diff --git "a/data_all_eng_slimpj/shuffled/split2/finalzzhcng" "b/data_all_eng_slimpj/shuffled/split2/finalzzhcng" new file mode 100644--- /dev/null +++ "b/data_all_eng_slimpj/shuffled/split2/finalzzhcng" @@ -0,0 +1,5 @@ +{"text":"\\section{Introduction}\n\n Dwarf novae (DNe) are a class of cataclysmic variables (CVs), which are\nclose binary systems consisting of a white dwarf and a red-dwarf secondary\ntransferring matter via the Roche-lobe overflow.\nSU UMa-type dwarf novae, a subclass of DNe, show superhumps during\ntheir long, bright outbursts (superoutbursts)\n[see e.g. \\citet{vog80suumastars}; \\citet{war85suuma}].\nThe origin of superhumps is basically understood as a result of\nvarying tidal dissipation in an eccentric accretion disk, whose\neccentricity is excited by the 3:1 orbital resonance\n(\\cite{whi88tidal}; \\cite{osa89suuma}; \\cite{osa96review}).\n\n Until the mid-1990's, the period of superhumps ($P_{\\rm SH}$)\nhad been considered to decrease during superoutburst\n(cf. \\cite{war85suuma}), which was explained as a result of\ndecreasing radius of the accretion disk\nduring superoutburst \\citep{osa85SHexcess}. In recent years,\nthe existence of objects with positive period derivatives\n($P_{\\rm dot} = \\dot{P}\/P$) of superhumps, particularly among systems\nwith short orbital periods ($P_{\\rm orb}$) has been established \n(see e.g. \\cite{kat01hvvir}). Since the superhump period, or its variation,\nis related to the radius of the accretion disk, or propagation of\nthe eccentricity wave (see e.g. \\cite{hir90SHexcess}; \\cite{lub91SHa};\n\\cite{kat98super}), the period variation is expected to provide\ndiagnostics of the dynamics in the outbursting accretion disk.\nA number of pieces of research have been issued in this perspective\n(e.g. \\cite{uem05tvcrv}; \\cite{ima06j0137}; \\cite{soe09asas1600}).\nIn particular, \\citet{uem05tvcrv} reported markedly different\n$P_{\\rm dot}$'s between different superoutbursts of TV Crv.\n\\citet{uem05tvcrv} proposed an interpretation that this difference\nis caused by the different mass (angular momentum) in the accretion disk\nat the onset of the superoutburst, following the theory by\n\\citet{osa03DNoutburst}.\nIf this is confirmed, $P_{\\rm dot}$ is expected to provide\nan observational measure of the mass in the disk.\n\n More recently, long-lasting superhumps with period unexpectedly\n($\\sim$0.5 \\%) longer than superhump periods during the\nslowly fading stage of WZ Sge-type superoutbursts have been\nestablished \\citep{kat08wzsgelateSH}.\n\\citet{kat08wzsgelateSH} suggested that\nthey are superhumps arising from the disk matter outside the\n3:1 resonance, or around the tidal truncation. \\citet{kat08wzsgelateSH}\nalso proposed the transient 2:1 resonance in the outer disk could\nregulate the excitation and propagation of the 3:1 resonance,\nleading to a novel interpretation of the variety of $P_{\\rm dot}$\nin different SU UMa-type dwarf novae.\n\n Motivated by these suggestions, we present a new systematic survey\nof $P_{\\rm dot}$ in SU UMa-type dwarf novae. The lack of published\ntimes of maxima in some of references having been one of the major\nobstacles in the research of period variations of superhumps, we present\ntimes of all measured superhumps for potential future analysis.\n\n In section \\ref{sec:obs}, we describe our observation and method\nof analysis. In section \\ref{sec:general}, we describe\ngeneral properties of period variation in superhumps. General\ndiscussions are given in section \\ref{sec:discussion}.\nSection \\ref{sec:wzsgestars} is dedicated to WZ Sge-type dwarf novae.\nThese sections are placed\nbefore section \\ref{sec:individual} (individual objects)\nbecause of the large amount of data presented in section\n\\ref{sec:individual}. We finally give section \\ref{sec:conclusion}\nfor a summary of new findings.\nThe names of the objects are sometimes abbreviated in\ntables, figures and sections \\ref{sec:general} and \\ref{sec:discussion};\nfor original names of these objects, refer to section \\ref{sec:individual}.\nAlternative designations were sometimes used when the original names\nwere difficult to abbreviate properly.\n\n\\section{Observation and Analysis}\\label{sec:obs}\n\n The data were obtained under campaigns led by the VSNET Collaboration\n\\citep{VSNET}. In some objects, we used archival data for published\npapers, and the public data from the AAVSO International Database\\footnote{\n$<$http:\/\/www.aavso.org\/data\/download\/$>$.\n}\nas a supplementary purpose. The majority of the data were acquired\nby time-resolved CCD photometry of with 30 cm-class telescopes, whose\nobservational details on individual objects will be presented in\nseparate papers dealing with in-depth analysis and discussion on\nindividual objects.\\footnote{\n During this analysis, it became evident that the KU computer\n lost ntp connection between 2008 May 16 and November 25.\n The times of observations\n during this period have been corrected by correlating with\n other simultaneous observations. The maximum correction amounted\n to 0.005 d and estimated maximum error of correction 0.001 d.\n The details of the corrections and these effects will be discussed\n in Ohshima et al., in preparation.\n The objects affected were V466 And, VY Aqr,\n KP Cas, V1251 Cyg, V630 Cyg, HO Del, V699 Oph, PV Per,\n UW Tri, DO Vul, NSV 5285, SDSS J1627, OT J0211, OT J0238,\n OT J1631 and OT J1914.\n The maximum uncertainty caused by these corrections were\n 0.00001--0.00002 d for periods of V466 And, V1251 Cyg and PV Per,\n and less than 0.00001 d for other objects.\n The maximum uncertainty for $P_{\\rm dot}$ was less than\n $1 \\times 10^{-5}$ .\n}\nWe generally restricted our analysis to superoutburst\nplateau and rapid fading stage. In a few very well-observed cases,\nwe dealt with post-superoutburst evolution of superhumps.\n\n After correction for systematic differences between observers, and\nsubtracting the general trend by fitting low-order (typically three\nto five) polynomials, we extracted times of superhump maxima by numerically\nfitting a template superhump light curve around the times of observed\nmaxima. We did not use the full superhump cycle but generally used\nphases $-$0.4 to 0.4 in order to minimize the contamination from\npotentially present secondary maxima. We employed a phase-averaged\n(and spline interpolated) light curve of superhumps of GW Lib as the\ntemplate, which is one of the best-sampled object among all SU UMa-type\ndwarf novae (figure \\ref{fig:gwsh}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig1.eps}\n \\end{center}\n \\caption{Template light curve (phase-averaged light curve of superhumps\n in GW Lib).}\n \\label{fig:gwsh}\n\\end{figure}\n\nThis usage of a fixed template has an advantage of much higher\nsignal-to-noise and thereby higher precision in determining maxima than\neye estimates (typically reducing the scatter by a factor of $\\sim$ 5)\nor than fitting using lower-quality template light curves prepared for\nindividual objects. The usage of a fixed template, however, has\na potential disadvantage of systematic errors caused by the variation\nin the superhump profile and the difference of the profile from\nthe template.\nThese potential effects have been examined by comparisons between previously\nreported times of maxima (referring to the same data) and\nthose determined in the present work.\nNo significant systematic differences were found to affect the\ndetermination of $P_{\\rm dot}$.\nIn some cases, comparisons with other authors have yielded significant\nconstant offsets (individually described in section \\ref{sec:individual}),\npresumably caused by different methods in extracting maxima.\nThese offsets were also found to be insensitive to determining $P_{\\rm dot}$\nafter adjustment by constant offsets.\n\n We generally used Phase Dispersion Minimization (PDM, \\cite{PDM})\nfor determining mean superhump periods described in the text. The values\ndetermined using linear regressions to times of superhump maxima\ncan be slightly different from those determined with the PDM.\nWhen segments (in $E$) are shown, these periods were derived from\na linear regression of maxima times of superhumps unless otherwise\nnoticed.\n\n Since we mainly focus on period variations of superhumps,\nwe only present superhump maxima and mostly omit individual light curves\nof outbursts, light curves of superhumps and results of PDM analysis\nto save space in section \\ref{sec:individual}.\nIndividual $O-C$ diagrams are not usually shown for the same reason;\nselected examples of $O-C$ diagrams are summarized in section\n\\ref{sec:general}. We, however, tried to include a comparison of\n$O-C$ diagrams if different superoutbursts of the same object were\nobserved, and tried to include the result of period analysis and\nthe superhump profile if they provide the first solid presentation.\nIn section \\ref{sec:individual}, we also included selected\nobservations of several superoutbursts not sufficiently covered to determine\n$P_{\\rm dot}$, if the determination of $P_{\\rm SH}$ is meaningful\nin itself or if the inclusion improves the statistical quality.\nWe also included partially observed superoutbursts for completeness,\nand this inclusion for future research is justified by a suggestion\nthat $P_{\\rm dot}$ can be measured from a combination of\ndifferent superoutbursts (subsection \\ref{sec:different}).\n\n We also calculated superhump periods and derivatives when times of\nsuperhump maxima were available in the literature. We employed the\nsame procedure as in the analysis of our own data. This work\ncomprises the largest homogeneous survey of variation of superhumps\nin SU UMa-type dwarf novae.\n\n\\begin{table*}\n\\caption{List of Superoutbursts.}\\label{tab:outobs}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references$^*$ \\\\\n\\hline\n\\ref{obj:foand} & FO And & 1994 & \\citet{kat95foand} \\\\\n\\ref{obj:kvand} & KV And & 1994 & \\citet{kat95kvand} \\\\\n & KV And & 2002 & Tor, KU, Tan \\\\\n\\ref{obj:lland} & LL And & 1993 & \\citet{kat04lland} \\\\\n & LL And & 2004 & KU, AAVSO, Mhh, Njh \\\\\n\\ref{obj:v402and} & V402 And & 2005 & Mhh, AAVSO \\\\\n & V402 And & 2006 & Mhh \\\\\n & V402 And & 2008 & Mhh \\\\\n\\ref{obj:v455and} & V455 And & 2007 & BSt, Mhh, KU, DRS, Ioh, HHO, AAVSO, Kis, PIE, Njh, \\\\\n & & & Mas, DPP, VAN, Nov, Nyr, OUS, GOT, RIT, BXS, DPV, LBr, \\\\\n & & & CTX, Hid, Boy, Kop, MEV, MNi \\\\\n\\ref{obj:v466and} & V466 And & 2008 & KU, HHO, Njh, DPV, PIE, Mhh, OUS, URB, JSh, AAVSO, \\\\\n & & & Nyr, RIT, CTX, Ost, BSt, MEV, Ter, VIR, DPP, Nov, Kis \\\\\n\\ref{obj:dhaql} & DH Aql & 2002 & OUS, RIX, KU, Mor, MLF, Nel, Kis, San, Cac \\\\\n & DH Aql & 2003 & KU, Tor \\\\\n & DH Aql & 2007 & Kis \\\\\n & DH Aql & 2008 & Kis \\\\\n\\ref{obj:v725aql} & V725 Aql & 1999 & \\citet{uem01v725aql} \\\\\n & V725 Aql & 2005 & AAVSO \\\\\n\\ref{obj:v1141aql} & V1141 Aql & 2002 & \\citet{ole03v1141aql} \\\\\n & V1141 Aql & 2003 & Hid, Kra, San \\\\\n\\ref{obj:vyaqr} & VY Aqr & 1986 & \\citet{pat93vyaqr} \\\\\n & VY Aqr & 2008 & MLF, Mhh, OUS, GBo, DPV, KU, GOT, Kis, Ioh, URB, \\\\\n & & & PIE, DPP, Kag, SAN \\\\\n\\ref{obj:egaqr} & EG Aqr & 2006 & \\citet{ima08egaqr} \\\\\n & EG Aqr & 2008 & Mhh, Njh, Ogm \\\\\n\\ref{obj:bfara} & BF Ara & 2002 & \\citet{kat03bfara} \\\\\n\\ref{obj:v663ara} & V663 Ara & 2004 & MLF \\\\\n\\ref{obj:v877ara} & V877 Ara & 2002 & \\citet{kat03v877arakktelpucma} \\\\\n\\ref{obj:bbari} & BB Ari & 2004 & KU, Hid, Mhh, OUS, Nyr, VAN, COO \\\\\n\\ref{obj:hvaur} & HV Aur & 2002 & Tor, OUS, Oud, KU, Nyr, DRS, Hid, Mas \\\\\n\\ref{obj:ttboo} & TT Boo & 2004 & COO, PIE, Hid, Njh, Mhh, Bil, Suc, \\citet{ole04ttboo} \\\\\n\\ref{obj:uzboo} & UZ Boo & 1994 & Oud \\\\\n & UZ Boo & 2003 & OUS, Njh, VAN, OKU, Nyr, Mhh, Ost, Njh, AAVSO \\\\\n\\ref{obj:nncam} & NN Cam & 2007 & DPV, VAN \\\\\n\\ref{obj:sycap} & SY Cap & 2008 & Njh, Mhh, Nel, KU \\\\\n\\ref{obj:axcap} & AX Cap & 2004 & MLF, Chi, KU, Hid, GBo \\\\\n-- & OY Car & 1980 & \\citet{krz85oycarsuper} \\\\\n\\hline\n \\multicolumn{4}{l}{$^*$ Key to observers:\nAth (Athens Univ.), \nBed$^\\dagger$ (J. Bedient), \nBil$^\\dagger$ (G. Billings), \nBoy$^\\dagger$ (D. Boyd),\nBSt$^\\dagger$ (B. Staels), \n}\\\\ \\multicolumn{4}{l}{\nBuc (D. Buczynski), \nBut (N. Butterworth), \nBXS (S. Brady), \nCOO$^\\dagger$ (L. Cook),\nCTX$^\\dagger$ (T. Crawford), \nChi (Concepcion),\n}\\\\ \\multicolumn{4}{l}{\nDPP$^\\dagger$ (P. de Ponthiere), \nDPV (P. Dubovsky), \nDRS (D. Starkey), \nFia (M. Fiaschi),\nGAR (G. Garradd), \nGBo (G. Bolt), \n}\\\\ \\multicolumn{4}{l}{\nGCO (C. Gualdoni), \nGGA (G. Good),\nGOT (T. Gomez), \nHHO (Higashi-Hiroshima Observatory), \nHea (B. Heathcote), \n}\\\\ \\multicolumn{4}{l}{\nHen$^\\dagger$ (A. Henden),\nHid (Hida Observatory), \nHMB (F. Hambsch), \nIMi (I. Miller),\nIoh (H. Itoh), \nJDW (D. West),\n}\\\\ \\multicolumn{4}{l}{\nJEN$^\\dagger$ (L. Jensen),\nJSh$^\\dagger$ (J. Shears), \nJWM (W. M. Julian II),\nKU (Kyoto University, campus observatory), \n}\\\\ \\multicolumn{4}{l}{\nKag (Kagoshima University), \nKeh (P. Kehusmaa),\nKGE$^\\dagger$ (K. Geary), \nKis (S. Kiyota), \nKop$^\\dagger$ (M. Koppelman), \n}\\\\ \\multicolumn{4}{l}{\nKra$^\\dagger$ (T. Krajci), \nKry (T. Kryachko et al.),\nLBr (L. Brat), \nLil$^\\dagger$ (W. Liller),\nMEV$^\\dagger$ (E. Morelle), \nMLF$^\\dagger$ (B. Monard), \n}\\\\ \\multicolumn{4}{l}{\nMNi (M. Nicholson),\nMar (B. Martin), \nMas (G. Masi), \nMhh (H. Maehara),\nMor (K. Morikawa), \nMyy (M. Moriyama),\n}\\\\ \\multicolumn{4}{l}{\nNDJ (N. James), \nNel (P. Nelson), \nNjh (K. Nakajima), \nNov (R. Nov\\'ak), \nNyr$^\\dagger$ (Nyrola and Hankasalmi Obs.), \n}\\\\ \\multicolumn{4}{l}{\nOgm$^\\dagger$ (Y. Ogmen),\nOKU (Osaka Kyoiku U.),\nOst (Ostrava team), \nOUS (Okayama University of Science), \n}\\\\ \\multicolumn{4}{l}{\nOud (Ouda station), \nPIE (J. Pietz), \nPav (E. Pavlenko et al.), \nPXR$^\\dagger$ (R. Pickard),\nRIT$^\\dagger$ (M. Richmond), \n}\\\\ \\multicolumn{4}{l}{\nRIX$^\\dagger$ (T. Richards), \nRes$^\\dagger$ (M. Reszelski), \nRet (A. Retter), \nRos (A. Rosenbush),\nSAN (R. Santallo), \n}\\\\ \\multicolumn{4}{l}{\nSAc (Seikei High School),\nSPA (San Pedro de Atacama), \nSXN (M. Simonsen),\nSan (Y. Sano), \nShu (S. Shugarov),\n}\\\\ \\multicolumn{4}{l}{\nSto (C. Stockdale), \nSuc (A. Sucker), \nTan (K. Tanabe), \nTer (Terskol Observatory), \nTor (K. Torii), \n}\\\\ \\multicolumn{4}{l}{\nUNAM (UNAM, Mexico), \nURB (L. Urbancok), \nVAN$^\\dagger$ (T. Vanmunster), \nVIR (J. Virtanen), \nWal (S. Walker), \n}\\\\ \\multicolumn{4}{l}{\nWar (Warsaw University), \nAAVSO (AAVSO database),\nASAS (ASAS-3 data)\n} \\\\\n \\multicolumn{4}{l}{$^\\dagger$ includes observations from the AAVSO database.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references \\\\\n\\hline\n\\ref{obj:gxcas} & GX Cas & 1994 & \\citet{nog98gxcasv419lyr} \\\\\n & GX Cas & 1996 & JEN \\\\\n & GX Cas & 1999 & KU \\\\\n & GX Cas & 2006 & KU, Njh \\\\\n\\ref{obj:htcas} & HT Cas & 1985 & \\citet{zha86htcas} \\\\\n\\ref{obj:kpcas} & KP Cas & 2008 & JSh, Boy, OUS, BSt, JWM, Nov, KU, Mhh, Njh \\\\\n\\ref{obj:v452cas} & V452 Cas & 1999 & KU \\\\\n & V452 Cas & 2007 & \\citet{she08v452cas} \\\\\n & V452 Cas & 2008 & Boy \\\\\n\\ref{obj:v359cen} & V359 Cen & 2002 & \\citet{kat02v359cen} \\\\\n-- & V436 Cen & 1978 & \\citet{sem80v436cen} \\\\\n\\ref{obj:v485cen} & V485 Cen & 1997 & \\citet{ole97v485cen} \\\\\n & V485 Cen & 2001 & KU, Ret \\\\\n & V485 Cen & 2004 & Nel, Hea \\\\\n\\ref{obj:v1040cen} & V1040 Cen & 2002 & MLF, GBo \\\\\n\\ref{obj:wxcet} & WX Cet & 1989 & \\citet{odo91wzsge} \\\\\n & WX Cet & 1998 & \\citet{kat01wxcet}, JEN \\\\\n & WX Cet & 2001 & KU, \\citet{ste07wxcet} \\\\\n & WX Cet & 2004 & Mhh, Njh \\\\\n-- & Z Cha & 1982 & \\citet{war88zcha} \\\\\n\\ref{obj:rxcha} & RX Cha & 2009 & Nel \\\\\n\\ref{obj:bzcir} & BZ Cir & 2004 & MLF, Chi \\\\\n\\ref{obj:cgcma} & CG CMa & 1999 & \\citet{kat99cgcma} \\\\\n\\ref{obj:pucma} & PU CMa & 2003 & Nel, MLF, SAN \\\\\n & PU CMa & 2005 & Mhh, Njh, AAVSO \\\\\n & PU CMa & 2008 & Nel, Njh, Kis, Mhh \\\\\n\\ref{obj:yzcnc} & YZ Cnc & 2007 & Njh \\\\\n\\ref{obj:akcnc} & AK Cnc & 1992 & \\citet{kat94akcnc} \\\\\n & AK Cnc & 1999 & JEN \\\\\n & AK Cnc & 2003 & Tor, PIE, KU, Tan, Nyr, Mhh \\\\\n\\ref{obj:cccnc} & CC Cnc & 2001 & \\citet{kat02cccnc} \\\\\n-- & EG Cnc & 1996 & \\citet{kat04egcnc}, \\citet{pat98egcnc} \\\\\n\\ref{obj:alcom} & AL Com & 1995 & \\citet{nog97alcom}, \\citet{how96alcom}, \\citet{pyc95alcom}, \\citet{pat96alcom} \\\\\n & AL Com & 2001 & \\citet{ish02wzsgeletter} \\\\\n & AL Com & 2008 & \\citet{uem08alcom} \\\\\n\\ref{obj:gocom} & GO Com & 2003 & \\citet{ima05gocom}, Pav \\\\\n & GO Com & 2005 & KU, Mhh, Njh, VAN, Boy \\\\\n & GO Com & 2006 & Njh, Kis, Mhh, GOT \\\\\n & GO Com & 2008 & Mhh, DPV \\\\\n\\ref{obj:v728cra} & V728 CrA & 2003 & MLF, Nel, SAN \\\\\n\\ref{obj:vwcrb} & VW CrB & 2001 & \\citet{nog04vwcrb} \\\\\n & VW CrB & 2003 & \\citet{nog04vwcrb} \\\\\n & VW CrB & 2006 & AAVSO \\\\\n\\ref{obj:tucrt} & TU Crt & 1998 & \\citet{men98tucrt} \\\\\n & TU Crt & 2001 & KU, Kis \\\\\n & TU Crt & 2009 & Njh, Kis \\\\\n\\ref{obj:tvcrv} & TV Crv & 2001 & \\citet{uem05tvcrv} \\\\\n & TV Crv & 2003 & \\citet{uem05tvcrv} \\\\\n & TV Crv & 2004 & \\citet{uem05tvcrv} \\\\\n\\ref{obj:v337cyg} & V337 Cyg & 2006 & Kra, Boy, VAN \\\\\n\\ref{obj:v503cyg} & V503 Cyg & 2002 & KU, DRS, PIE \\\\\n & V503 Cyg & 2008 & Njh, KU \\\\\n\\ref{obj:v550cyg} & V550 Cyg & 2000 & KU, Oud, PIE \\\\\n\\ref{obj:v630cyg} & V630 Cyg & 1996 & \\citet{nog01v630cyg} \\\\\n & V630 Cyg & 2008 & KU, Mhh, Ioh \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references \\\\\n\\hline\n\\ref{obj:v632cyg} & V632 Cyg & 2008 & DPV, Njh, AAVSO, VIR, Mhh \\\\\n\\ref{obj:v1028cyg} & V1028 Cyg & 1995 & \\citet{bab00v1028cyg}, AAVSO \\\\\n & V1028 Cyg & 1996 & Oud, AAVSO \\\\\n & V1028 Cyg & 1999 & KU, Buc \\\\\n & V1028 Cyg & 2001 & Bil \\\\\n & V1028 Cyg & 2002 & KU, OUS, Tor, Bil \\\\\n & V1028 Cyg & 2004 & Njh, Nyr, DRS \\\\\n & V1028 Cyg & 2008 & IMi, PXR \\\\\n\\ref{obj:v1113cyg} & V1113 Cyg & 1994 & \\citet{kat96v1113cyg} \\\\\n & V1113 Cyg & 2008 & Nov, Njh \\\\\n\\ref{obj:v1251cyg} & V1251 Cyg & 1991 & \\citet{kat95v1251cyg} \\\\\n & V1251 Cyg & 2008 & Mhh, Njh, HHO, IMi, KU, Ioh, CTX, Mas, \\\\\n & & & JSh, DPV, Keh, SAc \\\\\n\\ref{obj:v1316cyg} & V1316 Cyg & 2006 & \\citet{boy08v1316cyg} \\\\\n\\ref{obj:v1454cyg} & V1454 Cyg & 2006 & Njh, AAVSO \\\\\n\\ref{obj:v1504cyg} & V1504 Cyg & 1994 & \\citet{nog97v1504cyg} \\\\\n & V1504 Cyg & 2008 & Mhh, Ioh \\\\\n & V1504 Cyg & 2009 & KU \\\\\n\\ref{obj:v2176cyg} & V2176 Cyg & 1997 & AAVSO, \\citet{nov01v2176cyg}, \\citet{kwa98v2176cyg} \\\\\n\\ref{obj:hodel} & HO Del & 1994 & \\citet{kat03hodel} \\\\\n & HO Del & 2001 & \\citet{kat03hodel} \\\\\n & HO Del & 2008 & KU, DPV, Mhh, AAVSO, OUS, MEV, Kis \\\\\n\\ref{obj:bcdor} & BC Dor & 2003 & Nel, RIX \\\\\n\\ref{obj:cpdra} & CP Dra & 2003 & KU \\\\\n & CP Dra & 2009 & IMi, Boy, Mhh, Bst, Nyr \\\\\n\\ref{obj:dmdra} & DM Dra & 2003 & Tor, Tan, Hid \\\\\n\\ref{obj:dvdra} & DV Dra & 2005 & Njh, VAN, Mhh, Hid \\\\\n\\ref{obj:kvdra} & KV Dra & 2002 & KU, Tor, PIE, Nyr, OUS, DRS, COO, VAN, Bil \\\\\n & KV Dra & 2004 & KU, Mhh, OUS, Boy \\\\\n & KV Dra & 2005 & Mhh \\\\\n & KV Dra & 2009 & DPV, Njh, Mhh, OUS, KU, Ioh, Hyn \\\\\n\\ref{obj:mndra} & MN Dra & 2002a & \\citet{nog03var73dra} \\\\\n & MN Dra & 2002b & \\citet{nog03var73dra} \\\\\n & MN Dra & 2003 & Nyr \\\\\n & MN Dra & 2008 & MEV \\\\\n-- & IX Dra & 2003 & \\citet{ole04ixdra} \\\\\n\\ref{obj:xzeri} & XZ Eri & 2003a & \\citet{uem04xzeri} \\\\\n & XZ Eri & 2003b & KU, Njh \\\\\n & XZ Eri & 2007 & SPA, Njh, Mhh \\\\\n & XZ Eri & 2008 & AAVSO, Njh, Mhh, GBo, Kis \\\\\n\\ref{obj:aqeri} & AQ Eri & 1991 & \\citet{kat91aqeri} \\\\\n & AQ Eri & 1992 & Oud \\\\\n & AQ Eri & 2006 & Njh \\\\\n & AQ Eri & 2008 & Njh, Ioh, OUS, DPV, Kis, Nel, KU \\\\ \n\\ref{obj:uvgem} & UV Gem & 2003 & Oud, KU, PIE, VAN, Nyr, Tan \\\\\n & UV Gem & 2008 & Njh, KU \\\\\n\\ref{obj:awgem} & AW Gem & 1995 & \\citet{kat96awgem} \\\\\n & AW Gem & 2008 & Mhh, OUS \\\\\n & AW Gem & 2009 & Njh, AAVSO \\\\\n\\ref{obj:cigem} & CI Gem & 2005 & AAVSO, VAN, Njh \\\\\n\\ref{obj:irgem} & IR Gem & 1991 & \\citet{kat01irgem} \\\\\n & IR Gem & 2009 & Njh, OUS, SAc \\\\\n\\ref{obj:cigru} & CI Gru & 2004 & MLF \\\\\n-- & V592 Her & 1998 & \\citet{kat02v592her} \\\\\n-- & V660 Her & 2004 & \\citet{ole05v660her} \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references \\\\\n\\hline\n\\ref{obj:v844her} & V844 Her & 1997 & JEN \\\\\n & V844 Her & 1999 & \\citet{oiz07v844her} \\\\\n & V844 Her & 2002 & \\citet{oiz07v844her} \\\\\n & V844 Her & 2006 & \\citet{oiz07v844her} \\\\\n & V844 Her & 2008 & KU, DPV, Mhh \\\\\n\\ref{obj:v1108her} & V1108 Her & 2004 & AAVSO, VAN, KU, San, RIT, Hen, Kop, COO, Njh, Mhh, DRS, Boy, CTX \\\\\n\\ref{obj:ruhor} & RU Hor & 2003 & MLF, GBo \\\\\n & RU Hor & 2008 & MLF, GBo \\\\\n\\ref{obj:cthya} & CT Hya & 1999 & \\citet{kat99cthya} \\\\\n & CT Hya & 2000 & KU, Kis \\\\\n & CT Hya & 2002a & KU \\\\\n & CT Hya & 2002b & KU, Hid, Kis, Tor, Tan \\\\\n & CT Hya & 2009 & Njh, OUS, Kis \\\\\n\\ref{obj:mmhya} & MM Hya & 1998 & JEN, Oud \\\\\n & MM Hya & 2001 & SAAO, KU \\\\\n\\ref{obj:vwhyi} & VW Hyi & 1972 & \\citet{vog74vwhyi} \\\\\n & VW Hyi & 2000 & Lil \\\\\n\\ref{obj:rzleo} & RZ Leo & 2000 & \\citet{ish01rzleo}, AAVSO \\\\\n & RZ Leo & 2006 & Njh, Mhh, KU \\\\\n\\ref{obj:gwlib} & GW Lib & 2007 & MLF, HHO, KU, Kis, Mhh, Njh, Nel, Ioh, San \\\\\n\\ref{obj:rzlmi} & RZ LMi & 2004 & \\citet{ole08rzlmi} \\\\\n & RZ LMi & 2005 & COO \\\\\n\\ref{obj:sslmi} & SS LMi & 2006 & \\citet{she08sslmi} \\\\\n\\ref{obj:sxlmi} & SX LMi & 1994 & \\citet{nog97sxlmi} \\\\\n & SX LMi & 2001 & KU \\\\\n & SX LMi & 2002 & KU \\\\\n\\ref{obj:brlup} & BR Lup & 2003 & MLF, GBo, Nel \\\\\n & BR Lup & 2004 & MLF, RIX \\\\\n\\ref{obj:aylyr} & AY Lyr & 1987 & \\citet{uda88aylyr} \\\\\n & AY Lyr & 2008 & OUS, Ioh, Njh, SAc \\\\\n & AY Lyr & 2009 & OUS, Njh \\\\\n\\ref{obj:dmlyr} & DM Lyr & 1996 & \\citet{nog03dmlyr} \\\\\n & DM Lyr & 1997 & \\citet{nog03dmlyr} \\\\\n & DM Lyr & 2002 & Tor, KU \\\\\n\\ref{obj:v344lyr} & V344 Lyr & 1993 & \\citet{kat93v344lyr} \\\\\n\\ref{obj:v358lyr} & V358 Lyr & 2008 & KU, Njh, Mhh, Boy, AAVSO \\\\\n\\ref{obj:v419lyr} & V419 Lyr & 1999 & Nov, KU \\\\\n & V419 Lyr & 2006 & Boy, DPV, \\citet{rut07v419lyr} \\\\\n\\ref{obj:v585lyr} & V585 Lyr & 2003 & PIE, Nov, COO, KU, Tor, Kra, Nyr, Hid, Hen, War \\\\\n-- & TU Men & 1980 & \\citet{sto84tumen} \\\\\n\\ref{obj:admen} & AD Men & 2004 & MLF \\\\\n\\ref{obj:fqmon} & FQ Mon & 2004 & KU, Hid, Mas, Kis, MLF, PIE, Mhh, COO, Nyr \\\\\n & FQ Mon & 2006 & Kis, KU, Mhh, Njh \\\\\n & FQ Mon & 2007 & Njh, Mhh, Kis, GBo \\\\\n\\ref{obj:abnor} & AB Nor & 2002 & \\citet{kat04nsv10934mmscoabnorcal86} \\\\\n\\ref{obj:dtoct} & DT Oct & 2003a & \\citet{kat04nsv10934mmscoabnorcal86} \\\\\n & DT Oct & 2003b & Nel \\\\\n & DT Oct & 2008 & RIX \\\\\n\\ref{obj:v699oph} & V699 Oph & 2003 & San, Nel, Kra, DRS \\\\\n & V699 Oph & 2008 & KU, GBo \\\\\n\\ref{obj:v2051oph} & V2051 Oph & 1999 & GAR, Wal, KU \\\\\n & V2051 Oph & 2003 & Sto, SAN, Hea, Nel, MLF, San, Kis, Njh, Hid \\\\\n & V2051 Oph & 2009 & Kis, KU \\\\\n\\ref{obj:v2527oph} & V2527 Oph & 2004 & MLF, GBo, Chi, Hid, Mhh, KU, Kis \\\\\n & V2527 Oph & 2006 & Njh, Nel \\\\\n & V2527 Oph & 2008 & Mhh, Ioh, Njh \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references \\\\\n\\hline\n\\ref{obj:v1159ori} & V1159 Ori & 1993 & \\citet{pat95v1159ori} \\\\\n & V1159 Ori & 2002 & KU, Kis, Tor, Tan, Oud \\\\\n\\ref{obj:v344pav} & V344 Pav & 2004 & \\citet{uem04v344pav} \\\\\n\\ref{obj:efpeg} & EF Peg & 1991 & \\citet{kat02efpeg}, \\citet{how93efpeg} \\\\\n & EF Peg & 1997 & KU \\\\\n\\ref{obj:v364peg} & V364 Peg & 2004 & Kra, VAN \\\\\n\\ref{obj:v368peg} & V368 Peg & 2000 & KU, But, Nyr, Kra \\\\\n & V368 Peg & 2005 & Mhh, Njh, GCO \\\\\n & V368 Peg & 2006 & Njh, DPV \\\\\n\\ref{obj:v369peg} & V369 Peg & 1999 & \\citet{kat01v369peg}, JEN \\\\\n\\ref{obj:uvper} & UV Per & 1991 & Oud \\\\\n & UV Per & 2000 & KU, Tor, Buc, Mas, PIE, Mar \\\\\n & UV Per & 2003 & OUS, COO, AAVSO, VAN, PIE, Boy, Ost, Nyr, KU, Bil \\\\\n & UV Per & 2007 & DPV, OUS, MEV \\\\\n\\ref{obj:puper} & PU Per & 2009 & KU, Njh, Ioh, Mhh \\\\\n\\ref{obj:pvper} & PV Per & 2008 & KU, Mhh, Boy \\\\\n\\ref{obj:qyper} & QY Per & 1999 & KU, COO, Mar, VAN, Buc, JEN, AAVSO \\\\\n & QY Per & 2005 & Mhh, KU, Njh, OUS \\\\\n\\ref{obj:v518per} & V518 Per & 1992 & \\citet{kat95v518per} \\\\\n\\ref{obj:typsa} & TY PsA & 2008 & Njh, Ioh, SAc \\\\\n\\ref{obj:typsc} & TY Psc & 2005 & Mhh \\\\\n & TY Psc & 2008 & URB, Ost, Njh, OUS, Kis \\\\\n\\ref{obj:eipsc} & EI Psc & 2001 & \\citet{uem02j2329}, \\citet{ski02j2329} \\\\\n & EI Psc & 2005 & COO, Njh, Mhh \\\\\n\\ref{obj:vzpyx} & VZ Pyx & 1996 & \\citet{kat97vzpyx} \\\\\n & VZ Pyx & 2000 & Kis \\\\\n & VZ Pyx & 2004 & Kis \\\\\n & VZ Pyx & 2008 & Njh, Ioh, Kis \\\\\n\\ref{obj:dvsco} & DV Sco & 2004 & MLF, Chi, GBo \\\\\n & DV Sco & 2008 & MLF, GBo \\\\\n\\ref{obj:mmsco} & MM Sco & 2002 & \\citet{kat04nsv10934mmscoabnorcal86} \\\\\n\\ref{obj:nyser} & NY Ser & 1996 & \\citet{nog98nyser} \\\\\n-- & QW Ser & 2000 & \\citet{nog04qwser} \\\\\n & QW Ser & 2002 & \\citet{nog04qwser} \\\\\n\\ref{obj:rzsge} & RZ Sge & 1994 & \\citet{kat96rzsge} \\\\\n & RZ Sge & 1996 & Oud, \\citet{sem97rzsge} \\\\\n & RZ Sge & 2002 & KU \\\\\n\\ref{obj:wzsge} & WZ Sge & 1978 & \\citet{pat81wzsge}, \\citet{boh79wzsge}, \\citet{hei79wzsge}, \\citet{tar79wzsge} \\\\\n & WZ Sge & 2001 & KU, Oud, Mas, Mar, RIT, PIE, VAN, Nyr, DRS, Nov, \\\\\n & & & Mor, COO, Buc, UNAM, Ath, Kis, Kra, Hyn, GGA, San, \\\\\n & & & Boy, Fia, Myy, JDW, Dou \\citep{ish02wzsgeletter} \\\\\n\\ref{obj:awsge} & AW Sge & 2000 & Mas \\\\\n & AW Sge & 2006 & Kra, JSh \\\\\n\\ref{obj:v551sgr} & V551 Sgr & 2003 & MLF, SAN, Nel, GBo, Sto, Hid \\\\\n & V551 Sgr & 2004 & MLF \\\\\n\\ref{obj:v4140sgr} & V4140 Sgr & 2004 & Chi, MLF, Ret \\\\\n\\ref{obj:v701tau} & V701 Tau & 1995 & Oud \\\\\n & V701 Tau & 2005 & Mhh, Boy, GCO, JSh, VAN \\\\\n\\ref{obj:v1208tau} & V1208 Tau & 2000 & KU, GAR, Mas, COO \\\\\n & V1208 Tau & 2002 & Oud, Tan \\\\\n\\ref{obj:kktel} & KK Tel & 2002 & \\citet{kat03v877arakktelpucma} \\\\\n & KK Tel & 2003 & RIX \\\\\n & KK Tel & 2004 & MLF \\\\\n\\ref{obj:ektra} & EK TrA & 2007 & MLF \\\\\n-- & FL TrA & 2005 & \\citet{ima08fltractcv0549} \\\\\n\\ref{obj:uwtri} & UW Tri & 1995 & \\citet{kat01uwtri} \\\\\n & UW Tri & 2008 & KU, Ioh, Njh, Mhh, IMi, DRS, DPV, Bed, Nyr, Ogm, AAVSO \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references \\\\\n\\hline\n\\ref{obj:wytri} & WY Tri & 2000 & \\citet{van01wytri}, KU, Nov \\\\\n\\ref{obj:suuma} & SU UMa & 1989 & \\citet{uda90suuma} \\\\\n & SU UMa & 1999 & KU, Buc, Mhh \\\\\n\\ref{obj:swuma} & SW UMa & 1991 & Oud \\\\\n & SW UMa & 1996 & \\citet{sem97swuma}, \\citet{nog98swuma} \\\\\n & SW UMa & 1997 & JEN \\\\\n & SW UMa & 2000 & KU, JEN, Nov, Buc, Mar, Pav, Mas, AAVSO \\\\\n & SW UMa & 2002 & Tor, Tan \\\\\n & SW UMa & 2006 & IMi, Mhh, Nyr, DPV, Njh, GOT, KU, AAVSO \\\\\n\\ref{obj:bcuma} & BC UMa & 2000 & KU, Pav, NDJ \\\\\n & BC UMa & 2003 & KU, Oud, Boy, PIE, Ost, Kis, \\citet{mae07bcuma} \\\\\n\\ref{obj:bzuma} & BZ UMa & 2007 & VAN, PIE, AAVSO, Boy, Nyr, KU, Njh, Res, MEV, JSh, \\\\\n & & & DRS, Kop, Kra, DPV, Mhh \\\\\n\\ref{obj:ciuma} & CI UMa & 2001 & KU \\\\\n & CI UMa & 2003 & Hid, KU, PIE, Nyr, Tan \\\\\n & CI UMa & 2006 & DPV \\\\\n\\ref{obj:cyuma} & CY UMa & 1995 & \\citet{har95cyuma} \\\\\n & CY UMa & 1998 & JEN \\\\\n & CY UMa & 1999 & KU \\\\\n & CY UMa & 2009 & DPV, BSt, Njh, HMB, Ioh, VIR, AAVSO \\\\\n-- & DI UMa & 2007a & \\citet{rut08diuma} \\\\\n & & 2007b & \\citet{rut08diuma} \\\\\n\\ref{obj:dvuma} & DV UMa & 1997 & \\citet{pat00dvuma}, JEN, \\citet{nog01dvuma} \\\\\n & DV UMa & 1999 & KU, JEN \\\\\n & DV UMa & 2002 & KU, Nyr \\\\\n & DV UMa & 2005 & Mhh, Njh, KU \\\\\n & DV UMa & 2007 & IMi, Njh, Mhh, DPP, PXR, AAVSO \\\\\n\\ref{obj:eruma} & ER UMa & 1995 & \\citet{kat03erumaSH} \\\\\n\\ref{obj:iyuma} & IY UMa & 2000 & \\citet{uem00iyuma}, \\citet{pat00iyuma} \\\\\n & IY UMa & 2002 & KU, OUS, AAVSO \\\\\n & IY UMa & 2004 & Mhh, Nyr, KU, DPP, KGE \\\\\n & IY UMa & 2006 & Njh, Mhh, KU, Kra, DPV, RIT, Kop, AAVSO \\\\\n & IY UMa & 2007 & Mhh \\\\\n & IY UMa & 2009 & OUS, Njh, Ost, Ioh, SXN, Nyr \\\\\n\\ref{obj:ksuma} & KS UMa & 2003 & VAN, Tor, KU, PIE, Njh, Mhh, Mar, Ost, Nyr, DRS, \\citet{ole03ksuma} \\\\\n & KS UMa & 2007 & HHO, Njh, KU \\\\\n\\ref{obj:kvuma} & KV UMa & 2000 & \\citet{uem02j1118} \\\\\n\\ref{obj:mruma} & MR UMa & 2002 & KU, OUS \\\\\n & MR UMa & 2003 & KU, Tor, PIE, Hid, Nyr, War \\\\\n & MR UMa & 2007 & AAVSO \\\\\n-- & SS UMi & 2004 & \\citet{ole06ssumi} \\\\\n\\ref{obj:cuvel} & CU Vel & 2002 & Nel, GBo, Hea, RIX \\\\\n\\ref{obj:hsvir} & HS Vir & 1996 & \\citet{kat98hsvir} \\\\\n & HS Vir & 2008 & Nel \\\\\n\\ref{obj:hvvir} & HV Vir & 1992 & \\citet{kat01hvvir} \\\\\n & HV Vir & 2002 & \\citet{ish03hvvir} \\\\\n & HV Vir & 2008 & Njh, Kis, Mhh, KU, Ioh, Ros \\\\\n\\ref{obj:ouvir} & OU Vir & 2003 & KU, Tor, MLF, Hid, Kis, Kra, Njh, Hea, VAN, Mar, PIE, DRS, Nyr \\\\\n & OU Vir & 2008 & Ioh, DPV, Kis \\\\\n\\ref{obj:qzvir} & QZ Vir & 1993 & \\citet{kat97tleo}, \\citet{lem93tleo} \\\\\n & QZ Vir & 2005 & Mhh, Njh, Ost \\\\\n & QZ Vir & 2007 & Mhh, Njh, Kis \\citep{ohs09qzvir} \\\\\n & QZ Vir & 2008 & HHO, Njh, Kis, DPV, GBo, OUS \\citep{ohs09qzvir} \\\\\n & QZ Vir & 2009 & OUS, Njh, BSt, KU, Mhh, Ioh, HMB, Kis, Ogm \\citep{ohs09qzvir} \\\\\n\\ref{obj:rxvol} & RX Vol & 2003 & MLF, Nel, SAN \\\\\n\\ref{obj:tyvul} & TY Vul & 2003 & KU, PIE, AAVSO \\\\\n\\ref{obj:dovul} & DO Vul & 2008 & KU, Mhh \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or references & ID$^\\ddagger$ \\\\\n\\hline\n\\ref{obj:nsv4838} & NSV 4838 & 2005 & PIE, VAN, Boy & \\\\\n & NSV 4838 & 2007 & Mhh, KU, Njh & \\\\\n\\ref{obj:nsv5285} & NSV 5285 & 2008 & KU & \\\\\n\\ref{obj:nsv14652} & NSV 14652 & 2004 & PIE & \\\\\n\\ref{obj:j0232} & 1RXS J0232 & 2007 & Nel, GBo, AAVSO & Pi of the Sky \\\\\n\\ref{obj:j0423} & 1RXS J0423 & 2008 & BXS, JSh, IMi, BSt, DPV, Ioh, Mhh & \\\\\n\\ref{obj:j0532} & 1RXS J0532 & 2005 & KGE, Mhh, DPP, VAN, Nyr, JSh, COO & \\citet{ber05j0532} \\\\\n & 1RXS J0532 & 2008 & Njh, DPV, KU, Mhh & \\\\\n\\ref{obj:j0219} & 2QZ J0219 & 2005 & \\citet{ima06j0219} & \\\\\n & 2QZ J0219 & 2009 & Njh, Mhh, Ioh & \\\\\n\\ref{obj:asas0025} & ASAS J0025 & 2004 & Chi, COO, Mhh, MLF, Kis, & \\\\\n & & & KU, RIT, San, OUS, Nyr, & \\\\\n & & & Hid, DRS, PIE, Nel, Ret, & \\\\\n & & & Boy, GBo, Mas, PXR, Njh, & \\\\\n & & & Kop, VAN, Pav, CTX, AAVSO & \\\\\n\\ref{obj:asas0233} & ASAS J0233 & 2006 & Mhh, Kra, Njh, Kis, VAN, & \\\\\n & & & Boy, CTX, AAVSO & \\\\\n\\ref{obj:asas0918} & ASAS J0918 & 2005 & Mhh, Njh & \\\\\n\\ref{obj:asas1025} & ASAS J1025 & 2006 & Mhh, Kra, Njh, Kis, COO, MLF, & \\\\\n & & & AAVSO, Van, DPP, KU & \\\\\n\\ref{obj:asas1536} & ASAS J1536 & 2004 & KU, Kis, COO, Mhh, ASAS, Nyr, AAVSO & \\\\\n\\ref{obj:asas1600} & ASAS J1600 & 2005 & \\citet{soe09asas1600}, MLF, Nel & \\\\\n\\ref{obj:j0549} & CTCV J0549 & 2006 & \\citet{ima08fltractcv0549} & \\\\\n\\ref{obj:ha0242} & Ha 0242 & 2006 & Kra, Mhh, MLF & \\\\\n\\ref{obj:j0137} & SDSS J0137 & 2003 & \\citet{ima06j0137} & \\\\\n & SDSS J0137 & 2009 & Njh, Mhh & \\\\\n\\ref{obj:j0310} & SDSS J0310 & 2004 & MLF, Chi & \\\\\n\\ref{obj:j0334} & SDSS J0334 & 2009 & Mhh, KU & \\\\\n\\ref{obj:j0746} & SDSS J0746 & 2009 & KU, Njh, Mhh & \\\\\n-- & SDSS J0804 & 2006 & \\citet{kat09j0804} & \\\\\n\\ref{obj:j0812} & SDSS J0812 & 2008 & Mhh, Kis, Njh & \\\\\n\\ref{obj:j0824} & SDSS J0824 & 2007 & Njh, Boy, Mhh, JSh, BXS \\citep{boy08j0824} & \\\\\n\\ref{obj:j0838} & SDSS J0838 & 2007 & VAN & \\\\\n & SDSS J0838 & 2009 & Mhh, BSt, KU, Ioh & \\\\\n\\ref{obj:j1005} & SDSS J1005 & 2009 & Ioh, AAVSO, IMi, Mhh, Njh & \\\\\n\\ref{obj:j1100} & SDSS J1100 & 2009 & KU, PIE & \\\\\n\\ref{obj:j1227} & SDSS J1227 & 2007 & Mhh, DRS, \\citet{she08j1227} & \\\\\n\\ref{obj:j1524} & SDSS J1524 & 2009 & Nov, AAVSO, DPV, Mhh, Pav, Ioh, BSt, Njh & \\\\\n\\ref{obj:j1556} & SDSS J1556 & 2007 & Mhh, Njh, KU, Mas & \\\\\n\\ref{obj:j1627} & SDSS J1627 & 2008 & JSh, Kra, BXS, KU, GBo, Ogm, & \\\\\n & & & BSt, Njh, \\citet{she08j1627} & \\\\\n\\ref{obj:j1702} & SDSS J1702 & 2005 & Nyr, Boy, JSh, VAN, BXS \\citep{boy06j1702} & \\\\\n\\ref{obj:j1730} & SDSS J1730 & 2001 & KU, Nyr & \\\\\n & SDSS J1730 & 2002 & KU & \\\\\n & SDSS J1730 & 2004 & KU, War, COO, Ost & \\\\\n\\ref{obj:j2100} & SDSS J2100 & 2007 & Njh, Mhh & \\\\\n\\ref{obj:j2258} & SDSS J2258 & 2004 & MLF, Kis & \\\\\n & SDSS J2258 & 2008 & Njh, Mhh, Ioh, OUS, SAc & \\\\\n\\ref{obj:j0042} & OT J0042 & 2008 & KU, Mhh, Njh, Ioh, Kis & M31N 2008-11b \\\\\n\\ref{obj:j0113} & OT J0113 & 2008 & Mhh & CSS080922:011307$+$215250 \\\\\n\\ref{obj:j0211} & OT J0211 & 2008 & OUS, Mhh, KU & CSS080130:021110$+$171624 \\\\\n\\ref{obj:j0238} & OT J0238 & 2008 & Mhh, \\citet{shu08j0238}, KU, Njh & CSS081026:023839$+$355648 \\\\\n\\ref{obj:j0329} & OT J0329 & 2006 & \\citet{sha07j0329}, Kra, VAN, AAVSO, Boy, BXS & VS 0329$+$1250 \\\\\n\\ref{obj:j0406} & OT J0406 & 2008 & Mhh, OUS, GBo & Itagaki \\citep{yam08j0406cbet1463} \\\\\n\\hline\n \\multicolumn{5}{l}{$^\\ddagger$ Original identifications or discoverers.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{(continued) List of Superoutbursts.}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\nSubsection & Object & Year & Observers or reference & ID \\\\\n\\hline\n\\ref{obj:j0557} & OT J0557 & 2006 & \\citet{uem09j0557}, Boy, VAN, Nyr & \\citet{klo06j0557cbet777} \\\\\n\\ref{obj:j0747} & OT J0747 & 2008 & Kis, GBo, Njh, Mhh, Nel, BXS, DPP, & Itagaki \\citep{yam08j0747cbet1216} \\\\\n & & & JSh, CTX, Ioh, AAVSO & \\\\\n\\ref{obj:j0807} & OT J0807 & 2007 & Mhh, HHO, Kra, Njh, Kis, DPV & Itagaki \\\\\n\\ref{obj:j0814} & OT J0814 & 2008 & URB, DPV, Njh, KU & CSS080409:081419$-$005022 \\\\\n\\ref{obj:j0845} & OT J0845 & 2008 & Njh, Kis, Mhh & Itagaki \\citep{yam08j0845cbet1225} \\\\\n\\ref{obj:j0902} & OT J0902 & 2008 & KU, Mhh & CSS080304:090240$+$052501 \\\\\n\\ref{obj:j1021} & OT J1021 & 2006 & \\citet{uem08j1021}, AAVSO & \\citet{chr06j1021cbet746} \\\\\n\\ref{obj:j1026} & OT J1026 & 2009 & Njh & Itagaki \\citep{yam09j1026cbet1644} \\\\\n\\ref{obj:j1028} & OT J1028 & 2009 & GBo, KU, Mhh, Kis & CSS090331:102843$-$081927 \\\\\n\\ref{obj:j1112} & OT J1112 & 2007 & Ioh, GBo, Mhh, Kis & Pi of the Sky \\\\\n\\ref{obj:j1300} & OT J1300 & 2008 & GBo, Mhh, PIE & CSS080702:130030$+$115101 \\\\\n\\ref{obj:j1440} & OT J1440 & 2009 & IMi, Mhh, KU, OUS & CSS090530:144011$+$494734 \\\\\n\\ref{obj:j1443} & OT J1443 & 2009 & Njh, Ioh, Mhh, GBo, KU, Kis & CSS090418:144342$-$175550 \\\\\n\\ref{obj:j1631} & OT J1631 & 2008 & DPV, PIE, Mhh, KU, Njh & CSS080505:163121$+$103134 \\\\\n\\ref{obj:j1914} & OT J1914 & 2008 & Mhh, KU, Njh, DPV, Nyr, AAVSO & Itagaki \\citep{yam08j1914cbet1535} \\\\\n\\ref{obj:j1959} & OT J1959 & 2005 & VAN, KU, Njh & \\citet{ren05j1959iauc8591} \\\\\n\\ref{obj:j2131} & OT J2131 & 2008 & Mhh, Ioh, SAc & Itagaki \\citep{yam08j1631cbet1631} \\\\\n\\ref{obj:j2137} & OT J2137 & 2008 & GBo, Mhh, Njh, DPV, SAc, Kis, Kry & Itagaki \\\\\n\\ref{obj:j0222} & TSS J0222 & 2005 & \\citet{ima06tss0222} & \\citet{qui05tss0222atel658} \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\section{General Properties}\\label{sec:general}\n\n\\subsection{Distribution of Superhump Periods}\n\n Figure \\ref{fig:phist} shows the distribution of superhump periods\nin this survey. With the best statistics ever achieved, we can see\nthe maximum of the distribution close to $P_{\\rm SH} = 0.06$ d\nand a monotonous decrease in population towards longer periods.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig2.eps}\n \\end{center}\n \\caption{Distribution of superhump periods in this survey.\n }\n \\label{fig:phist}\n\\end{figure}\n\n\\subsection{General Tendency in Period Variations}\\label{sec:tendency}\n\n As already demonstrated by several authors (e.g. \\cite{ole03ksuma};\n\\cite{soe09asas1600}), short-$P_{\\rm SH}$ SU UMa-type dwarf novae\nusually show three distinct stages of period evolution\n(figure \\ref{fig:stage}):\n(A) early stage of superhump evolution having a longer $P_{\\rm SH}$,\n(B) middle segment with a stabilized period usually with a positive\n$P_{\\rm dot}$,\\footnote{\n This segment occasionally appears to be composed of two linear segments\n forming a ``V''-shaped dip. Although this could suggest that the\n stage B may not be a continuous entity, we preserve the current\n staging for simplicity and for direct comparison with earlier works.\n Such instances will be individually discussed in section\n \\ref{sec:individual}.\n} and (C) late stage with a shorter, stable superhump\nperiod.\nIn well-observed systems, the transitions between stages A and B,\nand stages B and C are usually abrupt, associated with discontinuous\nperiod changes. Although \\citet{ole03ksuma} referred these transitions\nto decreasing superhump periods, treating as if they are smooth\nvariations, we adopted the above phenomenological staging because the\ntransitions are usually discontinuous.\n\n Figure \\ref{fig:ocsamp} shows $O-C$ diagrams\nof representative systems taken from section \\ref{sec:individual}\nand from literature, in which systems all the three stages were observed.\nThe figures are arranged in the increasing order of superhump periods\n(the periods given in the figures refer to the mean periods during\nthe stage B). The thin lines are quadratic fits to the stage B.\nNote that the range of cycle counts ($E$) is different between\nfigures and that the start of stage B was defined to be $E=20$\nfor better visualization.\n\n We can see the following general tendency on these figures:\n(1) the period derivative during the stage B becomes systematically\nsmaller with increasing $P_{\\rm SH}$, and (2) the duration of the stage B\nbecomes systematically shorter with increasing $P_{\\rm SH}$ or\nthe fractional superhump excess $\\epsilon = P_{\\rm SH}\/P_{\\rm orb}-1$\n(figures \\ref{fig:bdur}, \\ref{fig:bdureps}).\n\n The last four long-$P_{\\rm SH}$ systems (SU UMa, DH Aql, SDSS J1556,\nUV Gem) and BZ Cir have nearly zero or negative $P_{\\rm dot}$,\nbut are included in this sequence of figures because they have\nall the three distinct stages and because the behavior in these objects\ncan be understood as a smooth extension of the tendency in\nshorter-$P_{\\rm SH}$ systems.\n\n Note also that a few historically controversial systems (V436 Cen:\n\\cite{sem80v436cen}, and \\cite{war83v436cen} for a discussion;\nOY Car: \\cite{krz85oycarsuper}, and \\cite{pat93vyaqr} for a discussion)\ncan well fit the present general tendency and no anomalies were apparent.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,130mm){fig3.eps}\n \\end{center}\n \\caption{Representative $O-C$ diagram showing three stages (A--C)\n of $O-C$ variation. The data were taken from the 2000 superoutburst\n of SW UMa. (Upper:) $O-C$ diagram. Three distinct stages\n (A -- evolutionary stage, B -- middle stage, and C -- stage after\n transition to a shorter period) and the location of the period break\n between stages B and C are shown. (Middle): Amplitude of superhumps.\n As shown in \\citet{soe09asas1600}, the maximum amplitudes of superhumps\n coincide with transitions between stages (A to B and B to C).\n (Lower:) Deviations from linear decline during the superoutburst\n plateau. As seen in \\citet{soe09asas1600} and \\citet{kat03hodel},\n rebrightening during the terminal plateau also corresponds to the\n transition from stage B to C.\n }\n \\label{fig:stage}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,175mm){fig4.eps}\n \\end{center}\n \\caption{$O-C$ diagrams of SU UMa-type dwarf novae showing three distinct\n stages.\n }\n \\label{fig:ocsamp}\n\\end{figure}\n\n\\addtocounter{figure}{-1}\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,175mm){fig5.eps}\n \\end{center}\n \\caption{$O-C$ diagrams of SU UMa-type dwarf novae showing three distinct\n stages (continued).\n }\n\\end{figure}\n\n\\addtocounter{figure}{-1}\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,175mm){fig6.eps}\n \\end{center}\n \\caption{$O-C$ diagrams of SU UMa-type dwarf novae showing three distinct\n stages (continued).\n }\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,100mm){fig7.eps}\n \\end{center}\n \\caption{Duration of stage B. The duration of stage B decreases with\n increasing $P_{\\rm SH}$ both in cycle numbers (upper) and\n time in days (lower). We used mean $P_{\\rm SH}$ during the stage B\n as the representative $P_{\\rm SH}$.\n }\n \\label{fig:bdur}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,100mm){fig8.eps}\n \\end{center}\n \\caption{Duration of stage B. The duration of stage B decreases with\n increasing $\\epsilon$ both in cycle numbers (upper) and\n time in days (lower). We used mean $P_{\\rm SH}$ during the stage B\n for evaluating $\\epsilon$.\n }\n \\label{fig:bdureps}\n\\end{figure}\n\n\\subsection{Transition to a Shorter Period}\n\n Following the stage B, most of well-observed objects\nshowed a transition to a stage with a shorter $P_{\\rm SH}$.\nWhen stage A was not observed or non-existent, this transition on\nthe $O-C$ diagram appears as a form of ``period break''. The corresponding\nlocation of this break is shown in figure \\ref{fig:stage}.\nFigure \\ref{fig:octrans} shows $O-C$ diagrams\nof selected systems taken from section \\ref{sec:individual}\nand literature,\nin which systems this transition (stage B to stage C) was recorded,\nbut stage A was not observed.\nThe durations of the stage B in these systems were not as exactly defined\nas in the objects treated in subsection \\ref{sec:tendency}.\n\n Combined with the objects is subsection \\ref{sec:tendency},\nthis transition found to be quite generally, if not always, seen in many\nSU UMa-type dwarf novae. In many well-observed objects, the periods\nof superhumps varied little after this transition, in contrast to\nthe systematic variation seen during the stage B.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,175mm){fig9.eps}\n \\end{center}\n \\caption{$O-C$ diagrams of SU UMa-type dwarf novae showing transition\n in the superhump period.\n }\n \\label{fig:octrans}\n\\end{figure}\n\n\\addtocounter{figure}{-1}\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,175mm){fig10.eps}\n \\end{center}\n \\caption{$O-C$ diagrams of SU UMa-type dwarf novae showing transition\n in the superhump period (continued).\n }\n\\end{figure}\n\n\\subsection{Global Period Derivatives}\n\n Several authors, including us, have pointed out that $P_{\\rm dot}$\nin SU UMa-type dwarf novae has a strong correlation with $P_{\\rm SH}$\n(e.g. \\cite{kat01hvvir}; \\cite{kat03v877arakktelpucma}; \\cite{uem05tvcrv};\n\\cite{rut07v419lyr}). These works, however, were based on results from\ndifferent segments of $O-C$ diagrams for extracting $P_{\\rm dot}$.\nOn the other hand, \\citet{pat93vyaqr} and their descendant papers\ncalculated $P_{\\rm SH}$ from the entire superoutburst (frequently\nconsisting of stages A--C), and led to a conclusion that almost all\n$P_{\\rm dot}$'s were negative or zero\n(see also a discussion in \\cite{ole03ksuma}).\n\n We nominally calculated $P_{\\rm dot}$ for the entire superoutburst\n(restricting to $0 \\le E \\le 200$ to avoid contaminations from\npost-superoutburst variations) and simulated the treatment by\n\\citet{pat93vyaqr}. The results presented in figure \\ref{fig:global}\\footnote{\n Individual values of $P_{\\rm dot}$ are not presented because this\n analysis is meaningful only in the context of statistical comparison\n with previous research, and because globally determined $P_{\\rm dot}$'s\n on highly structured $O-C$'s are no better than nominal values.\n Better-defined $P_{\\rm dot}$ for individual objects are discussed\n in \\ref{sec:pdotb} and later (sub)sections.\n}\nindicate that more than half of systems below $P_{\\rm SH} = 0.065$ d\nhave negative $P_{\\rm dot}$. The presence of systems with positive\n$P_{\\rm SH}$ and the decreasing trend of $P_{\\rm dot}$ with increasing\n$P_{\\rm SH}$ are already evident from this global determination.\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,140mm){fig11.eps}\n \\end{center}\n \\caption{Globally Determined $P_{\\rm dot}$.\n Several objects with extremely negative $P_{\\rm dot}$\n (e.g. AX Cap: $-83.0(10.5) \\times 10^{-5}$, $P_{\\rm SH}$ = 0.1131 d,\n MN Dra: $-165.9(17.7) \\times 10^{-5}$, $P_{\\rm SH}$ = 0.1077 d,\n NY Ser: $-143.7(7.8) \\times 10^{-5}$, 0.1072 d,\n GX Cas: $-66.3(15.2) \\times 10^{-5}$, 0.0939 d,\n UV Gem: $-53.4(3.8) \\times 10^{-5}$, 0.0931 d)\n are outside this figure.\n }\n \\label{fig:global}\n\\end{figure*}\n\n\\subsection{Period Derivatives during Stage B}\\label{sec:pdotb}\n\n Since the stages B and C were better studied than the stage A\nin many systems, and since they have general properties common to the\nmajority of superoutbursts, we first describe the stages B and C.\n\n We determined $P_{\\rm dot}$ for the stage B. This treatment corresponds\nto the analysis in \\citet{kat01hvvir} for short-$P_{\\rm SH}$ systems.\nThe values are listed in table \\ref{tab:perlist} as well as other\nparameters discussed in subsection \\ref{sec:pshstageb}.\\footnote{\n The intervals ($E_1$ and $E_2$) for the stages B and C given in the table\n sometimes overlap because of occasional observational ambiguity\n in determining the stages. The values of $P_{\\rm orb}$ are\n taken from \\citet{RitterCV7}.\n}\nThe results are shown in figures \\ref{fig:pdotpsh} and \\ref{fig:pdotpsh2}.\nThis figure is essentially an improvement of the corresponding figures\npresented in \\citet{kat01hvvir} and \\citet{kat03v877arakktelpucma},\nin that the present samples do not include globally determined $P_{\\rm dot}$\nor locally determined $P_{\\rm dot}$ around the transitions (stage A to B\nor stage B to C), and in that $P_{\\rm dot}$ were (re-)determined\nin a homogeneous way from the times of superhump maxima, either published\nin the literature or re-examined in this paper.\nNote, in particular, that two unusual systems,\nV485 Cen and EI Psc, now have more usual $P_{\\rm dot}$ in contrast to\n\\citet{kat01hvvir}. This was caused by an error in estimating\n$P_{\\rm dot}$ in the original paper (V485 Cen: \\cite{ole97v485cen})\nand a combination of two sets of published superhump maxima (EI Psc:\n\\cite{uem02j2329}; \\cite{ski02j2329}). The figure indicates that\nsystems with $P_{\\rm SH} < 0.08$ d have a general tendency\nof a positive $P_{\\rm dot}$ during the stage B.\n\n Figure \\ref{fig:pdoteps} shows the relation between $P_{\\rm dot}$\n(for the stage B) versus $\\epsilon$. The period derivative has a strong\ncorrelation with $\\epsilon$, which is believed to be an excellent\nmeasure for the mass ratio $q = M_2\/M_1$.\nIt would be worth noting that two systems with\nunusually short $P_{\\rm orb}$ (filled squares: EI Psc, V485 Cen)\nfollow the same relation as the rest of systems, suggesting that\n$P_{\\rm dot}$ is more dependent on $q$ than on $P_{\\rm orb}$.\n$P_{\\rm dot}$ reaches a maximum around $\\epsilon$ = 0.025\n(equivalent to $q$ = 0.12).\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(120mm,80mm){fig12.eps}\n \\end{center}\n \\caption{$P_{\\rm dot}$ for stage B versus the mean $P_{\\rm SH}$ during\n stage B.\n }\n \\label{fig:pdotpsh}\n\\end{figure*}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(120mm,80mm){fig13.eps}\n \\end{center}\n \\caption{$P_{\\rm dot}$ for stage B versus $P_{\\rm SH}$ (enlarged).\n }\n \\label{fig:pdotpsh2}\n\\end{figure*}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,140mm){fig14.eps}\n \\end{center}\n \\caption{$P_{\\rm dot}$ (for stage B) versus $\\epsilon$.\n $P_{\\rm dot}$ for stage B has a strong correlation with fractional\n superhump excess ($\\epsilon$), which is believed to be an excellent\n measure for $q$. The $\\epsilon$ was determined from the mean\n $P_{\\rm SH}$ during the stage B.\n Two systems with unusually short $P_{\\rm orb}$\n (filled squares: EI Psc, V485 Cen) follow the same relation as the\n rest of systems. One exceptionally large-$\\epsilon$ object\n (TU Men: $\\epsilon$ = 0.073, $P_{\\rm dot}$ = $-2.8(2.7) \\times 10^{-5}$)\n is located outside this figure.\n }\n \\label{fig:pdoteps}\n\\end{figure*}\n\n\\subsection{Superhump Periods during Stages B and C}\\label{sec:pshstageb}\n\n Figure \\ref{fig:dpporb} summarizes fractional decrease of the superhump\nperiod between stage B (hereafter period $P_1$) and\nstage C (hereafter period $P_2$) versus $P_{\\rm SH}$.\nThe superhump period usually decrease by $\\sim$0.5 \\% during\nthe transition from stage B to C.\nThere appears to be a weak relation between the fractional decrease\nand $P_{\\rm SH}$: the decrease is larger in longer-$P_{\\rm SH}$ systems.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig15.eps}\n \\end{center}\n \\caption{Fractional decrease of superhump period between stages B and C\n versus $P_{\\rm SH}$.\n }\n \\label{fig:dpporb}\n\\end{figure}\n\n Figure \\ref{fig:pstartporb} shows the relation between the fractional\nsuperhump excess at the beginning of the stage B (calculated using the\nmean $P_{\\rm SH}$ and $P_{\\rm dot}$) versus $P_{\\rm orb}$.\nThe figure was drawn for\nsystems with a well-defined stage B (corresponding to subsection\n\\ref{sec:tendency}) and with a known $P_{\\rm orb}$. The relation\nis tighter than the well-known relation between the global $P_{\\rm SH}$\nand $P_{\\rm orb}$ (e.g. \\cite{mol92SHexcess}).\nA linear regression to the data has yielded the following relation:\n\n\\begin{equation}\nP_{\\rm SH (start)}\/P_{\\rm orb}-1 = -0.033(6) + 0.87(9) P_{\\rm orb}\n\\label{equ:pstartporb}.\n\\end{equation}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig16.eps}\n \\end{center}\n \\caption{Fractional superhump excess at the beginning of stage B versus\n mean $P_{\\rm orb}$. The dashed line represents equation\n \\ref{equ:pstartporb}.\n }\n \\label{fig:pstartporb}\n\\end{figure}\n\n Figure \\ref{fig:pendporb} shows the relation between the fractional\nsuperhump excess at the end of the stage B, i.e. the longest superhump\nperiod for positive-$P_{\\rm dot}$ systems, versus mean $P_{\\rm orb}$.\nThis fractional period excess has, in contrast to one at the\nbeginning of the stage B, a fairly common value of $\\sim$0.03 (slightly\nincreasing with increasing $P_{\\rm orb}$, equation \\ref{equ:pendporb})\nbelow the period gap.\nThe difference in dependence to $P_{\\rm orb}$ between\nthese two periods is striking, and is most prominent at shorter\n$P_{\\rm orb}$ except extreme WZ Sge-type dwarf novae\n(for WZ Sge-type dwarf novae, see description and discussion\nin section \\ref{sec:wzsgestars}).\nThis difference appears to determine the $P_{\\rm dot}$ -- $P_{\\rm SH}$\nrelation (subsection \\ref{sec:pdotb}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig17.eps}\n \\end{center}\n \\caption{Fractional superhump excess at the end of the stage B versus\n the mean $P_{\\rm orb}$. The dashed line represents equation\n \\ref{equ:pendporb}. The figure is restricted to the displayed\n range for a comparison with figure \\ref{fig:pstartporb}.\n }\n \\label{fig:pendporb}\n\\end{figure}\n\n\\begin{equation}\nP_{\\rm SH (end)}\/P_{\\rm orb}-1 = 0.001(4) + 0.44(6) P_{\\rm orb}\n\\label{equ:pendporb}.\n\\end{equation}\n\n The superhump excesses (or periods) during the stage C are almost\nidentical to those at the start of the stage B (figure \\ref{fig:pstartp2}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig18.eps}\n \\end{center}\n \\caption{Comparison of fractional superhump excesses between the stage C\n and the start of the stage B.\n The open and filled circles represent fractional\n superhump excesses in the stage C and at the start of the stage B,\n respectively.\n The superhump excesses during the stage C are almost identical to those\n at the start of the stage B. The figure is restricted to the displayed\n range for better visibility.\n }\n \\label{fig:pstartp2}\n\\end{figure}\n\n For readers' convenience, we also provide relations between\n$P_1$ and $P_{\\rm orb}$ (equation \\ref{equ:p1porb}, the samples are the same\nas in figure \\ref{fig:pstartporb}) and $P_2$ and $P_{\\rm orb}$\n(equation \\ref{equ:p2porb}).\n\n\\begin{equation}\nP_1\/P_{\\rm orb}-1 = -0.017(7) + 0.66(10) P_{\\rm orb}\n\\label{equ:p1porb}.\n\\end{equation}\n\n\\begin{equation}\nP_2\/P_{\\rm orb}-1 = -0.012(4) + 0.56(5) P_{\\rm orb}\n\\label{equ:p2porb}.\n\\end{equation}\n\n These equations can be used for estimating $P_{\\rm orb}$ (as in\n\\cite{RitterCV7}) when superhump periods for specific stages are known.\nThe potential availability of $P_2$ for estimating $P_{\\rm orb}$\nwould provide an excellent alternative to $P_{\\rm SH}$ at the start of\nthe stage B, since the break between the stages B and C is easier to\ndetect than the start of the stage B, particularly when the superoutburst\nis detected during its later course.\n\n The overall behavior of the stages B and C in positive-$P_{\\rm dot}$\nsystems can be summarized:\n\n\\begin{itemize}\n\\item The superhumps during the stage B start with a short period,\nwhich is well correlated with $P_{\\rm orb}$.\n\\item The superhumps evolve during the stage B toward a longer period,\nwhich commonly has a $\\sim$ 3 \\% excess to $P_{\\rm orb}$.\n\\item The superhump period return to the initial period during the stage C.\n\\end{itemize}\n\n\\subsection{Superhump Periods during Stage A}\n\n The stage A usually constitutes $\\sim$20 superhump cycles.\nTable \\ref{tab:pera} and figure \\ref{fig:ppre} summarize the recorded\nsuperhump periods during the stage A.\nNote, however, the periods during this stage were not very\nprecisely determined because of the shortness of the interval, and\nbecause the amplitudes of superhumps are still small.\nFractional period excesses during this stage to the mean superhump\nperiod during the stage B tend to cluster around 1.0--1.5 \\%, with some\nexceptional systems having larger ($\\sim$3 \\%) excesses.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig19.eps}\n \\end{center}\n \\caption{Superhump periods during the stage A. Superhumps in this stage\n has a period typically 1.0--1.5 \\% longer than the one during the stage B.\n Some systems have still longer periods ($\\sim$3 \\% longer than the one\n during the stage B).\n }\n \\label{fig:ppre}\n\\end{figure}\n\n\\subsection{Difference Between Different Superoutbursts}\\label{sec:different}\n\n \\citet{uem05tvcrv} reported significantly different $P_{\\rm dot}$'s\nbetween different superoutbursts of the same object, TV Crv.\nSeveral authors, however, have reported results contrary to this\nfinding (e.g. \\cite{oiz07v844her}; \\cite{soe09swuma}; \\cite{ohs09qzvir}).\n\n We further examined different superoutbursts of the same objects,\nand found no convincing evidence for strong variation of\n$P_{\\rm dot}$ between different superoutbursts. On the contrary,\nthe behavior of superhump period in the same object appears to\nbe similar between different superoutbursts (e.g. figure\n\\ref{fig:uvpercomp}; figures in section \\ref{sec:individual}).\nThe difference reported in the past was apparently a result of\nobservation of different stages of superoutbursts (A--C) and the\ninsufficient coverage of the entire superoutburst.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig20.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of UV Per between different\n superoutbursts.\n }\n \\label{fig:uvpercomp}\n\\end{figure}\n\n A re-examination of the TV Crv case has also shown that the claim\nby \\citet{uem05tvcrv} was not convincing (figure \\ref{fig:tvcrvcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig21.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of TV Crv between 2001 and\n 2004 superoutbursts. $E=0$ corresponds to the start of the stage B.\n }\n \\label{fig:tvcrvcomp}\n\\end{figure}\n\n During the 2004 superoutburst of V2527 Oph, no anomalous behavior\nin $P_{\\rm dot}$ was observed even in the presence of a clear\nprecursor outburst.\nSimilar situations were observed in GO Com (2003), PU CMa (2008),\nAQ Eri (2009), QZ Vir (1993, 2009) and 1RXS J0532 (2005).\\footnote{\n The period evolution during the 2008 superoutburst of 1RXS J0423,\n which was associated with a precursor, was slow\n (subsection \\ref{sec:j0423}). It is not clear whether\n the existence of a precursor is responsible in this instance.\n}\nThe proposed relation between the presence of a precursor outburst\nand $P_{\\rm SH}$ \\citep{uem05tvcrv} is not supported by\nthese instances.\n\n Although further work is needed to exclude the presence of\ndifferent period behavior between different superoutbursts,\nthe close agreement of the behavior between different superoutbursts\nin many objects might be used to construct a combined $O-C$ diagram\nand to determine $P_{\\rm dot}$ from different superoutbursts even if\nobservational coverage of each outburst is incomplete.\n\n\\section{Discussion}\\label{sec:discussion}\n\n\\subsection{Existence of Stage B--C Transition}\n\n In section \\ref{sec:general}, we described that most of\nwell-observed systems show stage B--C transitions.\nThere are, however, some objects (or superoutbursts) without\nprominent stage B--C transitions even though the late stage of\nsuperoutbursts is well observed. WZ Sge-type dwarf novae with\nsmall $P_{\\rm dot}$, in particular, have tendency to lack the\nstage B--C transition (see also section \\ref{sec:individual}).\n\n We examined superoutbursts regarding the existence of stage B--C\ntransitions. The sample was selected by criteria of ``well-observed''\nquality (quality A or B) and observational coverage for at least\n50 superhump cycles.\nAs shown in figure \\ref{fig:stagec}, the existence of stage B--C\ntransitions is most strongly correlated with $\\epsilon$.\nIn systems with a small $\\epsilon$ (typically $\\epsilon < 0.015$),\nonly a few superoutbursts showed stage B--C transitions.\nThe result suggests that the appearance of this transition is\nstrongly dependent on $q$.\n\n In systems with $\\epsilon > 0.02$, there are some superoutbursts\nwithout a clear transition to the stage C. The best observed example\nmight be V844 Her in 2006 \\citep{oiz07v844her}. During this superoutburst,\nthere was no indication of a transition even after 146 superhump cycles,\nwhen the outburst just entered the rapid decline stage.\nIn this case, however, the transition may have occurred after the termination\nof the observation since a transition was recorded during the rapid fading\nand subsequent stage during the 2008 superoutburst of the same object.\nThe present statistical analysis may be similarly biased toward\nthe lower detection rate of the transition for systems with long-lasting\nstage B, i.e. systems with a shorter $P_{\\rm SH}$ or a smaller $\\epsilon$\n(subsection \\ref{sec:tendency}).\nEven considering this effect, the apparent rarity of the transition\nin small-$P_{\\rm dot}$ WZ Sge-type dwarf novae is likely significant,\nsince these objects were often observed even after the termination of their\nsuperoutbursts.\n\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives}\\label{tab:perlist}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ (d) & err & \\multicolumn{2}{c}{$E_1$$^*$} & $P_{\\rm dot}$$^\\dagger$ & err$^\\dagger$ & $P_2$ (d) & err & \\multicolumn{2}{c}{$E_2$$^*$} & $P_{\\rm orb}$ (d) & Q$^\\ddagger$ \\\\\n\\hline\nFO And & 1994 & 0.074554 & 0.000052 & 0 & 14 & -- & -- & 0.074018 & 0.000012 & 13 & 27 & 0.07161 & C \\\\\nKV And & 1994 & 0.074601 & 0.000122 & 0 & 55 & -- & -- & 0.074063 & -- & 55 & 95 & -- & C \\\\\nKV And & 2002 & 0.074501 & 0.000045 & 0 & 41 & -- & -- & 0.074155 & 0.000064 & 41 & 82 & -- & C \\\\\nLL And & 1993 & 0.056900 & 0.000088 & 0 & 56 & -- & -- & -- & -- & -- & -- & 0.055055 & C \\\\\nLL And & 2004 & 0.056583 & 0.000022 & 0 & 290 & 1.0 & 0.6 & 0.056223 & 0.000201 & 290 & 326 & 0.055055 & C \\\\\nV402 And & 2005 & 0.063230 & 0.000058 & 0 & 41 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV402 And & 2006 & 0.063439 & 0.000062 & 0 & 79 & 12.7 & 2.1 & -- & -- & -- & -- & -- & C \\\\\nV402 And & 2008 & 0.063532 & 0.000029 & 0 & 95 & 4.2 & 3.7 & -- & -- & -- & -- & -- & CG \\\\\nV455 And & 2007 & 0.057133 & 0.000010 & 23 & 128 & 4.7 & 1.2 & -- & -- & -- & -- & 0.056309 & A \\\\\nV466 And & 2008 & 0.057203 & 0.000015 & 20 & 194 & 5.7 & 0.7 & 0.057138 & 0.000024 & 208 & 349 & 0.056365 & AE \\\\\nDH Aql & 2002 & 0.080020 & 0.000017 & 12 & 52 & $-$6.9 & 3.7 & 0.079514 & 0.000034 & 76 & 128 & -- & A \\\\\nDH Aql & 2003 & -- & -- & -- & -- & -- & -- & 0.079593 & -- & 49 & 120 & -- & C \\\\\nDH Aql & 2007 & -- & -- & -- & -- & -- & -- & 0.079527 & 0.000044 & 0 & 76 & -- & C \\\\\nDH Aql & 2008 & -- & -- & -- & -- & -- & -- & 0.079493 & 0.000043 & 0 & 38 & -- & C \\\\\nV725 Aql & 1999 & -- & -- & -- & -- & -- & -- & 0.099134 & 0.000141 & 0 & 54 & -- & C \\\\\nV725 Aql & 2005 & 0.098525 & 0.000080 & 0 & 30 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV1141 Aql & 2002 & 0.063076 & 0.000032 & 0 & 79 & 9.3 & 4.3 & -- & -- & -- & -- & -- & B \\\\\nV1141 Aql & 2003 & 0.062961 & 0.000023 & 0 & 70 & 13.4 & 1.6 & -- & -- & -- & -- & -- & B \\\\\nVY Aqr & 1986 & 0.064867 & 0.000041 & 0 & 31 & -- & -- & 0.064288 & 0.000020 & 30 & 155 & 0.06309 & B \\\\\nVY Aqr & 2008 & 0.064657 & 0.000014 & 12 & 144 & 8.5 & 0.5 & 0.064272 & 0.000029 & 137 & 215 & 0.06309 & A \\\\\nEG Aqr & 2006 & 0.078958 & 0.000014 & 12 & 71 & $-$3.2 & 2.1 & 0.078505 & 0.000012 & 83 & 198 & -- & A \\\\\nEG Aqr & 2008 & 0.078760 & 0.000018 & 0 & 63 & $-$1.3 & 3.1 & -- & -- & -- & -- & -- & C \\\\\nBF Ara & 2002 & 0.087887 & 0.000019 & 0 & 102 & $-$2.8 & 1.6 & -- & -- & -- & -- & 0.08417 & C \\\\\nV663 Ara & 2004 & 0.076420 & 0.000061 & 0 & 40 & -- & -- & 0.076170 & 0.000144 & 37 & 52 & -- & C \\\\\nV877 Ara & 2002 & 0.083928 & 0.000023 & 24 & 98 & $-$5.7 & 2.9 & -- & -- & -- & -- & -- & CG2 \\\\\nBB Ari & 2004 & 0.072122 & 0.000026 & 0 & 75 & 1.6 & 3.0 & -- & -- & -- & -- & -- & C2 \\\\\nHV Aur & 2002 & 0.085563 & 0.000038 & 0 & 62 & $-$3.5 & 5.0 & -- & -- & -- & -- & -- & CG \\\\\nTT Boo & 2004 & 0.078085 & 0.000018 & 13 & 120 & 8.3 & 0.7 & 0.077666 & 0.000013 & 120 & 218 & -- & A \\\\\nUZ Boo & 1994 & 0.061743 & 0.000038 & 0 & 178 & $-$1.5 & 2.5 & -- & -- & -- & -- & -- & C \\\\\nUZ Boo & 2003 & 0.061922 & 0.000033 & 30 & 118 & $-$1.9 & 6.3 & -- & -- & -- & -- & -- & C \\\\\nNN Cam & 2007 & 0.074292 & 0.000021 & 0 & 28 & -- & -- & 0.073855 & 0.000018 & 24 & 82 & 0.0717 & B \\\\\nOY Car & 1980 & 0.064631 & 0.000026 & 0 & 126 & 8.9 & 1.6 & -- & -- & -- & -- & 0.063121 & B \\\\\nSY Cap & 2008 & 0.063759 & 0.000022 & 0 & 49 & $-$11.4 & 9.0 & -- & -- & -- & -- & -- & C \\\\\nAX Cap & 2004 & 0.115938 & 0.000356 & 8 & 34 & $-$86.5 & 65.3 & 0.111432 & 0.000091 & 34 & 99 & -- & C \\\\\nGX Cas & 1994 & -- & -- & -- & -- & -- & -- & 0.092947 & 0.000064 & 0 & 65 & -- & C \\\\\nGX Cas & 1996 & -- & -- & -- & -- & -- & -- & 0.093042 & 0.000014 & 44 & 109 & -- & C \\\\\nGX Cas & 1999 & 0.093525 & 0.000050 & 21 & 44 & -- & -- & 0.092958 & 0.000023 & 42 & 108 & -- & B \\\\\nGX Cas & 2006 & -- & -- & -- & -- & -- & -- & 0.092761 & 0.000143 & 52 & 74 & -- & C \\\\\nHT Cas & 1985 & 0.075920 & 0.000020 & 1 & 14 & -- & -- & -- & -- & -- & -- & 0.073647 & C2 \\\\\nKP Cas & 2008 & 0.085529 & 0.000060 & 0 & 15 & -- & -- & 0.085200 & 0.000021 & 15 & 53 & -- & B \\\\\nV452 Cas & 1999 & -- & -- & -- & -- & -- & -- & 0.088561 & 0.000061 & 0 & 57 & -- & C \\\\\nV452 Cas & 2007 & 0.089434 & 0.000072 & 0 & 21 & -- & -- & 0.088690 & 0.000017 & 20 & 102 & -- & B \\\\\nV452 Cas & 2008 & 0.089319 & 0.000026 & 0 & 34 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV359 Cen & 2002 & 0.081210 & 0.000072 & 22 & 50 & -- & -- & 0.080772 & 0.000028 & 49 & 104 & -- & B \\\\\nV436 Cen & 1978 & 0.063663 & 0.000014 & 16 & 81 & 5.2 & 1.9 & 0.063550 & 0.000033 & 81 & 160 & 0.062501 & B \\\\\nV485 Cen & 1997 & 0.042156 & 0.000008 & 0 & 188 & 2.8 & 0.3 & -- & -- & -- & -- & 0.040995 & B \\\\\nV485 Cen & 2001 & 0.042066 & 0.000024 & 0 & 103 & 1.2 & 4.5 & 0.041834 & 0.000159 & 100 & 127 & 0.040995 & C \\\\\nV485 Cen & 2004 & 0.042164 & 0.000010 & 0 & 167 & 3.1 & 0.9 & 0.041899 & 0.000028 & 166 & 190 & 0.040995 & B \\\\\nV1040 Cen & 2002 & 0.062179 & 0.000034 & 17 & 86 & 27.1 & 2.2 & 0.061751 & 0.000119 & 85 & 103 & 0.060296 & A \\\\\nWX Cet & 1989 & 0.059616 & 0.000050 & 33 & 185 & 10.3 & 1.4 & 0.059150 & 0.000110 & 184 & 201 & 0.058261 & B \\\\\n\\hline\n \\multicolumn{13}{l}{$^*$ Interval used for calculating the period (corresponding to $E$ in section \\ref{sec:individual}).} \\\\\n \\multicolumn{13}{l}{$^\\dagger$ Unit $10^{-5}$.} \\\\\n \\multicolumn{13}{l}{$^\\ddagger$ Data quality and comments. A: excellent, B: partial coverage or slightly low quality, C: insufficient coverage or}\\\\\n \\multicolumn{13}{l}{\\phantom{$^\\ddagger$} observations with large scatter, G: $P_{\\rm dot}$ denotes global $P_{\\rm dot}$, M: observational gap in middle stage,}\\\\\n \\multicolumn{13}{l}{\\phantom{$^\\ddagger$} 2: late-stage coverage, the listed period may refer to $P_2$, E: $P_{\\rm orb}$ refers to the period of early superhumps.} \\\\\n \\multicolumn{13}{l}{\\phantom{$^\\ddagger$} P: $P_{\\rm orb}$ refers to a shorter stable periodicity recorded in outburst.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nWX Cet & 1998 & 0.059529 & 0.000014 & 15 & 157 & 6.4 & 1.0 & 0.059217 & 0.000038 & 149 & 220 & 0.058261 & A \\\\\nWX Cet & 2001 & 0.059549 & 0.000028 & 0 & 129 & 7.5 & 1.1 & -- & -- & -- & -- & 0.058261 & B \\\\\nWX Cet & 2004 & 0.059534 & 0.000023 & 0 & 137 & 5.5 & 1.8 & 0.059047 & 0.000182 & 136 & 169 & 0.058261 & C \\\\\nZ Cha & 1982 & 0.077252 & 0.000064 & 0 & 38 & -- & -- & 0.076813 & 0.000063 & 38 & 65 & 0.074499 & B \\\\\nRX Cha & 2009 & 0.084921 & 0.000021 & 0 & 34 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nBZ Cir & 2004 & 0.076614 & 0.000019 & 13 & 68 & $-$0.5 & 3.8 & 0.076250 & 0.000010 & 66 & 146 & -- & B \\\\\nPU CMa & 2003 & 0.057962 & 0.000054 & 0 & 51 & -- & -- & 0.057587 & 0.000019 & 51 & 144 & 0.056694 & B \\\\\nPU CMa & 2005 & 0.058011 & 0.000024 & 0 & 93 & 11.4 & 1.8 & 0.057684 & 0.000022 & 91 & 231 & 0.056694 & B \\\\\nPU CMa & 2008 & 0.058033 & 0.000033 & 16 & 121 & 4.4 & 3.1 & -- & -- & -- & -- & 0.056694 & C \\\\\nYZ Cnc & 2007 & 0.090307 & 0.000046 & 0 & 66 & $-$5.1 & 4.7 & -- & -- & -- & -- & 0.0868 & C \\\\\nAK Cnc & 1992 & 0.067510 & 0.000183 & 0 & 17 & -- & -- & -- & -- & -- & -- & 0.0651 & C \\\\\nAK Cnc & 1999 & 0.067376 & 0.000040 & 0 & 88 & -- & -- & -- & -- & -- & -- & 0.0651 & C \\\\\nAK Cnc & 2003 & 0.067428 & 0.000032 & 0 & 100 & 4.8 & 3.2 & 0.066672 & 0.000084 & 100 & 120 & 0.0651 & C \\\\\nCC Cnc & 2001 & 0.075892 & 0.000089 & 0 & 53 & -- & -- & 0.075327 & 0.000046 & 51 & 119 & 0.07352 & B \\\\\nEG Cnc & 1996 & 0.060337 & 0.000006 & 0 & 157 & 0.8 & 0.5 & -- & -- & -- & -- & 0.05997 & A \\\\\nAL Com & 1995 & 0.057289 & 0.000010 & 24 & 229 & 1.9 & 0.5 & 0.057000 & -- & 229 & 264 & 0.056668 & A \\\\\nAL Com & 2001 & 0.057229 & 0.000014 & 28 & 222 & $-$0.2 & 0.8 & -- & -- & -- & -- & 0.056668 & C \\\\\nAL Com & 2008 & -- & -- & -- & -- & -- & -- & 0.057174 & 0.000006 & -- & -- & 0.056668 & C \\\\\nGO Com & 2003 & 0.063077 & 0.000025 & 16 & 115 & 15.5 & 2.3 & 0.062861 & 0.000042 & 113 & 262 & -- & A \\\\\nGO Com & 2005 & 0.063050 & 0.000018 & 0 & 142 & 6.9 & 1.5 & 0.062921 & 0.000058 & 142 & 191 & -- & B \\\\\nGO Com & 2006 & 0.063086 & 0.000043 & 0 & 153 & 4.6 & 3.4 & -- & -- & -- & -- & -- & C \\\\\nGO Com & 2008 & 0.063047 & 0.000059 & 0 & 48 & 15.5 & 11.2 & -- & -- & -- & -- & -- & C \\\\\nV728 CrA & 2003 & 0.082378 & 0.000020 & 0 & 50 & $-$2.3 & 3.4 & -- & -- & -- & -- & -- & C \\\\\nVW CrB & 2001 & -- & -- & -- & -- & -- & -- & 0.072504 & 0.000052 & 0 & 180 & -- & C \\\\\nVW CrB & 2003 & 0.072917 & 0.000037 & 0 & 142 & 7.7 & 0.8 & 0.072902 & 0.000036 & 142 & 238 & -- & B \\\\\nVW CrB & 2006 & 0.072679 & 0.000055 & 0 & 42 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nTU Crt & 1998 & 0.085321 & 0.000027 & 0 & 61 & -- & -- & 0.084947 & 0.000024 & 61 & 137 & 0.08209 & B \\\\\nTU Crt & 2001 & 0.085175 & 0.000087 & 0 & 71 & $-$12.3 & 9.3 & -- & -- & -- & -- & 0.08209 & B \\\\\nTU Crt & 2009 & 0.085280 & 0.000026 & 23 & 37 & -- & -- & -- & -- & -- & -- & 0.08209 & B \\\\\nTV Crv & 2001 & 0.065005 & 0.000017 & 13 & 109 & 6.2 & 1.5 & 0.064776 & 0.000068 & 108 & 168 & 0.0629 & B \\\\\nTV Crv & 2003 & 0.064948 & 0.000029 & 0 & 170 & -- & -- & -- & -- & -- & -- & 0.0629 & CGM \\\\\nTV Crv & 2004 & 0.065089 & 0.000027 & 16 & 103 & 9.5 & 3.1 & 0.064498 & 0.000272 & 102 & 118 & 0.0629 & C \\\\\nV337 Cyg & 2006 & 0.070003 & 0.000107 & 0 & 30 & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\nV503 Cyg & 2002 & 0.081391 & 0.000218 & 0 & 38 & -- & -- & 0.080979 & 0.000043 & 38 & 77 & 0.0777 & C \\\\\nV503 Cyg & 2008 & 0.081767 & 0.000045 & 0 & 49 & -- & -- & 0.081022 & 0.000018 & 49 & 110 & 0.0777 & C \\\\\nV550 Cyg & 2000 & 0.069172 & 0.000256 & 0 & 35 & -- & -- & 0.068479 & 0.000055 & 32 & 91 & -- & C \\\\\nV630 Cyg & 1996 & -- & -- & -- & -- & -- & -- & 0.078966 & 0.000061 & 0 & 16 & -- & C \\\\\nV630 Cyg & 2008 & 0.079182 & 0.000073 & 0 & 40 & 27.4 & 7.7 & 0.078442 & 0.000084 & 39 & 77 & -- & C \\\\\nV632 Cyg & 2008 & 0.065833 & 0.000027 & 16 & 82 & 17.4 & 3.0 & 0.065426 & 0.000034 & 80 & 157 & 0.06377 & BG \\\\\nV1028 Cyg & 1995 & 0.061749 & 0.000023 & 15 & 148 & 8.2 & 1.2 & 0.061532 & 0.000056 & 139 & 195 & -- & A \\\\\nV1028 Cyg & 1996 & -- & -- & -- & -- & -- & -- & 0.061536 & 0.000098 & 90 & 132 & -- & C \\\\\nV1028 Cyg & 1999 & 0.061696 & 0.000067 & 0 & 148 & 12.2 & 3.1 & -- & -- & -- & -- & -- & C \\\\\nV1028 Cyg & 2002 & 0.061772 & 0.000031 & 0 & 55 & 14.7 & 5.5 & 0.061518 & 0.000132 & 54 & 70 & -- & C \\\\\nV1028 Cyg & 2004 & 0.061770 & 0.000065 & 0 & 38 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV1028 Cyg & 2008 & 0.061833 & 0.000021 & 0 & 114 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV1113 Cyg & 1994 & 0.079059 & 0.000044 & 26 & 64 & -- & -- & 0.079059 & 0.000044 & 26 & 64 & -- & C \\\\\nV1113 Cyg & 2008 & 0.079051 & 0.000023 & 0 & 47 & $-$5.2 & 4.7 & -- & -- & -- & -- & -- & CG \\\\\nV1251 Cyg & 1991 & 0.076284 & 0.000074 & 0 & 16 & -- & -- & 0.075937 & 0.000079 & 14 & 42 & 0.07433 & CE \\\\\nV1251 Cyg & 2008 & 0.075973 & 0.000020 & 0 & 62 & 6.0 & 2.7 & 0.075663 & 0.000042 & 61 & 154 & 0.07433 & AE \\\\\nV1316 Cyg & 2006 & 0.076845 & 0.000026 & 0 & 70 & $-$5.1 & 2.8 & 0.076541 & 0.000014 & 94 & 273 & -- & A \\\\\nV1454 Cyg & 2006 & 0.061017 & 0.000048 & 113 & 196 & 15.0 & 4.3 & 0.060523 & 0.000086 & 195 & 278 & -- & C \\\\\nV1504 Cyg & 1994 & 0.072249 & 0.000022 & 0 & 43 & -- & -- & -- & -- & -- & -- & 0.06951 & C \\\\\nV1504 Cyg & 2008 & 0.072151 & 0.000053 & 0 & 14 & -- & -- & -- & -- & -- & -- & 0.06951 & C \\\\\nV1504 Cyg & 2009 & -- & -- & -- & -- & -- & -- & 0.071806 & 0.000039 & 0 & 42 & 0.06951 & C \\\\\nV2176 Cyg & 1997 & 0.056239 & 0.000012 & -- & -- & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nHO Del & 1994 & 0.064559 & 0.000056 & 0 & 49 & 10.0 & 15.4 & 0.064128 & 0.000054 & 47 & 94 & 0.06266 & C \\\\\nHO Del & 2001 & 0.064280 & 0.000120 & 0 & 2 & -- & -- & -- & -- & -- & -- & 0.06266 & C \\\\\nHO Del & 2008 & 0.064363 & 0.000017 & 11 & 96 & 6.4 & 1.5 & 0.063958 & 0.000044 & 95 & 165 & 0.06266 & B \\\\\nBC Dor & 2003 & 0.068473 & 0.000016 & 0 & 61 & -- & -- & 0.068021 & 0.000007 & 59 & 146 & -- & C \\\\\nCP Dra & 2003 & 0.083698 & 0.000028 & 0 & 15 & -- & -- & 0.082977 & 0.000162 & 36 & 49 & -- & C \\\\\nCP Dra & 2009 & 0.083822 & 0.000073 & 0 & 26 & -- & -- & 0.083362 & 0.000027 & 24 & 97 & -- & B \\\\\nDM Dra & 2003 & 0.075707 & 0.000051 & 0 & 40 & -- & -- & 0.075285 & 0.000044 & 38 & 81 & -- & C \\\\\nKV Dra & 2002 & 0.060295 & 0.000040 & 0 & 108 & 11.4 & 3.9 & 0.059956 & 0.000066 & 83 & 190 & -- & B \\\\\nKV Dra & 2004 & 0.060453 & 0.000076 & 0 & 96 & 43.4 & 8.5 & 0.059463 & 0.000208 & 94 & 118 & -- & B \\\\\nKV Dra & 2005 & 0.060341 & 0.000027 & 0 & 67 & 10.1 & 4.7 & -- & -- & -- & -- & -- & C \\\\\nKV Dra & 2009 & 0.060064 & 0.000061 & 7 & 42 & -- & -- & 0.060021 & 0.000110 & 105 & 124 & -- & CG \\\\\nMN Dra & 2002a & 0.104351 & 0.000368 & 0 & 16 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nMN Dra & 2002b & 0.108606 & 0.000307 & 10 & 27 & $-$10.0 & 12.0 & 0.105425 & 0.000191 & 27 & 51 & -- & B \\\\\nMN Dra & 2003 & 0.104796 & 0.000055 & 0 & 19 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nMN Dra & 2008 & 0.105140 & 0.000135 & 0 & 10 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nIX Dra & 2003 & 0.067003 & 0.000022 & 0 & 61 & 2.9 & 4.0 & 0.066692 & 0.000053 & 71 & 91 & -- & B \\\\\nXZ Eri & 2003a & 0.062955 & 0.000043 & 0 & 77 & 15.3 & 5.6 & 0.062578 & 0.000044 & 77 & 150 & 0.061159 & B \\\\\nXZ Eri & 2007 & 0.062807 & 0.000018 & 15 & 138 & 7.6 & 1.0 & 0.062653 & 0.000116 & 138 & 190 & 0.061159 & B \\\\\nXZ Eri & 2008 & 0.062796 & 0.000044 & 23 & 92 & 22.5 & 4.7 & 0.062722 & 0.000023 & 91 & 163 & 0.061159 & B \\\\\nAQ Eri & 1991 & 0.062250 & -- & -- & -- & -- & -- & -- & -- & -- & -- & 0.06094 & C \\\\\nAQ Eri & 1992 & 0.063810 & 0.000748 & 0 & 3 & -- & -- & 0.061634 & 0.000211 & 0 & 18 & 0.06094 & C \\\\\nAQ Eri & 2006 & 0.061681 & 0.000126 & 0 & 97 & 10.7 & 11.8 & -- & -- & -- & -- & 0.06094 & C \\\\\nAQ Eri & 2008 & 0.062359 & 0.000015 & 0 & 163 & 4.4 & 0.8 & -- & -- & -- & -- & 0.06094 & A \\\\\nUV Gem & 2003 & 0.093547 & 0.000076 & 12 & 34 & $-$35.9 & 21.5 & 0.092425 & 0.000040 & 33 & 81 & -- & A \\\\\nUV Gem & 2008 & -- & -- & -- & -- & -- & -- & 0.092758 & 0.000224 & 0 & 23 & -- & C \\\\\nAW Gem & 1995 & 0.079830 & 0.000113 & 12 & 25 & -- & -- & 0.079122 & 0.000044 & 25 & 51 & 0.07621 & C \\\\\nAW Gem & 2008 & 0.078990 & 0.000138 & 0 & 52 & -- & -- & -- & -- & -- & -- & 0.07621 & C \\\\\nAW Gem & 2009 & -- & -- & -- & -- & -- & -- & 0.078698 & 0.000056 & 63 & 114 & 0.07621 & C \\\\\nCI Gem & 2005 & 0.119309 & 0.000590 & 0 & 17 & -- & -- & 0.108501 & 0.001404 & 16 & 26 & -- & C \\\\\nIR Gem & 1991 & 0.070821 & 0.000144 & 0 & 15 & -- & -- & -- & -- & -- & -- & 0.0684 & C \\\\\nIR Gem & 2009 & 0.070925 & 0.000032 & 0 & 27 & -- & -- & 0.070299 & 0.000077 & 27 & 103 & 0.0684 & C \\\\\nCI Gru & 2004 & 0.054020 & 0.000140 & 0 & 5 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV592 Her & 1998 & 0.056498 & 0.000013 & 0 & 152 & 2.1 & 0.8 & -- & -- & -- & -- & -- & C \\\\\nV660 Her & 2004 & 0.080994 & 0.000012 & 0 & 67 & 1.6 & 2.2 & 0.080747 & 0.000073 & 67 & 116 & -- & C \\\\\nV844 Her & 1997 & 0.056007 & 0.000024 & 0 & 160 & 0.9 & 2.2 & -- & -- & -- & -- & 0.054643 & CM \\\\\nV844 Her & 1999 & 0.055906 & 0.000023 & 0 & 126 & 4.5 & 2.8 & -- & -- & -- & -- & 0.054643 & C \\\\\nV844 Her & 2002 & 0.055859 & 0.000023 & 0 & 129 & 4.4 & 1.2 & -- & -- & -- & -- & 0.054643 & C \\\\\nV844 Her & 2006 & 0.055868 & 0.000021 & 17 & 146 & 10.9 & 1.0 & -- & -- & -- & -- & 0.054643 & A \\\\\nV844 Her & 2008 & 0.055935 & 0.000023 & 0 & 149 & 7.1 & 0.4 & 0.055826 & 0.000043 & 149 & 179 & 0.054643 & B \\\\\nV1108 Her & 2004 & 0.057480 & 0.000034 & 29 & 97 & 1.6 & 6.8 & -- & -- & -- & -- & 0.05703 & B2P \\\\\nRU Hor & 2003 & 0.070950 & 0.000017 & 0 & 76 & 7.5 & 1.1 & 0.070478 & 0.000059 & 76 & 101 & -- & A \\\\\nRU Hor & 2008 & 0.071032 & 0.000017 & 1 & 44 & 6.5 & 3.2 & 0.070530 & 0.000020 & 43 & 114 & -- & B \\\\\nCT Hya & 1999 & 0.066425 & 0.000062 & 0 & 75 & 18.3 & 6.2 & 0.066164 & 0.000072 & 63 & 105 & -- & B \\\\\nCT Hya & 2000 & 0.066390 & 0.000035 & 0 & 78 & 9.6 & 5.2 & -- & -- & -- & -- & -- & C \\\\\nCT Hya & 2002a & 0.066384 & 0.000082 & 14 & 136 & 11.6 & 3.8 & -- & -- & -- & -- & -- & C \\\\\nCT Hya & 2002b & 0.066408 & 0.000036 & 0 & 90 & 13.2 & 3.1 & 0.066273 & 0.000081 & 90 & 151 & -- & C \\\\\nCT Hya & 2009 & 0.066630 & 0.000065 & 0 & 61 & 18.0 & 12.9 & -- & -- & -- & -- & -- & C \\\\\nMM Hya & 1998 & 0.058960 & 0.000071 & 0 & 52 & -- & -- & 0.058745 & 0.000316 & -- & -- & 0.057590 & C \\\\\nVW Hyi & 1972 & 0.076875 & 0.000033 & 0 & 65 & -- & -- & 0.076241 & 0.000177 & 65 & 79 & 0.074271 & B \\\\\nVW Hyi & 2000 & 0.076986 & 0.000055 & 0 & 60 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nRZ Leo & 2000 & 0.078658 & 0.000015 & 13 & 100 & 4.9 & 1.7 & 0.078225 & 0.000029 & 100 & 179 & 0.076038 & A \\\\\nRZ Leo & 2006 & 0.078428 & 0.000058 & 0 & 127 & -- & -- & -- & -- & -- & -- & 0.076038 & C \\\\\nGW Lib & 2007 & 0.054095 & 0.000010 & 51 & 278 & 4.0 & 0.1 & -- & -- & -- & -- & 0.05332 & A \\\\\nRZ LMi & 2004 & 0.059394 & 0.000030 & 10 & 86 & 13.5 & 1.3 & -- & -- & -- & -- & -- & B \\\\\nRZ LMi & 2005 & 0.059396 & 0.000011 & 0 & 86 & 2.3 & 1.1 & -- & -- & -- & -- & -- & C \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nSX LMi & 1994 & 0.069481 & 0.000017 & 0 & 45 & -- & -- & 0.069088 & 0.000025 & 45 & 118 & 0.06717 & B \\\\\nSX LMi & 2001 & 0.069144 & 0.000033 & 0 & 85 & 0.1 & 6.9 & 0.068935 & 0.000216 & 84 & 113 & 0.06717 & C \\\\\nSX LMi & 2002 & 0.069341 & 0.000004 & 14 & 115 & $-$0.7 & 0.5 & 0.069004 & 0.000030 & 115 & 130 & 0.06717 & C \\\\\nBR Lup & 2003 & 0.082284 & 0.000043 & 0 & 17 & -- & -- & 0.082000 & 0.000018 & 50 & 95 & 0.0795 & C \\\\\nBR Lup & 2004 & -- & -- & -- & -- & -- & -- & 0.082193 & 0.000038 & 0 & 96 & 0.0795 & C \\\\\nAY Lyr & 1987 & 0.075970 & 0.000018 & 0 & 92 & $-$0.1 & 2.0 & -- & -- & -- & -- & -- & B \\\\\nAY Lyr & 2008 & 0.076232 & 0.000099 & 0 & 28 & -- & -- & 0.075471 & 0.000077 & 27 & 54 & -- & B \\\\\nAY Lyr & 2009 & 0.076161 & 0.000065 & 0 & 28 & -- & -- & 0.075691 & 0.000030 & 26 & 94 & -- & C \\\\\nDM Lyr & 1996 & 0.067085 & 0.000050 & 0 & 32 & -- & -- & -- & -- & -- & -- & 0.065409 & C2 \\\\\nDM Lyr & 1997 & 0.067205 & 0.000248 & 0 & 46 & -- & -- & -- & -- & -- & -- & 0.065409 & C2 \\\\\nDM Lyr & 2002 & 0.067230 & 0.000054 & 0 & 59 & -- & -- & 0.067130 & 0.000043 & 58 & 134 & 0.065409 & C \\\\\nV344 Lyr & 1993 & 0.091354 & 0.000047 & 0 & 78 & $-$7.1 & 4.3 & -- & -- & -- & -- & -- & C \\\\\nV358 Lyr & 2008 & 0.055629 & 0.000032 & -- & -- & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV419 Lyr & 1999 & 0.090145 & 0.000140 & 3 & 38 & -- & -- & 0.089006 & 0.000073 & 36 & 78 & -- & C \\\\\nV419 Lyr & 2006 & 0.090060 & 0.000044 & 11 & 48 & -- & -- & 0.089745 & 0.000032 & 45 & 111 & -- & B \\\\\nV585 Lyr & 2003 & 0.060363 & 0.000018 & 32 & 150 & 10.7 & 1.2 & 0.060307 & 0.000067 & 150 & 181 & -- & A \\\\\nTU Men & 1980 & 0.125721 & 0.000035 & 0 & 96 & $-$2.8 & 2.7 & 0.124388 & 0.000033 & 96 & 120 & 0.1172 & B \\\\\nAD Men & 2004 & 0.096559 & 0.000228 & -- & -- & -- & -- & -- & -- & -- & -- & -- & C \\\\\nFQ Mon & 2004 & 0.073349 & 0.000035 & 0 & 111 & 9.2 & 2.4 & 0.072913 & 0.000054 & 109 & 205 & -- & B \\\\\nFQ Mon & 2006 & 0.073924 & 0.000103 & 0 & 51 & -- & -- & 0.072799 & 0.000071 & 51 & 134 & -- & C \\\\\nFQ Mon & 2007 & 0.073348 & 0.000022 & 0 & 124 & 5.4 & 1.3 & 0.073067 & 0.000083 & 122 & 164 & -- & B \\\\\nAB Nor & 2002 & 0.079620 & 0.000032 & 15 & 142 & $-$8.1 & 2.7 & -- & -- & -- & -- & -- & BG \\\\\nDT Oct & 2003 & 0.074755 & 0.000019 & 21 & 118 & $-$9.0 & 1.1 & -- & -- & -- & -- & -- & AG \\\\\nDT Oct & 2003b & 0.074893 & 0.000075 & 0 & 14 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nDT Oct & 2008 & 0.074554 & 0.000043 & 0 & 40 & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\nV699 Oph & 2003 & 0.070326 & 0.000038 & 0 & 43 & 14.2 & 7.7 & 0.070089 & 0.000061 & 42 & 68 & -- & B \\\\\nV699 Oph & 2008 & 0.070130 & 0.000014 & 14 & 87 & -- & -- & 0.069931 & 0.000060 & 87 & 129 & -- & C \\\\\nV2051 Oph & 1999 & 0.064367 & 0.000029 & 0 & 113 & 2.9 & 2.9 & -- & -- & -- & -- & 0.062428 & C \\\\\nV2051 Oph & 2003 & 0.064850 & 0.000085 & 0 & 17 & -- & -- & 0.063801 & 0.000083 & 16 & 48 & 0.062428 & C \\\\\nV2051 Oph & 2009 & 0.064179 & 0.000019 & 0 & 48 & -- & -- & -- & -- & -- & -- & 0.062428 & C \\\\\nV2527 Oph & 2004 & 0.072050 & 0.000016 & 29 & 103 & 6.0 & 1.7 & 0.071522 & 0.000020 & 103 & 168 & -- & A \\\\\nV2527 Oph & 2006 & 0.071942 & 0.000019 & 0 & 97 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV2527 Oph & 2008 & 0.071943 & 0.000062 & 0 & 111 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV1159 Ori & 1993 & 0.064201 & 0.000014 & 0 & 116 & 4.2 & 1.1 & 0.063905 & 0.000012 & 124 & 194 & 0.062178 & A \\\\\nV1159 Ori & 2002 & 0.064144 & 0.000049 & 0 & 63 & 14.9 & 5.4 & 0.064086 & 0.000046 & 93 & 249 & 0.062178 & B \\\\\nV344 Pav & 2004 & -- & -- & -- & -- & -- & -- & 0.079667 & 0.000152 & 0 & 51 & -- & C \\\\\nEF Peg & 1991 & 0.086930 & 0.000018 & 23 & 111 & $-$1.3 & 1.7 & 0.086623 & 0.000018 & 110 & 157 & -- & A \\\\\nEF Peg & 1997 & 0.087037 & 0.000025 & 0 & 91 & $-$4.2 & 2.1 & -- & -- & -- & -- & -- & BG \\\\\nV364 Peg & 2004 & 0.085338 & 0.000032 & 0 & 28 & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\nV368 Peg & 2000 & 0.070380 & 0.000008 & 0 & 86 & 0.5 & 1.2 & 0.070054 & 0.000052 & 85 & 142 & -- & B \\\\\nV368 Peg & 2005 & 0.070381 & 0.000026 & 70 & 97 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nV368 Peg & 2006 & -- & -- & -- & -- & -- & -- & 0.069945 & 0.000018 & 0 & 61 & -- & C \\\\\nV369 Peg & 1999 & 0.085694 & 0.000274 & 0 & 27 & -- & -- & 0.084854 & 0.000102 & 24 & 82 & -- & C \\\\\nUV Per & 2000 & 0.066627 & 0.000033 & 14 & 62 & 9.5 & 6.0 & 0.066288 & 0.000036 & 62 & 185 & 0.06489 & B \\\\\nUV Per & 2003 & 0.066671 & 0.000010 & 20 & 109 & 5.1 & 1.0 & 0.066251 & 0.000015 & 107 & 176 & 0.06489 & A \\\\\nUV Per & 2007 & 0.066319 & 0.000008 & 20 & 85 & 0.1 & 1.9 & 0.066017 & 0.000090 & 82 & 99 & 0.06489 & BG \\\\\nPU Per & 2009 & 0.068707 & 0.000280 & 0 & 18 & -- & -- & 0.067973 & 0.000099 & 18 & 90 & -- & C \\\\\nPV Per & 2008 & 0.080801 & 0.000018 & 0 & 36 & -- & -- & 0.080349 & 0.000050 & 35 & 161 & -- & B \\\\\nQY Per & 1999 & 0.078611 & 0.000022 & 5 & 69 & 7.8 & 3.1 & 0.078140 & 0.000052 & 67 & 123 & -- & A \\\\\nQY Per & 2005 & 0.078609 & 0.000058 & 0 & 54 & -- & -- & 0.078188 & 0.000018 & 54 & 117 & -- & C \\\\\nTY PsA & 2008 & 0.087990 & 0.000017 & 0 & 34 & -- & -- & 0.087730 & 0.000030 & 46 & 91 & 0.0841 & B \\\\\nTY Psc & 2005 & 0.070338 & 0.000013 & 0 & 43 & 1.5 & 3.0 & -- & -- & -- & -- & 0.06833 & CG \\\\\nTY Psc & 2008 & 0.070656 & 0.000022 & 0 & 82 & $-$5.2 & 1.9 & 0.070203 & 0.000034 & 82 & 133 & 0.06833 & A \\\\\nEI Psc & 2001 & 0.046349 & 0.000007 & 0 & 141 & 0.3 & 0.8 & 0.046090 & 0.000012 & 162 & 382 & 0.044567 & A \\\\\nEI Psc & 2005 & 0.046317 & 0.000007 & 0 & 73 & $-$2.8 & 2.0 & -- & -- & -- & -- & 0.044567 & B \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nVZ Pyx & 1996 & 0.075754 & 0.000012 & 0 & 27 & -- & -- & -- & -- & -- & -- & 0.07332 & C \\\\\nVZ Pyx & 2000 & -- & -- & -- & -- & -- & -- & 0.075492 & 0.000016 & 0 & 94 & 0.07332 & C \\\\\nVZ Pyx & 2004 & 0.075875 & 0.000060 & 0 & 52 & -- & -- & -- & -- & -- & -- & 0.07332 & C \\\\\nVZ Pyx & 2008 & 0.076045 & 0.000021 & 0 & 27 & -- & -- & 0.075379 & 0.000006 & 54 & 80 & 0.07332 & C \\\\\nDV Sco & 2004 & 0.099776 & 0.000202 & 0 & 17 & -- & -- & 0.099243 & 0.000032 & 17 & 53 & -- & C \\\\\nMM Sco & 2002 & 0.061324 & 0.000058 & 0 & 25 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nNY Ser & 1996 & 0.108610 & -- & -- & -- & -- & -- & 0.105677 & 0.000304 & 18 & 37 & -- & C \\\\\nQW Ser & 2000 & 0.077012 & 0.000014 & 0 & 79 & $-$1.1 & 1.5 & 0.076737 & 0.000051 & 78 & 116 & 0.07453 & B \\\\\nQW Ser & 2002 & 0.077032 & 0.000049 & 0 & 52 & 18.0 & 8.0 & 0.076637 & 0.000057 & 51 & 91 & 0.07453 & C \\\\\nRZ Sge & 1994 & 0.070575 & 0.000028 & 0 & 42 & -- & -- & 0.070104 & 0.000037 & 41 & 100 & 0.06828 & B \\\\\nRZ Sge & 1996 & 0.070645 & 0.000028 & 0 & 88 & 0.6 & 5.1 & 0.070082 & 0.000036 & 88 & 173 & 0.06828 & C \\\\\nRZ Sge & 2002 & 0.070441 & 0.000023 & 27 & 128 & -- & -- & 0.069970 & 0.000046 & 128 & 171 & 0.06828 & BG \\\\\nWZ Sge & 1978 & 0.057232 & 0.000014 & 0 & 228 & 0.4 & 0.8 & -- & -- & -- & -- & 0.056688 & B \\\\\nWZ Sge & 2001 & 0.057204 & 0.000005 & 27 & 177 & 2.0 & 0.4 & -- & -- & -- & -- & 0.056688 & A \\\\\nAW Sge & 2000 & 0.074519 & 0.000192 & 0 & 13 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nAW Sge & 2006 & 0.074528 & 0.000032 & 0 & 44 & $-$7.9 & 6.4 & -- & -- & -- & -- & -- & CG \\\\\nV551 Sgr & 2003 & 0.067600 & 0.000022 & 22 & 126 & 6.0 & 1.5 & -- & -- & -- & -- & -- & A \\\\\nV4140 Sgr & 2004 & 0.063510 & 0.000043 & 16 & 70 & 25.3 & 12.3 & 0.063092 & 0.000067 & 69 & 181 & 0.061430 & C \\\\\nV701 Tau & 1995 & 0.069080 & 0.000050 & 0 & 60 & -- & -- & 0.068885 & 0.000010 & 58 & 159 & -- & C \\\\\nV701 Tau & 2005 & 0.069036 & 0.000036 & 0 & 79 & 11.0 & 3.5 & -- & -- & -- & -- & -- & B \\\\\nV1208 Tau & 2000 & 0.070501 & 0.000032 & 0 & 80 & $-$2.8 & 4.1 & -- & -- & -- & -- & -- & C \\\\\nV1208 Tau & 2002 & 0.070537 & 0.000027 & 0 & 72 & $-$6.3 & 3.8 & -- & -- & -- & -- & -- & B \\\\\nKK Tel & 2002 & 0.087692 & 0.000066 & 22 & 47 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nKK Tel & 2003 & 0.087532 & 0.000050 & 0 & 13 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nKK Tel & 2004 & 0.087335 & 0.000068 & 0 & 14 & -- & -- & -- & -- & -- & -- & -- & CG \\\\\nEK TrA & 2007 & 0.064335 & 0.000011 & 0 & 250 & $-$0.5 & 0.5 & -- & -- & -- & -- & 0.06288 & B \\\\\nFL TrA & 2005 & 0.059850 & 0.000030 & 16 & 84 & 8.5 & 5.0 & -- & -- & -- & -- & -- & B \\\\\nUW Tri & 2008 & 0.054194 & 0.000025 & 0 & 288 & 3.7 & 0.6 & -- & -- & -- & -- & 0.05334 & BEM \\\\\nWY Tri & 2000 & 0.078427 & 0.000045 & 0 & 40 & -- & -- & 0.077706 & 0.000144 & 37 & 58 & -- & B \\\\\nSU UMa & 1989 & 0.079209 & 0.000094 & 0 & 14 & -- & -- & 0.078666 & 0.000022 & 12 & 63 & 0.07635 & B \\\\\nSU UMa & 1999 & 0.079091 & 0.000046 & 34 & 92 & 0.7 & 6.7 & 0.078777 & 0.000064 & 90 & 165 & 0.07635 & A \\\\\nSW UMa & 1991 & 0.058251 & 0.000024 & 52 & 88 & 8.1 & 8.0 & -- & -- & -- & -- & 0.056815 & C \\\\\nSW UMa & 1996 & 0.058189 & 0.000017 & 0 & 120 & 8.8 & 0.7 & -- & -- & -- & -- & 0.056815 & A \\\\\nSW UMa & 1997 & 0.058284 & 0.000048 & 0 & 140 & 8.6 & 0.5 & -- & -- & -- & -- & 0.056815 & C \\\\\nSW UMa & 2000 & 0.058258 & 0.000012 & 27 & 217 & 5.1 & 0.5 & 0.057721 & 0.000057 & 217 & 269 & 0.056815 & A \\\\\nSW UMa & 2002 & 0.058320 & 0.000021 & 0 & 142 & 9.9 & 0.9 & 0.057989 & 0.000049 & 142 & 228 & 0.056815 & AM \\\\\nSW UMa & 2006 & 0.058214 & 0.000031 & 33 & 189 & 9.5 & 0.6 & 0.057892 & 0.000018 & 188 & 338 & 0.056815 & B \\\\\nBC UMa & 2000 & 0.064555 & 0.000013 & 16 & 99 & 4.0 & 1.4 & 0.064121 & -- & 99 & 116 & 0.06261 & BG \\\\\nBC UMa & 2003 & 0.064571 & 0.000012 & 15 & 114 & 4.2 & 0.8 & 0.064183 & 0.000018 & 114 & 189 & 0.06261 & A \\\\\nBZ UMa & 2007 & 0.070180 & 0.000014 & 19 & 64 & 3.6 & 3.3 & 0.069793 & 0.000013 & 72 & 138 & 0.06799 & A \\\\\nCI UMa & 2001 & 0.062673 & 0.000098 & 0 & 32 & -- & -- & 0.062355 & 0.000108 & 31 & 65 & -- & C \\\\\nCI UMa & 2003 & 0.062688 & 0.000014 & 0 & 93 & 6.4 & 1.2 & 0.062466 & 0.000053 & 93 & 145 & -- & AM \\\\\nCI UMa & 2006 & -- & -- & -- & -- & -- & -- & 0.062479 & 0.000072 & 0 & 16 & -- & C \\\\\nCY UMa & 1995 & 0.072124 & 0.000009 & 0 & 73 & 2.7 & 1.0 & 0.071806 & 0.000020 & 70 & 153 & 0.06957 & A \\\\\nCY UMa & 1998 & 0.072460 & 0.000067 & 0 & 56 & -- & -- & 0.071936 & 0.000020 & 52 & 154 & 0.06957 & B \\\\\nCY UMa & 1999 & 0.072216 & 0.000032 & 0 & 43 & $-$5.9 & 9.5 & -- & -- & -- & -- & 0.06957 & CG \\\\\nCY UMa & 2009 & 0.072219 & 0.000017 & 0 & 37 & 2.5 & 5.2 & 0.071755 & 0.000028 & 44 & 116 & 0.06957 & B \\\\\nDI UMa & 2007a & 0.055322 & 0.000015 & 18 & 182 & 4.4 & 0.7 & -- & -- & -- & -- & 0.054579 & B \\\\\nDI UMa & 2007b & 0.055333 & 0.000022 & 0 & 126 & 6.0 & 1.6 & -- & -- & -- & -- & 0.054579 & B \\\\\nDV UMa & 1997 & 0.088800 & 0.000030 & 7 & 79 & $-$2.5 & 3.5 & 0.088414 & 0.000034 & 100 & 184 & 0.085853 & A \\\\\nDV UMa & 1999 & 0.088927 & 0.000032 & 0 & 80 & $-$4.7 & 3.4 & 0.088360 & 0.000084 & 78 & 129 & 0.085853 & B \\\\\nDV UMa & 2002 & 0.088743 & 0.000160 & 0 & 61 & -- & -- & 0.088404 & 0.000035 & 57 & 118 & 0.085853 & B \\\\\nDV UMa & 2005 & -- & -- & -- & -- & -- & -- & 0.088356 & 0.000098 & 100 & 168 & 0.085853 & C \\\\\nDV UMa & 2007 & 0.088539 & 0.000034 & 21 & 138 & $-$4.8 & 2.4 & -- & -- & -- & -- & 0.085853 & CG \\\\\nER UMa & 1995 & 0.065747 & 0.000024 & 0 & 123 & 4.1 & 2.1 & 0.065539 & 0.000020 & -- & -- & 0.06366 & B \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nIY UMa & 2000 & 0.075776 & 0.000015 & 23 & 101 & $-$1.8 & 2.2 & -- & -- & -- & -- & 0.073909 & A \\\\\nIY UMa & 2002 & 0.076009 & 0.000024 & 0 & 137 & 1.6 & 3.0 & 0.075287 & 0.000104 & 135 & 228 & 0.073909 & C \\\\\nIY UMa & 2004 & 0.076030 & 0.000011 & 0 & 130 & 0.1 & 0.9 & 0.075897 & 0.000022 & 126 & 169 & 0.073909 & C \\\\\nIY UMa & 2006 & 0.076082 & 0.000021 & 42 & 154 & 4.0 & 1.5 & 0.075830 & 0.000034 & 153 & 221 & 0.073909 & C \\\\\nIY UMa & 2007 & 0.075849 & 0.000071 & 0 & 15 & -- & -- & 0.075517 & 0.000043 & 13 & 54 & 0.073909 & C \\\\\nIY UMa & 2009 & 0.076233 & 0.000016 & 30 & 123 & $-$1.2 & 1.5 & 0.075823 & 0.000027 & 122 & 189 & 0.073909 & B \\\\\nKS UMa & 2003 & 0.070179 & 0.000009 & 15 & 95 & 2.2 & 1.1 & 0.069837 & 0.000021 & 95 & 147 & 0.06796 & A \\\\\nKS UMa & 2007 & 0.070265 & 0.000016 & 0 & 73 & 1.5 & 1.9 & -- & -- & -- & -- & 0.06796 & BM \\\\\nMR UMa & 2002 & 0.065157 & 0.000024 & 0 & 80 & 9.3 & 1.2 & 0.064743 & 0.000111 & 80 & 109 & -- & B \\\\\nMR UMa & 2003 & 0.065140 & 0.000018 & 0 & 84 & 6.0 & 2.3 & 0.064357 & 0.000066 & 84 & 144 & -- & B \\\\\nMR UMa & 2007 & 0.065115 & 0.000014 & 0 & 79 & 3.8 & 1.6 & 0.064887 & 0.000045 & 78 & 125 & -- & B \\\\\nSS UMi & 2004 & 0.070270 & 0.000062 & 13 & 57 & 25.0 & 5.0 & 0.070009 & 0.000017 & 55 & 113 & 0.06778 & B \\\\\nCU Vel & 2002 & 0.080941 & 0.000038 & 22 & 75 & $-$6.9 & 5.9 & 0.080609 & 0.000016 & 71 & 123 & 0.0785 & B \\\\\nHS Vir & 1996 & 0.080056 & 0.000032 & 23 & 99 & -- & -- & -- & -- & -- & -- & 0.0769 & C \\\\\nHS Vir & 2008 & 0.080028 & 0.000032 & 0 & 62 & -- & -- & -- & -- & -- & -- & 0.0769 & C2 \\\\\nHV Vir & 1992 & 0.058285 & 0.000017 & 0 & 165 & 5.7 & 0.6 & -- & -- & -- & -- & 0.057069 & A \\\\\nHV Vir & 2002 & 0.058266 & 0.000017 & 22 & 173 & 7.4 & 0.6 & 0.058012 & 0.000029 & 172 & 229 & 0.057069 & A \\\\\nHV Vir & 2008 & 0.058322 & 0.000027 & 18 & 157 & 7.1 & 1.9 & 0.058110 & 0.000059 & 157 & 226 & 0.057069 & A \\\\\nOU Vir & 2003 & 0.074912 & 0.000017 & 0 & 217 & $-$1.8 & 0.6 & -- & -- & -- & -- & 0.072706 & CG \\\\\nOU Vir & 2008 & 0.074962 & 0.000132 & 0 & 24 & -- & -- & -- & -- & -- & -- & 0.072706 & C \\\\\nQZ Vir & 1993 & 0.060345 & 0.000017 & 15 & 101 & 7.0 & 1.4 & 0.060087 & 0.000041 & 98 & 165 & 0.05882 & B \\\\\nQZ Vir & 2005 & 0.060488 & 0.000050 & 0 & 50 & -- & -- & -- & -- & -- & -- & 0.05882 & C \\\\\nQZ Vir & 2007 & 0.060481 & 0.000028 & 0 & 53 & 4.5 & 7.6 & 0.059984 & 0.000029 & 51 & 135 & 0.05882 & BM \\\\\nQZ Vir & 2008 & 0.060442 & 0.000015 & 0 & 85 & 4.7 & 1.9 & 0.059902 & 0.000040 & 85 & 168 & 0.05882 & A \\\\\nQZ Vir & 2009 & 0.060378 & 0.000022 & 0 & 91 & 11.4 & 1.8 & 0.059912 & 0.000010 & 88 & 251 & 0.05882 & A \\\\\nRX Vol & 2003 & 0.061364 & 0.000017 & 0 & 134 & 5.8 & 0.8 & -- & -- & -- & -- & -- & A \\\\\nTY Vul & 2003 & 0.081196 & 0.000205 & 0 & 42 & -- & -- & 0.080098 & 0.000067 & 42 & 120 & -- & C \\\\\nDO Vul & 2008 & 0.058204 & 0.000037 & 0 & 156 & 9.9 & 2.1 & -- & -- & -- & -- & -- & B \\\\\nNSV 4838 & 2005 & -- & -- & -- & -- & -- & -- & 0.069668 & 0.000086 & 0 & 86 & -- & C \\\\\nNSV 4838 & 2007 & 0.069916 & 0.000028 & 0 & 101 & 7.4 & 1.9 & 0.069604 & 0.000024 & 101 & 189 & -- & B \\\\\nNSV 5285 & 2008 & 0.087973 & 0.000086 & 0 & 34 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nNSV 14652 & 2004 & 0.081513 & 0.000016 & 0 & 50 & $-$3.0 & 3.6 & 0.081061 & 0.000149 & 50 & 61 & -- & B \\\\\n1RXS J0232 & 2007 & 0.066166 & 0.000011 & 0 & 106 & $-$1.7 & 0.7 & -- & -- & -- & -- & -- & B2 \\\\\n1RXS J0423 & 2008 & 0.078399 & 0.000036 & 30 & 68 & -- & -- & 0.078130 & 0.000023 & 67 & 171 & 0.07632 & B \\\\\n1RXS J0532 & 2005 & 0.057156 & 0.000013 & 0 & 162 & 5.7 & 0.8 & 0.056618 & 0.000044 & 162 & 246 & 0.05620 & A \\\\\n1RXS J0532 & 2008 & 0.057131 & 0.000024 & 0 & 138 & 10.2 & 0.8 & 0.056778 & 0.000085 & 138 & 173 & 0.05620 & A \\\\\n2QZ J0219 & 2005 & 0.081199 & 0.000036 & 0 & 74 & $-$1.9 & 3.9 & 0.080935 & 0.000034 & 74 & 123 & -- & B \\\\\n2QZ J0219 & 2009 & -- & -- & -- & -- & -- & -- & 0.081004 & 0.000013 & 0 & 74 & -- & C \\\\\nASAS J0025 & 2004 & 0.057093 & 0.000012 & 0 & 151 & 8.7 & 0.4 & 0.056823 & 0.000032 & 151 & 236 & 0.056540 & AP \\\\\nASAS J0233 & 2006 & 0.055987 & 0.000017 & 7 & 216 & 4.9 & 0.5 & 0.055840 & 0.000064 & 216 & 281 & 0.05490 & AE \\\\\nASAS J0918 & 2005 & 0.062893 & 0.000067 & 0 & 32 & -- & -- & 0.062526 & 0.000120 & 32 & 79 & -- & C \\\\\nASAS J1025 & 2006 & 0.063365 & 0.000016 & 27 & 142 & 10.9 & 0.6 & 0.063021 & 0.000016 & 141 & 251 & 0.06136 & AE \\\\\nASAS J1536 & 2004 & 0.064602 & 0.000024 & 30 & 139 & 2.4 & 2.1 & -- & -- & -- & -- & -- & A \\\\\nASAS J1600 & 2005 & 0.064970 & 0.000017 & 28 & 109 & 11.1 & 0.8 & 0.064597 & 0.000013 & 104 & 182 & 0.063381 & AE \\\\\nCTCV J0549 & 2006 & 0.084981 & 0.000157 & 23 & 36 & -- & -- & 0.084237 & 0.000049 & 35 & 119 & -- & B \\\\\nHa 0242 & 2006 & 0.077099 & 0.000022 & 0 & 43 & -- & -- & -- & -- & -- & -- & 0.074600 & C \\\\\nSDSS J0137 & 2003 & 0.056766 & 0.000013 & 0 & 98 & 2.3 & 1.7 & 0.056448 & 0.000016 & 98 & 231 & 0.055343 & A \\\\\nSDSS J0137 & 2009 & -- & -- & -- & -- & -- & -- & 0.056443 & 0.000008 & 0 & 160 & 0.055343 & C \\\\\nSDSS J0310 & 2004 & 0.068636 & 0.000037 & 0 & 161 & 2.0 & 2.7 & -- & -- & -- & -- & -- & CG \\\\\nSDSS J0334 & 2009 & 0.074773 & 0.000052 & 0 & 54 & $-$14.0 & 11.0 & -- & -- & -- & -- & -- & CG \\\\\nSDSS J0746 & 2009 & 0.066786 & 0.000031 & 0 & 78 & 9.3 & 2.5 & 0.066621 & 0.000048 & 76 & 139 & -- & C \\\\\nSDSS J0804 & 2006 & 0.059537 & 0.000031 & 0 & 40 & -- & -- & -- & -- & -- & -- & 0.059005 & C \\\\\nSDSS J0812 & 2008 & 0.084423 & 0.000095 & 0 & 60 & -- & -- & 0.083351 & 0.000259 & 59 & 95 & -- & B \\\\\nSDSS J0824 & 2007 & 0.069770 & 0.000033 & 0 & 110 & 8.0 & 2.5 & 0.069055 & 0.000083 & 110 & 168 & -- & B \\\\\nSDSS J0838 & 2009 & -- & -- & -- & -- & -- & -- & 0.071471 & 0.000023 & 101 & 155 & -- & CG \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\addtocounter{table}{-1}\n\\begin{table*}\n\\caption{Superhump Periods and Period Derivatives (continued)}\n\\begin{center}\n\\begin{tabular}{cccccccccccccc}\n\\hline\\hline\nObject & Year & $P_1$ & err & \\multicolumn{2}{c}{$E_1$} & $P_{\\rm dot}$ & err & $P_2$ & err & \\multicolumn{2}{c}{$E_2$} & $P_{\\rm orb}$ & Q \\\\\n\\hline\nSDSS J1005 & 2009 & -- & -- & -- & -- & -- & -- & 0.077469 & 0.000021 & 0 & 49 & -- & C \\\\\nSDSS J1100 & 2009 & 0.067569 & 0.000025 & 0 & 64 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nSDSS J1227 & 2007 & 0.064593 & 0.000022 & 33 & 129 & 6.1 & 2.1 & -- & -- & -- & -- & 0.062958 & B \\\\\nSDSS J1524 & 2009 & 0.067136 & 0.000023 & 0 & 89 & 8.2 & 2.6 & 0.066720 & 0.000035 & 88 & 163 & 0.065319 & B \\\\\nSDSS J1556 & 2007 & 0.082961 & 0.000022 & 12 & 85 & $-$7.6 & 2.3 & 0.082587 & 0.000038 & 85 & 145 & 0.08001 & B \\\\\nSDSS J1627 & 2008 & 0.109741 & 0.000087 & 15 & 50 & -- & -- & 0.108771 & 0.000022 & 49 & 150 & -- & A \\\\\nSDSS J1702 & 2005 & 0.105065 & 0.000083 & 0 & 85 & 15.8 & 4.2 & -- & -- & -- & -- & 0.100082 & B \\\\\nSDSS J1730 & 2001 & 0.079413 & 0.000102 & 0 & 86 & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\nSDSS J1730 & 2002 & 0.079390 & 0.000051 & 0 & 140 & 2.0 & 3.5 & -- & -- & -- & -- & -- & C2 \\\\\nSDSS J1730 & 2004 & 0.080068 & 0.000241 & 0 & 9 & -- & -- & 0.079455 & 0.000017 & 5 & 64 & -- & B \\\\\nSDSS J2100 & 2007 & 0.086960 & 0.000150 & 44 & 56 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nSDSS J2258 & 2004 & -- & -- & -- & -- & -- & -- & 0.085900 & 0.000086 & 0 & 24 & -- & C \\\\\nSDSS J2258 & 2008 & -- & -- & -- & -- & -- & -- & 0.086141 & 0.000025 & 0 & 98 & -- & B \\\\\nOT J0042 & 2008 & 0.056892 & 0.000028 & 0 & 162 & 4.0 & 1.8 & -- & -- & -- & -- & 0.05550 & BE \\\\\nOT J0113 & 2008 & 0.094325 & 0.000076 & 0 & 43 & -- & -- & -- & -- & -- & -- & -- & C2 \\\\\nOT J0211 & 2008 & 0.081643 & 0.000313 & 0 & 14 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nOT J0238 & 2008 & 0.053658 & 0.000007 & 67 & 350 & 2.0 & 0.2 & 0.053202 & 0.000117 & 350 & 405 & 0.05281 & BE \\\\\nOT J0329 & 2006 & 0.053405 & 0.000006 & 0 & 139 & 2.8 & 0.3 & -- & -- & -- & -- & -- & B \\\\\nOT J0406 & 2008 & 0.079947 & 0.000025 & 0 & 61 & 2.8 & 3.4 & -- & -- & -- & -- & -- & C2 \\\\\nOT J0557 & 2006 & 0.053509 & 0.000021 & 0 & 110 & 9.0 & 2.1 & 0.053258 & 0.000030 & 109 & 260 & -- & B \\\\\nOT J0747 & 2008 & 0.060736 & 0.000009 & 0 & 109 & 4.0 & 0.8 & -- & -- & -- & -- & -- & B \\\\\nOT J0807 & 2007 & 0.061050 & 0.000039 & 0 & 89 & 9.5 & 4.8 & 0.060656 & 0.000039 & 70 & 187 & -- & B \\\\\nOT J0814 & 2008 & 0.076518 & 0.000021 & 0 & 79 & -- & -- & 0.075739 & 0.000145 & 79 & 141 & -- & C \\\\\nOT J0845 & 2008 & 0.060473 & 0.000037 & 66 & 167 & 6.7 & 3.4 & -- & -- & -- & -- & -- & C \\\\\nOT J1021 & 2006 & 0.056312 & 0.000012 & 0 & 240 & 0.4 & 0.8 & 0.056043 & 0.000065 & 237 & 298 & -- & B \\\\\nOT J1026 & 2009 & -- & -- & -- & -- & -- & -- & 0.067520 & 0.000900 & 0 & 46 & -- & C \\\\\nOT J1028 & 2009 & 0.038145 & 0.000025 & 0 & 59 & 11.6 & 8.5 & -- & -- & -- & -- & -- & C \\\\\nOT J1112 & 2007 & 0.058965 & 0.000009 & 16 & 287 & 0.9 & 0.4 & -- & -- & -- & -- & 0.05847 & BE \\\\\nOT J1300 & 2008 & 0.064388 & 0.000036 & 14 & 109 & 14.4 & 1.5 & -- & -- & -- & -- & -- & C \\\\\nOT J1440 & 2009 & -- & -- & -- & -- & -- & -- & 0.064736 & 0.000059 & 15 & 39 & -- & C \\\\\nOT J1443 & 2009 & 0.072180 & 0.000028 & 12 & 112 & 10.0 & 1.3 & 0.071756 & 0.000057 & 110 & 180 & -- & B \\\\\nOT J1631 & 2008 & 0.064125 & 0.000022 & 0 & 96 & 12.5 & 1.3 & 0.064087 & 0.000076 & 96 & 138 & -- & A \\\\\nOT J1914 & 2008 & 0.071348 & 0.000028 & 0 & 82 & 9.6 & 2.6 & 0.070927 & 0.000078 & 82 & 168 & -- & B \\\\\nOT J1959 & 2005 & 0.059919 & 0.000036 & 0 & 93 & $-$0.7 & 5.2 & -- & -- & -- & -- & -- & C \\\\\nOT J2131 & 2008 & 0.064630 & 0.000030 & 0 & 62 & -- & -- & -- & -- & -- & -- & -- & C \\\\\nOT J2137 & 2008 & 0.099451 & -- & 0 & 5 & -- & -- & 0.097675 & 0.000025 & 5 & 61 & -- & B \\\\\nTSS J0222 & 2005 & 0.055585 & 0.000022 & 37 & 197 & 2.2 & 1.5 & -- & -- & -- & -- & 0.054868 & BE \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(180mm,70mm){fig22.eps}\n \\end{center}\n \\caption{Existence of stage B--C transition versus $P_{\\rm SH}$,\n $P_{\\rm dot}$ and $\\epsilon$. The gray color indicates superoutbursts\n with a stage B--C transition. The existence of stage B--C\n transitions is most strongly correlated with $\\epsilon$.\n }\n \\label{fig:stagec}\n\\end{figure*}\n\n\\subsection{Relation between stage C Superhumps and Late Superhumps}\n\n During the final stage of a superoutburst and the subsequent\npost-superoutburst stages, some SU UMa-type dwarf nova have been\nreported to exhibit modulations having approximately the same period as\n$P_{\\rm SH}$, but having a maximum phase $\\sim$0.5 offset from those\nof usual superhumps. These modulations have been traditionally called\n``late superhumps'' (\\cite{hae79lateSH}; \\cite{vog83lateSH};\n\\cite{vanderwoe88lateSH}; \\cite{hes92lateSH}).\nWe, however, could not find very convincing evidence for this\nphenomenon in many well-sampled objects\n(see e.g. QZ Vir: \\cite{ohs09qzvir}).\nInstead, there seems to be almost ubiquitous presence of a transition\nfrom the stage B to C associated with a period shortening\n(section \\ref{sec:pshstageb})\nand the continuity of superhump phases in well-observed systems\n(see also \\cite{ohs09qzvir}).\n\n This might suggest that at least some of claimed ``late superhumps''\nin the literature actually referred to superhumps during the stage C.\nThe $P_{\\rm SH} (= P_2)$ being typically $\\sim$ 0.5--1.0 \\% shorter than in\nearlier stages ($P_1$), a observational gap in $\\sim$ 30--50 cycles\n($\\sim$2--3 d) can result a phase shift of 0.15--0.5, and it may have\nbeen attributed to a $\\sim$0.5 phase offset.\nAlthough it would be already difficult to\nre-examine historical observations reporting late superhumps, we should\npay attention to this possibility and avoid attributing the term\n``late superhumps'' simply because a phase offset is detected.\nIf this interpretation is indeed the case, the term ``late superhumps''\nshould better be attributed to superhumps during the stage C ($P_2$).\\footnote{\n Note, however, we used ``late superhumps'' for late-stage superhumps\n different from ordinary ones in WZ Sge-type dwarf novae\n \\citep{kat08wzsgelateSH}.\n}\n\n There is some evidence of traditional late superhumps in\nDT Oct (subsection \\ref{sec:dtoct}) and HS Vir (subsection \\ref{sec:hsvir}).\nIt may be that this type of traditional late superhumps is only\nobserved in systems with a high mass-transfer rate, enabling sufficient\nluminosity from the hot spot.\n\n\\subsection{Implications of Period Transition in Interpreting Observations}\\label{sec:transimplication}\n\n One of the important consequences of the period transition between stages B\nand C in interpreting observations is that this appearance of a new,\nstable, period is sometimes confused with the orbital period\n(see likely examples,\nIX Dra: \\cite{ole04ixdra}, OT J102146.4$+$234926: \\cite{uem08j1021}).\nPhotometrically claimed orbital periods during superoutbursts,\nespecially those giving $\\epsilon <1$ \\% need to be carefully\nre-examined.\n\n Furthermore, the presence of two distinct periods with fair stability\nmight be problematic in identifying multiple periodicity by\nanalyzing power spectra of the entire data (e.g. \\cite{pat03suumas}).\n\n A typical difference of 0.5--1.0\\% in $P_{\\rm SH}$ between\n$P_1$ and $P_2$ corresponds to a difference of 0.03--0.05 in\n$q$ \\citep{pat05SH}.\nThis difference could result a systematic error in calibrating\n$\\epsilon$--$q$ relation, or estimating $q$ depending on the stage\nwhen $P_{\\rm SH}$ is measured. The situation could be worse if the\nrelation is applied to superhump periods obtained around the termination\nof the stage B (subsection \\ref{sec:pdotb}, figure \\ref{fig:pendporb}).\nThis issue is further discussed in subsection \\ref{sec:epsq}.\n\n\\subsection{Minimum Superhump Period and 3:1 Resonance}\n\n Among surveyed sets of parameters, we have noticed that the\nfractional period excess for minimum $P_{\\rm SH}$ of\na given superoutburst (either $P_2$ or $P_{\\rm SH}$ at the start of\nthe stage B for $P_{\\rm dot} > 0$ systems) of a given system\nis most smoothly and tightly correlated with other system parameters\n(figures \\ref{fig:pminpsh}, \\ref{fig:pmineps}; for a comparison of\nother representative $P_{\\rm SH}$, see figure \\ref{fig:pothereps}).\nIn figure \\ref{fig:pmineps}, we give $\\epsilon$ expected for\ndynamical precession rate at the 3:1 resonance ($\\epsilon_{3:1}$),\nusing the $\\epsilon$--$q$ relation (\\cite{pat05SH}, using the updated\none discussed in subsection \\ref{sec:epsq}) and angular velocity\nof disk precession formulated by \\citet{osa85SHexcess}.\nThe $\\epsilon$ for the minimum $P_{\\rm SH}$ best parallels the expected \n$\\epsilon$ for the 3:1 resonance. We therefore regard that the\nminimum $P_{\\rm SH}$ represents the precession at the 3:1 resonance.\nThis interpretation can naturally explain the ubiquitous presence of\nthe stage C and the stability of the superhump period during the stage C.\nThe systematic difference between $\\epsilon_{3:1}$ and observed values\nis likely attributed to the scaling problem in interpreting hydrodynamical\nprecession rate of a disk as a whole by single-particle dynamical precession\n(see \\cite{smi07SH}) rather than the real difference.\n\n In systems lacking the stage C, such as many of extreme\nWZ Sge-type dwarf novae, the $P_{\\rm SH}$ appears to always reflect\nthe precession rate at the 3:1 resonance.\nThe stability of the $P_{\\rm SH}$ in such systems can then be naturally\nexplained. In positive $P_{\\rm dot}$ systems, $P_{\\rm SH}$ at the\nstart of the stage B is almost identical to $P_2$\n(subsection \\ref{sec:pshstageb}). This can be understood as\nsuperhumps excited at the 3:1 resonance quickly dominates at the start\nof the stage B in these systems.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig23.eps}\n \\end{center}\n \\caption{Relation between the fractional period excess for the\n minimum $P_{\\rm SH}$ and $P_{\\rm SH}$ ($P_1$).\n }\n \\label{fig:pminpsh}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig24.eps}\n \\end{center}\n \\caption{Relation between the fractional period excess for the\n minimum $P_{\\rm SH}$ and $q$, scaled from $P_1$.\n The dashed line represents fractional excess expected for single\n particle dynamical precession rate at 1:3 resonance.\n }\n \\label{fig:pmineps}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig25.eps}\n \\end{center}\n \\caption{Relation between the fractional period excess for the\n different epochs of stage B $P_{\\rm SH}$ and $q$, scaled from $P_1$.\n The dashed line is the same as in figure \\ref{fig:pmineps}.\n }\n \\label{fig:pothereps}\n\\end{figure}\n\n\\subsection{Maximum Superhump Period and Disk Radius}\\label{sec:maxradius}\n\n By assuming this interpretation and assuming the radial dependence of\nprecession rate \\citep{mur00SHprecession}, we can calculate the disk\nradius from $\\epsilon$ at other epochs.\\footnote{\n In scaling the radius, we used the radius of single-particle\n dynamical 3:1 resonance for simplicity.\n This radius may be systematically too large \\citep{smi07SH}.\n Other factors proposed to affect superhump periods include \n changes in temperature or pressure (\\cite{hir93SHperiod};\n \\cite{mur98SH}; \\cite{mon01SH}; \\cite{pea06SH}.\n Since the disk temperature is expected to decrease\n during the decline phase, a slowing effect on the precession due to\n the pressure forces is expected to decrease \\citet{mon01SH}.\n This expectation is contrary to the global period decrease generally\n observed, and we regard that the variation in the disk temperature\n is unlikely the primary cause of the period variation.\n We therefore focus on dynamical precession and did not consider\n other effects for simplicity.\n}\n\n The radii calculated for the end of stage B for systems with\n$P_{\\rm dot} > 0$, corresponding to the maximum radii, are given in\ntable \\ref{tab:pendr} and figure \\ref{fig:pendr}.\nThe radii at the end of stage B for positive\n$P_{\\rm dot}$ systems are reasonably situated, considering the errors\nand the simplified treatment, around the radii of tidal truncation or slightly\nbeyond this. This result can lead to a picture that superhumps are\ninitially excited at the 3:1 resonance, whose outward propagation\n(if there is sufficient matter outside the 3:1 resonance)\nis limited by tidal truncation. This probably determines the maximum\nattainable $P_{\\rm SH}$ in positive $P_{\\rm dot}$ systems.\nSince the superhumps usually quickly decay near the end of stage B,\nthe large dissipation at large radius seems to quickly quench\nthe eccentricity power.\n\n\\begin{table}\n\\caption{Superhump Periods during Stage A}\\label{tab:pera}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nObject & Year & period (d) & err \\\\\n\\hline\nV455 And & 2007 & 0.05803 & 0.00008 \\\\\nV466 And & 2008 & 0.05815 & 0.00008 \\\\\nDH Aql & 2003 & 0.08079 & 0.00012 \\\\\nVY Aqr & 2008 & 0.06558 & 0.00026 \\\\\nEG Aqr & 2006 & 0.08128 & 0.00018 \\\\\nTT Boo & 2004 & 0.07911 & 0.00009 \\\\\nUZ Boo & 2003 & 0.06354 & 0.00024 \\\\\nAX Cap & 2004 & 0.12279 & 0.00277 \\\\\nGX Cas & 1996 & 0.09690 & 0.00055 \\\\\nV1040 Cen & 2002 & 0.06243 & 0.00007 \\\\\nWX Cet & 1989 & 0.06031 & 0.00003 \\\\\nWX Cet & 1998 & 0.06027 & 0.00014 \\\\\nRX Cha & 2009 & 0.08710 & -- \\\\\nBZ Cir & 2004 & 0.07692 & 0.00005 \\\\\nPU CMa & 2008 & 0.05901 & 0.00022 \\\\\nAL Com & 1995 & 0.05799 & 0.00014 \\\\\nAL Com & 2001 & 0.05791 & 0.00022 \\\\\nGO Com & 2003 & 0.06323 & 0.00010 \\\\\nV632 Cyg & 2008 & 0.06628 & 0.00007 \\\\\nV1028 Cyg & 1995 & 0.06269 & 0.00011 \\\\\nV1113 Cyg & 1994 & 0.07963 & 0.00007 \\\\\nKV Dra & 2009 & 0.06109 & 0.00026 \\\\\nXZ Eri & 2008 & 0.06519 & 0.00021 \\\\\nUV Gem & 2003 & 0.09635 & 0.00030 \\\\\nAW Gem & 1995 & 0.08276 & 0.00053 \\\\\nAW Gem & 2009 & 0.08185 & 0.00038 \\\\\nV844 Her & 2006 & 0.05649 & 0.00005 \\\\\nMM Hya & 2001 & 0.06032 & 0.00025 \\\\\nRZ Leo & 2000 & 0.08046 & 0.00053 \\\\\nGW Lib & 2007 & 0.05473 & 0.00007 \\\\\nV419 Lyr & 2006 & 0.09131 & 0.00009 \\\\\nV585 Lyr & 2003 & 0.06113 & 0.00008 \\\\\nAB Nor & 2002 & 0.08174 & 0.00027 \\\\\nDT Oct & 2003 & 0.07650 & 0.00017 \\\\\nV2527 Oph & 2004 & 0.07226 & 0.00008 \\\\\nV368 Peg & 2005 & 0.07130 & -- \\\\\nUV Per & 2003 & 0.06813 & 0.00009 \\\\\nUV Per & 2007 & 0.06659 & 0.00002 \\\\\nQY Per & 1999 & 0.08037 & 0.00032 \\\\\nWZ Sge & 2001 & 0.05838 & 0.00006 \\\\\nSU UMa & 1999 & 0.08054 & 0.00021 \\\\\nSW UMa & 1991 & 0.05908 & 0.00014 \\\\\nSW UMa & 2000 & 0.05877 & 0.00006 \\\\\nSW UMa & 2006 & 0.05894 & 0.00005 \\\\\nBC UMa & 2003 & 0.06512 & 0.00006 \\\\\nBZ UMa & 2007 & 0.07113 & 0.00039 \\\\\nDV UMa & 2005 & 0.08929 & -- \\\\\nDV UMa & 2007 & 0.08926 & 0.00018 \\\\\nIY UMa & 2000 & 0.07666 & 0.00015 \\\\\nKS UMa & 2003 & 0.07095 & 0.00009 \\\\\nHS Vir & 1996 & 0.08118 & 0.00021 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump Periods during Stage A (continued)}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nObject & Year & period (d) & err \\\\\n\\hline\nHV Vir & 2002 & 0.05864 & 0.00002 \\\\\n1RXS J0423 & 2008 & 0.07970 & 0.00010 \\\\\nASAS J0233 & 2006 & 0.05676 & 0.00007 \\\\\nASAS J1025 & 2006 & 0.06407 & 0.00010 \\\\\nASAS J1536 & 2004 & 0.06557 & 0.00014 \\\\\nASAS J1600 & 2005 & 0.06653 & 0.00012 \\\\\nCTCV J0549 & 2006 & 0.08650 & 0.00026 \\\\\nSDSS J1556 & 2007 & 0.08395 & 0.00014 \\\\\nSDSS J1627 & 2008 & 0.11269 & 0.00067 \\\\\nOT J1443 & 2009 & 0.07461 & 0.00055 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Estimated disk radius at the end of stage B.}\\label{tab:pendr}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\nObject & Year & $\\epsilon$ & $r$$^a$ & err$^b$ \\\\\n\\hline\nV1108 Her & 2004 & 0.008 & 0.499 & 0.149 \\\\\nOT J1112 & 2007 & 0.008 & 0.526 & 0.036 \\\\\nWZ Sge & 2001 & 0.009 & 0.534 & 0.019 \\\\\nAL Com & 1995 & 0.011 & 0.600 & 0.042 \\\\\nTSS J0222 & 2005 & 0.013 & 0.520 & 0.050 \\\\\nDI UMa & 2007a & 0.014 & 0.569 & 0.027 \\\\\nGW Lib & 2007 & 0.015 & 0.587 & 0.005 \\\\\nV455 And & 2007 & 0.015 & 0.532 & 0.024 \\\\\nV466 And & 2008 & 0.015 & 0.595 & 0.029 \\\\\nOT J0238 & 2008 & 0.016 & 0.600 & 0.018 \\\\\nV436 Cen & 1978 & 0.019 & 0.501 & 0.017 \\\\\nASAS J0233 & 2006 & 0.020 & 0.564 & 0.017 \\\\\nHV Vir & 2002 & 0.021 & 0.567 & 0.014 \\\\\nWX Cet & 1998 & 0.022 & 0.551 & 0.020 \\\\\nHV Vir & 2008 & 0.022 & 0.550 & 0.036 \\\\\nUV Per & 2007 & 0.022 & 0.510 & 0.017 \\\\\nV844 Her & 2006 & 0.022 & 0.585 & 0.020 \\\\\nWX Cet & 1989 & 0.023 & 0.593 & 0.033 \\\\\nPU CMa & 2008 & 0.024 & 0.500 & 0.036 \\\\\nSW UMa & 2006 & 0.025 & 0.579 & 0.013 \\\\\nVY Aqr & 2008 & 0.025 & 0.553 & 0.008 \\\\\nASAS J1600 & 2005 & 0.025 & 0.544 & 0.008 \\\\\nSW UMa & 1991 & 0.025 & 0.485 & 0.028 \\\\\nSW UMa & 2000 & 0.025 & 0.581 & 0.014 \\\\\nQZ Vir & 1993 & 0.026 & 0.518 & 0.013 \\\\\nSDSS J1227 & 2007 & 0.026 & 0.505 & 0.020 \\\\\nXZ Eri & 2008 & 0.027 & 0.574 & 0.040 \\\\\nUV Per & 2000 & 0.027 & 0.518 & 0.031 \\\\\nXZ Eri & 2007 & 0.027 & 0.529 & 0.013 \\\\\nHO Del & 2008 & 0.027 & 0.530 & 0.014 \\\\\nUV Per & 2003 & 0.027 & 0.527 & 0.010 \\\\\nIY UMa & 2006 & 0.029 & 0.497 & 0.015 \\\\\nBC UMa & 2000 & 0.031 & 0.517 & 0.011 \\\\\nV1040 Cen & 2002 & 0.031 & 0.577 & 0.016 \\\\\nBC UMa & 2003 & 0.031 & 0.514 & 0.007 \\\\\nBZ UMa & 2007 & 0.032 & 0.501 & 0.013 \\\\\nV632 Cyg & 2008 & 0.032 & 0.531 & 0.018 \\\\\nKS UMa & 2003 & 0.033 & 0.496 & 0.007 \\\\\nASAS J1025 & 2006 & 0.033 & 0.533 & 0.006 \\\\\nTV Crv & 2001 & 0.033 & 0.496 & 0.011 \\\\\nV4140 Sgr & 2004 & 0.034 & 0.537 & 0.057 \\\\\nRZ Leo & 2000 & 0.034 & 0.504 & 0.012 \\\\\nTV Crv & 2004 & 0.035 & 0.539 & 0.024 \\\\\nSU UMa & 1999 & 0.036 & 0.481 & 0.028 \\\\\nSS UMi & 2004 & 0.037 & 0.514 & 0.016 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ Estimated disk radius at the end of stage B.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Error in the radius.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Estimated disk radius at the start of stage B.}\\label{tab:pstartr}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\nObject & Year & $\\epsilon$ & $r$$^a$ & err$^b$ \\\\\n\\hline\nV1108 Her & 2004 & 0.008 & 0.474 & 0.149 \\\\\nOT J1112 & 2007 & 0.008 & 0.474 & 0.036 \\\\\nWZ Sge & 2001 & 0.009 & 0.474 & 0.019 \\\\\nAL Com & 2001 & 0.010 & 0.472 & 0.036 \\\\\nAL Com & 1995 & 0.011 & 0.552 & 0.042 \\\\\nTSS J0222 & 2005 & 0.013 & 0.471 & 0.050 \\\\\nDI UMa & 2007a & 0.014 & 0.472 & 0.027 \\\\\nGW Lib & 2007 & 0.015 & 0.472 & 0.005 \\\\\nV455 And & 2007 & 0.015 & 0.470 & 0.024 \\\\\nV466 And & 2008 & 0.015 & 0.472 & 0.029 \\\\\nOT J0238 & 2008 & 0.016 & 0.575 & 0.018 \\\\\nV436 Cen & 1978 & 0.019 & 0.468 & 0.017 \\\\\nASAS J0233 & 2006 & 0.020 & 0.469 & 0.017 \\\\\nHV Vir & 2002 & 0.021 & 0.468 & 0.014 \\\\\nWX Cet & 1998 & 0.022 & 0.474 & 0.020 \\\\\nHV Vir & 2008 & 0.022 & 0.467 & 0.036 \\\\\nUV Per & 2007 & 0.022 & 0.509 & 0.017 \\\\\nV844 Her & 2006 & 0.022 & 0.468 & 0.020 \\\\\nWX Cet & 1989 & 0.023 & 0.468 & 0.033 \\\\\nPU CMa & 2008 & 0.024 & 0.464 & 0.036 \\\\\nSW UMa & 2006 & 0.025 & 0.467 & 0.013 \\\\\nVY Aqr & 2008 & 0.025 & 0.469 & 0.008 \\\\\nASAS J1600 & 2005 & 0.025 & 0.477 & 0.008 \\\\\nIY UMa & 2000 & 0.025 & 0.461 & 0.015 \\\\\nSW UMa & 1991 & 0.025 & 0.463 & 0.028 \\\\\nSW UMa & 2000 & 0.025 & 0.512 & 0.014 \\\\\nQZ Vir & 1993 & 0.026 & 0.475 & 0.013 \\\\\nSDSS J1227 & 2007 & 0.026 & 0.463 & 0.020 \\\\\nXZ Eri & 2008 & 0.027 & 0.466 & 0.040 \\\\\nUV Per & 2000 & 0.027 & 0.487 & 0.031 \\\\\nXZ Eri & 2007 & 0.027 & 0.464 & 0.013 \\\\\nHO Del & 2008 & 0.027 & 0.493 & 0.014 \\\\\nUV Per & 2003 & 0.027 & 0.497 & 0.010 \\\\\nIY UMa & 2006 & 0.029 & 0.469 & 0.015 \\\\\nBC UMa & 2000 & 0.031 & 0.498 & 0.011 \\\\\nCU Vel & 2002 & 0.031 & 0.498 & 0.027 \\\\\nV1040 Cen & 2002 & 0.031 & 0.464 & 0.016 \\\\\nDV UMa & 2007 & 0.031 & 0.457 & 0.019 \\\\\nBC UMa & 2003 & 0.031 & 0.489 & 0.007 \\\\\nIY UMa & 2009 & 0.031 & 0.500 & 0.012 \\\\\nBZ UMa & 2007 & 0.032 & 0.492 & 0.013 \\\\\nSX LMi & 2002 & 0.032 & 0.493 & 0.004 \\\\\nV632 Cyg & 2008 & 0.032 & 0.465 & 0.018 \\\\\nKS UMa & 2003 & 0.033 & 0.485 & 0.007 \\\\\nASAS J1025 & 2006 & 0.033 & 0.461 & 0.006 \\\\\nTV Crv & 2001 & 0.033 & 0.462 & 0.011 \\\\\nV4140 Sgr & 2004 & 0.034 & 0.461 & 0.057 \\\\\nDV UMa & 1997 & 0.034 & 0.489 & 0.019 \\\\\nRZ Leo & 2000 & 0.034 & 0.481 & 0.012 \\\\\nTV Crv & 2004 & 0.035 & 0.495 & 0.024 \\\\\nSU UMa & 1999 & 0.036 & 0.479 & 0.028 \\\\\nSS UMi & 2004 & 0.037 & 0.458 & 0.016 \\\\\nSDSS J1556 & 2007 & 0.037 & 0.496 & 0.012 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ Estimated disk radius at the start of stage B.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Error in the radius.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig26.eps}\n \\end{center}\n \\caption{Disk radius at the end of stage B scaled from ratios of\n $\\epsilon$ (for $P_1$) between the end of stage B and\n the minimum $P_{\\rm SH}$.\n The locations of various resonances and limits are the same as\n in \\citet{kat08wzsgelateSH}.\n }\n \\label{fig:pendr}\n\\end{figure}\n\n This picture generally well applies to systems with $\\epsilon > 0.02$\n(corresponding to $q > 0.11$). Objects with smaller $\\epsilon$ tend to\ndeviate from this trend. These objects include extreme WZ Sge-type dwarf\nnovae (WZ Sge, V455 And, AL Com) while some of\n(what are usually regarded as) WZ Sge-type dwarf novae (GW Lib, HV Vir)\nhave a similar tendency to ordinary SU UMa-type dwarf novae.\nThe small radii for V436 Cen, UV Per (2007) and others may have been\na result of undersampling of superhump timings; the case for UV Per\nis particularly likely because other well-sampled superoutbursts of the\nsame object generally gave larger radii.\n\n The difference among WZ Sge-type dwarf novae can be attributed to\nthe matter left beyond the 3:1 resonance \\citep{kat08wzsgelateSH}:\nif the 2:1 resonance is strong enough to accrete much of the matter\nbeyond the radius of 3:1 resonance, the propagation of the eccentricity\nwave beyond the 3:1 resonance would not produce a strong superhump\nsignal with a longer period. Further observations, however, are\nespecially needed in these cases whether different types of superoutbursts\n(cf. \\cite{uem08alcom}) in the same WZ Sge-type object lead to different\nbehavior of $P_{\\rm SH}$.\n\n\\subsection{Superhump Period at the Start of Stage B}\n\n The radii calculated for the start of stage B are given in\ntable \\ref{tab:pstartr} and figure \\ref{fig:pstartr}.\nIn systems with positive $P_{\\rm dot}$, these radii match the\nsupposed 3:1 resonance. The exceptions, AL Com in 1995 and\nOT J0238 in 2008, are likely a result of the poorly determined\nstage C superhumps.\nIn negative $P_{\\rm dot}$ systems (generally corresponding to\n$\\epsilon > 0.025$), the decrease in the $P_{\\rm SH}$ can be explained\nif superhumps are initially excited slightly outside the 3:1 resonance.\nIn such systems, the large tidal torque caused by the large $q$ might\nenable eccentricity wave originating even outside the 3:1 resonance.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig27.eps}\n \\end{center}\n \\caption{Disk radius at the start of stage B scaled from ratios of\n $\\epsilon$ between the end of the stage B and the minimum $P_{\\rm SH}$.\n }\n \\label{fig:pstartr}\n\\end{figure}\n\n\\subsection{Stage C Superhumps in Positive $P_{\\rm dot}$ Systems}\\label{sec:stagec}\n\n In our interpretation, the stage C superhumps in positive $P_{\\rm dot}$\nare regarded as superhumps stably originating from the radius of the\n3:1 resonance. It looks as if superhumps\nare newly excited around the radius of 3:1 resonance after the original\nsuperhumps reached a larger radius (limiting radius as discussed in\nsubsection \\ref{sec:maxradius}) and their eccentric power is quenched.\nIt may be that superhumps can be rejuvenized if the eccentricity\nof the original superhumps become sufficiently weak and there is\nstill sufficient matter around the 3:1 resonance. Such a condition\ncould be realized when the matter beyond the 3:1 resonance still\nremains after the termination of a superoutburst\n(cf. \\cite{kat08wzsgelateSH}) and if this matter is efficiently\naccreted inward. The brightening associated with the appearance\n(or regrowth) of superhumps at the start of the stage C can be naturally\nexplained by this accretion and increased dissipation due to\na renewed tidal instability.\n\n\\subsection{Stage A Superhumps}\n\n We similarly calculated the radii for the start of the stage A\n(figure \\ref{fig:pstagear}). In some systems, the fractional superhump\nexcesses exceed the range in \\citet{mur00SHprecession},\nand they are shown in lower limits. The periods of stage A superhumps\ncan be understood if they originate from the outermost disk.\nSince stage A and B superhumps show a smooth transition in phase,\nthe eccentricity excited during the stage A in the outside the disk\nappears to efficiently excite the strong eccentricity at the radius\nof the 3:1 resonance. It may be that the eccentricity invoked during\nthe stage A can efficiently work as a seed perturbation at the radius\nof the 3:1 resonance.\nThe situation might be the same for the stage B--C transition.\n\n Although many of very well observed superoutbursts show stage A,\nsome superoutbursts showed different behavior. Among them, QZ Vir in 1993\nand 1RXS J0532 in 2005 associated with precursor outbursts did not show\nlong-period superhumps as in usual stage A. The initial period of\nsuperhumps during the 1993 superoutburst of QZ Vir was close to the\norbital period \\citep{kat97tleo}, an exceptional case in this study.\nThe existence of a prominent precursor in these superoutburst can be\nunderstood as a result of a small disk-mass at the onset of superoutbursts\n\\citep{osa03DNoutburst}. In these superoutbursts, the disk mass may\nhave been so small that virtually no mass was present beyond the\n3:1 resonance.\n\n Note, however, stage A with long-period superhumps was\ndefinitely recorded during superoutbursts of GO Com in 2003\n\\citep{ima05gocom} and PU CMa in 2008 (subsection \\ref{tab:pucma}).\nThe condition whether stage A appears or not may depend on other factors.\n\n With smoothed particle hydrodynamics (SPH), \\citet{mur98SH} reported\na longer superhump period during the early stage of eccentricity growth.\nAlthough this might correspond to stage A superhumps, the exact\nidentification should await further investigation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig28.eps}\n \\end{center}\n \\caption{Disk radius during the stage A scaled from ratios of\n $\\epsilon$ between the end of stage B and the minimum $P_{\\rm SH}$.\n Upper arrow show lower limits.\n }\n \\label{fig:pstagear}\n\\end{figure}\n\n\\subsection{ER UMa Stars}\\label{sec:erumastars}\n\n ER UMa stars are a subgroup of SU UMa-type dwarf novae characterized\nby the shortness (19--50 d) of their supercycles\n(\\cite{kat95eruma}; \\cite{rob95eruma}; \\cite{mis95PGCV};\n\\cite{nog95rzlmi}; \\cite{osa95eruma}).\nIt has been demonstrated that at least some of\nER UMa stars show large-amplitude superhumps at the onset of superoutbursts\n\\citep{kat96erumaSH} and a phase reversal of superhumps during the\nearly plateau stage \\citep{kat03erumaSH}. \\citet{osa03DNoutburst}\ninterpreted large-amplitude superhumps in the early stage is a consequence\nof tidal heating at the outer edge by the continuous presence of tidal\ninstability, resulting a superoutburst driven by the tidal instability.\nThe origin of the phase reversal is not yet well understood.\n\\citet{kat03erumaSH} suspected that a movement of the location of\nthe strongest tidal dissipation to the opposite direction somehow\nhappened, while \\citet{ole04ixdra} considered a beat between the superhump\nand orbital periods.\\footnote{\n As discussed in subsection \\ref{sec:transimplication} this ``orbital\n period'' likely referred to $P_2$ rather than the true $P_{\\rm orb}$.\n}\n\n Due to the complexity in the hump profile and limited availability\nof high-quality raw data, we do not discuss on these objects in detail.\nAn $O-C$ analysis for ER UMa is presented here, and brief discussions\non V1159 Ori and RZ LMi are given in Appendix section \\ref{sec:individual}.\n\n Upon examination of the data used in\n\\citet{kat03erumaSH}, we noticed that the early-stage superhumps\ncan be tracked for a while even after the occurrence of the\nreported phase reversal (figure \\ref{fig:erumahumpall}, open circles).\nThese superhumps appear to comfortably follow a positive $P_{\\rm dot}$\nexpected for this $P_{\\rm SH}$. In ER UMa, the stage C appeared to\nhave started earlier than in ordinary SU UMa-type dwarf novae, and was\nobserved as a regrowth of superhumps associated with a phase reversal\n(figure \\ref{fig:erumahumpall}, filled circles). It may be that\na combination of a large mass-transfer rate from the secondary,\nand the small amount of disk matter beyond the 3:1 resonance in ER UMa\nstars \\citep{osa03DNoutburst} serves a condition enabling early\nrejuvenization of superhumps (cf. subsection \\ref{sec:stagec}).\nIt is not known why only ER UMa stars show a $\\sim$0.5 phase shift\nat the onset of the stage C. Detailed observations of ER UMa stars\nmight provide a clue to understanding the nature of the stage B--C\ntransition.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig29.eps}\n \\end{center}\n \\caption{$O-C$ variation in ER UMa (1995). (Upper) $O-C$.\n The open and filled circles represent early-stage and later-stage\n superhumps described in \\citet{kat03erumaSH}.\n (Lower) Light curve.\n }\n \\label{fig:erumahumpall}\n\\end{figure}\n\n The behavior of superhumps in RZ LMi is still poorly known.\n\\citet{ole08rzlmi} reported that its superhump periods were almost constant\nother than one well-observed, 2004 superoutburst. \\citet{ole08rzlmi}\nclaimed that the phases of superhumps were even coherent between\ndifferent superoutbursts. We should, however, note that many of\nobservations by \\citet{ole08rzlmi} covered only a few days of\nindividual superoutbursts, making it difficult to estimate\n$P_{\\rm dot}$ for individual superoutbursts. Instead, reported\nsuperhump maxima in \\citet{ole08rzlmi} can be reasonably well\nexpressed by a slightly positive $P_{\\rm dot}$, by the same\noverlaying method used in subsection \\ref{sec:different}\n(figure \\ref{fig:rzlmiocadd}). We consider that the $P_{\\rm dot}$\nobserved during the 2004 superoutburst is typical for this object\nand the slight difference in $P_{\\rm SH}$ between different\nsuperoutbursts \\citep{ole08rzlmi} was a result of observation of\ndifferent phase of superoutbursts. This interpretation needs to\nbe tested by continuous observation throughout different superoutbursts.\nIt would be intriguing to see whether or not the stage C is present\nin RZ LMi (see subsection \\ref{sec:rzlmi}),\nwhich might provide a clue why superoutbursts in RZ LMi\nare quenched so early (cf. \\cite{osa95rzlmi}; \\cite{hel01eruma}).\n\n Most recently, \\citet{rut08diuma} reported a positive, but a relatively\nsmall $P_{\\rm dot}$ in another ultra-short $P_{\\rm SH}$ ER UMa star,\nDI UMa. \\citet{rut08diuma} also reported superhump-like variations during\nthe rising stage but were shifted in phase by $\\sim$0.5 $P_{\\rm SH}$.\nThese variations may have been stage A superhumps, and we obtained\na period of 0.0569(2) d by assuming the phase continuity.\nThe exact identification of their nature should await a further study.\nIf the superhumps were evolving in period during the rising stage of\nDI UMa, as in the stage A in ordinary SU UMa-type dwarf novae, the onset\nof tidal instability likely coincides with the ignition of the outburst,\non the contrary to the expectation in \\citet{osa03DNoutburst} that\ntidal instability triggers ER UMa-type superoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig30.eps}\n \\end{center}\n \\caption{$O-C$ variation in RZ LMi. The hump maxima are taken\n from \\citet{ole08rzlmi} and are shifted so that the start of\n individual superoutburst corresponds to $E=0$.\n }\n \\label{fig:rzlmiocadd}\n\\end{figure}\n\n\\subsection{Long-Period Systems}\\label{sec:longp}\n\n The period variation of superhumps in long-period ($P_{\\rm SH}$)\nsystems appears to vary from system to system.\nSome systems, such as MN Dra and UV Gem, show smoothly decreasing\n$P_{\\rm SH}$ (figure \\ref{fig:lp1}), while others, such as\nAX Cap and SDSS J1627, show stage transitions (accompanied by\na break in the $O-C$ diagram and a well-defined stage C superhumps\nwith a fairly constant period) as in short-$P_{\\rm SH}$\nsystems (figure \\ref{fig:lp2}).\nNote, however, the degree of period variation is strongly\ndifferent from system to system. Although the global pattern of\nperiod variation is similar between AX Cap and SDSS J1627, the amplitude\nof $O-C$'s are several times larger in the former system.\nThere are apparently a class of systems with a much smaller period\nvariation, such as TU Men, EF Peg, BF Ara and V725 Aql.\nAlthough further confirmation is necessary, SDSS J1702 (and possibly\nV725 Aql) even appears to have a positive period derivative.\n\n The systems with smoothly decreasing $P_{\\rm SH}$ look like to have\nmore frequent normal outbursts than in systems with stage transitions.\nThe latter class of long-$P_{\\rm SH}$ SU UMa-type dwarf novae\nseems to somehow mimic short-$P_{\\rm SH}$ SU UMa-type dwarf novae\nwith infrequent superoutbursts. Whether there is a difference in\n$q$ or other system parameters, or whether suppression of normal\noutbursts somehow works in the latter class need to be tested\nby further observations.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig31.eps}\n \\end{center}\n \\caption{$O-C$ variations of Long-$P_{\\rm SH}$ systems with\n smooth period variations.}\n \\label{fig:lp1}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig32.eps}\n \\end{center}\n \\caption{$O-C$ variations of Long-$P_{\\rm SH}$ systems with\n period breaks.}\n \\label{fig:lp2}\n\\end{figure}\n\n\\subsection{Superhumps in Black-Hole X-Ray Transients}\\label{sec:BHXT}\n\n Black-hole X-ray transients (BHXTs) are known to show superhumps\n(cf. \\cite{bai92gumus}; \\cite{kat95v518per}; \\cite{odo96BHXNSH};\n\\cite{has01BHXNSH}; \\cite{uem02j1118}).\n\n KV UMa (=XTE J1118$+$480) is the best studied superhumping system\namong BHXTs. The $O-C$ diagram (figure \\ref{fig:kvumaoc}, see\nsubsection \\ref{sec:kvuma} for the data)\nclosely resemble those of SU UMa-type dwarf novae with intermediate\n$P_{\\rm orb}$.\nThe similarity of the $O-C$ variation between SU UMa-type dwarf novae\nand a BHXT suggests that the evolution mechanism of superhumps\nis similar between these systems. The degree of period variation,\nsuch as $P_2\/P_1-1$ = 0.001 and\nglobal $P_{\\rm dot}$ = $-0.43(0.05) \\times 10^{-5}$, is an order of\nmagnitude smaller than those of typical SU UMa-type dwarf novae.\nThis difference may be attributed to the difference in the emission\nmechanism of superhumps between CVs and BHXTs \\citep{has01BHXNSH}.\nIn BHXTs, the outer region of the accretion disk may be efficiently\nshadowed by the inner region and may not be sufficiently ionized\nfor the eccentricity wave to propagate. A study of period variation\nof superhumps in BHXTs is expected to provide additional clue in\nunderstanding the origin of superhumps in these systems and might\nserve as a potential tool for studying the structure of the outer\naccretion disks in these systems.\n\n An updated analysis for V518 Per is also presented in subsection\n\\ref{sec:v518per}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig33.eps}\n \\end{center}\n \\caption{$O-C$ diagram of KV UMa (=XTE J1118$+$480) during the 2000\n outburst.}\n \\label{fig:kvumaoc}\n\\end{figure}\n\n\\subsection{$\\epsilon$-$q$ Relation}\\label{sec:epsq}\n\n Since it has become more evident that the shortest $P_{\\rm SH}$\n(in many cases, this agrees with $P_2$), rather than mean $P_{\\rm SH}$,\nrepresents the characteristic $P_{\\rm SH}$ for SU UMa-type superoutbursts,\nwe re-calibrated the $\\epsilon$-$q$ relation using the shortest $P_{\\rm SH}$\nas in the way in \\citet{pat05SH}. The data are given in table\n\\ref{tab:epsq} (the $q$ and $\\epsilon$ for DW UMa and UU Aqr are from\n\\cite{pat05SH}; $\\epsilon$ for other objects are newly determined\nin this work). The updated $\\epsilon$-$q$ is shown in equation\n\\ref{equ:epsq} and figure \\ref{fig:epsq}.\n\n\\begin{equation}\n\\epsilon = 0.16(2)q + 0.25(7)q^2\n\\label{equ:epsq}.\n\\end{equation}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig34.eps}\n \\end{center}\n \\caption{Fractional superhump excess versus mass-ratio.\n $\\epsilon$ denotes fractional superhump excess for the minimum $P_{\\rm SH}$.}\n \\label{fig:epsq}\n\\end{figure}\n\n\\begin{table}\n\\caption{Fractional superhump excess versus mass-ratio}\\label{tab:epsq}\n\\begin{center}\n\\begin{tabular}{ccc}\n\\hline\\hline\nObject & $\\epsilon$ & $q$ \\\\\n\\hline\nKV UMa & 0.0026(2) & 0.037(7) \\\\\nWZ Sge & 0.0089(1) & 0.050(15) \\\\\nXZ Eri & 0.0238(4) & 0.110(2) \\\\\nIY UMa & 0.0238(18) & 0.125(8) \\\\\nZ Cha & 0.0311(8) & 0.145(15) \\\\\nDV UMa & 0.0295(2) & 0.150(1) \\\\\nOU Vir & 0.0303(2) & 0.175(25) \\\\\nDW UMa & 0.0644(20) & 0.28(4) \\\\\nUU Aqr & 0.0702(19) & 0.30(7) \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{$\\epsilon$-$P_{\\rm orb}$ Relation}\\label{sec:epsporb}\n\n The improved relation between $\\epsilon$ and $P_{\\rm orb}$ is\nshown in figure \\ref{fig:epsporb}. The predicted location of\nRoche-lobe filling zero-age main sequence is also shown following\n\\citet{pat03suumas}. Although the new calibration on the $\\epsilon$-$q$\nrelation seems to slightly improve the deviation between observed and\npredicted $\\epsilon$, there still remains significant disagreement\nbetween them. The disagreement is the greatest where the period minimum \nappears to reside: $-1.27 < log(P_{\\rm orb}) < -1.25$\n($0.053 < P_{\\rm orb} < 0.056$ d).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig35.eps}\n \\end{center}\n \\caption{Fractional superhump excess versus orbital period.\n $\\epsilon$ denotes fractional superhump excess for the minimum $P_{\\rm SH}$.\n The two set of curves and dashed curves represent predicted $\\epsilon$\n for zero-age main-sequence following figure 20 of \\citet{pat03suumas};\n the upper (thin) curve represents the relation in \\citet{pat03suumas} and\n the lower (thick) curve represents the relation based on the improved\n $\\epsilon$-$q$ relation.\n }\n \\label{fig:epsporb}\n\\end{figure}\n\n\\section{Period Variation of Superhumps in WZ Sge-Type Dwarf Novae}\\label{sec:wzsgestars}\n\n\\subsection{Late-Stage Superhumps in WZ Sge-Type Dwarf Novae: Case Studies}\\label{sec:latestage}\n\n WZ Sge-type dwarf novae (see e.g. \\cite{bai79wzsge}; \\cite{dow90wxcet};\n\\cite{kat01hvvir}) are a subgroup of SU UMa-type dwarf novae\ncharacterized by large-amplitude (typically $\\sim$ 8 mag) superoutbursts\nwith very long (typically $\\sim$ 10 yr) recurrence times.\n\n Some SU UMa-type dwarf novae with long recurrence times, most notably\nWZ Sge-type dwarf novae, are known to\nexhibit long-enduring superhumps during the late post-superoutburst stage.\nWe will examine selected special cases (though the discussion\nmay not be necessarily applicable to general cases) which provide\nnew insight into the relation of late-stage superhumps and other\nperiodicities.\n\n The first case is GW Lib in 2007.\nDuring the late post-superoutburst stage, this object showed\nvery stable superhumps whose period is $\\sim$0.5 \\% longer than\nthose of the ordinary superhumps \\citep{kat08wzsgelateSH}.\nThese superhumps during the late post-superoutburst stage appear to be\non a smooth extension of the $O-C$ diagram of the stage B\n(figure \\ref{fig:gwlibhumpall}). This suggests\nthat these superhumps are intrinsically of the same origin, and\nthe transition to the stage C around the termination of the\nsuperoutburst looks like a disturbance in the $O-C$ diagram.\n\n This temporary emergence of a new periodicity is in reality\nattributed to orbital humps (cf. subsection \\ref{sec:gwlib}).\nSimilar behavior was also recorded in well-observed WZ Sge-type systems\nV455 And (subsection \\ref{sec:v455and}) and WZ Sge\n(subsection \\ref{sec:wzsge}). This phenomenon thus appears\ncommon to many WZ Sge-type dwarf novae, but apparently not very striking\nin usual SU UMa-type dwarf novae. \\citet{osa02wzsgehump} presented\nan interpretation that the orbital humps observed in WZ Sge-type\nsuperoutbursts can be well reproduced by a projection effect of the\nsuperhump source, rather than by an enhanced hot spot. Our observation\nin SDSS J080434.20$+$510349.2 (hereafter SDSS J0804)\nsupports this interpretation \\citep{kat09j0804}.\nThere appears to be a condition that this mechanism strongly works\nduring the late stage of WZ Sge-type superoutbursts. There also remains\na possibility that a mechanism similar to early superhumps\nworks in this phase (see subsection \\ref{sec:gwlib}).\n\n Following \\citet{kat08wzsgelateSH},\nlate post-superoutburst superhumps are supposed to originate from\nthe precessing eccentric disk near the tidal truncation.\nThis leads to a picture that the eccentric disk continues to slowly\nexpand after the end of stage B, and finally reaches the tidal truncation\nwhere the period stabilizes. This picture is a natural extension\nof the explanation of ``late superhumps'' in WZ Sge-type dwarf novae\nproposed by \\citet{kat08wzsgelateSH}.\nDuring the plateau stage when the\ndisk is still bright enough, newly excited superhumps\n(stage C superhumps) can temporarily dominate over the superhump\nsignal arising from the outer, relatively faint, disk, and\nbehaves as a temporarily disturbance until the entire disk returns\nto the cool state. This interpretation, however, needs to be\nverified by more detailed study and by a comparison with numerical\nsimulations of superhumps incorporating the thermal instability.\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,160mm){fig36.eps}\n \\end{center}\n \\caption{$O-C$ variation in GW Lib (2007). (Upper) $O-C$;\n (Lower) Light curve. The early stage of the superoutburst, when\n ordinary superhump were not observed, is outside ($E < 0$) the figure.\n }\n \\label{fig:gwlibhumpall}\n\\end{figure*}\n\n The second case is ASAS J002511$+$1217.2\n(figure \\ref{fig:asas0025humpall}). Following a typical\nstage B--C evolution, the object showed double-humped superhumps\nwith a shorter period between the end of the superoutburst plateau\nand the rebrightening. Outside this stage, superhumps during the\nlate post-superoutburst stage are on a smooth extension of the stage C\nsuperhumps (see subsection \\ref{sec:asas0025} for details).\nAlthough the situation looks somewhat different from GW Lib,\nsuperhumps during the late post-superoutburst stage appears to\nhave evolved from the stage C superhumps. The early post-superoutburst\nstage and the rebrightening acted like a disturbance as in GW Lib,\nalthough the emergence of orbital period was not yet confirmed in\nthis case.\nIt may be that $m=2$ waves were transiently excited in the inner disk,\nand the phenomenological difference from GW Lib may be associated with\nthe presence of a rebrightening. It would be worth noting that both\nGW Lib and ASAS J002511$+$1217.2 did not show a $\\sim$0.5 phase shift\nduring the late stages.\n\n We give a summary of late-stage superhumps in WZ Sge-type dwarf novae\nin table \\ref{tab:latehump}. The values of late-stage superhumps\n($P_{\\rm late}$) listed in the table are representative periods.\nSince $P_1$ here represents a mean period of stage B, not one\nat its beginning, $P_{\\rm late}$ can be shorter than $P_1$\nin large $P_{\\rm dot}$ systems (e.g. ASAS J0025), \nSee subsections of individual objects for the details.\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,160mm){fig37.eps}\n \\end{center}\n \\caption{$O-C$ variation in ASAS J0025 (2004). (Upper) $O-C$.\n Different symbols refer to humps of different categories\n (see subsection \\ref{sec:asas0025});\n (Lower) Light curve. The earliest stage of the superoutburst\n was not observed.\n }\n \\label{fig:asas0025humpall}\n\\end{figure*}\n\n\\begin{table*}\n\\caption{Late-stage superhumps in WZ Sge-type dwarf novae.}\\label{tab:latehump}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\nObject & $P_{\\rm orb}$ (d) & $P_1$ (d) & $P_{\\rm late}$ (d) & source \\\\\n\\hline\nV455 And & 0.056309 & 0.057144(11) & 0.057188(6) & this work \\\\\nEG Cnc & 0.05997 & 0.060337(6) & 0.06051(2) & this work, \\citet{pat98egcnc} \\\\\nGW Lib & 0.05332 & 0.054095(10) & 0.054156(1) & this work \\\\\nWZ Sge & 0.056688 & 0.057204(5) & 0.057488(14) & this work \\\\\nASAS J0025 & 0.056540$^*$ & 0.057093(12) & 0.056995(3) & this work \\\\\nASAS J1536 & -- & 0.064602(24) & 0.064729(13) & this work \\\\\nSDSS J0804 & 0.059005 & 0.059539(11) & 0.059659(5) & \\citet{kat09j0804} \\\\\nOT J0747 & -- & 0.060750(7) & 0.060771(3) & this work \\\\\n\\hline\n \\multicolumn{4}{l}{$^*$ candidate $P_{\\rm orb}$.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n\\subsection{Period Variation in WZ Sge-Type Dwarf Novae}\n\n Although the borderline between WZ Sge-type dwarf novae and ordinary\nSU UMa-type dwarf novae is somewhat ambiguous, it has been proposed\nthat a 2:1 orbital resonance in low-$q$ systems is responsible\nfor the phenomenon \\citep{osa02wzsgehump}. As already introduced in\n\\citet{kat08wzsgelateSH}, early superhumps (double-wave humps with\na period close to $P_{\\rm orb}$ seen during the earliest stages of\nWZ Sge-type superoutbursts; see also \\cite{kat02wzsgeESH}) are\nconsidered to be a manifestation of the 2:1 resonance\n\\citep{osa02wzsgehump}. By the inferred mechanism, the existence of early\nsuperhumps might a best feature in discriminating WZ Sge-type dwarf\nnovae from ordinary SU UMa-type dwarf novae (in low-inclination systems,\nthough, the amplitudes of early superhumps can be too low to detect;\ne.g. GW Lib, Imada et al., in preparation). In this paper, we deal\nwith objects with early superhumps or objects with very rare\n(less than once in several years) and large-amplitude superoutbursts\nas WZ Sge-type dwarf novae and analogs.\n\n \\citet{kat08wzsgelateSH} also listed nearly constant to positive\n$P_{\\rm dot}$ as one of the common properties of WZ Sge-type dwarf novae.\nWe examine this further in this subsection.\n\n Table \\ref{tab:wztab} summarizes properties of superoutbursts of\nWZ Sge-type dwarf novae. The quiescent magnitudes were mainly taken\nfrom the on-line version of \\citet{RitterCV7}, supplemented for\nV1251 Cyg (Henden, AAVSO-discussion 14842), V592 Her, HV Vir\n(SDSS $g$ values), GW Lib (typical quiescent magnitudes reported\nto VSNET). The maximum magnitudes were mean magnitudes around maximum\nfrom reports to VSNET and other literature; $V$-band measurements are\npreferentially used whenever available. $P_{\\rm SH}$ refers to $P_1$.\n\n\\begin{table*}\n\\caption{Parameters of WZ Sge-type superoutbursts.}\\label{tab:wztab}\n\\begin{center}\n\\begin{tabular}{cccccccccccc}\n\\hline\\hline\nObject & Year & $P_{\\rm SH}$ & $P_{\\rm orb}$ & $P_{\\rm dot}$$^*$ & err$^*$ & $\\epsilon$ & Type$^\\dagger$ & $N_{\\rm reb}$$^\\ddagger$ & delay$^\\S$ & Max & Min \\\\\n\\hline\nLL And & 1993 & 0.056900 & 0.055055 & -- & -- & 0.034 & D? & 0? & -- & 14.3 & 20.0 \\\\\nLL And & 2004 & 0.056583 & 0.055055 & 1.0 & 0.6 & 0.028 & D? & 0? & -- & 12.6 & 20.0 \\\\\nV455 And & 2007 & 0.057133 & 0.056309 & 4.7 & 1.2 & 0.015 & D & 0 & 10 & 8.7 & 16.1 \\\\\nV466 And & 2008 & 0.057203 & 0.056365 & 5.7 & 0.7 & 0.015 & D & 0 & $>$12 & 12.7 & 21.2 \\\\\nUZ Boo & 1994 & 0.061743 & -- & $-$1.5 & 2.5 & -- & B & 2: & 1--5 & 11.7 & 20.4 \\\\\nUZ Boo & 2003 & 0.061922 & -- & $-$1.9 & 6.3 & -- & B & 4 & 3: & 12.8 & 20.4 \\\\\nCG CMa & 1999 & -- & 0.063275 & -- & -- & -- & A\/B & 1\/2 & -- & 13.7 & [22 \\\\\nEG Cnc & 1996 & 0.060337 & 0.05997 & 0.8 & 0.5 & 0.006 & B & 6 & $>$5 & 11.9 & 19.1 \\\\\nAL Com & 1995 & 0.057289 & 0.056668 & 1.9 & 0.5 & 0.011 & A & 1 & 9 & 12.7 & 20.8 \\\\\nAL Com & 2001 & 0.057229 & 0.056668 & $-$0.2 & 0.8 & 0.010 & A & 1 & 10--14 & 12.8 & 20.8 \\\\\nAL Com & 2008 & 0.057174 & 0.056668 & -- & -- & 0.009 & B & $\\ge$4 & -- & 13.2 & 20.8 \\\\\nV1251 Cyg & 1991 & 0.076284 & 0.07433 & -- & -- & 0.026 & D? & 0? & 3--9 & 12.4 & 20.6 \\\\\nV1251 Cyg & 2008 & 0.075973 & 0.07433 & 6.0 & 2.7 & 0.022 & C & 1 & 5 & 12.6 & 20.6 \\\\\nV2176 Cyg & 1997 & 0.056239 & -- & -- & -- & -- & A & 1 & -- & ]13.3 & 19.9 \\\\\nDV Dra & 2005 & -- & 0.05883 & -- & -- & -- & -- & -- & $>$6 & 15.0 & 21.0 \\\\\nV592 Her & 1998 & 0.056498 & -- & 2.1 & 0.8 & -- & D & 0 & 7: & 12.0 & 21.3 \\\\\nV1108 Her & 2004 & 0.057480 & 0.05703 & 1.6 & 6.8 & 0.008 & D & 0 & -- & 11.2 & 17.1 \\\\\nRZ Leo & 2000 & 0.078658 & 0.076038 & 4.9 & 1.7 & 0.034 & C & 1 & 3: & 12.1 & 18.5 \\\\\nRZ Leo & 2006 & 0.078428 & 0.076038 & -- & -- & 0.031 & C & 1 & -- & ]12.5 & 18.5 \\\\\nGW Lib & 2007 & 0.054095 & 0.05332 & 4.0 & 0.1 & 0.015 & D & 0 & 10 & 8.2 & 16.6 \\\\\nSS LMi & 2006 & -- & 0.056637 & -- & -- & -- & -- & -- & -- & ]16.2 & 21.7 \\\\\nV358 Lyr & 2008 & 0.055629 & -- & -- & -- & -- & A & 1 & -- & ]16.1 & [23 \\\\\nWZ Sge & 1978 & 0.057232 & 0.056688 & 0.4 & 0.8 & 0.010 & A & 1($>$6) & 11 & 7.8 & 15.0 \\\\\nWZ Sge & 2001 & 0.057204 & 0.056688 & 2.0 & 0.4 & 0.009 & A & 1(12) & 12 & 8.2 & 15.0 \\\\\nUW Tri & 1995 & -- & 0.05330 & -- & -- & -- & -- & -- & $>$8 & 14.7 & 22.6 \\\\\nUW Tri & 2008 & 0.054194 & 0.05334 & 3.7 & 0.6 & 0.016 & -- & -- & 10 & 14.3 & 22.6 \\\\\nBC UMa & 2000 & 0.064555 & 0.06261 & 4.0 & 1.4 & 0.031 & C & 1 & 4 & 11.6 & 18.6 \\\\\nBC UMa & 2003 & 0.064571 & 0.06261 & 4.2 & 0.8 & 0.031 & C & 1 & 2 & 12.5 & 18.6 \\\\\nHV Vir & 1992 & 0.058285 & 0.057069 & 5.7 & 0.6 & 0.021 & D\/C & 1? & 10 & 11.5 & 19.2 \\\\\nHV Vir & 2002 & 0.058266 & 0.057069 & 7.4 & 0.6 & 0.021 & D & 0 & 2--5 & 13.0 & 19.2 \\\\\nHV Vir & 2008 & 0.058322 & 0.057069 & 7.1 & 1.9 & 0.022 & D? & 0 & 6 & 12.3 & 19.2 \\\\\n1RXS J0232 & 2007 & 0.066166 & -- & $-$1.7 & 0.7 & -- & B & 4 & -- & 10.5 & 18.8 \\\\\nASAS J0233 & 2006 & 0.055987 & 0.05490 & 4.9 & 0.5 & 0.020 & D? & 0? & 8 & 12.0 & 18.2 \\\\\nASAS J1025 & 2006 & 0.063365 & 0.06136 & 10.9 & 0.6 & 0.033 & C & 1 & 3 & 12.2 & 19.3 \\\\\nASAS J1600 & 2005 & 0.064970 & 0.063381 & 11.1 & 0.8 & 0.025 & C & 1 & 2--7 & 12.7 & 17.9 \\\\\nSDSS J0804 & 2006 & 0.059537 & 0.059005 & -- & -- & 0.009 & B & 11 & -- & ]14 & 17.8 \\\\\nOT J0042 & 2008 & 0.056892 & 0.05550 & 4.0 & 1.8 & 0.025 & C? & 1? & 10--12 & 14.5 & 22.8 \\\\\nOT J0238 & 2008 & 0.053658 & 0.05281 & 2.0 & 0.2 & 0.016 & D & 0 & $>$9 & ]14.1 & 21.7 \\\\\nOT J0747 & 2008 & 0.060736 & -- & 4.0 & 0.8 & -- & B & 6 & $<$13 & 11.4 & 19.5 \\\\\nOT J0807 & 2007 & 0.061050 & -- & 9.5 & 4.8 & -- & D? & 0? & -- & ]13.6 & 20.9 \\\\\nOT J0902 & 2008 & -- & 0.05652 & -- & -- & -- & -- & -- & -- & ]16.3 & 23.2 \\\\\nOT J1021 & 2006 & 0.056312 & -- & 0.4 & 0.8 & -- & A & 1 & -- & ]13.9 & 19.7 \\\\\nOT J1112 & 2007 & 0.058965 & 0.05847 & 0.9 & 0.4 & 0.008 & D? & 0? & 21: & 11.5 & [20 \\\\\nOT J1959 & 2005 & 0.059919 & -- & $-$0.7 & 5.2 & -- & C & 1 & $<$6 & 14.7 & 22.5 \\\\\nTSS J0222 & 2005 & 0.055585 & 0.054868 & 2.2 & 1.5 & 0.013 & A & 1 & 6 & 15.5 & 19.5 \\\\\n\\hline\n \\multicolumn{12}{l}{$^*$ Unit $10^{-5}$.} \\\\\n \\multicolumn{12}{l}{$^\\dagger$ A: long-lasting rebrightening; B: multiple rebegitehnings; C: single rebrightening; D: no rebrightening.} \\\\\n \\multicolumn{12}{l}{$^\\ddagger$ Number of rebrightenings.} \\\\\n \\multicolumn{12}{l}{$^\\S$ Days before ordinary superhumps appeared.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table*}\n\n Figure \\ref{fig:wzpdoteps} shows the relation between $P_{\\rm dot}$\nversus $\\epsilon$ for WZ Sge-type dwarf novae.\nFor systems with $\\epsilon < 0.026$, $P_{\\rm dot}$\nis a strong function of $\\epsilon$ (equation \\ref{equ:wzpdoteps}).\nIf $\\epsilon$ indeed reflects $q$, the low $q$, rather than $P_{\\rm orb}$,\nis most responsible for smaller $P_{\\rm dot}$. Systems with nearly zero\n$P_{\\rm dot}$ appear to represent a population with low-mass secondaries.\nCombined with figure \\ref{fig:wzpdottype}, low-$P_{\\rm dot}$ systems with\n$P_{\\rm SH} < 0.057$ d can be considered as a consequence of terminal\nevolution of CVs around the period minimum. Two long-$P_{\\rm SH}$ objects\n(OT J1112 and EG Cnc\\footnote{\n The $P_{\\rm orb}$ has been controversial \\citep{kat04egcnc}. The present\n analysis of $P_{\\rm dot}$--$\\epsilon$ relation seems to support\n the period identification of \\citet{pat98egcnc}. Accurate determination\n of the period of early superhumps, as well as independent estimates\n of $P_{\\rm dot}$ in future superoutbursts is still wanted.\n}) are either good candidates for ``period bouncers'',\nor the period minimum is broader than had been considered and these\nobjects are presently reaching the period minimum at these\n$P_{\\rm orb}$.\nWe should note, however, this empirical calibration implicitly assume that\nall superhumps in WZ Sge-type dwarf novae during the plateau stage B\nsuperhumps. If some systems show stage C superhump even in this phase,\n$P_{\\rm dot}$, and hence $q$ might be underestimated (see a discussion\nin 1RXS J0232, subsection \\ref{sec:j0232}).\nAmong our sample, 1RXS J0232 is a single candidate for a period\nbouncer having a longer superhump period than 0.0603 d (EG Cnc).\nThe relative lack of promising candidates for period bouncers with\nlong superhump periods, despite the greatly improved statistics,\nshould be worth noting.\n\n\\begin{equation}\nP_{\\rm dot} = -0.00002(1) + 0.0040(6) \\epsilon\n\\label{equ:wzpdoteps}.\n\\end{equation}\n\n Some object with WZ Sge-type characteristics (early superhumps and\nlarge outburst amplitudes) are present in a range of $\\epsilon > 0.026$\n(BC UMa, V1251 Cyg, RZ Leo). These objects do not follow the relation\nin equation \\ref{equ:wzpdoteps} and appear to have higher $q$.\nThese object may either consist ``borderline'' WZ Sge-type dwarf\nnovae (cf. \\cite{pat03suumas}), or the existence of a large disk-mass\nat the onset of superoutbursts may enable the 2:1 resonance to appear\nin some high-$q$ systems.\n\n\\subsection{Period Variation versus Outburst Type}\\label{sec:wzsgeouttype}\n\n WZ Sge-type dwarf novae are known to exhibit a wide variety of\noutburst morphology, especially in post-outburst rebrightenings\n(\\cite{kat04egcnc}; \\cite{ima06tss0222}).\n\n Figure \\ref{fig:wzpdottype} shows the relation between $P_{\\rm dot}$\nversus $P_{\\rm SH}$ and outburst type, where the nomenclature of\nclassification is after \\citet{ima06tss0222}\\footnote{\n Although the original classification \\citet{ima06tss0222} was for\n WZ Sge (SU UMa)-type dwarf novae, it should be worth noting that\n these types of rebrightenings sometimes appear in X-ray transients\n \\citep{kuu96TOAD}.\n} and type-D represents\noutbursts without a rebrightening (figure \\ref{fig:outtype}).\nThe $P_{\\rm dot}$ tends to decrease with decreasing $P_{\\rm SH}$.\nThere appear to be two populations among WZ Sge-type dwarf novae: systems\nwith $P_{\\rm dot}$ nearly zero ($P_{\\rm dot} < +2 \\times 10^{-5}$)\nand systems with larger $P_{\\rm dot}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,160mm){fig38.eps}\n \\end{center}\n \\caption{Types of WZ Sge-type outbursts. A: WZ Sge (2001),\n B: EG Cnc (1996, data from \\cite{kat04egcnc}), C: ASAS J0025 (2004),\n D: GW Lib (2007).\n }\n \\label{fig:outtype}\n\\end{figure}\n\n Type-A outbursts (filled circles; long-duration rebrightening)\nare restricted to a region with short $P_{\\rm SH}$ and small $P_{\\rm dot}$.\nType-B outbursts (filled squares; multiple rebrightenings)\ntend to be located in a region with small $P_{\\rm dot}$ but with larger\n$P_{\\rm SH}$ than type-A.\nType-C outbursts (open triangles; single rebrightening) are located\nin a region with middle-to-longer $P_{\\rm SH}$ and larger $P_{\\rm dot}$.\nType-D outbursts (open circles; no rebrightening) tend to have a small\n$P_{\\rm SH}$ and a various $P_{\\rm dot}$.\nIt should be noted that these classifications are not always the\nproperty unique for each objects, but can be different between\nsuperoutbursts of the same object \\citep{uem08alcom}.\n\n The distinction between type-A and type-D outbursts in short $P_{\\rm orb}$\nsystems may be understood in a scenario presented in\n\\citet{kat08wzsgelateSH}. That is, in most extreme WZ Sge-type systems,\nthe 2:1 resonance can be strong enough to accrete much of the matter\nbeyond the 3:1 resonance and leave no room for a positive $P_{\\rm dot}$.\nIn less extreme systems, the remnant matter beyond the 3:1 resonance\nenables outward propagation of the eccentricity wave and resulting\na positive $P_{\\rm dot}$.\n\n If $P_{\\rm dot}$ indeed reflects $q$, the location of type-B\noutbursts would indicate that these objects have small $q$, comparable\nto those with type-A outbursts, but longer $P_{\\rm orb}$.\nIn these type-B superoutbursts, the intervals between superoutbursts\ntend to be shorter than in objects with type-A outbursts,\nand the delay in appearance of ordinary superhumps is generally\nshorter. It may be that type-B outbursts are a variety of\ntype-A outbursts with a smaller disk mass at the onset of the\noutbursts. The presence of a type-B outburst in AL Com with\na possibly fainter maximum \\citep{uem08alcom} seems to support\nthis interpretation.\nThe presence of low-amplitude outbursts during the 1978 and\n2001 superoutbursts of WZ Sge (\\cite{pat81wzsge}; \\cite{pat02wzsge})\nwould be a signature of a smooth transition between type-A and type-B\noutbursts (see also \\cite{osa02wzsgehump}).\nThe relatively long $P_{\\rm orb}$ in type-B objects might suggest\nthat the binary configuration in these systems is somehow responsible\nfor an early ignition of a superoutburst than in objects with\ntype-A outbursts.\nAnother potential interpretation is that objects with type-B outbursts\nhave a lower $q$ (cf. \\cite{pat98egcnc}) than in other systems.\nIf this is the case, a smaller tidal torque in low-$q$ systems\nmight be insufficient to sustain a long-duration type-A rebrightening.\nThe apparent presence of a higher $\\epsilon$ system (SDSS J0804:\n\\cite{kat09j0804} and \\cite{zha08j0804})\namong objects with type-B outbursts, however, would indicate that\nnot all type-B outbursts can be attributed to the low $q$.\n\n Type-C outbursts are less featured than other types of outbursts;\nthese outbursts resemble more usual superoutbursts with\na rebrightening frequently seen in a broader spectrum of\nSU UMa-type dwarf novae. A further explanation would be needed why\nshort-$P_{\\rm orb}$ systems have little tendency to show type-C outbursts,\ndespite the apparent presence of sufficient matter beyond the 3:1\nresonance.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig39.eps}\n \\end{center}\n \\caption{$P_{\\rm dot}$ versus $\\epsilon$ for WZ Sge-type\n dwarf novae. ASAS J0025 was excluded from this figure due to the\n uncertain $P_{\\rm orb}$.\n The dashed line represents equation \\ref{equ:wzpdoteps}.\n }\n \\label{fig:wzpdoteps}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig40.eps}\n \\end{center}\n \\caption{$P_{\\rm dot}$ versus $P_{\\rm SH}$ for WZ Sge-type\n dwarf novae. Symbols represent the type of outburst:\n type-A (filled circles), type-B (filled squares),\n type-C (open triangles), type-D (open circles).\n }\n \\label{fig:wzpdottype}\n\\end{figure}\n\n\\subsection{Delay of Appearance of Superhumps in WZ Sge-Type Dwarf Novae: Relation with Outburst Type}\\label{sec:wzsgedelay}\n\n \\citet{kat08wzsgelateSH} suggested that the long delays of appearance\nof ordinary superhumps in WZ Sge-type superoutburst can be attributed\nto the suppression of the 3:1 resonance by the 2:1 resonance, rather than\nthese delays reflect the long growth time of the 3:1 resonance in\nlow-$q$ systems. The similarity of the duration of the stage A\n($\\sim$ 20 cycles), which can be considered as the growth time of\nsuperhumps, between SU UMa-type dwarf novae and WZ Sge-type dwarf novae\nwould also support this interpretation.\nWe also surveyed these delay times in WZ Sge-type outbursts\nfor better statistics, and included them in table \\ref{tab:wztab}.\nIn several cases, the delay times could not be well constrained due to\nthe gap in observations, or due to the apparent delay in detection\nof the outburst. In such cases, the possible ranges of the delay times\nare given. Since the development of superhumps usually takes $\\sim$1 d,\nthe values have $\\sim$ 1 d uncertainty even in well-observed systems,\nand they may be different from values given in the different literature.\n\n It is noteworthy that all well-observed type-A and type-D superoutbursts\nhave longer (6--12 d, or even longer) delay times than in type-C superoutbursts\n(typically $\\sim$ 5 d). Many of type-B superoutburst were, unfortunately,\nnot sampled very well, but they appear to have shorter (1--5 d) delay\ntimes. These results strengthen the similarity between type-A and type-D\nsuperoutbursts (subsection \\ref{sec:wzsgeouttype}). Following\n\\citet{kat08wzsgelateSH}, the 2:1 resonance in these outbursts are\nstrong enough to accrete most of the matter beyond the 3:1 resonance,\nand the the small $P_{\\rm dot}$ and the lack of type-C rebrightening\nmay be a natural consequence.\nShorter delay times in type-C superoutbursts and the strongly positive\n$P_{\\rm dot}$ can be interpreted as a result of a smaller mass and\na smaller effect of the 2:1 resonance, leaving significant amount\nof matter beyond the 3:1 resonance \\citep{kat08wzsgelateSH}.\n\n Type-B superoutbursts appear to have intermediate delay times\nbetween type-A\/D and ordinary SU UMa-type superoutbursts (1--3 d).\nThis would suggest that the matter beyond the 3:1 resonance is smaller,\nand the 2:1 resonance is weaker than in type-A\/D superoutbursts.\nThe origin of type-B superoutbursts with low $P_{\\rm dot}$'s can then\nbe understood as a consequence of small mass outside the 3:1 resonance\n(although the 2:1 resonance still works, the small mass in the outer disk\ndoes not allow sufficient outward propagation of the eccentricity wave),\nrather than a consequence of extremely low-$q$ expected for period bouncers.\nFurther detailed observations of type-B superoutbursts and determination\nof $P_{\\rm orb}$ would discriminate these possibilities.\n\n\\subsection{Delay of Appearance of Superhumps: Comparison between Different Superoutbursts}\n\n \\citet{kat08wzsgelateSH} also suggested superoutbursts with\na different extent are expected to show different delay times.\nIn the present survey, HV Vir appears to perfectly fit\nthis expectation. A fainter superoutburst in 2002 led to a shorter\ngrowth time compared to the 1992 one. In WX Cet, the delay time ($\\ge 4d$)\nin the bright superoutburst in 1989 was longer than $\\sim$ 2 d\nin the 1998 superoutburst (\\cite{kat01wxcet}; subsection \\ref{sec:wxcet}).\nDifferent superoutbursts of SW UMa (subsection \\ref{sec:swuma})\nalso followed this tendency (see also \\cite{soe09swuma}).\nOhshima et al. (in preparation) also suggested that the delay time in\nV844 Her during the bright superoutburst in 2008 appears to be longer\nthan those in other superoutbursts of the same object\n(see also subsection \\ref{sec:v844her}).\nIn BC UMa (subsection \\ref{sec:bcuma}), the duration of\nthe stage B was dependent on the extent of the superoutburst.\n\n In summary, the present survey generally strengthened the expectations\nin \\citet{kat08wzsgelateSH}.\n\n\\section{Individual Objects}\\label{sec:individual}\n\n\\subsection{FO Andromedae}\\label{obj:foand}\n\n We reanalyzed the data in \\citet{kat95foand}. The times of\nsuperhump maxima are listed in table \\ref{tab:foandoc1994}.\nThis observation covered the late stage of the superoutburst and\nmost likely caught the stage B--C transition.\nThe mean periods were 0.07455(5) d for $E \\le 14$ (stage B)\nand 0.07402(1) d for $13 \\le E \\le 27$ (stage C).\n\n\\begin{table}\n\\caption{Superhump maxima of FO And (1994).}\\label{tab:foandoc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49578.1462 & 0.0008 & $-$0.0033 & 23 \\\\\n13 & 49579.1158 & 0.0006 & 0.0022 & 49 \\\\\n14 & 49579.1896 & 0.0007 & 0.0018 & 31 \\\\\n26 & 49580.0778 & 0.0007 & 0.0001 & 34 \\\\\n27 & 49580.1520 & 0.0006 & 0.0001 & 48 \\\\\n68 & 49583.1917 & 0.0014 & $-$0.0009 & 42 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449578.1495 + 0.074163 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{KV Andromedae}\\label{obj:kvand}\n\n KV And was originally reported as a large-amplitude dwarf nova\n\\citep{kur77kvandkwand}. \\citet{kat94kvand} and \\citet{kat95kvand}\nreported the detection of superhumps, whose period suggested a more\nusual dwarf nova rather than a short-period, WZ Sge-like object.\n\n We have analyzed two superoutbursts in 1994 (reanalysis of\n\\cite{kat95kvand}) and 2002. The results are presented\nin tables \\ref{tab:kvandoc1994} and \\ref{tab:kvandoc2002}.\nDuring both outbursts, the superhump period likely decreased.\nThe global $P_{\\rm dot}$'s were $-12.8(6.0) \\times 10^{-5}$\nand $-8.2(2.9) \\times 10^{-5}$, respectively. The period changes\ncan be also interpreted as a result of transition from stage B to C\n(see table \\ref{tab:perlist}).\n\n\\begin{table}\n\\caption{Superhump maxima of KV And (1994).}\\label{tab:kvandoc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49576.2102 & 0.0077 & 0.0012 & 16 \\\\\n1 & 49576.2723 & 0.0022 & $-$0.0110 & 9 \\\\\n27 & 49578.2175 & 0.0011 & $-$0.0002 & 45 \\\\\n28 & 49578.3010 & 0.0017 & 0.0089 & 21 \\\\\n41 & 49579.2609 & 0.0005 & 0.0016 & 49 \\\\\n55 & 49580.3074 & 0.0021 & 0.0065 & 48 \\\\\n95 & 49583.2699 & 0.0017 & $-$0.0069 & 43 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449576.2090 + 0.074398 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KV And (2002).}\\label{tab:kvandoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52584.1913 & 0.0005 & $-$0.0030 & 337 \\\\\n1 & 52584.2647 & 0.0005 & $-$0.0040 & 326 \\\\\n2 & 52584.3449 & 0.0014 & 0.0019 & 126 \\\\\n13 & 52585.1613 & 0.0007 & 0.0009 & 346 \\\\\n14 & 52585.2402 & 0.0028 & 0.0055 & 254 \\\\\n27 & 52586.1978 & 0.0033 & $-$0.0030 & 72 \\\\\n40 & 52587.1639 & 0.0020 & $-$0.0029 & 186 \\\\\n41 & 52587.2449 & 0.0041 & 0.0038 & 197 \\\\\n42 & 52587.3158 & 0.0015 & 0.0004 & 58 \\\\\n53 & 52588.1312 & 0.0032 & $-$0.0016 & 135 \\\\\n54 & 52588.2100 & 0.0010 & 0.0028 & 145 \\\\\n55 & 52588.2863 & 0.0016 & 0.0049 & 114 \\\\\n67 & 52589.1712 & 0.0017 & $-$0.0019 & 228 \\\\\n68 & 52589.2474 & 0.0018 & $-$0.0000 & 115 \\\\\n69 & 52589.3196 & 0.0021 & $-$0.0022 & 115 \\\\\n80 & 52590.1372 & 0.0019 & $-$0.0019 & 62 \\\\\n81 & 52590.2109 & 0.0034 & $-$0.0025 & 93 \\\\\n82 & 52590.2907 & 0.0062 & 0.0029 & 95 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452584.1944 + 0.074310 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{LL Andromedae}\\label{sec:lland}\\label{obj:lland}\n\n LL And is an eruptive object discovered in 1979 \\citep{wil79lland}.\nLittle had been known until its first-ever outburst since the discovery\nin 1993, during which \\citet{kat04lland} established the SU UMa-type\nnature of this object, and reported a superhump period of 0.05697(3) d.\nThe superhump maxima\ndetermined from these observations are listed in table\n\\ref{tab:llandoc1993}. Excluding $E = 37$ with a large error and\na significant deviation in $O-C$, the overall $P_{\\rm dot}$ was\n$+19.7(17.3) \\times 10^{-5}$.\n\n The object underwent another superoutburst in 2004 May--June.\nThe object was very unfavorably situated for long time-series photometry.\nThe data were unavoidably taken at a large air-mass, $f(z)$.\nWe subtracted the first-order atmospheric extinction term, $c f(z)$,\nwhere $c$ was numerically determined for each observer by minimizing\nthe deviation of the subtracted result from the general fading trend.\nWith the help of the superhump\nperiod obtained in 1993, we selected the most likely mean superhump\nperiod of 0.05658(2) d with PDM analysis (figure \\ref{fig:llandshpdm}).\nThe times of superhump maxima\ndetermined using this period are given in table \\ref{tab:llandoc2004}.\nThe period and period derivative determined from $0 \\leq E \\leq 290$\nwere 0.05658(2) d and $P_{\\rm dot}$ = $+1.0(0.6) \\times 10^{-5}$,\nrespectively. The resultant $\\epsilon$ of 2.8 \\% is still large for\nthis $P_{\\rm orb}$ (see a discussion in \\cite{kat04lland}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig41.eps}\n \\end{center}\n \\caption{Superhumps in LL And (2004). (Upper): PDM analysis.\n The selection of the period was based on the 1993 observation.\n (Lower): Phase-averaged profile.}\n \\label{fig:llandshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of LL And (1993).}\\label{tab:llandoc1993}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49330.9100 & 0.0142 & 0.0028 & 22 \\\\\n1 & 49330.9592 & 0.0058 & $-$0.0048 & 22 \\\\\n36 & 49332.9513 & 0.0011 & $-$0.0043 & 22 \\\\\n37 & 49333.0232 & 0.0056 & 0.0108 & 10 \\\\\n53 & 49333.9219 & 0.0016 & $-$0.0009 & 21 \\\\\n54 & 49333.9759 & 0.0018 & $-$0.0039 & 21 \\\\\n55 & 49334.0375 & 0.0014 & 0.0008 & 20 \\\\\n56 & 49334.0931 & 0.0019 & $-$0.0005 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449330.9072 + 0.056900 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of LL And (2004).}\\label{tab:llandoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53152.8407 & 0.0049 & 0.0031 & 55 \\\\\n84 & 53157.5827 & 0.0030 & $-$0.0045 & 51 \\\\\n95 & 53158.2028 & 0.0020 & $-$0.0064 & 71 \\\\\n96 & 53158.2636 & 0.0011 & $-$0.0022 & 115 \\\\\n131 & 53160.2482 & 0.0018 & 0.0034 & 207 \\\\\n149 & 53161.2683 & 0.0016 & 0.0058 & 80 \\\\\n172 & 53162.5636 & 0.0069 & 0.0005 & 47 \\\\\n290 & 53169.2458 & 0.0066 & 0.0107 & 84 \\\\\n308 & 53170.2472 & 0.0036 & $-$0.0057 & 140 \\\\\n325 & 53171.2115 & 0.0043 & $-$0.0026 & 103 \\\\\n326 & 53171.2684 & 0.0134 & $-$0.0022 & 58 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453152.8376 + 0.056543 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V402 Andromedae}\\label{obj:v402and}\n\n V402 And is a dwarf nova discovered by \\citet{ant98v1008herv402andv369peg}.\nThe SU UMa-type nature was confirmed during the 2000 superoutburst\n(vsnet-alert 5274).\nWe analyzed the 2005, 2006 and 2008 superoutbursts (tables\n\\ref{tab:v402andoc2005}, \\ref{tab:v402andoc2006}, \\ref{tab:v402andoc2008}).\nThe 2005 and 2006 superoutbursts were observed during their early stages\nand the 2008 one was observed during its middle stage.\nThe resultant $P_{\\rm dot}$ were $+12.7(2.1) \\times 10^{-5}$ for the 2006\nsuperoutburst and $+4.2(3.7) \\times 10^{-5}$ for the 2008, respectively.\nA shorter mean $P_{\\rm SH}$ for the 2005 superoutburst during its early\nstage is also consistent with the positive $P_{\\rm dot}$.\nA combined $O-C$ diagram is presented in figure \\ref{fig:v402andcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig42.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V402 And between different\n superoutbursts. A period of 0.06350 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v402andcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V402 And (2005).}\\label{tab:v402andoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53671.0724 & 0.0005 & 0.0020 & 107 \\\\\n1 & 53671.1326 & 0.0006 & $-$0.0010 & 134 \\\\\n17 & 53672.1439 & 0.0010 & $-$0.0014 & 117 \\\\\n39 & 53673.5338 & 0.0036 & $-$0.0026 & 13 \\\\\n40 & 53673.5992 & 0.0015 & $-$0.0004 & 22 \\\\\n41 & 53673.6663 & 0.0075 & 0.0035 & 19 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453671.0704 + 0.063230 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V402 And (2006).}\\label{tab:v402andoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53952.2426 & 0.0030 & 0.0029 & 125 \\\\\n16 & 53953.2541 & 0.0011 & $-$0.0006 & 130 \\\\\n31 & 53954.2024 & 0.0013 & $-$0.0039 & 105 \\\\\n79 & 53957.2531 & 0.0016 & 0.0017 & 135 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453952.2397 + 0.063439 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V402 And (2008).}\\label{tab:v402andoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54755.0811 & 0.0007 & 0.0010 & 103 \\\\\n1 & 54755.1458 & 0.0006 & 0.0022 & 136 \\\\\n2 & 54755.2058 & 0.0020 & $-$0.0013 & 72 \\\\\n15 & 54756.0331 & 0.0011 & 0.0000 & 98 \\\\\n16 & 54756.0995 & 0.0021 & 0.0029 & 54 \\\\\n32 & 54757.1103 & 0.0006 & $-$0.0028 & 113 \\\\\n33 & 54757.1721 & 0.0009 & $-$0.0046 & 128 \\\\\n80 & 54760.1659 & 0.0014 & 0.0033 & 135 \\\\\n95 & 54761.1149 & 0.0017 & $-$0.0007 & 100 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454755.0801 + 0.063532 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V455 Andromedae}\\label{sec:v455and}\\label{obj:v455and}\n\n V455 And = HS 2331$+$3905 \\citep{ara05v455and} underwent\na spectacular superoutburst, the first time in its history, in 2007\n(H. Maehara, vsnet-alert 9530; \\cite{tem07v455andcbet1053}).\nFollowing a rapidly rising stage, the object developed early superhumps\n(vsnet-alert 9543) similar to those in WZ Sge. \nAfter about eleven days, ordinary superhumps appeared\n(vsnet-alert 9582, 9584). Representative mean periods of early and\nordinary superhumps were 0.0562675(18) d (figure \\ref{fig:v455andeshpdm})\nand 0.0572038(14) d (figure \\ref{fig:v455andshpdm}), respectively.\n\n The maxima times of ordinary superhumps (tables \\ref{tab:v455andoc2007})\nwere obtained after subtracting phase-averaged orbital variations\n(mean orbital variations were determined from averages for 3--5 d during the\nmain outburst and fading stage, 10 d for the post-superoutburst stage).\nDuring BJD 2454356--2454357.3, sporadic humps having a period close to\nsuperhumps were observed in addition to early superhumps.\nNo apparent superhump signal was detected before this epoch.\nFor the interval $E \\le 20$, clear stage A evolution was observed\nwith a mean period of 0.05803(8) d (disregarding $E=3$ and $E=11$).\nWe determined $P_{\\rm dot}$ of $+4.7(1.2) \\times 10^{-5}$ from\nmaxima of $23 \\le E \\le 128$, after which the phases of maxima\ncoincide with orbital humps and were disregarded (see a discussion in\nWZ Sge, subsection \\ref{sec:wzsge}).\n\n In contrast to WZ Sge, the orbital variations were so\nstrong (figure \\ref{fig:v455postorb}) that it was practically impossible\nto directly extract the times of superhump maxima from the light curve\nduring the post-superoutburst stage.\nWe therefore measured the times of superhump maxima during the\nthis stage after subtracting the orbital light curve\n(table \\ref{tab:v455andoc2007post}). A relatively large scatter in\nthe $O-C$'s was probably a result from the interfering orbital variation.\nThere was an apparent change in the period around $E=170$.\nThe mean superhump periods (disregarding maxima coinciding orbital\nhumps and discrepant ones deviating by more than 0.018 d from the\nmean trend) before and after the change were 0.057295(2) d\nand 0.057154(1) d, respectively. These periods were longer than the\n$P_{\\rm SH}$ during the main superoutburst (cf. \\cite{kat08wzsgelateSH}).\nFigure \\ref{fig:v455postpdm} shows period analysis and mean superhump\nprofiles during the post-superoutburst stage.\n\n The overall evolution of $O-C$'s was remarkably similar to that of GW Lib\n(figure \\ref{fig:v455humpall}; only the first half of the post-superoutburst\nstage is shown for better visibility of the general feature).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig43.eps}\n \\end{center}\n \\caption{Early superhumps in V455 And (2007) for BJD 2454349--2454356.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v455andeshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig44.eps}\n \\end{center}\n \\caption{Ordinary superhumps in V455 And (2007) for BJD 2454357.3--2454366.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v455andshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig45.eps}\n \\end{center}\n \\caption{Averaged orbital light curve of V455 And during the\n post-superoutburst stage.}\n \\label{fig:v455postorb}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,180mm){fig46.eps}\n \\end{center}\n \\caption{Period analysis of V455 And (2007) during the post-superoutburst\n stage. Upper two figures represent the PDM analysis and mean superhump\n profile (after subtracting the orbital variation) before BJD 2454377,\n the epoch of the period change. Lower two figures represent the\n PDM analysis and mean superhump profile after BJD 2454377.}\n \\label{fig:v455postpdm}\n\\end{figure}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,160mm){fig47.eps}\n \\end{center}\n \\caption{$O-C$ variation in V455 And (2007). (Upper) $O-C$.\n Open squares indicate humps coinciding with the phase of orbital humps.\n Filled squares are humps outside the phase of orbital humps.\n We used a period of 0.05714 d for calculating the $O-C$'s.\n The global evolution of the $O-C$ diagram is remarkably similar\n to that of GW Lib (figure \\ref{fig:gwlibhumpall}).\n (Lower) Light curve.\n }\n \\label{fig:v455humpall}\n\\end{figure*}\n\n A full analysis of the observation will be presented in Maehara et al.,\nin preparation.\n\n\\begin{table}\n\\caption{Superhump maxima of V455 And (2007).}\\label{tab:v455andoc2007}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 54357.3037 & 0.0005 & $-$0.0134 & 0.23 & 466 \\\\\n1 & 54357.3682 & 0.0002 & $-$0.0061 & 0.37 & 703 \\\\\n2 & 54357.4275 & 0.0002 & $-$0.0041 & 0.43 & 832 \\\\\n3 & 54357.4686 & 0.0003 & $-$0.0203 & 0.16 & 829 \\\\\n4 & 54357.5446 & 0.0002 & $-$0.0014 & 0.51 & 659 \\\\\n5 & 54357.5949 & 0.0002 & $-$0.0083 & 0.40 & 836 \\\\\n6 & 54357.6563 & 0.0001 & $-$0.0042 & 0.49 & 859 \\\\\n7 & 54357.7128 & 0.0004 & $-$0.0049 & 0.49 & 120 \\\\\n11 & 54357.9321 & 0.0005 & $-$0.0146 & 0.39 & 243 \\\\\n12 & 54358.0050 & 0.0002 & 0.0011 & 0.68 & 410 \\\\\n13 & 54358.0637 & 0.0003 & 0.0026 & 0.72 & 506 \\\\\n14 & 54358.1192 & 0.0015 & 0.0009 & 0.71 & 569 \\\\\n15 & 54358.1788 & 0.0003 & 0.0033 & 0.77 & 538 \\\\\n16 & 54358.2351 & 0.0003 & 0.0023 & 0.77 & 291 \\\\\n17 & 54358.2984 & 0.0004 & 0.0083 & 0.89 & 463 \\\\\n18 & 54358.3517 & 0.0003 & 0.0044 & 0.84 & 300 \\\\\n19 & 54358.4109 & 0.0003 & 0.0064 & 0.89 & 341 \\\\\n20 & 54358.4698 & 0.0002 & 0.0081 & 0.94 & 94 \\\\\n21 & 54358.5262 & 0.0002 & 0.0073 & 0.94 & 42 \\\\\n23 & 54358.6427 & 0.0003 & 0.0093 & 0.01 & 93 \\\\\n29 & 54358.9829 & 0.0008 & 0.0061 & 0.05 & 324 \\\\\n30 & 54359.0410 & 0.0003 & 0.0070 & 0.08 & 583 \\\\\n31 & 54359.0966 & 0.0001 & 0.0054 & 0.07 & 550 \\\\\n32 & 54359.1547 & 0.0002 & 0.0063 & 0.10 & 1031 \\\\\n33 & 54359.2083 & 0.0001 & 0.0026 & 0.05 & 783 \\\\\n34 & 54359.2650 & 0.0002 & 0.0021 & 0.06 & 430 \\\\\n35 & 54359.3261 & 0.0002 & 0.0059 & 0.14 & 546 \\\\\n36 & 54359.3815 & 0.0002 & 0.0042 & 0.13 & 410 \\\\\n37 & 54359.4377 & 0.0002 & 0.0031 & 0.13 & 447 \\\\\n38 & 54359.4956 & 0.0002 & 0.0038 & 0.15 & 307 \\\\\n39 & 54359.5522 & 0.0004 & 0.0032 & 0.16 & 317 \\\\\n40 & 54359.6114 & 0.0003 & 0.0051 & 0.21 & 356 \\\\\n41 & 54359.6639 & 0.0004 & 0.0004 & 0.14 & 91 \\\\\n47 & 54360.0096 & 0.0004 & 0.0027 & 0.28 & 168 \\\\\n48 & 54360.0653 & 0.0002 & 0.0012 & 0.27 & 698 \\\\\n49 & 54360.1246 & 0.0001 & 0.0033 & 0.32 & 943 \\\\\n50 & 54360.1830 & 0.0003 & 0.0044 & 0.36 & 316 \\\\\n51 & 54360.2378 & 0.0003 & 0.0021 & 0.34 & 295 \\\\\n52 & 54360.2930 & 0.0002 & $-$0.0001 & 0.31 & 646 \\\\\n53 & 54360.3494 & 0.0001 & $-$0.0009 & 0.32 & 617 \\\\\n54 & 54360.4102 & 0.0004 & 0.0027 & 0.40 & 500 \\\\\n55 & 54360.4658 & 0.0004 & 0.0011 & 0.38 & 337 \\\\\n56 & 54360.5223 & 0.0002 & 0.0004 & 0.39 & 465 \\\\\n57 & 54360.5790 & 0.0003 & $-$0.0001 & 0.40 & 435 \\\\\n58 & 54360.6379 & 0.0004 & 0.0015 & 0.44 & 194 \\\\\n64 & 54360.9825 & 0.0009 & 0.0027 & 0.56 & 92 \\\\\n65 & 54361.0420 & 0.0016 & 0.0050 & 0.62 & 80 \\\\\n66 & 54361.0961 & 0.0009 & 0.0019 & 0.58 & 111 \\\\\n67 & 54361.1538 & 0.0012 & 0.0024 & 0.60 & 94 \\\\\n68 & 54361.2058 & 0.0011 & $-$0.0028 & 0.53 & 80 \\\\\n69 & 54361.2632 & 0.0009 & $-$0.0027 & 0.54 & 62 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2454357.3171 + 0.057228 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n70 & 54361.3261 & 0.0003 & 0.0030 & 0.66 & 542 \\\\\n71 & 54361.3869 & 0.0004 & 0.0065 & 0.74 & 500 \\\\\n72 & 54361.4393 & 0.0003 & 0.0017 & 0.67 & 408 \\\\\n74 & 54361.5549 & 0.0004 & 0.0028 & 0.72 & 288 \\\\\n75 & 54361.6121 & 0.0004 & 0.0028 & 0.74 & 440 \\\\\n76 & 54361.6690 & 0.0006 & 0.0025 & 0.75 & 236 \\\\\n81 & 54361.9530 & 0.0003 & 0.0004 & 0.80 & 534 \\\\\n82 & 54362.0070 & 0.0002 & $-$0.0028 & 0.76 & 526 \\\\\n83 & 54362.0682 & 0.0002 & 0.0012 & 0.84 & 785 \\\\\n84 & 54362.1233 & 0.0001 & $-$0.0011 & 0.82 & 788 \\\\\n85 & 54362.1805 & 0.0001 & $-$0.0010 & 0.84 & 862 \\\\\n86 & 54362.2372 & 0.0001 & $-$0.0016 & 0.84 & 824 \\\\\n87 & 54362.2954 & 0.0003 & $-$0.0005 & 0.88 & 406 \\\\\n88 & 54362.3494 & 0.0002 & $-$0.0038 & 0.84 & 207 \\\\\n89 & 54362.4077 & 0.0002 & $-$0.0028 & 0.87 & 267 \\\\\n90 & 54362.4660 & 0.0003 & $-$0.0017 & 0.91 & 166 \\\\\n91 & 54362.5206 & 0.0002 & $-$0.0043 & 0.88 & 265 \\\\\n92 & 54362.5786 & 0.0002 & $-$0.0036 & 0.91 & 310 \\\\\n93 & 54362.6329 & 0.0002 & $-$0.0064 & 0.87 & 183 \\\\\n94 & 54362.6917 & 0.0002 & $-$0.0049 & 0.91 & 150 \\\\\n95 & 54362.7495 & 0.0004 & $-$0.0044 & 0.94 & 89 \\\\\n96 & 54362.8061 & 0.0002 & $-$0.0050 & 0.95 & 171 \\\\\n97 & 54362.8639 & 0.0002 & $-$0.0044 & 0.97 & 144 \\\\\n98 & 54362.9199 & 0.0004 & $-$0.0056 & 0.97 & 119 \\\\\n99 & 54362.9780 & 0.0003 & $-$0.0047 & 1.00 & 164 \\\\\n100 & 54363.0369 & 0.0002 & $-$0.0031 & 0.04 & 98 \\\\\n101 & 54363.0929 & 0.0003 & $-$0.0043 & 0.04 & 111 \\\\\n102 & 54363.1483 & 0.0008 & $-$0.0061 & 0.02 & 104 \\\\\n103 & 54363.2051 & 0.0006 & $-$0.0066 & 0.03 & 70 \\\\\n105 & 54363.3222 & 0.0002 & $-$0.0039 & 0.11 & 614 \\\\\n106 & 54363.3771 & 0.0001 & $-$0.0062 & 0.09 & 648 \\\\\n107 & 54363.4358 & 0.0002 & $-$0.0048 & 0.13 & 464 \\\\\n108 & 54363.4939 & 0.0002 & $-$0.0039 & 0.16 & 274 \\\\\n109 & 54363.5512 & 0.0002 & $-$0.0038 & 0.18 & 793 \\\\\n110 & 54363.6063 & 0.0003 & $-$0.0059 & 0.16 & 593 \\\\\n111 & 54363.6636 & 0.0002 & $-$0.0058 & 0.17 & 320 \\\\\n112 & 54363.7236 & 0.0004 & $-$0.0031 & 0.24 & 209 \\\\\n113 & 54363.7776 & 0.0004 & $-$0.0063 & 0.20 & 142 \\\\\n114 & 54363.8364 & 0.0005 & $-$0.0047 & 0.24 & 142 \\\\\n115 & 54363.8950 & 0.0006 & $-$0.0034 & 0.28 & 132 \\\\\n116 & 54363.9499 & 0.0002 & $-$0.0057 & 0.26 & 395 \\\\\n117 & 54364.0095 & 0.0003 & $-$0.0033 & 0.32 & 419 \\\\\n118 & 54364.0666 & 0.0003 & $-$0.0035 & 0.33 & 368 \\\\\n119 & 54364.1243 & 0.0004 & $-$0.0030 & 0.36 & 304 \\\\\n120 & 54364.1801 & 0.0004 & $-$0.0045 & 0.35 & 186 \\\\\n121 & 54364.2398 & 0.0006 & $-$0.0020 & 0.41 & 216 \\\\\n122 & 54364.3006 & 0.0007 & 0.0016 & 0.49 & 489 \\\\\n123 & 54364.3585 & 0.0005 & 0.0023 & 0.52 & 391 \\\\\n124 & 54364.4055 & 0.0003 & $-$0.0079 & 0.35 & 290 \\\\\n125 & 54364.4726 & 0.0010 & 0.0019 & 0.54 & 265 \\\\\n126 & 54364.5262 & 0.0004 & $-$0.0016 & 0.49 & 359 \\\\\n127 & 54364.5883 & 0.0005 & 0.0032 & 0.60 & 505 \\\\\n128 & 54364.6432 & 0.0005 & 0.0008 & 0.57 & 556 \\\\\n133 & 54364.9369 & 0.0002 & 0.0084 & 0.79 & 172 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n134 & 54364.9943 & 0.0003 & 0.0086 & 0.81 & 173 \\\\\n135 & 54365.0494 & 0.0002 & 0.0065 & 0.79 & 314 \\\\\n136 & 54365.1085 & 0.0003 & 0.0083 & 0.83 & 275 \\\\\n137 & 54365.1631 & 0.0003 & 0.0057 & 0.80 & 347 \\\\\n138 & 54365.2185 & 0.0003 & 0.0039 & 0.79 & 432 \\\\\n139 & 54365.2757 & 0.0006 & 0.0038 & 0.80 & 325 \\\\\n140 & 54365.3337 & 0.0003 & 0.0046 & 0.83 & 447 \\\\\n141 & 54365.3910 & 0.0003 & 0.0046 & 0.85 & 237 \\\\\n142 & 54365.4472 & 0.0003 & 0.0036 & 0.85 & 207 \\\\\n143 & 54365.5042 & 0.0005 & 0.0034 & 0.86 & 235 \\\\\n144 & 54365.5634 & 0.0007 & 0.0054 & 0.91 & 220 \\\\\n145 & 54365.6164 & 0.0003 & 0.0012 & 0.85 & 316 \\\\\n146 & 54365.6753 & 0.0004 & 0.0029 & 0.90 & 159 \\\\\n147 & 54365.7308 & 0.0003 & 0.0011 & 0.89 & 160 \\\\\n148 & 54365.7882 & 0.0003 & 0.0013 & 0.90 & 119 \\\\\n149 & 54365.8467 & 0.0005 & 0.0025 & 0.94 & 127 \\\\\n150 & 54365.9029 & 0.0007 & 0.0015 & 0.94 & 124 \\\\\n151 & 54365.9589 & 0.0002 & 0.0003 & 0.94 & 748 \\\\\n152 & 54366.0151 & 0.0013 & $-$0.0007 & 0.93 & 480 \\\\\n153 & 54366.0705 & 0.0004 & $-$0.0025 & 0.92 & 529 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007).}\\label{tab:v455andoc2007post}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 54367.2376 & 0.0052 & $-$0.0213 & 0.65 & 88 \\\\\n1 & 54367.3004 & 0.0010 & $-$0.0157 & 0.76 & 240 \\\\\n2 & 54367.3639 & 0.0006 & $-$0.0093 & 0.89 & 168 \\\\\n4 & 54367.4756 & 0.0004 & $-$0.0119 & 0.87 & 85 \\\\\n5 & 54367.5306 & 0.0005 & $-$0.0141 & 0.85 & 179 \\\\\n6 & 54367.5895 & 0.0004 & $-$0.0123 & 0.89 & 323 \\\\\n7 & 54367.6474 & 0.0004 & $-$0.0116 & 0.92 & 214 \\\\\n8 & 54367.6998 & 0.0003 & $-$0.0163 & 0.85 & 244 \\\\\n9 & 54367.7597 & 0.0003 & $-$0.0136 & 0.92 & 161 \\\\\n10 & 54367.8174 & 0.0003 & $-$0.0131 & 0.94 & 165 \\\\\n11 & 54367.8711 & 0.0002 & $-$0.0165 & 0.90 & 170 \\\\\n12 & 54367.9438 & 0.0029 & $-$0.0009 & 0.19 & 40 \\\\\n20 & 54368.3873 & 0.0003 & $-$0.0146 & 0.06 & 455 \\\\\n21 & 54368.4418 & 0.0005 & $-$0.0172 & 0.03 & 374 \\\\\n22 & 54368.5004 & 0.0005 & $-$0.0158 & 0.07 & 186 \\\\\n23 & 54368.5582 & 0.0006 & $-$0.0152 & 0.10 & 196 \\\\\n24 & 54368.6176 & 0.0006 & $-$0.0129 & 0.15 & 84 \\\\\n26 & 54368.7300 & 0.0005 & $-$0.0148 & 0.15 & 71 \\\\\n30 & 54368.9625 & 0.0006 & $-$0.0110 & 0.28 & 313 \\\\\n31 & 54369.0182 & 0.0006 & $-$0.0123 & 0.27 & 343 \\\\\n32 & 54369.0883 & 0.0023 & 0.0006 & 0.51 & 273 \\\\\n33 & 54369.1426 & 0.0006 & $-$0.0022 & 0.48 & 162 \\\\\n34 & 54369.1916 & 0.0007 & $-$0.0104 & 0.35 & 119 \\\\\n35 & 54369.2552 & 0.0005 & $-$0.0039 & 0.48 & 219 \\\\\n36 & 54369.3017 & 0.0003 & $-$0.0146 & 0.30 & 300 \\\\\n37 & 54369.3615 & 0.0003 & $-$0.0120 & 0.36 & 111 \\\\\n38 & 54369.4285 & 0.0016 & $-$0.0021 & 0.55 & 77 \\\\\n39 & 54369.4816 & 0.0012 & $-$0.0062 & 0.50 & 72 \\\\\n41 & 54369.5926 & 0.0015 & $-$0.0095 & 0.47 & 63 \\\\\n42 & 54369.6495 & 0.0015 & $-$0.0097 & 0.48 & 65 \\\\\n43 & 54369.7184 & 0.0007 & 0.0020 & 0.70 & 68 \\\\\n44 & 54369.7761 & 0.0004 & 0.0026 & 0.73 & 68 \\\\\n45 & 54369.8306 & 0.0005 & $-$0.0000 & 0.70 & 69 \\\\\n46 & 54369.8887 & 0.0007 & 0.0008 & 0.73 & 69 \\\\\n47 & 54369.9441 & 0.0004 & $-$0.0009 & 0.71 & 67 \\\\\n52 & 54370.2317 & 0.0007 & 0.0010 & 0.82 & 121 \\\\\n58 & 54370.5696 & 0.0004 & $-$0.0040 & 0.82 & 87 \\\\\n59 & 54370.6276 & 0.0002 & $-$0.0031 & 0.85 & 135 \\\\\n60 & 54370.6840 & 0.0003 & $-$0.0039 & 0.85 & 119 \\\\\n61 & 54370.7419 & 0.0003 & $-$0.0032 & 0.88 & 98 \\\\\n62 & 54370.7960 & 0.0005 & $-$0.0062 & 0.84 & 66 \\\\\n63 & 54370.8542 & 0.0005 & $-$0.0052 & 0.87 & 67 \\\\\n64 & 54370.9116 & 0.0003 & $-$0.0049 & 0.89 & 66 \\\\\n65 & 54370.9683 & 0.0010 & $-$0.0054 & 0.90 & 95 \\\\\n66 & 54371.0331 & 0.0008 & 0.0023 & 0.05 & 86 \\\\\n70 & 54371.2523 & 0.0005 & $-$0.0071 & 0.94 & 137 \\\\\n71 & 54371.3043 & 0.0004 & $-$0.0123 & 0.87 & 147 \\\\\n72 & 54371.3735 & 0.0013 & $-$0.0002 & 0.09 & 35 \\\\\n83 & 54372.0082 & 0.0067 & 0.0059 & 0.37 & 87 \\\\\n94 & 54372.6343 & 0.0005 & 0.0033 & 0.49 & 167 \\\\\n107 & 54373.3843 & 0.0019 & 0.0104 & 0.81 & 30 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2454367.5448 + 0.057162 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n108 & 54373.4425 & 0.0009 & 0.0114 & 0.84 & 28 \\\\\n109 & 54373.4987 & 0.0016 & 0.0105 & 0.84 & 74 \\\\\n110 & 54373.5539 & 0.0006 & 0.0085 & 0.82 & 99 \\\\\n123 & 54374.2885 & 0.0011 & 0.0002 & 0.86 & 58 \\\\\n124 & 54374.3461 & 0.0009 & 0.0007 & 0.89 & 83 \\\\\n125 & 54374.4001 & 0.0006 & $-$0.0025 & 0.85 & 86 \\\\\n126 & 54374.4567 & 0.0008 & $-$0.0030 & 0.85 & 77 \\\\\n127 & 54374.5199 & 0.0010 & 0.0030 & 0.97 & 30 \\\\\n128 & 54374.5763 & 0.0017 & 0.0023 & 0.97 & 63 \\\\\n129 & 54374.6306 & 0.0016 & $-$0.0006 & 0.94 & 91 \\\\\n130 & 54374.6872 & 0.0009 & $-$0.0012 & 0.94 & 71 \\\\\n131 & 54374.7410 & 0.0006 & $-$0.0045 & 0.90 & 70 \\\\\n132 & 54374.7991 & 0.0009 & $-$0.0036 & 0.93 & 70 \\\\\n133 & 54374.8610 & 0.0011 & 0.0012 & 0.03 & 66 \\\\\n134 & 54374.9184 & 0.0008 & 0.0015 & 0.05 & 69 \\\\\n141 & 54375.3256 & 0.0016 & 0.0086 & 0.28 & 29 \\\\\n145 & 54375.5512 & 0.0011 & 0.0056 & 0.29 & 27 \\\\\n152 & 54375.9385 & 0.0003 & $-$0.0071 & 0.17 & 248 \\\\\n152 & 54375.9651 & 0.0002 & 0.0195 & 0.64 & 363 \\\\\n153 & 54376.0099 & 0.0005 & 0.0072 & 0.43 & 366 \\\\\n163 & 54376.5909 & 0.0005 & 0.0166 & 0.75 & 66 \\\\\n164 & 54376.6421 & 0.0009 & 0.0107 & 0.66 & 70 \\\\\n165 & 54376.7003 & 0.0022 & 0.0117 & 0.69 & 70 \\\\\n166 & 54376.7621 & 0.0005 & 0.0164 & 0.79 & 70 \\\\\n167 & 54376.8138 & 0.0005 & 0.0110 & 0.71 & 69 \\\\\n168 & 54376.8737 & 0.0005 & 0.0137 & 0.77 & 68 \\\\\n169 & 54376.9282 & 0.0016 & 0.0110 & 0.74 & 70 \\\\\n172 & 54377.1025 & 0.0005 & 0.0139 & 0.84 & 121 \\\\\n173 & 54377.1596 & 0.0009 & 0.0139 & 0.85 & 133 \\\\\n174 & 54377.2149 & 0.0004 & 0.0120 & 0.83 & 132 \\\\\n175 & 54377.2698 & 0.0004 & 0.0097 & 0.81 & 132 \\\\\n176 & 54377.3255 & 0.0007 & 0.0083 & 0.80 & 65 \\\\\n180 & 54377.5529 & 0.0003 & 0.0071 & 0.84 & 196 \\\\\n181 & 54377.5964 & 0.0010 & $-$0.0066 & 0.61 & 110 \\\\\n182 & 54377.6662 & 0.0005 & 0.0060 & 0.85 & 62 \\\\\n183 & 54377.7248 & 0.0006 & 0.0075 & 0.89 & 66 \\\\\n184 & 54377.7773 & 0.0005 & 0.0029 & 0.82 & 68 \\\\\n185 & 54377.8339 & 0.0005 & 0.0023 & 0.83 & 68 \\\\\n186 & 54377.8921 & 0.0004 & 0.0034 & 0.86 & 68 \\\\\n187 & 54377.9458 & 0.0005 & $-$0.0000 & 0.81 & 64 \\\\\n193 & 54378.2893 & 0.0004 & 0.0006 & 0.91 & 82 \\\\\n194 & 54378.3407 & 0.0010 & $-$0.0052 & 0.83 & 83 \\\\\n195 & 54378.4133 & 0.0020 & 0.0102 & 0.11 & 94 \\\\\n196 & 54378.4595 & 0.0008 & $-$0.0007 & 0.94 & 161 \\\\\n197 & 54378.5156 & 0.0011 & $-$0.0018 & 0.93 & 214 \\\\\n198 & 54378.5696 & 0.0004 & $-$0.0049 & 0.89 & 112 \\\\\n199 & 54378.6255 & 0.0003 & $-$0.0061 & 0.88 & 243 \\\\\n200 & 54378.6782 & 0.0011 & $-$0.0106 & 0.82 & 140 \\\\\n201 & 54378.7412 & 0.0008 & $-$0.0047 & 0.94 & 72 \\\\\n204 & 54378.9128 & 0.0007 & $-$0.0045 & 0.99 & 201 \\\\\n205 & 54378.9748 & 0.0005 & 0.0002 & 0.09 & 460 \\\\\n206 & 54379.0327 & 0.0011 & 0.0010 & 0.12 & 441 \\\\\n207 & 54379.0912 & 0.0006 & 0.0024 & 0.15 & 459 \\\\\n208 & 54379.1535 & 0.0030 & 0.0075 & 0.26 & 207 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n209 & 54379.1986 & 0.0005 & $-$0.0046 & 0.06 & 435 \\\\\n210 & 54379.2470 & 0.0010 & $-$0.0133 & 0.92 & 364 \\\\\n212 & 54379.3782 & 0.0005 & 0.0036 & 0.25 & 279 \\\\\n213 & 54379.4322 & 0.0006 & 0.0004 & 0.21 & 278 \\\\\n214 & 54379.4949 & 0.0012 & 0.0060 & 0.32 & 163 \\\\\n215 & 54379.5460 & 0.0004 & $-$0.0000 & 0.23 & 399 \\\\\n216 & 54379.6081 & 0.0008 & 0.0049 & 0.33 & 529 \\\\\n220 & 54379.8001 & 0.0006 & $-$0.0317 & 0.74 & 68 \\\\\n221 & 54379.8551 & 0.0007 & $-$0.0338 & 0.72 & 68 \\\\\n222 & 54379.9402 & 0.0008 & $-$0.0058 & 0.23 & 383 \\\\\n223 & 54380.0034 & 0.0003 & 0.0002 & 0.35 & 557 \\\\\n226 & 54380.1728 & 0.0011 & $-$0.0019 & 0.36 & 364 \\\\\n227 & 54380.2211 & 0.0007 & $-$0.0107 & 0.22 & 274 \\\\\n228 & 54380.2790 & 0.0012 & $-$0.0099 & 0.25 & 293 \\\\\n228 & 54380.3108 & 0.0003 & 0.0218 & 0.81 & 279 \\\\\n229 & 54380.3640 & 0.0003 & 0.0179 & 0.76 & 278 \\\\\n230 & 54380.4154 & 0.0004 & 0.0122 & 0.67 & 270 \\\\\n231 & 54380.4635 & 0.0006 & 0.0031 & 0.53 & 275 \\\\\n232 & 54380.5235 & 0.0015 & 0.0059 & 0.59 & 251 \\\\\n240 & 54380.9853 & 0.0013 & 0.0105 & 0.79 & 96 \\\\\n241 & 54381.0421 & 0.0007 & 0.0102 & 0.80 & 93 \\\\\n242 & 54381.1003 & 0.0007 & 0.0113 & 0.83 & 72 \\\\\n243 & 54381.1577 & 0.0005 & 0.0114 & 0.85 & 84 \\\\\n246 & 54381.3291 & 0.0002 & 0.0115 & 0.90 & 303 \\\\\n247 & 54381.3838 & 0.0004 & 0.0090 & 0.87 & 298 \\\\\n248 & 54381.4315 & 0.0002 & $-$0.0004 & 0.72 & 282 \\\\\n249 & 54381.4944 & 0.0004 & 0.0053 & 0.83 & 309 \\\\\n250 & 54381.5513 & 0.0005 & 0.0050 & 0.84 & 234 \\\\\n251 & 54381.6006 & 0.0008 & $-$0.0028 & 0.72 & 96 \\\\\n266 & 54382.4532 & 0.0033 & $-$0.0075 & 0.86 & 42 \\\\\n268 & 54382.5658 & 0.0009 & $-$0.0092 & 0.86 & 206 \\\\\n269 & 54382.6202 & 0.0004 & $-$0.0118 & 0.83 & 280 \\\\\n270 & 54382.6646 & 0.0006 & $-$0.0247 & 0.61 & 88 \\\\\n271 & 54382.7442 & 0.0034 & $-$0.0022 & 0.03 & 68 \\\\\n281 & 54383.3122 & 0.0009 & $-$0.0057 & 0.12 & 241 \\\\\n285 & 54383.5676 & 0.0009 & 0.0211 & 0.65 & 232 \\\\\n286 & 54383.6169 & 0.0003 & 0.0133 & 0.53 & 212 \\\\\n287 & 54383.6514 & 0.0009 & $-$0.0094 & 0.14 & 222 \\\\\n288 & 54383.7252 & 0.0011 & 0.0073 & 0.45 & 58 \\\\\n289 & 54383.7814 & 0.0017 & 0.0063 & 0.45 & 70 \\\\\n290 & 54383.8539 & 0.0009 & 0.0217 & 0.74 & 69 \\\\\n292 & 54383.9548 & 0.0006 & 0.0083 & 0.53 & 131 \\\\\n293 & 54384.0067 & 0.0004 & 0.0030 & 0.45 & 132 \\\\\n294 & 54384.0590 & 0.0014 & $-$0.0018 & 0.38 & 225 \\\\\n295 & 54384.1246 & 0.0007 & 0.0066 & 0.54 & 206 \\\\\n296 & 54384.1904 & 0.0005 & 0.0152 & 0.71 & 136 \\\\\n297 & 54384.2521 & 0.0007 & 0.0199 & 0.81 & 182 \\\\\n299 & 54384.3195 & 0.0009 & $-$0.0271 & 0.00 & 175 \\\\\n303 & 54384.5882 & 0.0007 & 0.0131 & 0.78 & 68 \\\\\n304 & 54384.6427 & 0.0005 & 0.0104 & 0.74 & 68 \\\\\n305 & 54384.7065 & 0.0011 & 0.0171 & 0.88 & 70 \\\\\n306 & 54384.7686 & 0.0010 & 0.0220 & 0.98 & 68 \\\\\n307 & 54384.8216 & 0.0007 & 0.0178 & 0.92 & 70 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n309 & 54384.9306 & 0.0005 & 0.0125 & 0.86 & 160 \\\\\n310 & 54384.9850 & 0.0004 & 0.0098 & 0.82 & 355 \\\\\n311 & 54385.0440 & 0.0002 & 0.0117 & 0.87 & 377 \\\\\n312 & 54385.0932 & 0.0004 & 0.0037 & 0.74 & 326 \\\\\n314 & 54385.2160 & 0.0004 & 0.0122 & 0.92 & 376 \\\\\n315 & 54385.2644 & 0.0005 & 0.0035 & 0.79 & 223 \\\\\n321 & 54385.6065 & 0.0009 & 0.0027 & 0.86 & 67 \\\\\n322 & 54385.6626 & 0.0018 & 0.0016 & 0.86 & 68 \\\\\n323 & 54385.7111 & 0.0010 & $-$0.0071 & 0.72 & 69 \\\\\n325 & 54385.8368 & 0.0008 & 0.0043 & 0.95 & 68 \\\\\n326 & 54385.8888 & 0.0009 & $-$0.0008 & 0.87 & 69 \\\\\n328 & 54385.9958 & 0.0026 & $-$0.0081 & 0.77 & 65 \\\\\n329 & 54386.0590 & 0.0031 & $-$0.0020 & 0.90 & 67 \\\\\n330 & 54386.1156 & 0.0017 & $-$0.0026 & 0.90 & 42 \\\\\n335 & 54386.4172 & 0.0009 & 0.0133 & 0.26 & 60 \\\\\n336 & 54386.4696 & 0.0007 & 0.0086 & 0.19 & 60 \\\\\n337 & 54386.5282 & 0.0009 & 0.0100 & 0.23 & 58 \\\\\n351 & 54387.2852 & 0.0008 & $-$0.0331 & 0.67 & 99 \\\\\n352 & 54387.3462 & 0.0013 & $-$0.0293 & 0.75 & 64 \\\\\n368 & 54388.3009 & 0.0008 & 0.0111 & 0.71 & 136 \\\\\n369 & 54388.3549 & 0.0003 & 0.0079 & 0.67 & 124 \\\\\n370 & 54388.4158 & 0.0004 & 0.0116 & 0.75 & 109 \\\\\n372 & 54388.4825 & 0.0005 & $-$0.0359 & 0.94 & 181 \\\\\n372 & 54388.5334 & 0.0004 & 0.0149 & 0.84 & 182 \\\\\n374 & 54388.6438 & 0.0003 & 0.0110 & 0.80 & 172 \\\\\n380 & 54388.9844 & 0.0039 & 0.0088 & 0.85 & 151 \\\\\n381 & 54389.0447 & 0.0013 & 0.0119 & 0.92 & 377 \\\\\n382 & 54389.0961 & 0.0006 & 0.0061 & 0.83 & 308 \\\\\n383 & 54389.1523 & 0.0011 & 0.0052 & 0.83 & 377 \\\\\n384 & 54389.2021 & 0.0008 & $-$0.0022 & 0.71 & 330 \\\\\n400 & 54390.1431 & 0.0028 & 0.0244 & 0.43 & 35 \\\\\n404 & 54390.3163 & 0.0007 & $-$0.0310 & 0.50 & 84 \\\\\n405 & 54390.4139 & 0.0014 & 0.0095 & 0.23 & 84 \\\\\n407 & 54390.4877 & 0.0017 & $-$0.0310 & 0.55 & 84 \\\\\n407 & 54390.5323 & 0.0017 & 0.0136 & 0.34 & 80 \\\\\n412 & 54390.8071 & 0.0015 & 0.0027 & 0.22 & 68 \\\\\n413 & 54390.8705 & 0.0006 & 0.0089 & 0.34 & 68 \\\\\n415 & 54390.9797 & 0.0011 & 0.0038 & 0.28 & 127 \\\\\n416 & 54391.0329 & 0.0016 & $-$0.0001 & 0.23 & 144 \\\\\n417 & 54391.0895 & 0.0025 & $-$0.0007 & 0.23 & 171 \\\\\n418 & 54391.1324 & 0.0019 & $-$0.0149 & 1.00 & 140 \\\\\n423 & 54391.4284 & 0.0014 & $-$0.0046 & 0.25 & 62 \\\\\n447 & 54392.7733 & 0.0032 & $-$0.0313 & 0.14 & 67 \\\\\n447 & 54392.8236 & 0.0015 & 0.0189 & 0.03 & 59 \\\\\n448 & 54392.8764 & 0.0009 & 0.0146 & 0.97 & 65 \\\\\n466 & 54393.8981 & 0.0005 & 0.0076 & 0.11 & 64 \\\\\n468 & 54394.0171 & 0.0005 & 0.0123 & 0.22 & 184 \\\\\n469 & 54394.0617 & 0.0015 & $-$0.0002 & 0.02 & 380 \\\\\n471 & 54394.1956 & 0.0015 & 0.0194 & 0.39 & 527 \\\\\n472 & 54394.2438 & 0.0021 & 0.0104 & 0.25 & 400 \\\\\n473 & 54394.2947 & 0.0008 & 0.0042 & 0.15 & 174 \\\\\n476 & 54394.4834 & 0.0009 & 0.0214 & 0.51 & 122 \\\\\n479 & 54394.6500 & 0.0005 & 0.0166 & 0.46 & 177 \\\\\n480 & 54394.6893 & 0.0007 & $-$0.0012 & 0.16 & 174 \\\\\n485 & 54394.9449 & 0.0010 & $-$0.0314 & 0.70 & 222 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n485 & 54394.9930 & 0.0006 & 0.0167 & 0.56 & 232 \\\\\n486 & 54395.0338 & 0.0007 & 0.0003 & 0.28 & 197 \\\\\n487 & 54395.0864 & 0.0016 & $-$0.0042 & 0.21 & 165 \\\\\n489 & 54395.2112 & 0.0018 & 0.0063 & 0.43 & 51 \\\\\n490 & 54395.2625 & 0.0023 & 0.0004 & 0.34 & 79 \\\\\n497 & 54395.6482 & 0.0010 & $-$0.0139 & 0.19 & 68 \\\\\n509 & 54396.3290 & 0.0011 & $-$0.0189 & 0.28 & 122 \\\\\n510 & 54396.3885 & 0.0006 & $-$0.0165 & 0.34 & 122 \\\\\n511 & 54396.4523 & 0.0012 & $-$0.0098 & 0.47 & 123 \\\\\n515 & 54396.7136 & 0.0016 & 0.0228 & 0.11 & 67 \\\\\n517 & 54396.7774 & 0.0008 & $-$0.0277 & 0.24 & 69 \\\\\n520 & 54396.9561 & 0.0009 & $-$0.0204 & 0.42 & 144 \\\\\n521 & 54397.0329 & 0.0008 & $-$0.0007 & 0.78 & 223 \\\\\n522 & 54397.0918 & 0.0016 & 0.0009 & 0.83 & 176 \\\\\n523 & 54397.1584 & 0.0033 & 0.0104 & 0.01 & 128 \\\\\n524 & 54397.2294 & 0.0018 & 0.0243 & 0.27 & 154 \\\\\n550 & 54398.6891 & 0.0008 & $-$0.0019 & 0.20 & 68 \\\\\n551 & 54398.7464 & 0.0008 & $-$0.0017 & 0.21 & 70 \\\\\n552 & 54398.8078 & 0.0022 & 0.0025 & 0.30 & 69 \\\\\n553 & 54398.8672 & 0.0017 & 0.0047 & 0.36 & 69 \\\\\n566 & 54399.5986 & 0.0014 & $-$0.0068 & 0.35 & 68 \\\\\n567 & 54399.6570 & 0.0012 & $-$0.0056 & 0.38 & 70 \\\\\n568 & 54399.7116 & 0.0012 & $-$0.0081 & 0.35 & 69 \\\\\n569 & 54399.7686 & 0.0008 & $-$0.0082 & 0.37 & 68 \\\\\n570 & 54399.8487 & 0.0027 & 0.0147 & 0.79 & 68 \\\\\n618 & 54402.5771 & 0.0018 & $-$0.0001 & 0.24 & 68 \\\\\n619 & 54402.6349 & 0.0009 & 0.0006 & 0.27 & 69 \\\\\n620 & 54402.7059 & 0.0012 & 0.0144 & 0.53 & 70 \\\\\n621 & 54402.7438 & 0.0011 & $-$0.0048 & 0.20 & 70 \\\\\n622 & 54402.8160 & 0.0009 & 0.0102 & 0.48 & 70 \\\\\n623 & 54402.8862 & 0.0015 & 0.0233 & 0.73 & 54 \\\\\n626 & 54403.0402 & 0.0015 & 0.0059 & 0.47 & 90 \\\\\n627 & 54403.0972 & 0.0014 & 0.0057 & 0.48 & 79 \\\\\n660 & 54404.9795 & 0.0008 & 0.0021 & 0.91 & 126 \\\\\n661 & 54405.0351 & 0.0009 & 0.0006 & 0.89 & 87 \\\\\n662 & 54405.1088 & 0.0065 & 0.0171 & 0.20 & 59 \\\\\n670 & 54405.5667 & 0.0032 & 0.0178 & 0.34 & 68 \\\\\n671 & 54405.6199 & 0.0013 & 0.0138 & 0.28 & 51 \\\\\n672 & 54405.6729 & 0.0015 & 0.0097 & 0.22 & 67 \\\\\n673 & 54405.7252 & 0.0076 & 0.0048 & 0.15 & 68 \\\\\n674 & 54405.7827 & 0.0010 & 0.0052 & 0.17 & 60 \\\\\n675 & 54405.8333 & 0.0017 & $-$0.0014 & 0.07 & 66 \\\\\n690 & 54406.6919 & 0.0007 & 0.0000 & 0.32 & 60 \\\\\n695 & 54406.9441 & 0.0016 & $-$0.0336 & 0.80 & 69 \\\\\n696 & 54406.9976 & 0.0017 & $-$0.0372 & 0.75 & 79 \\\\\n696 & 54407.0427 & 0.0010 & 0.0079 & 0.55 & 92 \\\\\n698 & 54407.1198 & 0.0012 & $-$0.0293 & 0.92 & 92 \\\\\n699 & 54407.1793 & 0.0016 & $-$0.0270 & 0.97 & 89 \\\\\n705 & 54407.5621 & 0.0006 & 0.0130 & 0.77 & 72 \\\\\n707 & 54407.6838 & 0.0009 & 0.0203 & 0.93 & 76 \\\\\n708 & 54407.7326 & 0.0010 & 0.0120 & 0.80 & 77 \\\\\n709 & 54407.7848 & 0.0035 & 0.0070 & 0.73 & 71 \\\\\n710 & 54407.8205 & 0.0012 & $-$0.0144 & 0.36 & 77 \\\\\n711 & 54407.8711 & 0.0007 & $-$0.0209 & 0.26 & 52 \\\\\n713 & 54408.0200 & 0.0011 & 0.0137 & 0.90 & 86 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n715 & 54408.0882 & 0.0006 & $-$0.0325 & 0.11 & 91 \\\\\n715 & 54408.1401 & 0.0015 & 0.0194 & 0.04 & 92 \\\\\n725 & 54408.7080 & 0.0011 & 0.0159 & 0.12 & 77 \\\\\n730 & 54408.9503 & 0.0025 & $-$0.0276 & 0.42 & 79 \\\\\n742 & 54409.6787 & 0.0005 & 0.0150 & 0.36 & 77 \\\\\n744 & 54409.7458 & 0.0004 & $-$0.0321 & 0.55 & 76 \\\\\n744 & 54409.7826 & 0.0016 & 0.0047 & 0.21 & 74 \\\\\n745 & 54409.8415 & 0.0011 & 0.0064 & 0.25 & 77 \\\\\n778 & 54411.7051 & 0.0007 & $-$0.0160 & 0.35 & 21 \\\\\n779 & 54411.7451 & 0.0012 & $-$0.0331 & 0.06 & 58 \\\\\n780 & 54411.8182 & 0.0008 & $-$0.0171 & 0.36 & 99 \\\\\n782 & 54411.9668 & 0.0016 & 0.0172 & 1.00 & 221 \\\\\n787 & 54412.2265 & 0.0032 & $-$0.0089 & 0.61 & 67 \\\\\n798 & 54412.8325 & 0.0013 & $-$0.0315 & 0.37 & 74 \\\\\n814 & 54413.7843 & 0.0015 & 0.0059 & 0.27 & 79 \\\\\n815 & 54413.8399 & 0.0011 & 0.0043 & 0.26 & 73 \\\\\n884 & 54417.7831 & 0.0009 & 0.0042 & 0.29 & 79 \\\\\n885 & 54417.8362 & 0.0018 & 0.0002 & 0.23 & 78 \\\\\n887 & 54417.9551 & 0.0010 & 0.0048 & 0.34 & 81 \\\\\n888 & 54418.0135 & 0.0010 & 0.0061 & 0.38 & 100 \\\\\n889 & 54418.0621 & 0.0043 & $-$0.0025 & 0.24 & 140 \\\\\n890 & 54418.1102 & 0.0026 & $-$0.0115 & 0.10 & 116 \\\\\n904 & 54418.9231 & 0.0008 & 0.0012 & 0.53 & 70 \\\\\n905 & 54418.9700 & 0.0020 & $-$0.0089 & 0.37 & 82 \\\\\n906 & 54419.0309 & 0.0014 & $-$0.0052 & 0.45 & 105 \\\\\n907 & 54419.0968 & 0.0028 & 0.0035 & 0.62 & 112 \\\\\n908 & 54419.1505 & 0.0010 & 0.0001 & 0.57 & 109 \\\\\n909 & 54419.2033 & 0.0022 & $-$0.0043 & 0.51 & 83 \\\\\n919 & 54419.7762 & 0.0018 & $-$0.0028 & 0.68 & 74 \\\\\n920 & 54419.8253 & 0.0011 & $-$0.0109 & 0.55 & 74 \\\\\n940 & 54420.9911 & 0.0010 & 0.0119 & 0.26 & 94 \\\\\n941 & 54421.0319 & 0.0009 & $-$0.0045 & 0.98 & 78 \\\\\n944 & 54421.2073 & 0.0006 & $-$0.0005 & 0.10 & 82 \\\\\n957 & 54421.9139 & 0.0011 & $-$0.0368 & 0.65 & 77 \\\\\n957 & 54421.9613 & 0.0008 & 0.0106 & 0.49 & 80 \\\\\n994 & 54424.0840 & 0.0012 & 0.0187 & 0.18 & 92 \\\\\n1009 & 54424.9177 & 0.0026 & $-$0.0048 & 0.99 & 79 \\\\\n1011 & 54425.0344 & 0.0017 & $-$0.0024 & 0.06 & 81 \\\\\n1029 & 54426.0711 & 0.0023 & 0.0056 & 0.47 & 69 \\\\\n1030 & 54426.1341 & 0.0017 & 0.0115 & 0.59 & 75 \\\\\n1062 & 54427.9455 & 0.0011 & $-$0.0059 & 0.76 & 147 \\\\\n1063 & 54428.0024 & 0.0032 & $-$0.0061 & 0.77 & 172 \\\\\n1064 & 54428.0748 & 0.0089 & 0.0091 & 0.06 & 164 \\\\\n1080 & 54428.9456 & 0.0008 & $-$0.0345 & 0.52 & 162 \\\\\n1081 & 54429.0459 & 0.0014 & 0.0087 & 0.30 & 92 \\\\\n1091 & 54429.6224 & 0.0017 & 0.0137 & 0.54 & 76 \\\\\n1092 & 54429.6651 & 0.0035 & $-$0.0008 & 0.30 & 76 \\\\\n1093 & 54429.7452 & 0.0088 & 0.0221 & 0.72 & 77 \\\\\n1094 & 54429.7790 & 0.0236 & $-$0.0011 & 0.32 & 77 \\\\\n1096 & 54429.8967 & 0.0009 & 0.0022 & 0.41 & 81 \\\\\n1097 & 54429.9560 & 0.0031 & 0.0044 & 0.47 & 81 \\\\\n1125 & 54431.5670 & 0.0019 & 0.0152 & 0.08 & 77 \\\\\n1126 & 54431.6214 & 0.0027 & 0.0124 & 0.04 & 78 \\\\\n1160 & 54433.5612 & 0.0008 & 0.0092 & 0.49 & 77 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V455 And during the Post-Superoutburst Stage (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n1161 & 54433.6227 & 0.0011 & 0.0136 & 0.58 & 78 \\\\\n1201 & 54435.8936 & 0.0061 & $-$0.0016 & 0.91 & 62 \\\\\n1202 & 54435.9601 & 0.0010 & 0.0078 & 0.09 & 81 \\\\\n1204 & 54436.0419 & 0.0009 & $-$0.0246 & 0.55 & 165 \\\\\n1204 & 54436.0933 & 0.0027 & 0.0267 & 0.46 & 111 \\\\\n1239 & 54438.0607 & 0.0026 & $-$0.0061 & 0.40 & 52 \\\\\n1272 & 54439.9187 & 0.0010 & $-$0.0340 & 0.40 & 82 \\\\\n1272 & 54439.9763 & 0.0013 & 0.0236 & 0.42 & 81 \\\\\n1274 & 54440.0474 & 0.0024 & $-$0.0196 & 0.68 & 102 \\\\\n1289 & 54440.9335 & 0.0010 & 0.0092 & 0.42 & 81 \\\\\n1290 & 54440.9862 & 0.0038 & 0.0048 & 0.35 & 34 \\\\\n1291 & 54441.0517 & 0.0012 & 0.0131 & 0.52 & 149 \\\\\n1292 & 54441.0985 & 0.0058 & 0.0027 & 0.35 & 84 \\\\\n1293 & 54441.1525 & 0.0009 & $-$0.0004 & 0.31 & 55 \\\\\n1307 & 54441.9501 & 0.0011 & $-$0.0029 & 0.47 & 65 \\\\\n1323 & 54442.8889 & 0.0008 & 0.0216 & 0.14 & 81 \\\\\n1324 & 54442.9489 & 0.0021 & 0.0244 & 0.21 & 76 \\\\\n1342 & 54443.9433 & 0.0041 & $-$0.0099 & 0.87 & 182 \\\\\n1343 & 54443.9874 & 0.0016 & $-$0.0229 & 0.65 & 260 \\\\\n1343 & 54444.0293 & 0.0006 & 0.0190 & 0.40 & 145 \\\\\n1344 & 54444.0791 & 0.0014 & 0.0116 & 0.28 & 74 \\\\\n1358 & 54444.8856 & 0.0009 & 0.0180 & 0.60 & 76 \\\\\n1359 & 54444.9252 & 0.0015 & 0.0005 & 0.31 & 81 \\\\\n1360 & 54444.9678 & 0.0021 & $-$0.0141 & 0.06 & 81 \\\\\n1405 & 54447.5704 & 0.0006 & 0.0168 & 0.28 & 77 \\\\\n1406 & 54447.6291 & 0.0008 & 0.0184 & 0.33 & 74 \\\\\n1448 & 54449.9846 & 0.0020 & $-$0.0264 & 0.16 & 125 \\\\\n1449 & 54450.0945 & 0.0022 & 0.0263 & 0.11 & 80 \\\\\n1458 & 54450.5688 & 0.0012 & $-$0.0137 & 0.53 & 56 \\\\\n1464 & 54450.9005 & 0.0012 & $-$0.0249 & 0.42 & 44 \\\\\n1465 & 54450.9585 & 0.0012 & $-$0.0240 & 0.45 & 44 \\\\\n1475 & 54451.5628 & 0.0014 & 0.0088 & 0.18 & 75 \\\\\n1481 & 54451.9163 & 0.0010 & 0.0193 & 0.46 & 44 \\\\\n1482 & 54451.9780 & 0.0016 & 0.0240 & 0.56 & 45 \\\\\n1639 & 54460.9315 & 0.0033 & 0.0050 & 0.56 & 43 \\\\\n1640 & 54460.9821 & 0.0023 & $-$0.0015 & 0.46 & 116 \\\\\n1641 & 54461.0252 & 0.0027 & $-$0.0156 & 0.23 & 122 \\\\\n1691 & 54463.9164 & 0.0025 & 0.0181 & 0.57 & 43 \\\\\n1692 & 54463.9730 & 0.0012 & 0.0176 & 0.58 & 43 \\\\\n1780 & 54468.9547 & 0.0022 & $-$0.0298 & 0.05 & 74 \\\\\n1781 & 54469.0230 & 0.0009 & $-$0.0187 & 0.26 & 73 \\\\\n1797 & 54469.9389 & 0.0008 & $-$0.0172 & 0.53 & 37 \\\\\n1837 & 54472.2254 & 0.0066 & $-$0.0167 & 0.13 & 48 \\\\\n1838 & 54472.3032 & 0.0012 & 0.0040 & 0.51 & 49 \\\\\n1839 & 54472.3606 & 0.0026 & 0.0042 & 0.53 & 43 \\\\\n1902 & 54475.9420 & 0.0013 & $-$0.0148 & 0.13 & 93 \\\\\n1954 & 54478.9490 & 0.0010 & 0.0205 & 0.54 & 83 \\\\\n2182 & 54491.9374 & 0.0009 & $-$0.0211 & 0.20 & 77 \\\\\n2183 & 54491.9920 & 0.0026 & $-$0.0237 & 0.17 & 75 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V466 Andromedae}\\label{obj:v466and}\n\n The object was discovered by K. Itagaki \\citep{yam08v466andiauc8971}.\nThe object was soon recognized as a WZ Sge-type dwarf nova based on\nthe presence of early superhumps with a period of 0.056365(7) d\n(vsnet-alert 10518; period refined in this paper,\nfigure \\ref{fig:v466eshpdm}).\nThe object later developed ordinary superhumps (mean period\n0.057203(10) d with the PDM method; figure \\ref{fig:v466shpdm}).\nWe only deal with ordinary superhumps here (table \\ref{tab:v466andoc2008}).\nThe $O-C$ diagram (figure \\ref{fig:v466andoc}) shows the clear presence\nof stages A--C.\nThe $P_{\\rm dot}$ during stage B was $+5.7(0.7) \\times 10^{-5}$\n($20 \\le E \\le 194$). More detailed discussion will be presented in\nOhshima et al., in preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig48.eps}\n \\end{center}\n \\caption{Early superhumps in V466 And (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v466eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig49.eps}\n \\end{center}\n \\caption{Ordinary superhumps in V466 And (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v466shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig50.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps V466 And (2008).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($20 \\le E \\le 194$, thin curve).\n (Lower): Light curve.\n }\n \\label{fig:v466andoc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V466 And (2008).}\\label{tab:v466andoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54722.2300 & 0.0039 & $-$0.0115 & 207 \\\\\n3 & 54722.4050 & 0.0013 & $-$0.0081 & 68 \\\\\n4 & 54722.4628 & 0.0010 & $-$0.0076 & 33 \\\\\n6 & 54722.5761 & 0.0029 & $-$0.0087 & 11 \\\\\n7 & 54722.6373 & 0.0018 & $-$0.0048 & 21 \\\\\n10 & 54722.8118 & 0.0010 & $-$0.0019 & 35 \\\\\n11 & 54722.8712 & 0.0010 & 0.0003 & 38 \\\\\n20 & 54723.3924 & 0.0005 & 0.0066 & 115 \\\\\n21 & 54723.4483 & 0.0004 & 0.0053 & 147 \\\\\n22 & 54723.5056 & 0.0004 & 0.0054 & 165 \\\\\n23 & 54723.5635 & 0.0004 & 0.0061 & 77 \\\\\n24 & 54723.6211 & 0.0004 & 0.0065 & 55 \\\\\n33 & 54724.1305 & 0.0003 & 0.0009 & 120 \\\\\n38 & 54724.4181 & 0.0008 & 0.0025 & 42 \\\\\n39 & 54724.4763 & 0.0006 & 0.0035 & 42 \\\\\n40 & 54724.5330 & 0.0005 & 0.0030 & 42 \\\\\n41 & 54724.5903 & 0.0005 & 0.0031 & 42 \\\\\n45 & 54724.8198 & 0.0006 & 0.0037 & 57 \\\\\n46 & 54724.8752 & 0.0006 & 0.0019 & 35 \\\\\n47 & 54724.9312 & 0.0011 & 0.0007 & 48 \\\\\n68 & 54726.1274 & 0.0007 & $-$0.0046 & 282 \\\\\n69 & 54726.1881 & 0.0008 & $-$0.0011 & 264 \\\\\n70 & 54726.2445 & 0.0007 & $-$0.0019 & 273 \\\\\n71 & 54726.3018 & 0.0034 & $-$0.0018 & 65 \\\\\n111 & 54728.5877 & 0.0014 & $-$0.0044 & 91 \\\\\n112 & 54728.6430 & 0.0010 & $-$0.0063 & 95 \\\\\n122 & 54729.2158 & 0.0012 & $-$0.0056 & 222 \\\\\n125 & 54729.3924 & 0.0028 & $-$0.0006 & 41 \\\\\n142 & 54730.3642 & 0.0020 & $-$0.0015 & 61 \\\\\n143 & 54730.4239 & 0.0042 & 0.0010 & 48 \\\\\n144 & 54730.4760 & 0.0012 & $-$0.0041 & 65 \\\\\n173 & 54732.1408 & 0.0020 & 0.0016 & 285 \\\\\n174 & 54732.1956 & 0.0008 & $-$0.0008 & 270 \\\\\n175 & 54732.2545 & 0.0025 & 0.0009 & 257 \\\\\n176 & 54732.3082 & 0.0019 & $-$0.0027 & 140 \\\\\n193 & 54733.2941 & 0.0029 & 0.0106 & 64 \\\\\n194 & 54733.3555 & 0.0018 & 0.0149 & 61 \\\\\n208 & 54734.1451 & 0.0013 & 0.0035 & 123 \\\\\n209 & 54734.2072 & 0.0165 & 0.0083 & 103 \\\\\n210 & 54734.2650 & 0.0035 & 0.0090 & 132 \\\\\n211 & 54734.3149 & 0.0033 & 0.0016 & 135 \\\\\n300 & 54739.4015 & 0.0016 & $-$0.0036 & 24 \\\\\n301 & 54739.4519 & 0.0014 & $-$0.0104 & 23 \\\\\n302 & 54739.5220 & 0.0018 & 0.0024 & 21 \\\\\n347 & 54742.0880 & 0.0058 & $-$0.0060 & 109 \\\\\n348 & 54742.1463 & 0.0032 & $-$0.0050 & 113 \\\\\n349 & 54742.2080 & 0.0087 & $-$0.0005 & 110 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454722.2415 + 0.057212 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DH Aquilae}\\label{obj:dhaql}\n\n \\citet{nog95dhaql} established the SU UMa-type nature of this object.\nWe further observed the 2002, 2003 and 2008 superoutbursts\n(tables \\ref{tab:dhaqloc2002}, \\ref{tab:dhaqloc2003}, \\ref{tab:dhaqloc2008}).\nThe global $P_{\\rm dot}$ during the 2002 superoutburst was\n$-8.4(0.8) \\times 10^{-5}$, excluding $E = 0$ taken during the\nearly evolutionary stage (cf. figure \\ref{fig:ocsamp}).\nA likely stage B--C transition was recorded during the 2003 superoutburst.\nThe 2007 and 2008 observations most likely recorded stage C superhumps.\nMean periods 0.07952(4) d and 0.07949(4) d, respectively, determined with\nthe PDM method were adopted in table \\ref{tab:perlist}.\n\n A comparison of $O-C$ diagrams of DH Aql between different\nsuperoutbursts is shown in figure \\ref{fig:dhaqlcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig51.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of DH Aql between different\n superoutbursts. A period of 0.08000 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used. Since the start of the 2007 superoutburst\n was not well constrained, we shifted the $O-C$ diagrams\n to best fit the others.\n }\n \\label{fig:dhaqlcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhumps Maxima of DH Aql (2002).}\\label{tab:dhaqloc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52483.9809 & 0.0013 & $-$0.0272 & 93 \\\\\n12 & 52484.9615 & 0.0001 & $-$0.0037 & 267 \\\\\n13 & 52485.0443 & 0.0001 & $-$0.0006 & 256 \\\\\n14 & 52485.1212 & 0.0002 & $-$0.0035 & 250 \\\\\n16 & 52485.2822 & 0.0007 & $-$0.0021 & 135 \\\\\n17 & 52485.3642 & 0.0001 & 0.0003 & 222 \\\\\n18 & 52485.4433 & 0.0001 & $-$0.0005 & 223 \\\\\n19 & 52485.5233 & 0.0002 & $-$0.0002 & 221 \\\\\n24 & 52485.9234 & 0.0001 & 0.0012 & 290 \\\\\n25 & 52486.0043 & 0.0001 & 0.0023 & 472 \\\\\n26 & 52486.0839 & 0.0002 & 0.0021 & 748 \\\\\n27 & 52486.1638 & 0.0003 & 0.0023 & 628 \\\\\n38 & 52487.0443 & 0.0004 & 0.0055 & 306 \\\\\n39 & 52487.1229 & 0.0003 & 0.0044 & 376 \\\\\n40 & 52487.2037 & 0.0002 & 0.0054 & 584 \\\\\n50 & 52488.0036 & 0.0004 & 0.0078 & 228 \\\\\n51 & 52488.0838 & 0.0003 & 0.0082 & 331 \\\\\n52 & 52488.1630 & 0.0003 & 0.0076 & 430 \\\\\n76 & 52490.0748 & 0.0004 & 0.0054 & 221 \\\\\n77 & 52490.1572 & 0.0004 & 0.0080 & 207 \\\\\n89 & 52491.1113 & 0.0009 & 0.0050 & 147 \\\\\n90 & 52491.1859 & 0.0005 & $-$0.0001 & 281 \\\\\n101 & 52492.0616 & 0.0009 & $-$0.0017 & 127 \\\\\n102 & 52492.1443 & 0.0006 & 0.0013 & 152 \\\\\n103 & 52492.2209 & 0.0014 & $-$0.0019 & 120 \\\\\n114 & 52493.0958 & 0.0011 & $-$0.0043 & 151 \\\\\n115 & 52493.1746 & 0.0022 & $-$0.0053 & 136 \\\\\n126 & 52494.0544 & 0.0014 & $-$0.0027 & 117 \\\\\n127 & 52494.1315 & 0.0010 & $-$0.0053 & 325 \\\\\n128 & 52494.2091 & 0.0021 & $-$0.0076 & 128 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452484.0082 + 0.079754 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhumps Maxima of DH Aql (2003).}\\label{tab:dhaqloc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52886.0802 & 0.0060 & $-$0.0154 & 81 \\\\\n12 & 52887.0571 & 0.0002 & 0.0008 & 124 \\\\\n13 & 52887.1374 & 0.0003 & 0.0010 & 150 \\\\\n49 & 52890.0418 & 0.0007 & 0.0233 & 76 \\\\\n120 & 52895.6929 & 0.0020 & $-$0.0097 & 76 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452886.0957 + 0.080058 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhumps Maxima of DH Aql (2007).}\\label{tab:dhaqloc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54232.2271 & 0.0005 & $-$0.0058 & 121 \\\\\n25 & 54234.2183 & 0.0008 & $-$0.0016 & 138 \\\\\n37 & 54235.1824 & 0.0146 & 0.0087 & 125 \\\\\n38 & 54235.2582 & 0.0024 & 0.0050 & 88 \\\\\n51 & 54236.2859 & 0.0018 & $-$0.0005 & 80 \\\\\n76 & 54238.2676 & 0.0011 & $-$0.0059 & 84 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454232.2329 + 0.079481 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhumps Maxima of DH Aql (2008).}\\label{tab:dhaqloc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54628.1832 & 0.0041 & $-$0.0005 & 60 \\\\\n25 & 54630.1736 & 0.0006 & 0.0016 & 142 \\\\\n37 & 54631.1240 & 0.0013 & $-$0.0025 & 138 \\\\\n38 & 54631.2073 & 0.0012 & 0.0014 & 86 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454628.1837 + 0.079534 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V725 Aquilae}\\label{sec:v725aql}\\label{obj:v725aql}\n\n We have reanalyzed the 1999 superoutburst \\citep{uem01v725aql}.\nThe times of superhump maxima are listed in table \\ref{tab:v725aqloc1999}.\nAs shown in \\citet{uem01v725aql}, superhumps were only sufficiently\nobserved mainly after the brightening before termination of the plateau,\npresumably corresponding to the stage C. This would explain the apparently\nzero period derivative in \\citet{uem01v725aql}. Although the present\ndata nominally yielded an overall positive $P_{\\rm dot}$ of\n$+34.9(15.4) \\times 10^{-5}$, the times of maxima for $E \\ge 20$ are\nwell-expressed by a constant period of 0.09977(13) d.\nThere seems to have been a transition in the period of superhumps\naround $E = 20$, associated by a lengthening, rather than shortening\nin many SU UMa-type dwarf novae (see also SDSS J1702 for a possible\nlengthening of the superhump period in a long-$P_{\\rm SH}$ system,\nsubsection \\ref{sec:j1702}).\nA better coverage of the early stage of a next superoutburst\nis vital to test whether this object indeed has a nearly zero\n$P_{\\rm dot}$.\nThe times of superhump maxima during the 2005 superoutburst are\nalso listed in table \\ref{tab:v725aqloc2005}.\nA combined $O-C$ diagram (figure \\ref{fig:v725aqlcomp}) suggests\na positive $P_{\\rm dot}$, which needs to be confirmed by further\nobservations.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig52.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V725 Aql between different\n superoutbursts. A period of 0.06350 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v725aqlcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V725 Aql (1999).}\\label{tab:v725aqloc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51447.9596 & 0.0066 & 0.0008 & 116 \\\\\n1 & 51448.0635 & 0.0038 & 0.0055 & 137 \\\\\n2 & 51448.1632 & 0.0072 & 0.0062 & 85 \\\\\n4 & 51448.3580 & 0.0009 & 0.0026 & 56 \\\\\n10 & 51448.9388 & 0.0019 & $-$0.0113 & 157 \\\\\n11 & 51449.0486 & 0.0077 & $-$0.0006 & 185 \\\\\n12 & 51449.1689 & 0.0132 & 0.0205 & 147 \\\\\n20 & 51449.9295 & 0.0046 & $-$0.0120 & 141 \\\\\n21 & 51450.0275 & 0.0091 & $-$0.0131 & 181 \\\\\n24 & 51450.3365 & 0.0016 & $-$0.0015 & 25 \\\\\n30 & 51450.9305 & 0.0040 & $-$0.0023 & 143 \\\\\n31 & 51451.0263 & 0.0199 & $-$0.0056 & 178 \\\\\n32 & 51451.1225 & 0.0087 & $-$0.0086 & 160 \\\\\n33 & 51451.2305 & 0.0024 & 0.0003 & 30 \\\\\n34 & 51451.3325 & 0.0010 & 0.0032 & 53 \\\\\n44 & 51452.3266 & 0.0021 & 0.0059 & 33 \\\\\n54 & 51453.3220 & 0.0027 & 0.0100 & 36 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451447.9588 + 0.099134 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V725 Aql (2005).}\\label{tab:v725aqloc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53685.5353 & 0.0022 & 0.0013 & 120 \\\\\n1 & 53685.6311 & 0.0023 & $-$0.0014 & 97 \\\\\n30 & 53688.4897 & 0.0139 & 0.0000 & 30 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453685.5339 + 0.098525 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1141 Aquilae}\\label{obj:v1141aql}\n\n \\citet{ole03v1141aql} reported the detection of superhumps during\nthe 2002 superoutburst. The reported period was 0.05930(5) d.\nAlthough \\citet{ole03v1141aql} attempted to make a comparison with\nthe system SW UMa, which has similar outburst properties and superhump\nperiod, they failed to detect a positive period derivative.\n\n During the 2003 superoutburst, we performed time-series\nphotometry on consecutive five nights. The resultant timings of\nsuperhump maxima are presented in table \\ref{tab:v1141aqloc}.\nThe period by \\citet{ole03v1141aql} did not well fit our\nobservations; instead, a period of 0.06296(2) d well expressed our\nobservations (figure \\ref{fig:v1141aqlshpdm}).\nThe cycle numbers given in table \\ref{tab:v1141aqloc}\nrefer to this period. The observed times were well expressed by\na $P_{\\rm dot}$ of $+13.4(1.6) \\times 10^{-5}$.\n\n A comparison of $O-C$ diagrams of V1141 Aql between different\nsuperoutbursts is shown in figure \\ref{fig:v1141aqlcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig53.eps}\n \\end{center}\n \\caption{Superhumps in V1141 Aql (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v1141aqlshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig54.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V1141 Aql between different\n superoutbursts. A period of 0.06296 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v1141aqlcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V1141 Aql (2003).}\\label{tab:v1141aqloc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C$ & $N^b$ \\\\\n\\hline\n0 & 52823.0212 & 0.0005 & 0.0021 & 137 \\\\\n1 & 52823.0831 & 0.0005 & 0.0011 & 102 \\\\\n2 & 52823.1465 & 0.0007 & 0.0015 & 81 \\\\\n4 & 52823.2723 & 0.0015 & 0.0013 & 17 \\\\\n5 & 52823.3340 & 0.0011 & 0.0001 & 18 \\\\\n6 & 52823.3961 & 0.0011 & $-$0.0008 & 18 \\\\\n21 & 52824.3373 & 0.0025 & $-$0.0040 & 17 \\\\\n37 & 52825.3465 & 0.0010 & $-$0.0021 & 17 \\\\\n38 & 52825.4087 & 0.0016 & $-$0.0028 & 17 \\\\\n53 & 52826.3558 & 0.0008 & $-$0.0002 & 17 \\\\\n54 & 52826.4178 & 0.0012 & $-$0.0011 & 17 \\\\\n69 & 52827.3654 & 0.0011 & 0.0020 & 17 \\\\\n70 & 52827.4291 & 0.0014 & 0.0028 & 17 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n By correctly identifying the cycle numbers based on this period,\nthe reported times of maxima in\n\\citet{ole03v1141aql} can also be well fit by a mean period of\n0.06308(3) d and $P_{\\rm dot}$ of $+9.3(4.3) \\times 10^{-5}$.\nThese period derivatives are indeed similar to that of SW UMa.\nThe new period is also compatible with the proposed orbital\nperiod of 0.0620 d from single-night quiescent photometry\n\\citep{hae04v1141aql}. By literally adopting this proposed orbital\nperiod, we obtain a fractional superhump excess of 1.5\\%.\nA comparison of $O-C$ diagrams between 2002 and 2003 superoutbursts\nis shown in figure \\ref{fig:v1141aqlcomp}.\n\n\\subsection{VY Aquarii}\\label{obj:vyaqr}\n\n VY Aqr had long been supposed to be a recurrent nova that erupted\nin 1907 and 1962 (\\cite{str62vyaqr}; \\cite{hut62vyaqr}).\nWhile the detection of the 1973 outburst \\citep{mcn82vyaqr} suggested\na shorter recurrence time, the detection of additional outbursts\n(\\cite{ric83vyaqr}; \\cite{ric83vyaqraditional}; \\cite{lil83vyaqr})\nled to a more likely classification as a WZ Sge-type dwarf nova.\nFurther outbursts were recorded almost yearly (e.g. \\cite{mca83vyaqriauc};\n\\cite{lub86vyaqriauc}; \\cite{hur87vyaqriauc}), confirming the\ndwarf nova-type classification. \\citet{pat93vyaqr} first established\nthe SU UMa-type classification based on photoelectric observations\nduring the 1986 outburst.\n\n The only available timing observation of superhumps in the past\n\\citep{pat93vyaqr} reported a negative $P_{\\rm dot}$.\nThe existence of a negative $P_{\\rm dot}$\nwith this relatively short superhump period had been a mystery.\nThe fresh outburst in 2008 has enabled us to finally establish\n$P_{\\rm dot}$ of this object. The outburst was well-observed\nduring the entire superoutburst plateau and subsequent decline,\na rebrightening, and final fading. We only deal with superhumps\nduring the plateau phase (table \\ref{tab:vyaqroc2008}). The $O-C$ diagram\nshows all the distinct stages A--C (figure \\ref{fig:vyaqr2008oc}).\nThe $P_{\\rm dot}$ during stage B was $+8.5(0.5) \\times 10^{-5}$\n($12 \\le E \\le 144$).\n\nThe times of superhump maxima of the 1986 superoutburst\ndetermined from the scanned figure are given in table \\ref{tab:vyaqroc1986}.\nThe negative $P_{\\rm dot}$ in \\citet{pat93vyaqr} was probably a\nresult of the stage B--C transition around $E=30-31$\n(figure \\ref{fig:vyaqrcomp}).\nFor more details of this outburst, see Ohshima et al., in preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig55.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps VY Aqr (2008).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($12 \\le E \\le 144$, thin curve)\n (Lower): Light curve. A brightening associated with the start of the\n stage C is clearly seen.\n }\n \\label{fig:vyaqr2008oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig56.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of VY Aqr between different\n superoutbursts. A period of 0.06464 d was used to draw this figure.\n Approximate cycle counts ($E$) after the estimated appearance of the\n superhumps were used.\n }\n \\label{fig:vyaqrcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of VY Aqr (2008).}\\label{tab:vyaqroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54649.3119 & 0.0005 & $-$0.0075 & 122 \\\\\n1 & 54649.3815 & 0.0006 & $-$0.0025 & 122 \\\\\n2 & 54649.4430 & 0.0004 & $-$0.0056 & 41 \\\\\n3 & 54649.5132 & 0.0002 & $-$0.0002 & 412 \\\\\n4 & 54649.5757 & 0.0001 & $-$0.0022 & 378 \\\\\n5 & 54649.6453 & 0.0001 & 0.0028 & 286 \\\\\n12 & 54650.1000 & 0.0002 & 0.0051 & 109 \\\\\n13 & 54650.1646 & 0.0002 & 0.0051 & 115 \\\\\n14 & 54650.2284 & 0.0003 & 0.0043 & 70 \\\\\n18 & 54650.4881 & 0.0001 & 0.0055 & 658 \\\\\n19 & 54650.5522 & 0.0001 & 0.0050 & 388 \\\\\n20 & 54650.6166 & 0.0001 & 0.0048 & 267 \\\\\n29 & 54651.1956 & 0.0002 & 0.0022 & 304 \\\\\n30 & 54651.2578 & 0.0002 & $-$0.0003 & 310 \\\\\n34 & 54651.5178 & 0.0002 & 0.0013 & 335 \\\\\n35 & 54651.5820 & 0.0001 & 0.0009 & 285 \\\\\n36 & 54651.6460 & 0.0001 & 0.0003 & 276 \\\\\n42 & 54652.0349 & 0.0004 & 0.0014 & 85 \\\\\n43 & 54652.1010 & 0.0027 & 0.0029 & 117 \\\\\n44 & 54652.1636 & 0.0005 & 0.0009 & 221 \\\\\n45 & 54652.2252 & 0.0004 & $-$0.0021 & 285 \\\\\n49 & 54652.4843 & 0.0002 & $-$0.0015 & 250 \\\\\n50 & 54652.5488 & 0.0001 & $-$0.0017 & 299 \\\\\n51 & 54652.6130 & 0.0001 & $-$0.0021 & 276 \\\\\n52 & 54652.6777 & 0.0002 & $-$0.0020 & 171 \\\\\n59 & 54653.1312 & 0.0005 & $-$0.0008 & 258 \\\\\n60 & 54653.1931 & 0.0002 & $-$0.0035 & 535 \\\\\n61 & 54653.2598 & 0.0003 & $-$0.0014 & 237 \\\\\n62 & 54653.3223 & 0.0002 & $-$0.0035 & 105 \\\\\n63 & 54653.3863 & 0.0002 & $-$0.0042 & 137 \\\\\n64 & 54653.4516 & 0.0001 & $-$0.0035 & 357 \\\\\n65 & 54653.5148 & 0.0001 & $-$0.0049 & 528 \\\\\n66 & 54653.5793 & 0.0001 & $-$0.0050 & 283 \\\\\n67 & 54653.6440 & 0.0001 & $-$0.0049 & 272 \\\\\n75 & 54654.1606 & 0.0002 & $-$0.0053 & 398 \\\\\n76 & 54654.2257 & 0.0002 & $-$0.0049 & 398 \\\\\n77 & 54654.2904 & 0.0003 & $-$0.0048 & 238 \\\\\n78 & 54654.3549 & 0.0003 & $-$0.0049 & 194 \\\\\n79 & 54654.4193 & 0.0002 & $-$0.0051 & 487 \\\\\n80 & 54654.4856 & 0.0002 & $-$0.0034 & 533 \\\\\n90 & 54655.1280 & 0.0069 & $-$0.0072 & 85 \\\\\n91 & 54655.1952 & 0.0020 & $-$0.0046 & 122 \\\\\n95 & 54655.4556 & 0.0005 & $-$0.0027 & 48 \\\\\n96 & 54655.5200 & 0.0006 & $-$0.0030 & 54 \\\\\n106 & 54656.1690 & 0.0002 & $-$0.0001 & 241 \\\\\n107 & 54656.2327 & 0.0004 & $-$0.0010 & 339 \\\\\n108 & 54656.3000 & 0.0011 & 0.0016 & 114 \\\\\n111 & 54656.4952 & 0.0010 & 0.0030 & 65 \\\\\n121 & 54657.1410 & 0.0009 & 0.0026 & 119 \\\\\n122 & 54657.2070 & 0.0005 & 0.0040 & 201 \\\\\n123 & 54657.2710 & 0.0005 & 0.0034 & 161 \\\\\n125 & 54657.4035 & 0.0003 & 0.0067 & 258 \\\\\n126 & 54657.4675 & 0.0002 & 0.0060 & 462 \\\\\n127 & 54657.5326 & 0.0002 & 0.0065 & 291 \\\\\n128 & 54657.5973 & 0.0002 & 0.0066 & 285 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454649.3195 + 0.064619 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of VY Aqr (2008). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n129 & 54657.6612 & 0.0002 & 0.0059 & 218 \\\\\n137 & 54658.1813 & 0.0004 & 0.0090 & 158 \\\\\n138 & 54658.2437 & 0.0005 & 0.0068 & 157 \\\\\n141 & 54658.4386 & 0.0005 & 0.0078 & 406 \\\\\n142 & 54658.5041 & 0.0005 & 0.0087 & 320 \\\\\n143 & 54658.5670 & 0.0002 & 0.0070 & 278 \\\\\n144 & 54658.6321 & 0.0002 & 0.0075 & 272 \\\\\n151 & 54659.0791 & 0.0018 & 0.0021 & 136 \\\\\n152 & 54659.1486 & 0.0003 & 0.0070 & 506 \\\\\n153 & 54659.2100 & 0.0002 & 0.0037 & 358 \\\\\n154 & 54659.2741 & 0.0007 & 0.0033 & 130 \\\\\n157 & 54659.4653 & 0.0004 & 0.0006 & 145 \\\\\n158 & 54659.5326 & 0.0004 & 0.0032 & 195 \\\\\n167 & 54660.1131 & 0.0017 & 0.0022 & 93 \\\\\n168 & 54660.1747 & 0.0003 & $-$0.0008 & 290 \\\\\n169 & 54660.2369 & 0.0005 & $-$0.0032 & 221 \\\\\n172 & 54660.4263 & 0.0023 & $-$0.0077 & 40 \\\\\n173 & 54660.4972 & 0.0008 & $-$0.0014 & 57 \\\\\n188 & 54661.4626 & 0.0010 & $-$0.0053 & 63 \\\\\n204 & 54662.4928 & 0.0014 & $-$0.0091 & 64 \\\\\n215 & 54663.1890 & 0.0054 & $-$0.0236 & 119 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VY Aqr (1986).}\\label{tab:vyaqroc1986}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ \\\\\n\\hline\n0 & 46559.9687 & 0.0011 & $-$0.0113 \\\\\n15 & 46560.9427 & 0.0011 & $-$0.0028 \\\\\n30 & 46561.9140 & 0.0010 & 0.0030 \\\\\n31 & 46561.9806 & 0.0011 & 0.0053 \\\\\n62 & 46563.9742 & 0.0008 & 0.0035 \\\\\n77 & 46564.9402 & 0.0012 & 0.0040 \\\\\n92 & 46565.9050 & 0.0016 & 0.0033 \\\\\n93 & 46565.9700 & 0.0013 & 0.0040 \\\\\n108 & 46566.9338 & 0.0009 & 0.0023 \\\\\n124 & 46567.9619 & 0.0009 & 0.0006 \\\\\n139 & 46568.9205 & 0.0030 & $-$0.0063 \\\\\n155 & 46569.9512 & 0.0020 & $-$0.0055 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2446559.9800 + 0.064365 E$.} \\\\\n \\multicolumn{4}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{EG Aquarii}\\label{obj:egaqr}\n\n The 2006 superoutburst of this object was extensively studied\nby \\citet{ima08egaqr}. We further observed the 2008 superoutburst\n(table \\ref{tab:egaqroc2008}).\nSince the outburst detection was not noticed early enough, the observation\nonly covered the middle part of the superoutburst. The resultant\n$P_{\\rm dot}$ was similar to that obtained during the 2006\nsuperoutburst. The supercycle of this object is likely $\\sim$ 750 d.\n\n\\begin{table}\n\\caption{Superhump maxima of EG Aqr (2008).}\\label{tab:egaqroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54802.9893 & 0.0003 & $-$0.0014 & 216 \\\\\n3 & 54803.2277 & 0.0006 & 0.0007 & 46 \\\\\n12 & 54803.9365 & 0.0004 & 0.0006 & 262 \\\\\n13 & 54804.0154 & 0.0005 & 0.0007 & 173 \\\\\n38 & 54805.9831 & 0.0004 & $-$0.0006 & 242 \\\\\n63 & 54807.9527 & 0.0006 & 0.0000 & 244 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454802.9908 + 0.078760 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BF Arae}\\label{obj:bfara}\n\n \\citet{kat03bfara} studied the 2002 superoutburst of this object.\nA reanalysis of the same data has yielded improved determination of\nsuperhump maxima than those obtained by eye estimates\n(table \\ref{tab:bfaraoc}). The resultant $P_{\\rm dot}$ was\n$-2.8(1.6) \\times 10^{-5}$, giving a slightly smaller value in\n\\citet{kat03bfara}. \\citet{ole07bfara} obtained photometry in\nquiescence and yielded a likely orbital period of 0.084176(21) d,\ngiving a fractional superhump excess of 4.4 \\%.\n\n\\begin{table}\n\\caption{Superhump maxima of BF Ara (2002).}\\label{tab:bfaraoc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52504.9878 & 0.0005 & $-$0.0031 & 143 \\\\\n1 & 52505.0774 & 0.0005 & $-$0.0014 & 120 \\\\\n2 & 52505.1643 & 0.0005 & $-$0.0023 & 114 \\\\\n12 & 52506.0456 & 0.0007 & 0.0001 & 87 \\\\\n13 & 52506.1311 & 0.0005 & $-$0.0023 & 89 \\\\\n14 & 52506.2266 & 0.0024 & 0.0053 & 49 \\\\\n23 & 52507.0148 & 0.0008 & 0.0025 & 82 \\\\\n24 & 52507.1025 & 0.0007 & 0.0024 & 83 \\\\\n25 & 52507.1869 & 0.0008 & $-$0.0012 & 89 \\\\\n35 & 52508.0672 & 0.0006 & 0.0003 & 88 \\\\\n36 & 52508.1565 & 0.0008 & 0.0017 & 88 \\\\\n60 & 52510.2640 & 0.0014 & $-$0.0001 & 102 \\\\\n61 & 52510.3510 & 0.0014 & $-$0.0010 & 100 \\\\\n80 & 52512.0207 & 0.0016 & $-$0.0011 & 30 \\\\\n90 & 52512.9025 & 0.0023 & 0.0018 & 22 \\\\\n91 & 52512.9920 & 0.0017 & 0.0034 & 25 \\\\\n102 & 52513.9504 & 0.0021 & $-$0.0050 & 27 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452504.9909 + 0.087887 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V663 Arae}\\label{obj:v663ara}\n\n V663 Ara was discovered by \\citet{ges74v663ara} as a long-period\nvariable star. \\citet{DownesCVatlas3} listed this object as a CV.\nThe SU UMa-type nature of this object was established by B. Monard\n(vsnet-alert 8231, 8232).\nWe obtained a mean superhump period of 0.07639(2) d from observations\non four nights (figure \\ref{fig:v663arashpdm}).\nThe times of superhump maxima are listed in table\n\\ref{tab:v663araoc2004}. The resultant $P_{\\rm dot}$ was\n$-6.2(9.4) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig57.eps}\n \\end{center}\n \\caption{Superhumps in V663 Ara (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v663arashpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V663 Ara (2004).}\\label{tab:v663araoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53195.4364 & 0.0007 & 0.0001 & 82 \\\\\n11 & 53196.2782 & 0.0013 & 0.0020 & 63 \\\\\n12 & 53196.3546 & 0.0010 & 0.0020 & 83 \\\\\n13 & 53196.4265 & 0.0015 & $-$0.0025 & 81 \\\\\n14 & 53196.5017 & 0.0018 & $-$0.0037 & 81 \\\\\n37 & 53198.2603 & 0.0112 & $-$0.0015 & 47 \\\\\n38 & 53198.3415 & 0.0016 & 0.0033 & 86 \\\\\n39 & 53198.4187 & 0.0020 & 0.0042 & 86 \\\\\n40 & 53198.4907 & 0.0016 & $-$0.0002 & 84 \\\\\n50 & 53199.2517 & 0.0021 & $-$0.0029 & 76 \\\\\n51 & 53199.3304 & 0.0015 & $-$0.0005 & 81 \\\\\n52 & 53199.4068 & 0.0055 & $-$0.0005 & 35 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453195.4362 + 0.076366 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V877 Arae}\\label{sec:v877ara}\\label{obj:v877ara}\n\n \\citet{kat03v877arakktelpucma} observed the 2002 superoutburst\nand reported a strongly negative period derivative. The variation\nof the superhump period occurred during the earliest stage of the\nsuperoutburst, and the originally reported $P_{\\rm dot}$ more likely\nreflected the early stage of period shift from the stage A to B,\nas seen in the similar long-period system DT Oct\n(subsection \\ref{sec:dtoct}).\nThe refined superhump maxima are listed in table \\ref{tab:v877ara}.\nBy neglecting the early portion ($E < 24$), we obtained a\n$P_{\\rm dot}$ of $-5.7(2.9) \\times 10^{-5}$, typical for an usual\nSU UMa-type dwarf nova.\n\n\\begin{table}\n\\caption{Superhump maxima of V877 Ara (2002).}\\label{tab:v877ara}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52434.9582 & 0.0011 & $-$0.0123 & 61 \\\\\n1 & 52435.0470 & 0.0003 & $-$0.0076 & 84 \\\\\n24 & 52436.9922 & 0.0011 & 0.0045 & 64 \\\\\n25 & 52437.0757 & 0.0007 & 0.0039 & 111 \\\\\n26 & 52437.1645 & 0.0005 & 0.0087 & 87 \\\\\n27 & 52437.2473 & 0.0007 & 0.0075 & 86 \\\\\n72 & 52441.0235 & 0.0015 & 0.0013 & 46 \\\\\n73 & 52441.1103 & 0.0008 & 0.0041 & 69 \\\\\n74 & 52441.1923 & 0.0007 & 0.0021 & 65 \\\\\n95 & 52442.9508 & 0.0013 & $-$0.0044 & 23 \\\\\n96 & 52443.0389 & 0.0017 & $-$0.0004 & 24 \\\\\n97 & 52443.1186 & 0.0012 & $-$0.0047 & 51 \\\\\n98 & 52443.2047 & 0.0009 & $-$0.0027 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452434.9704 + 0.084050 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BB Arietis}\\label{sec:bbari}\\label{obj:bbari}\n\n This object was recognized during the identification project of\nthe New Catalogue of Suspected Variable Stars (NSV, \\cite{NSV})\nobjects against ROSAT X-ray source (Kato, vsnet-chat 3317).\nThe proximity of a ROSAT source to the position of NSV 907,\na large-amplitude variable star, suggested that the object may be\na dwarf nova, as we have seen in\nDT Oct = NSV 10934 \\citep{kat02gzcncnsv10934}.\n\n The object has been monitored since, and the first outburst was\ndetected by P. Schmeer on 2004 March 2 at an unfiltered CCD magnitude\nof 13.5. It is unclear how long this outburst lasted.\nOn 2004 November 1, P. Schmeer detected another outburst at magnitude\n13.7. Following this alert, we started time-resolved photometry and\ndetected superhumps. A PDM analysis yielded a mean superhump period\nof 0.07209(1) d (figure \\ref{fig:bbarishpdm}).\nThe times of superhump maxima are listed in\ntable \\ref{tab:bbarioc2004}. We obtained $P_{\\rm dot}$ =\n$+1.6(3.0) \\times 10^{-5}$. Since the superoutburst was likely detected\nduring its final stage, the superhump period and period derivative most\nlikely reflect the behavior after transition to the stage C.\nAlthough the object has been well monitored since, only two normal\noutbursts was recorded in 2006 November in 2009 February.\nThe outburst frequency may be as low as UV Per and VY Aqr,\nhaving similar superhump periods.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig58.eps}\n \\end{center}\n \\caption{Superhumps in BB Ari (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:bbarishpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of BB Ari (2004).}\\label{tab:bbarioc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53311.4608 & 0.0004 & $-$0.0005 & 77 \\\\\n1 & 53311.5325 & 0.0005 & $-$0.0009 & 44 \\\\\n12 & 53312.3280 & 0.0011 & 0.0012 & 113 \\\\\n22 & 53313.0479 & 0.0012 & $-$0.0001 & 166 \\\\\n23 & 53313.1210 & 0.0006 & 0.0009 & 183 \\\\\n24 & 53313.1933 & 0.0008 & 0.0011 & 305 \\\\\n25 & 53313.2648 & 0.0007 & 0.0005 & 366 \\\\\n35 & 53313.9865 & 0.0005 & 0.0009 & 131 \\\\\n36 & 53314.0586 & 0.0005 & 0.0010 & 260 \\\\\n37 & 53314.1318 & 0.0003 & 0.0020 & 320 \\\\\n38 & 53314.2018 & 0.0005 & $-$0.0002 & 226 \\\\\n39 & 53314.2753 & 0.0003 & 0.0013 & 304 \\\\\n42 & 53314.4881 & 0.0007 & $-$0.0023 & 71 \\\\\n43 & 53314.5592 & 0.0008 & $-$0.0034 & 71 \\\\\n60 & 53315.7811 & 0.0020 & $-$0.0075 & 16 \\\\\n61 & 53315.8605 & 0.0017 & $-$0.0002 & 17 \\\\\n73 & 53316.7295 & 0.0028 & 0.0033 & 22 \\\\\n74 & 53316.8010 & 0.0014 & 0.0027 & 23 \\\\\n75 & 53316.8705 & 0.0021 & 0.0000 & 16 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453311.4613 + 0.072122 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{HV Aurigae}\\label{obj:hvaur}\n\n \\citet{nog95hvaur} reported a superhump period of 0.0855(1) d.\nDuring the 2002 superoutburst, we undertook an observing campaign.\nThe observation confirmed\nthe periodicity in \\citet{nog95hvaur}. The measured superhump maxima\nare listed in table \\ref{tab:hvauroc}. The data did not show a clear\ntendency of period changes. A high-quality subset ($O-C$'s with errors\nless than 0.0015 d) of superhump times gives a virtually zero\n($-3.5(5.0) \\times 10^{-5}$) period change. The object looks similar\nto BF Ara, another long-period system with a relatively constant\nsuperhump period, although we can not exclude the possibility that we\nobserved only the stage C superhumps since the start of the outburst\nwas unknown.\n\n\\begin{table}\n\\caption{Superhump maxima of HV Aur (2002).}\\label{tab:hvauroc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52605.9359 & 0.0038 & $-$0.0044 & 83 \\\\\n1 & 52606.0296 & 0.0049 & 0.0037 & 106 \\\\\n2 & 52606.1087 & 0.0022 & $-$0.0028 & 148 \\\\\n13 & 52607.0547 & 0.0009 & 0.0020 & 477 \\\\\n14 & 52607.1391 & 0.0010 & 0.0009 & 316 \\\\\n15 & 52607.2239 & 0.0008 & 0.0001 & 579 \\\\\n16 & 52607.3117 & 0.0020 & 0.0023 & 437 \\\\\n17 & 52607.3956 & 0.0006 & 0.0007 & 71 \\\\\n18 & 52607.4795 & 0.0007 & $-$0.0009 & 60 \\\\\n20 & 52607.6508 & 0.0006 & $-$0.0008 & 58 \\\\\n24 & 52607.9912 & 0.0044 & $-$0.0026 & 214 \\\\\n25 & 52608.0808 & 0.0010 & 0.0015 & 217 \\\\\n29 & 52608.4213 & 0.0005 & $-$0.0003 & 140 \\\\\n30 & 52608.5063 & 0.0005 & $-$0.0009 & 139 \\\\\n32 & 52608.6785 & 0.0006 & 0.0001 & 44 \\\\\n33 & 52608.7650 & 0.0008 & 0.0011 & 40 \\\\\n41 & 52609.4485 & 0.0003 & 0.0001 & 88 \\\\\n42 & 52609.5330 & 0.0003 & $-$0.0009 & 68 \\\\\n47 & 52609.9713 & 0.0050 & 0.0095 & 134 \\\\\n48 & 52610.0441 & 0.0038 & $-$0.0033 & 166 \\\\\n50 & 52610.2187 & 0.0009 & 0.0002 & 160 \\\\\n51 & 52610.2989 & 0.0041 & $-$0.0052 & 223 \\\\\n59 & 52610.9945 & 0.0045 & 0.0060 & 161 \\\\\n60 & 52611.0745 & 0.0024 & 0.0004 & 119 \\\\\n62 & 52611.2385 & 0.0050 & $-$0.0067 & 224 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452605.9403 + 0.085563 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TT Bootis}\\label{obj:ttboo}\n\n \\citet{ole04ttboo} reported on period variation during the 2004\nsuperoutburst. We observed the same superoutburst and obtained\nsuperhump maxima with higher precision than those in \\citet{ole04ttboo}.\nA combined list of superhump maxima and the $O-C$ diagram are given\nin table \\ref{tab:ttboooc2004} and figure \\ref{fig:ocsamp}.\nWe applied a systematic correction of $+$0.0031 d to the times of\n\\citet{ole04ttboo} and disregarded maxima measured using Cook's\nobservations, which are included in our own data set and were analyzed\nwith a higher precision. Although \\citet{ole04ttboo} proposed\na different treatment in dividing the $O-C$ diagram, we derived\n$P_{\\rm dot}$ = $+8.3(0.7) \\times 10^{-5}$ from the segment\n$13 \\le E \\le 120$ (stage B) by analogy with other systems with similar\n$O-C$ behavior (subsection \\ref{sec:tendency}).\nThe extreme values in \\citet{ole04ttboo} reflected\na transition from the stage A to B\nwith positive $P_{\\rm dot}$, and a transition to the stage C\nobserved during the late course of the superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of TT Boo (2004).}\\label{tab:ttboooc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53161.7568 & 0.0004 & $-$0.0150 & 141 \\\\\n1 & 53161.8360 & 0.0003 & $-$0.0138 & 213 \\\\\n2 & 53161.9152 & 0.0003 & $-$0.0126 & 158 \\\\\n9 & 53162.4705 & 0.0004 & $-$0.0029 & 80 \\\\\n13 & 53162.7845 & 0.0002 & $-$0.0007 & 157 \\\\\n14 & 53162.8624 & 0.0002 & $-$0.0008 & 138 \\\\\n15 & 53162.9406 & 0.0002 & $-$0.0006 & 123 \\\\\n22 & 53163.4858 & 0.0003 & $-$0.0010 & 64 \\\\\n22 & 53163.4841 & 0.0015 & $-$0.0027 & 0 \\\\\n34 & 53164.4176 & 0.0005 & $-$0.0047 & 53 \\\\\n35 & 53164.4986 & 0.0008 & $-$0.0016 & 42 \\\\\n35 & 53164.4973 & 0.0025 & $-$0.0029 & 0 \\\\\n47 & 53165.4303 & 0.0004 & $-$0.0053 & 81 \\\\\n47 & 53165.4321 & 0.0020 & $-$0.0036 & 0 \\\\\n48 & 53165.5111 & 0.0080 & $-$0.0025 & 0 \\\\\n59 & 53166.3676 & 0.0015 & $-$0.0035 & 0 \\\\\n60 & 53166.4451 & 0.0030 & $-$0.0040 & 0 \\\\\n61 & 53166.5243 & 0.0017 & $-$0.0027 & 0 \\\\\n73 & 53167.4573 & 0.0020 & $-$0.0051 & 0 \\\\\n98 & 53169.4156 & 0.0025 & 0.0043 & 0 \\\\\n99 & 53169.4954 & 0.0020 & 0.0062 & 0 \\\\\n106 & 53170.0422 & 0.0014 & 0.0073 & 130 \\\\\n107 & 53170.1215 & 0.0010 & 0.0087 & 188 \\\\\n108 & 53170.1960 & 0.0017 & 0.0052 & 68 \\\\\n111 & 53170.4354 & 0.0008 & 0.0107 & 85 \\\\\n111 & 53170.4339 & 0.0015 & 0.0092 & 0 \\\\\n112 & 53170.5131 & 0.0025 & 0.0105 & 0 \\\\\n119 & 53171.0603 & 0.0004 & 0.0120 & 136 \\\\\n120 & 53171.1384 & 0.0003 & 0.0122 & 182 \\\\\n124 & 53171.4490 & 0.0005 & 0.0110 & 79 \\\\\n129 & 53171.8395 & 0.0004 & 0.0117 & 138 \\\\\n130 & 53171.9188 & 0.0013 & 0.0130 & 77 \\\\\n132 & 53172.0715 & 0.0004 & 0.0099 & 182 \\\\\n133 & 53172.1503 & 0.0004 & 0.0107 & 150 \\\\\n141 & 53172.7718 & 0.0003 & 0.0086 & 162 \\\\\n142 & 53172.8488 & 0.0004 & 0.0076 & 158 \\\\\n143 & 53172.9272 & 0.0007 & 0.0080 & 123 \\\\\n144 & 53173.0028 & 0.0020 & 0.0057 & 98 \\\\\n145 & 53173.0765 & 0.0010 & 0.0015 & 215 \\\\\n150 & 53173.4702 & 0.0005 & 0.0053 & 76 \\\\\n153 & 53173.7031 & 0.0008 & 0.0045 & 94 \\\\\n154 & 53173.7821 & 0.0005 & 0.0055 & 140 \\\\\n155 & 53173.8586 & 0.0004 & 0.0040 & 100 \\\\\n167 & 53174.7902 & 0.0005 & 0.0002 & 121 \\\\\n188 & 53176.4183 & 0.0010 & $-$0.0087 & 60 \\\\\n189 & 53176.5000 & 0.0013 & $-$0.0050 & 80 \\\\\n192 & 53176.7321 & 0.0010 & $-$0.0067 & 77 \\\\\n205 & 53177.7458 & 0.0007 & $-$0.0065 & 103 \\\\\n206 & 53177.8227 & 0.0009 & $-$0.0075 & 107 \\\\\n207 & 53177.8939 & 0.0016 & $-$0.0143 & 91 \\\\\n213 & 53178.3623 & 0.0040 & $-$0.0136 & 0 \\\\\n214 & 53178.4416 & 0.0030 & $-$0.0122 & 0 \\\\\n215 & 53178.5173 & 0.0030 & $-$0.0145 & 0 \\\\\n218 & 53178.7474 & 0.0007 & $-$0.0182 & 104 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453161.7719 + 0.077953 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N=0$ refers to \\citet{ole04ttboo}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{UZ Bootis}\\label{obj:uzboo}\n\n UZ Boo had long been suspected to be a WZ Sge-type dwarf nova\n\\citep{bai79wzsge}. Due to the lack of an outburst since 1978,\nit was only in 1994 when the SU UMa-type nature of this object was\nestablished (cf. \\cite{kat01hvvir}).\n\n The 2003--2004 superoutburst was detected by P. Dubovsky on 2003\nDecember 5 (vsnet-alert 7937). The true superhump period was finally\nidentified (vsnet-alert 7952). The object underwent four rebrightenings\n(vsnet-alert 7954, 7960, 7962, 7967) following the main\nsuperoutburst (figure \\ref{fig:uzboo2003lc}).\\footnote{\n The 1994 superoutburst possibly had two rebrightenings \\citep{kuu96TOAD}.\n}\nDue to the poor seasonal location, the quality of the observation\nwas not always very good. We selected the superhump period of\n0.06191(2) d with the PDM method (figure \\ref{fig:uzbooshpdm})\nfor the best sampled segment between BJD 2452983 and 2452991.\nThe times of superhump maxima and cycle counts identified with this\nperiod are listed in table \\ref{tab:uzboooc2003}.\nAlthough the superhump period was almost constant for $E \\ge 30$\n(with mean $P_{\\rm SH}$ and $P_{\\rm dot}$ of 0.06192(3) d and\n$-1.9(6.3) \\times 10^{-5}$, respectively), there was clear evidence\nof period evolution before $E = 30$. We identified this segment\nto be stage A with a mean $P_{\\rm SH}$ of 0.0635(2) d, lasting for\n$\\sim$ 30 superhump cycles.\nThe relatively long $P_{\\rm SH}$, the lack of period\nvariation during the stage B and the presence of multiple rebrightenings\nmake UZ Boo a system analogous to EG Cnc\n(\\cite{pat98egcnc}; \\cite{kat04egcnc}).\n\n The times of superhump maxima during the 1994 superoutburst were\nanalyzed using the $P_{\\rm SH}$ identified during the 2003 superoutburst\n(table \\ref{tab:uzboooc1994}). Although the maximum at $E=0$ was on\na smooth extrapolation of later maxima, this could have been an\nearly superhump. The resultant $P_{\\rm SH}$ and\n$P_{\\rm dot}$ were 0.06174(4) d and $-1.5(2.5) \\times 10^{-5}$,\nrespectively.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig59.eps}\n \\end{center}\n \\caption{Superoutburst of UZ Boo in 2003--2004. The data are a combination\n of our observations (filled squares), and AAVSO and VSNET observations\n (filled squares; the ``V''-marks indicate upper limits).\n Four post-superoutburst rebrightenings were recorded.}\n \\label{fig:uzboo2003lc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig60.eps}\n \\end{center}\n \\caption{Superhumps in UZ Boo (2003). (Upper): PDM analysis between\n BJD 2452983 and 2452991.\n (Lower): Phase-averaged profile.}\n \\label{fig:uzbooshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of UZ Boo (1994).}\\label{tab:uzboooc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49582.9956 & 0.0009 & $-$0.0012 & 106 \\\\\n81 & 49587.9933 & 0.0019 & $-$0.0047 & 40 \\\\\n97 & 49588.9930 & 0.0036 & 0.0071 & 41 \\\\\n161 & 49592.9429 & 0.0027 & 0.0055 & 63 \\\\\n177 & 49593.9195 & 0.0077 & $-$0.0058 & 57 \\\\\n178 & 49593.9862 & 0.0019 & $-$0.0009 & 48 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449582.9968 + 0.061743 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of UZ Boo (2003--2004).}\\label{tab:uzboooc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52981.7156 & 0.0009 & $-$0.0263 & 79 \\\\\n10 & 52982.3523 & 0.0029 & $-$0.0109 & 90 \\\\\n16 & 52982.7409 & 0.0007 & 0.0049 & 72 \\\\\n30 & 52983.6210 & 0.0007 & 0.0153 & 34 \\\\\n31 & 52983.6789 & 0.0005 & 0.0111 & 82 \\\\\n32 & 52983.7415 & 0.0005 & 0.0116 & 74 \\\\\n58 & 52985.3526 & 0.0020 & 0.0073 & 35 \\\\\n90 & 52987.3377 & 0.0009 & 0.0044 & 239 \\\\\n106 & 52988.3281 & 0.0016 & 0.0008 & 225 \\\\\n107 & 52988.3793 & 0.0033 & $-$0.0101 & 92 \\\\\n117 & 52989.0067 & 0.0042 & $-$0.0040 & 76 \\\\\n118 & 52989.0687 & 0.0006 & $-$0.0042 & 87 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452981.7419 + 0.062127 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{NN Camelopardalis}\\label{obj:nncam}\n\n NN Cam = NSV 1485 is a recently identified SU UMa-type dwarf nova\n(\\cite{khr05nsv1485}; for more historical information, see\nvsnet-alert 9557), whose outburst was detected\non 2007 September 11. Although this outburst rapidly faded,\na genuine superoutburst followed after eight days (vsnet-alert 9598).\n\n The times of superhump maxima obtained during this superoutburst\nare listed in table \\ref{tab:nncamoc2007}. A stage B--C transition was\nprobably recorded. Using the orbital period of 0.0717 d determined\nphotometrically (vsnet-alert 9557), we obtained a fractional superhump\nexcess for $P_2$ of 3.0 \\%.\nDuring the precursor, low-amplitude modulations\nwere observed (figure \\ref{fig:nncamprec}). Although the duration of\nthe observation was not long enough, the period of the variations is\nconsistent with the suggested orbital period. If this period is\nconfirmed, the outburst makes the second example of a transition from\nthe orbital period to the superhump period after the case of\nthe 1993 superoutburst of QZ Vir \\citep{kat97tleo}.\n\n The object underwent normal outbursts in 2008 March and October\n(vsnet-alert 10588). Photometric observations during the 2008 October\noutburst did not record modulations similar to those recorded during\nthe precursor outburst in 2007 September. This suggests that some\nkind of (immature) superhumps were indeed excited during this\nprecursor outburst in 2007.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig61.eps}\n \\end{center}\n \\caption{Precursor outburst of NN Cam in 2007 (Upper): Light curve.\n (Lower): Phase-averaged profile referring to the orbital period.}\n \\label{fig:nncamprec}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of NN Cam.}\\label{tab:nncamoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54363.5492 & 0.0004 & $-$0.0070 & 83 \\\\\n13 & 54364.5159 & 0.0002 & $-$0.0014 & 260 \\\\\n14 & 54364.5891 & 0.0003 & $-$0.0022 & 301 \\\\\n24 & 54365.3323 & 0.0005 & 0.0017 & 57 \\\\\n25 & 54365.4071 & 0.0006 & 0.0026 & 83 \\\\\n26 & 54365.4816 & 0.0005 & 0.0032 & 173 \\\\\n27 & 54365.5551 & 0.0003 & 0.0027 & 387 \\\\\n28 & 54365.6289 & 0.0006 & 0.0025 & 191 \\\\\n39 & 54366.4393 & 0.0003 & $-$0.0003 & 87 \\\\\n40 & 54366.5162 & 0.0003 & 0.0027 & 324 \\\\\n41 & 54366.5879 & 0.0002 & 0.0005 & 402 \\\\\n54 & 54367.5477 & 0.0005 & $-$0.0009 & 207 \\\\\n55 & 54367.6229 & 0.0003 & 0.0004 & 250 \\\\\n66 & 54368.4375 & 0.0006 & 0.0016 & 87 \\\\\n67 & 54368.5094 & 0.0005 & $-$0.0004 & 86 \\\\\n81 & 54369.5403 & 0.0007 & $-$0.0046 & 267 \\\\\n82 & 54369.6179 & 0.0007 & $-$0.0009 & 218 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454363.5562 + 0.073935 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SY Capriconi}\\label{obj:sycap}\n\n SY Cap was originally classified as a long-period variable \\citep{GCVS}.\nThe dwarf nova-type nature was pointed out by one of the authors\n(T. Kato, vsnet-alert 10025). Observations during the 2008 outburst\nestablished the SU UMa-type nature of this object (vsnet-alert 10453,\nfigure \\ref{fig:sycapshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:sycapoc2008}.\nThe mean superhump period and global $P_{\\rm dot}$ were 0.06376(2) d and\n$-11.4(9.0) \\times 10^{-5}$, respectively. The negative value of\n$P_{\\rm dot}$ is probably a result of transition between stages B and C.\nThe object resembles CI UMa in its short supercycles, combined with\nrelatively few normal outbursts and the short duration of superoutbursts\n(cf. \\cite{nog97ciuma}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig62.eps}\n \\end{center}\n \\caption{Superhumps in SY Cap (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:sycapshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SY Cap (2008).}\\label{tab:sycapoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54700.0560 & 0.0006 & $-$0.0009 & 121 \\\\\n1 & 54700.1206 & 0.0006 & 0.0000 & 120 \\\\\n2 & 54700.1844 & 0.0009 & 0.0000 & 81 \\\\\n14 & 54700.9505 & 0.0005 & 0.0011 & 78 \\\\\n47 & 54703.0539 & 0.0018 & 0.0004 & 70 \\\\\n48 & 54703.1186 & 0.0006 & 0.0013 & 92 \\\\\n49 & 54703.1790 & 0.0010 & $-$0.0020 & 99 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454700.0568 + 0.063759 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AX Capriconi}\\label{obj:axcap}\n\n AX Cap was serendipitously discovered as a dwarf nova during a\nsearch for asteroids \\citep{how94CVspec3}. \\citet{how94CVspec3}\nreported a spectrum during a faint outburst. An exceptionally\nbright (15.4 mag) outburst was reported on 2004 July 17 (R. Stubbings,\nvsnet-obs 50216). The confirmation of superhumps (vsnet-campaign-dn 4337)\nled to a classification as a long-$P_{\\rm SH}$ SU UMa-type dwarf nova.\nTable \\ref{tab:axcapoc2004} lists the observed superhump maxima.\nDuring $E \\le 2$, the superhumps were still evolving. The period smoothly\ndecreased with a large negative $P_{\\rm dot}$ until $E=34$, then\nit apparently shifted to a shorter one (figure \\ref{fig:lp2}).\nThe $P_{\\rm dot}$ for the former interval ($8 \\le E \\le 34$) was\n$P_{\\rm dot} = -87(65) \\times 10^{-5}$.\n\n Among SU UMa-type dwarf novae, AX Cap has the second longest\n$P_{\\rm SH}$ next to TU Men. Together with the large period variation\nsimilar to MN Dra, this object certainly deserves a further detailed\nstudy.\n\n\\begin{table}\n\\caption{Superhump maxima of AX Cap (2004).}\\label{tab:axcapoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53204.3758 & 0.0069 & $-$0.0824 & 259 \\\\\n1 & 53204.4990 & 0.0101 & $-$0.0722 & 265 \\\\\n2 & 53204.6508 & 0.0042 & $-$0.0336 & 194 \\\\\n8 & 53205.3625 & 0.0044 & $-$0.0007 & 176 \\\\\n9 & 53205.4690 & 0.0026 & $-$0.0073 & 256 \\\\\n10 & 53205.5742 & 0.0053 & $-$0.0153 & 258 \\\\\n15 & 53206.1685 & 0.0033 & 0.0134 & 62 \\\\\n17 & 53206.4050 & 0.0014 & 0.0237 & 260 \\\\\n18 & 53206.5227 & 0.0031 & 0.0282 & 373 \\\\\n19 & 53206.6365 & 0.0016 & 0.0290 & 239 \\\\\n34 & 53208.3657 & 0.0007 & 0.0612 & 257 \\\\\n35 & 53208.4751 & 0.0007 & 0.0575 & 258 \\\\\n36 & 53208.5862 & 0.0011 & 0.0554 & 213 \\\\\n50 & 53210.1405 & 0.0024 & 0.0259 & 200 \\\\\n51 & 53210.2576 & 0.0058 & 0.0299 & 119 \\\\\n85 & 53214.0435 & 0.0034 & $-$0.0305 & 116 \\\\\n86 & 53214.1470 & 0.0061 & $-$0.0401 & 317 \\\\\n99 & 53215.6157 & 0.0066 & $-$0.0421 & 155 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453204.4582 + 0.113128 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{GX Cassiopeiae}\\label{obj:gxcas}\n\n The object has one of the longest superhump periods among known\nSU UMa-type dwarf novae. \\citet{nog98gxcasv419lyr} reported the detection\nof superhumps during the 1994 superoutburst.\n\n We further observed the 1999 and 2006 superoutbursts from the start of\nthe appearance of superhumps. We also analyzed the AAVSO data of the\n1996 superoutburst.\nThe determined times of superhump maxima are listed in\ntables \\ref{tab:gxcasoc1994}, \\ref{tab:gxcasoc1996}, \\ref{tab:gxcasoc1999} and\n\\ref{tab:gxcasoc2006}.\n\n The early and late stages were observed during the 1996 superoutburst.\nBased on the identification of the $P_{\\rm SH}$ during other superoutbursts,\nwe can unambiguously determine $E$ for each superhumps. The results\ndemonstrate the clear presence of stages A and C. The parameters are\nlisted in table \\ref{tab:perlist}. It might be worth noting that a PDM\nanalysis gave a false period (0.0862 d) due to the strong period variation,\nsimilar to the case in CTCV J0549$-$4921 \\citep{ima08fltractcv0549}.\n\n During the 1999 superoutburst, the object showed\na significantly longer period ($P > 0.0964$ d) for $E < 21$,\nprobably reflecting the stage A as in the 1996 superoutburst.\nThe rest of the superoutburst showed a relatively regular decrease of\nthe superhump period.\nThe mean $P_{\\rm dot}$ was $-7.6(2.5) \\times 10^{-5}$.\nThe present analysis confirmed the period identification\nin \\citet{nog98gxcasv419lyr}.\n\n The 2006 superoutburst showed a similar tendency of a\nlarge period change during the early stage. Such large variations\nof superhump periods appear to be common in long-period SU UMa-type\ndwarf novae (cf. subsection \\ref{sec:longp}; \\cite{rut07v419lyr}).\n\n A combined $O-C$ diagram (figure \\ref{fig:gxcascomp}) now clearly\nillustrates the period variation of superhumps in this system.\nHaving observed $\\sim$ 5 d after the outburst detection, the 1994\nobservation recorded the stage C superhumps.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig63.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of GX Cas between different\n superoutbursts. A period of 0.09320 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the superoutburst\n were used.\n }\n \\label{fig:gxcascomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of GX Cas (1994).}\\label{tab:gxcasoc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49585.1684 & 0.0003 & $-$0.0021 & 48 \\\\\n1 & 49585.2681 & 0.0011 & 0.0046 & 20 \\\\\n32 & 49588.1412 & 0.0014 & $-$0.0037 & 126 \\\\\n42 & 49589.0743 & 0.0013 & $-$0.0000 & 49 \\\\\n43 & 49589.1647 & 0.0012 & $-$0.0026 & 65 \\\\\n44 & 49589.2590 & 0.0017 & $-$0.0013 & 67 \\\\\n53 & 49590.0924 & 0.0046 & $-$0.0044 & 33 \\\\\n54 & 49590.1920 & 0.0018 & 0.0023 & 32 \\\\\n55 & 49590.2910 & 0.0020 & 0.0083 & 49 \\\\\n65 & 49591.2112 & 0.0035 & $-$0.0010 & 39 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449585.1706 + 0.092947 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GX Cas (1996).}\\label{tab:gxcasoc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50358.5124 & 0.0018 & $-$0.0199 & 28 \\\\\n1 & 50358.6074 & 0.0014 & $-$0.0185 & 27 \\\\\n2 & 50358.6980 & 0.0016 & $-$0.0216 & 11 \\\\\n10 & 50359.4792 & 0.0009 & 0.0104 & 38 \\\\\n44 & 50362.6771 & 0.0006 & 0.0242 & 26 \\\\\n45 & 50362.7700 & 0.0007 & 0.0234 & 26 \\\\\n54 & 50363.6082 & 0.0007 & 0.0187 & 22 \\\\\n55 & 50363.7016 & 0.0007 & 0.0185 & 21 \\\\\n65 & 50364.6287 & 0.0027 & 0.0091 & 11 \\\\\n107 & 50368.5394 & 0.0014 & $-$0.0136 & 22 \\\\\n108 & 50368.6320 & 0.0017 & $-$0.0147 & 20 \\\\\n109 & 50368.7243 & 0.0016 & $-$0.0160 & 22 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450358.5323 + 0.093652 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GX Cas (1999).}\\label{tab:gxcasoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51472.1436 & 0.0027 & $-$0.0416 & 140 \\\\\n1 & 51472.2314 & 0.0022 & $-$0.0472 & 188 \\\\\n21 & 51474.1645 & 0.0005 & 0.0167 & 187 \\\\\n22 & 51474.2580 & 0.0014 & 0.0168 & 142 \\\\\n32 & 51475.1919 & 0.0006 & 0.0160 & 187 \\\\\n33 & 51475.2853 & 0.0008 & 0.0160 & 165 \\\\\n42 & 51476.1268 & 0.0009 & 0.0164 & 121 \\\\\n43 & 51476.2217 & 0.0005 & 0.0178 & 185 \\\\\n44 & 51476.3169 & 0.0008 & 0.0195 & 121 \\\\\n53 & 51477.1493 & 0.0005 & 0.0107 & 187 \\\\\n54 & 51477.2421 & 0.0005 & 0.0101 & 187 \\\\\n86 & 51480.2181 & 0.0031 & $-$0.0046 & 181 \\\\\n87 & 51480.3092 & 0.0023 & $-$0.0070 & 138 \\\\\n97 & 51481.2400 & 0.0034 & $-$0.0108 & 143 \\\\\n107 & 51482.1691 & 0.0023 & $-$0.0162 & 184 \\\\\n108 & 51482.2663 & 0.0026 & $-$0.0125 & 188 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451472.1852 + 0.093459 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GX Cas (2006).}\\label{tab:gxcasoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54069.0790 & 0.0049 & $-$0.0240 & 66 \\\\\n20 & 54071.0076 & 0.0006 & 0.0266 & 78 \\\\\n52 & 54073.9927 & 0.0004 & 0.0068 & 99 \\\\\n53 & 54074.0917 & 0.0010 & 0.0119 & 72 \\\\\n63 & 54075.0165 & 0.0009 & $-$0.0023 & 130 \\\\\n64 & 54075.1092 & 0.0009 & $-$0.0035 & 136 \\\\\n74 & 54076.0362 & 0.0012 & $-$0.0155 & 129 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 54069.1030 + 0.093902 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{HT Cassiopeiae}\\label{obj:htcas}\n\n The only superoutburst observed for superhumps was in 1985\n\\citep{zha86htcas}, who reported $P_{\\rm SH}$ of 0.076077 d without\ngiving details. Although this observations were based on only two\nnights, we extracted the observations from the published light curves\nby referring to published times of eclipses and obtained times of\nsuperhump maxima (table \\ref{tab:htcasoc1985}). Since the determination\nof the maximum at $E=0$ was affected by the lack of observations before\nthe maximum, we calculated the period by using two remaining maxima.\nThe nominal $P_{\\rm SH}$ was 0.07592(2) d, giving a slightly smaller\n$\\epsilon$ of 3.0 \\% than in \\citet{zha86htcas}.\n\n\\begin{table}\n\\caption{Superhump maxima of HT Cas (1985).}\\label{tab:htcasoc1985}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ \\\\\n\\hline\n0 & 46084.5704 & 0.0004 & $-$0.0069 \\\\\n1 & 46084.6612 & 0.0001 & 0.0074 \\\\\n14 & 46085.6482 & 0.0001 & $-$0.0005 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2446084.5773 + 0.076529 E$.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{KP Cassiopeiae}\\label{obj:kpcas}\n\n Little had been known about KP Cas before the detection of a bright\noutburst by Y. Sano (vsnet-alert 10629). The outburst soon turned\nout to be a superoutburst. The mean superhump period with the PDM\nmethod was 0.085283(12) d (figure \\ref{fig:kpcasshpdm}).\nThe times of superhump maxima are listed\nin table \\ref{tab:kpcasoc2008}. The outburst was apparently detected\nduring the middle-to-late stage, and a clear transition of the superhump\nperiod (stage B to C) was detected around $E = 15$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig64.eps}\n \\end{center}\n \\caption{Superhumps in KP Cas (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:kpcasshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of KP Cas (2008).}\\label{tab:kpcasoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54767.0256 & 0.0003 & $-$0.0020 & 130 \\\\\n1 & 54767.1100 & 0.0004 & $-$0.0029 & 133 \\\\\n3 & 54767.2827 & 0.0005 & $-$0.0008 & 71 \\\\\n4 & 54767.3600 & 0.0014 & $-$0.0087 & 139 \\\\\n5 & 54767.4551 & 0.0014 & 0.0011 & 183 \\\\\n6 & 54767.5440 & 0.0012 & 0.0047 & 136 \\\\\n8 & 54767.7096 & 0.0005 & $-$0.0002 & 37 \\\\\n9 & 54767.7945 & 0.0005 & $-$0.0006 & 41 \\\\\n10 & 54767.8798 & 0.0005 & $-$0.0005 & 43 \\\\\n11 & 54767.9668 & 0.0006 & 0.0011 & 123 \\\\\n12 & 54768.0512 & 0.0006 & 0.0003 & 179 \\\\\n14 & 54768.2228 & 0.0011 & 0.0014 & 137 \\\\\n15 & 54768.3094 & 0.0004 & 0.0027 & 89 \\\\\n16 & 54768.3930 & 0.0005 & 0.0010 & 120 \\\\\n17 & 54768.4785 & 0.0002 & 0.0013 & 259 \\\\\n18 & 54768.5623 & 0.0003 & $-$0.0003 & 184 \\\\\n19 & 54768.6481 & 0.0025 & 0.0003 & 24 \\\\\n23 & 54768.9903 & 0.0007 & 0.0014 & 85 \\\\\n24 & 54769.0774 & 0.0014 & 0.0032 & 54 \\\\\n27 & 54769.3304 & 0.0003 & 0.0004 & 174 \\\\\n31 & 54769.6712 & 0.0005 & 0.0001 & 41 \\\\\n32 & 54769.7581 & 0.0005 & 0.0018 & 42 \\\\\n33 & 54769.8435 & 0.0005 & 0.0019 & 41 \\\\\n34 & 54769.9293 & 0.0008 & 0.0024 & 153 \\\\\n35 & 54770.0107 & 0.0008 & $-$0.0015 & 164 \\\\\n36 & 54770.0967 & 0.0006 & $-$0.0008 & 165 \\\\\n37 & 54770.1849 & 0.0013 & 0.0022 & 109 \\\\\n39 & 54770.3527 & 0.0004 & $-$0.0005 & 474 \\\\\n40 & 54770.4389 & 0.0004 & 0.0004 & 374 \\\\\n41 & 54770.5233 & 0.0002 & $-$0.0005 & 271 \\\\\n42 & 54770.6073 & 0.0004 & $-$0.0018 & 97 \\\\\n43 & 54770.6938 & 0.0004 & $-$0.0006 & 37 \\\\\n44 & 54770.7784 & 0.0005 & $-$0.0012 & 41 \\\\\n45 & 54770.8638 & 0.0005 & $-$0.0011 & 42 \\\\\n46 & 54770.9488 & 0.0009 & $-$0.0014 & 29 \\\\\n50 & 54771.2907 & 0.0004 & $-$0.0005 & 223 \\\\\n51 & 54771.3755 & 0.0005 & $-$0.0010 & 223 \\\\\n52 & 54771.4594 & 0.0004 & $-$0.0024 & 259 \\\\\n53 & 54771.5484 & 0.0038 & 0.0013 & 265 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454767.0276 + 0.085273 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V452 Cassiopeiae}\\label{obj:v452cas}\n\n In addition to \\citet{she08v452cas}, we analyzed the 1999 superoutburst\nand the AAVSO data during the 2008 December superoutburst (tables\n\\ref{tab:v452casoc1999}, \\ref{tab:v452casoc2008}).\nThe 1999 observation covered the middle-to-late stage of the superoutburst.\nA PDM analysis yielded a mean $P_{\\rm SH}$ of 0.08856(6) d, which\nprobably corresponds to the stage C superhumps.\nThe 2008 observations recorded the early part of this superoutburst\nand yielded a slightly shorter $P_{\\rm SH}$ of 0.08932(3) d than\nin \\citet{she08v452cas}. A combined $O-C$ diagram is shown in\nfigure \\ref{fig:v452cascomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig65.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V452 Cas between different\n superoutbursts. A period of 0.08880 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the superoutburst\n were used.\n }\n \\label{fig:v452cascomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V452 Cas (1999).}\\label{tab:v452casoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51496.2273 & 0.0043 & $-$0.0067 & 153 \\\\\n1 & 51496.3314 & 0.0072 & 0.0088 & 121 \\\\\n46 & 51500.2964 & 0.0026 & $-$0.0100 & 17 \\\\\n57 & 51501.2882 & 0.0061 & 0.0079 & 54 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451496.2340 + 0.088532 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V452 Cas (2008).}\\label{tab:v452casoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54805.3812 & 0.0005 & 0.0000 & 76 \\\\\n33 & 54808.3282 & 0.0009 & $-$0.0005 & 100 \\\\\n34 & 54808.4186 & 0.0012 & 0.0005 & 74 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454805.3812 + 0.089319 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V359 Centauri}\\label{obj:v359cen}\n\n We reanalyzed the data of the 2002 superoutburst\n\\citep{kat02v359cen}. The result (table \\ref{tab:v359cenoc2002})\ngenerally confirmed the conclusion\nin \\citet{kat02v359cen}: the global $P_{\\rm dot}$ was\n$-16.3(1.7) \\times 10^{-5}$ while $P_{\\rm dot}$ for $E > 22$\nwas $-9.4(3.0) \\times 10^{-5}$ (see discussion in \\cite{kat02v359cen}\nfor a selection of the interval). We adopted the latter as being\nthe representative $P_{\\rm dot}$ for this object.\n\n\\begin{table}\n\\caption{Superhump maxima of V359 Cen (2002).}\\label{tab:v359cenoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52423.9416 & 0.0004 & $-$0.0137 & 106 \\\\\n1 & 52424.0235 & 0.0003 & $-$0.0129 & 130 \\\\\n23 & 52425.8215 & 0.0004 & 0.0025 & 109 \\\\\n35 & 52426.7972 & 0.0007 & 0.0058 & 94 \\\\\n36 & 52426.8804 & 0.0006 & 0.0080 & 195 \\\\\n37 & 52426.9619 & 0.0009 & 0.0084 & 71 \\\\\n49 & 52427.9337 & 0.0004 & 0.0078 & 166 \\\\\n50 & 52428.0149 & 0.0009 & 0.0080 & 107 \\\\\n62 & 52428.9865 & 0.0004 & 0.0072 & 86 \\\\\n84 & 52430.7602 & 0.0007 & $-$0.0018 & 47 \\\\\n85 & 52430.8391 & 0.0018 & $-$0.0040 & 11 \\\\\n102 & 52432.2163 & 0.0008 & $-$0.0043 & 91 \\\\\n103 & 52432.2971 & 0.0009 & $-$0.0046 & 92 \\\\\n104 & 52432.3762 & 0.0012 & $-$0.0065 & 92 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452423.9553 + 0.081033 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V485 Centauri}\\label{obj:v485cen}\n\n The period evolution of this ultrashort-$P_{\\rm orb}$ SU UMa-type\ndwarf nova was studied by \\citet{ole97v485cen}, yielding a positive\n$P_{\\rm dot}$ (the value has been corrected in this paper, see\nsubsection \\ref{sec:pdotb}).\n\nWe observed the 2001 superoutburst (table \\ref{tab:v485cenoc2001}).\nAlthough the data were rather sparse, there was again no indication of\nan exceptionally large $P_{\\rm dot}$.\n\nWe also examined the 2004 superoutburst using the AAVSO data\n(table \\ref{tab:v485cenoc2004}). The data clearly showed a stage B--C\ntransition around $E=166$. The $P_{\\rm dot}$ during the stage B was\n$+3.1(0.9) \\times 10^{-5}$, strengthening our interpretation that\nthis object has an usual $P_{\\rm dot}$. The existence of the stage C\nhas been demonstrated for this class of objects first time in this\nsuperoutburst.\n\nA comparison of $O-C$ diagrams between different superoutbursts\nis presented in figure \\ref{fig:v485cencomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig66.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V485 Cen between different\n superoutbursts. A period of 0.04212 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the superoutburst\n were used.\n }\n \\label{fig:v485cencomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V485 Cen (2001).}\\label{tab:v485cenoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51999.8526 & 0.0004 & $-$0.0019 & 37 \\\\\n1 & 51999.8954 & 0.0004 & $-$0.0012 & 39 \\\\\n2 & 51999.9380 & 0.0004 & $-$0.0006 & 40 \\\\\n5 & 52000.0668 & 0.0027 & 0.0020 & 79 \\\\\n6 & 52000.1049 & 0.0014 & $-$0.0019 & 82 \\\\\n7 & 52000.1464 & 0.0016 & $-$0.0024 & 82 \\\\\n8 & 52000.1976 & 0.0034 & 0.0068 & 65 \\\\\n9 & 52000.2314 & 0.0025 & $-$0.0016 & 53 \\\\\n30 & 52001.1127 & 0.0029 & $-$0.0033 & 75 \\\\\n32 & 52001.2030 & 0.0030 & 0.0029 & 68 \\\\\n53 & 52002.0686 & 0.0058 & $-$0.0146 & 60 \\\\\n54 & 52002.1269 & 0.0048 & 0.0018 & 76 \\\\\n55 & 52002.1729 & 0.0027 & 0.0056 & 71 \\\\\n73 & 52002.9267 & 0.0007 & 0.0025 & 38 \\\\\n74 & 52002.9696 & 0.0007 & 0.0034 & 39 \\\\\n75 & 52003.0099 & 0.0005 & 0.0017 & 40 \\\\\n76 & 52003.0509 & 0.0017 & 0.0006 & 21 \\\\\n77 & 52003.0952 & 0.0036 & 0.0029 & 76 \\\\\n78 & 52003.1359 & 0.0022 & 0.0016 & 71 \\\\\n79 & 52003.1789 & 0.0035 & 0.0025 & 44 \\\\\n80 & 52003.2139 & 0.0037 & $-$0.0046 & 82 \\\\\n100 & 52004.0632 & 0.0055 & 0.0037 & 81 \\\\\n101 & 52004.1037 & 0.0036 & 0.0022 & 82 \\\\\n102 & 52004.1467 & 0.0056 & 0.0031 & 81 \\\\\n103 & 52004.1813 & 0.0028 & $-$0.0043 & 81 \\\\\n125 & 52005.1122 & 0.0022 & 0.0014 & 78 \\\\\n127 & 52005.1864 & 0.0040 & $-$0.0085 & 74 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451999.8544 + 0.042050 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V485 Cen (2004).}\\label{tab:v485cenoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53140.0437 & 0.0003 & 0.0000 & 74 \\\\\n1 & 53140.0853 & 0.0002 & $-$0.0006 & 66 \\\\\n2 & 53140.1271 & 0.0003 & $-$0.0009 & 74 \\\\\n3 & 53140.1719 & 0.0004 & 0.0018 & 39 \\\\\n98 & 53144.1718 & 0.0007 & $-$0.0024 & 42 \\\\\n166 & 53147.0436 & 0.0012 & 0.0034 & 37 \\\\\n167 & 53147.0857 & 0.0015 & 0.0033 & 38 \\\\\n189 & 53148.0081 & 0.0008 & $-$0.0016 & 33 \\\\\n190 & 53148.0487 & 0.0021 & $-$0.0031 & 41 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453140.0437 + 0.042148 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1040 Centauri}\\label{obj:v1040cen}\n\n V1040 Cen (=RX J1155.4$-$5641) is an ROSAT-selected CV\n\\citep{mot98ROSATCV}. \\citet{pat03suumas} reported a $P_{\\rm SH}$\nof 0.06215(10) d for the 2002 superoutburst. We analyzed the same\nsuperoutburst using the available data. The times of superhump maxima\nare listed in table \\ref{tab:v1040cenoc2002}. Except $50 \\le E \\le 54$,\nthe overall $O-C$ diagram showed typical stage A--C transitions.\nThe epochs of $50 \\le E \\le 54$ were affected by strong variation\nin the superhump profile (broad maxima), which may be due to overlapping\norbital signals. Disregarding these epochs, we obtained a strongly\npositive $P_{\\rm dot}$ of $+27.1(2.2) \\times 10^{-5}$\n($17 \\le E \\le 86$). Other parameters are listed in table\n\\ref{tab:perlist}. The behavior is somewhat reminiscent to ER UMa\nstars (subsection \\ref{sec:erumastars}). A further analysis and\nobservations might shed light to further understanding period variations\nand the evolution of stage C superhumps in this object and ER UMa stars.\n\n We used BJD 2452383--2452402 (post-outburst\nrebrightening and subsequent phase) and obtained a refined photometric\nperiod of 0.060296(8) d, which has been attributed to $P_{\\rm orb}$\n\\citep{pat03suumas}. No strong superhump signals were evident during\nthis stage. This period, however, was not dominant during the quiescence\nin 2008 (BJD 2454547--2454574). The exact identification of $P_{\\rm orb}$\nshould await a spectroscopic study.\n\n\\begin{table}\n\\caption{Superhump maxima of V1040 Cen (2002).}\\label{tab:v1040cenoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52366.2446 & 0.0002 & 0.0006 & 93 \\\\\n1 & 52366.3075 & 0.0001 & 0.0013 & 92 \\\\\n2 & 52366.3688 & 0.0003 & 0.0004 & 93 \\\\\n3 & 52366.4303 & 0.0003 & $-$0.0002 & 93 \\\\\n4 & 52366.4925 & 0.0003 & $-$0.0002 & 93 \\\\\n5 & 52366.5560 & 0.0003 & 0.0012 & 93 \\\\\n6 & 52366.6173 & 0.0003 & 0.0003 & 93 \\\\\n17 & 52367.3057 & 0.0005 & 0.0051 & 131 \\\\\n18 & 52367.3668 & 0.0003 & 0.0041 & 165 \\\\\n19 & 52367.4287 & 0.0003 & 0.0038 & 161 \\\\\n20 & 52367.4882 & 0.0004 & 0.0012 & 116 \\\\\n22 & 52367.6126 & 0.0004 & 0.0013 & 164 \\\\\n32 & 52368.2284 & 0.0002 & $-$0.0045 & 160 \\\\\n33 & 52368.2919 & 0.0002 & $-$0.0031 & 154 \\\\\n34 & 52368.3528 & 0.0002 & $-$0.0044 & 163 \\\\\n47 & 52369.1609 & 0.0005 & $-$0.0042 & 187 \\\\\n48 & 52369.2231 & 0.0003 & $-$0.0041 & 338 \\\\\n49 & 52369.2840 & 0.0003 & $-$0.0054 & 346 \\\\\n50 & 52369.3512 & 0.0005 & $-$0.0003 & 351 \\\\\n51 & 52369.4163 & 0.0009 & 0.0026 & 164 \\\\\n52 & 52369.4793 & 0.0006 & 0.0034 & 165 \\\\\n53 & 52369.5359 & 0.0006 & $-$0.0022 & 164 \\\\\n54 & 52369.6009 & 0.0009 & 0.0007 & 165 \\\\\n61 & 52370.0311 & 0.0004 & $-$0.0041 & 154 \\\\\n62 & 52370.0948 & 0.0003 & $-$0.0025 & 154 \\\\\n63 & 52370.1570 & 0.0004 & $-$0.0025 & 153 \\\\\n64 & 52370.2191 & 0.0004 & $-$0.0026 & 238 \\\\\n65 & 52370.2834 & 0.0004 & $-$0.0005 & 246 \\\\\n66 & 52370.3437 & 0.0004 & $-$0.0023 & 234 \\\\\n67 & 52370.4058 & 0.0006 & $-$0.0024 & 93 \\\\\n68 & 52370.4657 & 0.0009 & $-$0.0046 & 93 \\\\\n69 & 52370.5342 & 0.0009 & 0.0018 & 93 \\\\\n70 & 52370.5928 & 0.0007 & $-$0.0018 & 92 \\\\\n78 & 52371.0964 & 0.0005 & 0.0046 & 112 \\\\\n79 & 52371.1568 & 0.0004 & 0.0028 & 104 \\\\\n83 & 52371.4064 & 0.0008 & 0.0039 & 46 \\\\\n84 & 52371.4716 & 0.0006 & 0.0069 & 93 \\\\\n85 & 52371.5304 & 0.0004 & 0.0036 & 89 \\\\\n86 & 52371.5957 & 0.0004 & 0.0067 & 47 \\\\\n101 & 52372.5226 & 0.0008 & 0.0013 & 93 \\\\\n102 & 52372.5812 & 0.0006 & $-$0.0022 & 93 \\\\\n103 & 52372.6424 & 0.0014 & $-$0.0032 & 67 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452366.2440 + 0.062151 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{WX Ceti}\\label{sec:wxcet}\\label{obj:wxcet}\n\n We reanalyzed the 1998 data in \\citet{kat01wxcet} combined with the AAVSO\ndata and obtained refined times of maxima (table \\ref{tab:wxcetoc1998}).\nSeveral newly determined maxima are also included.\nThe new $O-C$ diagram basically confirms the finding in \\citet{kat01wxcet},\nbut now clearly shows three stages of A--C.\nThe timings of ``late superhumps'' in \\citet{kat01wxcet} were\nsomewhat contaminated by the incorrect phase identification in the\nstage C. We obtained $P_{\\rm dot}$ = $+6.4(1.0) \\times 10^{-5}$ for the\nstage B ($15 \\le E \\le 157$).\n\n We analyzed the 2001 superoutburst after combining our data and\nthose in \\citet{ste07wxcet}. The resultant times of maxima are\nlisted in table \\ref{tab:wxcetoc2001}. The observation well covered\nthe middle part of the superoutburst and yielded\n$P_{\\rm dot}$ = $+7.5(1.1) \\times 10^{-5}$.\n\n The 2004 observation (table \\ref{tab:wxcetoc2004}) also covered\nthe stages A--C. The $P_{\\rm dot}$ of the stage B was\n$+5.5(1.8) \\times 10^{-5}$ ($E \\le 137$).\n\n We also analyzed the data for the 1989 superoutburst\n\\citep{odo91wzsge} after extracting the data from the scanned figure.\nAlthough systematic errors may be significantly larger than the errors\ngiven in the table, we could extract times of superhump maxima\n(table \\ref{tab:wxcetoc1989}). The $O-C$ diagram clearly exhibits\nstages A--C. The $P_{\\rm dot}$ of the stage B was\n$+10.3(1.4) \\times 10^{-5}$ ($33 \\le E \\le 185$).\nThe difficulty in determining the period in \\citet{odo91wzsge} was\nprobably a result from this strong period variation.\n\n In summary, all observed superoutbursts of WX Cet showed a similar\npattern of $O-C$ and $P_{\\rm dot}$ was always positive in the\nmiddle of the plateau phase (figure \\ref{fig:wxcetcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig67.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of WX Cet between different\n superoutbursts. A period of 0.05955 d was used to draw this figure.\n Estimated cycle counts ($E$) after the appearance of the\n superhumps were used.\n }\n \\label{fig:wxcetcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of WX Cet (1998).}\\label{tab:wxcetoc1998}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51129.0492 & 0.0067 & $-$0.0100 & 114 \\\\\n5 & 51129.3533 & 0.0016 & $-$0.0034 & 35 \\\\\n6 & 51129.4112 & 0.0009 & $-$0.0050 & 34 \\\\\n15 & 51129.9537 & 0.0005 & 0.0020 & 138 \\\\\n16 & 51130.0153 & 0.0005 & 0.0041 & 128 \\\\\n17 & 51130.0743 & 0.0006 & 0.0037 & 85 \\\\\n18 & 51130.1364 & 0.0006 & 0.0062 & 118 \\\\\n19 & 51130.1919 & 0.0023 & 0.0022 & 22 \\\\\n33 & 51131.0254 & 0.0005 & 0.0028 & 184 \\\\\n34 & 51131.0836 & 0.0006 & 0.0015 & 87 \\\\\n36 & 51131.2074 & 0.0062 & 0.0063 & 29 \\\\\n48 & 51131.9130 & 0.0011 & $-$0.0021 & 73 \\\\\n49 & 51131.9730 & 0.0004 & $-$0.0016 & 227 \\\\\n50 & 51132.0329 & 0.0004 & $-$0.0011 & 181 \\\\\n51 & 51132.0915 & 0.0009 & $-$0.0021 & 69 \\\\\n52 & 51132.1483 & 0.0014 & $-$0.0047 & 80 \\\\\n65 & 51132.9243 & 0.0010 & $-$0.0022 & 149 \\\\\n66 & 51132.9806 & 0.0005 & $-$0.0054 & 259 \\\\\n67 & 51133.0390 & 0.0014 & $-$0.0065 & 193 \\\\\n68 & 51133.0999 & 0.0023 & $-$0.0051 & 63 \\\\\n69 & 51133.1603 & 0.0017 & $-$0.0042 & 87 \\\\\n101 & 51135.0619 & 0.0008 & $-$0.0066 & 112 \\\\\n102 & 51135.1238 & 0.0017 & $-$0.0041 & 141 \\\\\n103 & 51135.1791 & 0.0012 & $-$0.0083 & 115 \\\\\n115 & 51135.9051 & 0.0008 & 0.0037 & 116 \\\\\n116 & 51135.9652 & 0.0010 & 0.0042 & 110 \\\\\n117 & 51136.0238 & 0.0006 & 0.0034 & 112 \\\\\n118 & 51136.0814 & 0.0007 & 0.0015 & 142 \\\\\n119 & 51136.1407 & 0.0016 & 0.0013 & 140 \\\\\n120 & 51136.1994 & 0.0029 & 0.0004 & 91 \\\\\n122 & 51136.3256 & 0.0036 & 0.0077 & 34 \\\\\n123 & 51136.3784 & 0.0023 & 0.0010 & 24 \\\\\n133 & 51136.9784 & 0.0024 & 0.0061 & 40 \\\\\n134 & 51137.0315 & 0.0012 & $-$0.0004 & 169 \\\\\n135 & 51137.0928 & 0.0008 & 0.0014 & 246 \\\\\n136 & 51137.1522 & 0.0009 & 0.0013 & 204 \\\\\n138 & 51137.2770 & 0.0013 & 0.0072 & 24 \\\\\n139 & 51137.3346 & 0.0038 & 0.0052 & 35 \\\\\n140 & 51137.3918 & 0.0015 & 0.0029 & 31 \\\\\n149 & 51137.9314 & 0.0027 & 0.0071 & 94 \\\\\n150 & 51137.9905 & 0.0011 & 0.0067 & 110 \\\\\n151 & 51138.0484 & 0.0040 & 0.0051 & 78 \\\\\n155 & 51138.2930 & 0.0024 & 0.0117 & 34 \\\\\n156 & 51138.3461 & 0.0009 & 0.0053 & 34 \\\\\n157 & 51138.4034 & 0.0027 & 0.0031 & 30 \\\\\n184 & 51139.9982 & 0.0071 & $-$0.0086 & 50 \\\\\n185 & 51140.0671 & 0.0007 & 0.0009 & 117 \\\\\n186 & 51140.1228 & 0.0010 & $-$0.0029 & 118 \\\\\n187 & 51140.1787 & 0.0052 & $-$0.0065 & 88 \\\\\n202 & 51141.0700 & 0.0045 & $-$0.0077 & 109 \\\\\n203 & 51141.1322 & 0.0021 & $-$0.0050 & 82 \\\\\n220 & 51142.1362 & 0.0026 & $-$0.0124 & 119 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451129.0592 + 0.059498 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WX Cet (2001).}\\label{tab:wxcetoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52092.2687 & 0.0019 & 0.0099 & 41 \\\\\n17 & 52093.2717 & 0.0027 & 0.0006 & 50 \\\\\n27 & 52093.8664 & 0.0002 & $-$0.0002 & 73 \\\\\n28 & 52093.9244 & 0.0002 & $-$0.0017 & 67 \\\\\n34 & 52094.2857 & 0.0019 & 0.0022 & 72 \\\\\n44 & 52094.8760 & 0.0002 & $-$0.0030 & 72 \\\\\n45 & 52094.9362 & 0.0003 & $-$0.0023 & 58 \\\\\n50 & 52095.2327 & 0.0026 & $-$0.0035 & 54 \\\\\n60 & 52095.8291 & 0.0005 & $-$0.0026 & 12 \\\\\n61 & 52095.8865 & 0.0010 & $-$0.0047 & 15 \\\\\n77 & 52096.8433 & 0.0010 & $-$0.0008 & 15 \\\\\n78 & 52096.9022 & 0.0004 & $-$0.0014 & 67 \\\\\n94 & 52097.8553 & 0.0006 & $-$0.0011 & 58 \\\\\n128 & 52099.8851 & 0.0004 & 0.0041 & 62 \\\\\n129 & 52099.9450 & 0.0004 & 0.0044 & 40 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452092.2588 + 0.059549 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WX Cet (2004).}\\label{tab:wxcetoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53347.9434 & 0.0001 & 0.0007 & 282 \\\\\n1 & 53348.0017 & 0.0002 & $-$0.0005 & 279 \\\\\n2 & 53348.0614 & 0.0002 & $-$0.0002 & 331 \\\\\n34 & 53349.9591 & 0.0002 & $-$0.0055 & 322 \\\\\n101 & 53353.9518 & 0.0007 & 0.0029 & 213 \\\\\n136 & 53356.0365 & 0.0004 & 0.0062 & 213 \\\\\n137 & 53356.1009 & 0.0006 & 0.0112 & 108 \\\\\n167 & 53357.8609 & 0.0038 & $-$0.0129 & 196 \\\\\n168 & 53357.9318 & 0.0008 & $-$0.0014 & 304 \\\\\n169 & 53357.9921 & 0.0020 & $-$0.0006 & 262 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453347.9427 + 0.0594678 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WX Cet (1989).}\\label{tab:wxcetoc1989}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ \\\\\n\\hline\n0 & 47683.6324 & 0.0009 & $-$0.0105 \\\\\n17 & 47684.6569 & 0.0024 & 0.0003 \\\\\n33 & 47685.6227 & 0.0006 & 0.0120 \\\\\n50 & 47686.6355 & 0.0006 & 0.0109 \\\\\n67 & 47687.6429 & 0.0003 & 0.0045 \\\\\n84 & 47688.6507 & 0.0003 & $-$0.0015 \\\\\n101 & 47689.6571 & 0.0006 & $-$0.0089 \\\\\n117 & 47690.6117 & 0.0003 & $-$0.0084 \\\\\n118 & 47690.6711 & 0.0012 & $-$0.0087 \\\\\n183 & 47694.5645 & 0.0015 & 0.0084 \\\\\n184 & 47694.6209 & 0.0039 & 0.0052 \\\\\n185 & 47694.6789 & 0.0009 & 0.0036 \\\\\n200 & 47695.5650 & 0.0021 & $-$0.0049 \\\\\n201 & 47695.6275 & 0.0012 & $-$0.0020 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2447683.6428 + 0.059635 E$.} \\\\\n \\multicolumn{4}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RX Chameleontis}\\label{obj:rxcha}\n\n \\citet{kat01rxcha} analyzed the 1998 outburst and reported a superhump\nperiod of 0.084 d. We observed the 2009 superoutburst during the early\nstage (table \\ref{tab:rxchaoc2009}). The $O-C$ diagram showed a typical\nstage A--B transition. The mean superhump period during the stage B\nwith the PDM method was 0.08492(2) d (figure \\ref{fig:rxchashpdm}),\nconfirming the long-$P_{\\rm SH}$ nature claimed in \\citet{kat01rxcha}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig68.eps}\n \\end{center}\n \\caption{Superhumps in RX Cha (2009). (Upper): PDM analysis excluding\n the early evolutionary stage before BJD 2454857.5).\n (Lower): Phase-averaged profile.}\n \\label{fig:rxchashpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of RX Cha (2009).}\\label{tab:rxchaoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54857.1087 & 0.0007 & $-$0.0077 & 106 \\\\\n10 & 54857.9797 & 0.0007 & 0.0087 & 76 \\\\\n22 & 54859.0007 & 0.0003 & 0.0043 & 140 \\\\\n34 & 54860.0165 & 0.0004 & $-$0.0054 & 110 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454857.1164 + 0.085455 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BZ Circini}\\label{obj:bzcir}\n\n BZ Cir is an X-ray selected CV (=1E 1449.7$-$6804:\n\\cite{gri87bzciriauc}; \\cite{her90XrayCVs}).\nThe first recorded outburst was detected by B. Monard in 2004 June\n(vsnet-alert 8194). The outburst soon turned out to be a superoutburst\n(vsnet-alert 8201). We analyzed this superoutburst.\nThe mean superhump period with the PDM method was 0.076422(5) d\n(figure \\ref{fig:bzcirshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:bzciroc2004}.\nWhile the global $P_{\\rm dot}$ corresponds to\n$-6.9(0.5) \\times 10^{-5}$, there was an apparent transition\nof periods around $E = 68$. The $P_{\\rm dot}$ of the\nmiddle segment ($13 \\le E \\le 68$) was $-0.5(3.8) \\times 10^{-5}$\n(cf. figure \\ref{fig:ocsamp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig69.eps}\n \\end{center}\n \\caption{Superhumps in BZ Cir (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:bzcirshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of BZ Cir (2004).}\\label{tab:bzciroc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53183.2842 & 0.0004 & $-$0.0102 & 86 \\\\\n13 & 53184.2835 & 0.0002 & $-$0.0044 & 142 \\\\\n14 & 53184.3612 & 0.0002 & $-$0.0031 & 172 \\\\\n15 & 53184.4375 & 0.0002 & $-$0.0033 & 163 \\\\\n16 & 53184.5156 & 0.0004 & $-$0.0016 & 114 \\\\\n26 & 53185.2797 & 0.0003 & $-$0.0017 & 173 \\\\\n27 & 53185.3597 & 0.0006 & 0.0019 & 83 \\\\\n42 & 53186.5081 & 0.0009 & 0.0040 & 92 \\\\\n43 & 53186.5809 & 0.0019 & 0.0003 & 75 \\\\\n53 & 53187.3473 & 0.0004 & 0.0025 & 155 \\\\\n54 & 53187.4272 & 0.0007 & 0.0060 & 137 \\\\\n66 & 53188.3453 & 0.0005 & 0.0070 & 155 \\\\\n67 & 53188.4219 & 0.0004 & 0.0072 & 171 \\\\\n68 & 53188.4986 & 0.0007 & 0.0075 & 108 \\\\\n94 & 53190.4820 & 0.0005 & 0.0039 & 172 \\\\\n132 & 53193.3791 & 0.0011 & $-$0.0030 & 145 \\\\\n145 & 53194.3683 & 0.0006 & $-$0.0074 & 166 \\\\\n146 & 53194.4465 & 0.0004 & $-$0.0056 & 167 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453183.2944 + 0.076422 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CG Canis Majoris}\\label{obj:cgcma}\n\n CG CMa was originally classified as a classical nova in 1934\n\\citep{due87novaatlas}. A new outburst in 1999 finally led to\na classification as a WZ Sge-type dwarf nova (\\cite{due99cgcma};\n\\cite{kat99cgcma}). We reanalyzed photometric data reported in\n\\citet{kat99cgcma}. The period around $\\sim$0.063 d reported in\n\\citet{kat99cgcma} appears viable, although the faintness of\nthe object and the existence of a close companion made the uncertainty\nlarge. We determined $O-C$'s based on this period selection\n(table \\ref{tab:cgcmaoc1999}). If this period is the true\nperiod, the $P_{\\rm dot}$ is almost zero at $+0.5(1.6) \\times 10^{-5}$.\nSince this variation was detected during the early stage of the\noutburst, this period likely refers to that of early superhumps,\nrather than superhumps suggested in \\citet{kat99cgcma}.\nOther candidate periods could not express observations well.\n\n\\begin{table}\n\\caption{Maxima of (Early) Superhumps in CG CMa (1999).}\\label{tab:cgcmaoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51232.1013 & 0.0077 & 0.0005 & 101 \\\\\n45 & 51234.9526 & 0.0036 & 0.0045 & 127 \\\\\n47 & 51235.0719 & 0.0042 & $-$0.0027 & 121 \\\\\n78 & 51237.0438 & 0.0048 & 0.0076 & 56 \\\\\n79 & 51237.0974 & 0.0036 & $-$0.0020 & 62 \\\\\n92 & 51237.9213 & 0.0130 & $-$0.0007 & 59 \\\\\n94 & 51238.0369 & 0.0066 & $-$0.0117 & 127 \\\\\n95 & 51238.1084 & 0.0058 & $-$0.0034 & 78 \\\\\n108 & 51238.9387 & 0.0054 & 0.0044 & 127 \\\\\n110 & 51239.0654 & 0.0036 & 0.0044 & 102 \\\\\n141 & 51241.0137 & 0.0039 & $-$0.0088 & 118 \\\\\n171 & 51242.9313 & 0.0123 & 0.0107 & 62 \\\\\n173 & 51243.0503 & 0.0036 & 0.0031 & 36 \\\\\n187 & 51243.9274 & 0.0049 & $-$0.0057 & 81 \\\\\n189 & 51244.0595 & 0.0053 & $-$0.0002 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451232.1007 + 0.063275 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{PU Canis Majoris}\\label{tab:pucma}\\label{obj:pucma}\n\n The SU UMa-type nature of PU CMa was pointed out by\n\\citet{kat03v877arakktelpucma}, but they were unable to uniquely\ndetermine the superhump period. Thanks to three superoutbursts\nin 2003, 2005 and 2008, we have been able to firmly establish the\nsuperhump period. The times of superhump maxima are summarized\nin tables \\ref{tab:pucmaoc2003}, \\ref{tab:pucmaoc2005} and\n\\ref{tab:pucmaoc2008}.\n\nThe 2003 superoutburst was observed during its later course\nand a clear transition from the stage B to C was observed.\nWe also included some of post-outburst hump maxima having the\nsame phase as in stage C superhumps. No clear phase shift,\nexpected for traditional ``late superhumps'',\nwas observed during and soon after the rapidly fading stage.\n\nThe 2005 and 2008 superoutbursts were observed during their earlier\nstages and the superhump period showed an increase during\nthe superoutburst plateau. The $P_{\\rm dot}$'s were\n$+11.4(1.8) \\times 10^{-5}$ and $+4.4(3.1) \\times 10^{-5}$,\nrespectively. The 2005 superoutburst showed a clear transition\nto the stage C (figure \\ref{fig:pucma2005oc};\n$P_2 =$ 0.05768(2) d, disregarding $E=196$ and $E=215$).\n\nThe 2008 superoutburst was preceded by a distinct\nprecursor (corresponding to $E \\le 17$), during which a longer\n$P_{\\rm SH}$ was observed (figure \\ref{fig:pucma2008oc}).\nThe fractional superhump excess\nwas 2.3 \\% (mean period) against the orbital period by\n\\citet{tho03kxaqlftcampucmav660herdmlyr}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig70.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps PU CMa (2005).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($E \\le 93$, thin curve)\n (Lower): Light curve. Large dots are our CCD observations and small\n dots are visual observation from the VSNET database.}\n \\label{fig:pucma2005oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig71.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps PU CMa (2008).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($16 \\le E \\le 121$, thin curve)\n (Lower): Light curve. Large dots are our CCD observations and small\n dots are visual observation from the VSNET database.}\n \\label{fig:pucma2008oc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of PU CMa (2003).}\\label{tab:pucmaoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52784.8969 & 0.0007 & $-$0.0104 & 248 \\\\\n23 & 52786.2337 & 0.0007 & $-$0.0005 & 187 \\\\\n40 & 52787.2190 & 0.0003 & 0.0041 & 116 \\\\\n49 & 52787.7365 & 0.0005 & 0.0024 & 127 \\\\\n51 & 52787.8539 & 0.0006 & 0.0045 & 215 \\\\\n57 & 52788.1995 & 0.0005 & 0.0040 & 131 \\\\\n69 & 52788.8885 & 0.0004 & 0.0007 & 356 \\\\\n74 & 52789.1770 & 0.0009 & 0.0007 & 92 \\\\\n86 & 52789.8705 & 0.0004 & 0.0020 & 232 \\\\\n92 & 52790.2129 & 0.0005 & $-$0.0017 & 132 \\\\\n109 & 52791.1955 & 0.0021 & 0.0002 & 59 \\\\\n144 & 52793.2083 & 0.0008 & $-$0.0060 & 34 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452784.9074 + 0.057688 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of PU CMa (2005).}\\label{tab:pucmaoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53401.6702 & 0.0002 & $-$0.0033 & 45 \\\\\n1 & 53401.7285 & 0.0002 & $-$0.0029 & 57 \\\\\n5 & 53401.9608 & 0.0004 & $-$0.0019 & 60 \\\\\n6 & 53402.0195 & 0.0006 & $-$0.0011 & 37 \\\\\n7 & 53402.0742 & 0.0004 & $-$0.0042 & 90 \\\\\n8 & 53402.1319 & 0.0003 & $-$0.0044 & 106 \\\\\n17 & 53402.6534 & 0.0003 & $-$0.0034 & 56 \\\\\n18 & 53402.7106 & 0.0003 & $-$0.0041 & 56 \\\\\n23 & 53403.0002 & 0.0004 & $-$0.0037 & 167 \\\\\n24 & 53403.0578 & 0.0004 & $-$0.0040 & 261 \\\\\n25 & 53403.1167 & 0.0004 & $-$0.0029 & 226 \\\\\n41 & 53404.0427 & 0.0003 & $-$0.0023 & 161 \\\\\n42 & 53404.1023 & 0.0003 & $-$0.0006 & 251 \\\\\n43 & 53404.1593 & 0.0008 & $-$0.0014 & 122 \\\\\n58 & 53405.0286 & 0.0006 & 0.0002 & 201 \\\\\n59 & 53405.0871 & 0.0004 & 0.0009 & 266 \\\\\n76 & 53406.0729 & 0.0008 & 0.0033 & 180 \\\\\n91 & 53406.9469 & 0.0022 & 0.0097 & 58 \\\\\n92 & 53407.0135 & 0.0008 & 0.0185 & 85 \\\\\n93 & 53407.0657 & 0.0010 & 0.0129 & 84 \\\\\n111 & 53408.1069 & 0.0015 & 0.0129 & 82 \\\\\n144 & 53410.0103 & 0.0012 & 0.0074 & 57 \\\\\n177 & 53411.9160 & 0.0016 & 0.0043 & 59 \\\\\n179 & 53412.0252 & 0.0011 & $-$0.0021 & 80 \\\\\n196 & 53413.0222 & 0.0016 & 0.0116 & 74 \\\\\n197 & 53413.0678 & 0.0010 & $-$0.0007 & 80 \\\\\n215 & 53414.0804 & 0.0012 & $-$0.0292 & 85 \\\\\n231 & 53415.0256 & 0.0020 & $-$0.0095 & 81 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453401.6735 + 0.057842 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of PU CMa (2008).}\\label{tab:pucmaoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54760.2505 & 0.0022 & $-$0.0132 & 154 \\\\\n1 & 54760.3128 & 0.0005 & $-$0.0090 & 255 \\\\\n16 & 54761.1995 & 0.0012 & 0.0073 & 86 \\\\\n17 & 54761.2523 & 0.0045 & 0.0020 & 58 \\\\\n31 & 54762.0691 & 0.0002 & 0.0064 & 214 \\\\\n66 & 54764.0955 & 0.0003 & 0.0018 & 177 \\\\\n67 & 54764.1538 & 0.0002 & 0.0021 & 166 \\\\\n121 & 54767.2920 & 0.0010 & 0.0068 & 110 \\\\\n137 & 54768.2144 & 0.0009 & 0.0007 & 56 \\\\\n171 & 54770.1899 & 0.0011 & 0.0032 & 37 \\\\\n257 & 54775.1667 & 0.0020 & $-$0.0104 & 38 \\\\\n258 & 54775.2358 & 0.0009 & 0.0007 & 59 \\\\\n259 & 54775.2948 & 0.0011 & 0.0016 & 59 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454760.2158 + 0.057977 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{YZ Cancri}\\label{obj:yzcnc}\n\n YZ Cnc is one of the oldest known SU UMa-type dwarf nova.\nThe superhump period of 0.09204 d \\citep{pat79SH} has long been\nwidely used. We, however, noticed that this period was incorrect.\nWe obtained the times of superhump maxima from the observations of\nthe 2007 February superoutburst (table \\ref{tab:yzcncoc}).\nThe period 0.09204 d could not fit the observation.\nA PDM analysis and superhump timing analysis yielded mean periods\nof 0.09042(4) d and 0.09031(5) d, respectively.\nThe corresponding fractional superhump excess was 4.0 \\%.\nThe $P_{\\rm dot}$ was $-5.1(4.7) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of YZ Cnc (2007).}\\label{tab:yzcncoc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54144.0639 & 0.0006 & $-$0.0017 & 112 \\\\\n1 & 54144.1553 & 0.0008 & $-$0.0006 & 110 \\\\\n22 & 54146.0535 & 0.0010 & 0.0012 & 104 \\\\\n23 & 54146.1421 & 0.0007 & $-$0.0005 & 110 \\\\\n34 & 54147.1341 & 0.0022 & $-$0.0019 & 81 \\\\\n35 & 54147.2321 & 0.0025 & 0.0058 & 49 \\\\\n65 & 54149.9319 & 0.0031 & $-$0.0036 & 77 \\\\\n66 & 54150.0270 & 0.0014 & 0.0012 & 113 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454144.0656 + 0.090307 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AK Cancri}\\label{obj:akcnc}\n\n \\citet{kat94akcnc} first detected superhumps in this object, and\nreported a period of 0.06735(5) d. We measured times of superhump maxima\nfrom these observations (table \\ref{tab:akcncoc1992}). The first\ntwo nights of the observation were likely taken during stage B,\nwhile the last night was likely during stage C.\n\\citet{men96akcnc} further observed the 1995 superoutburst and yielded\na mean period of 0.06749(1) d.\n\n We analyzed the 1999 superoutburst using the AAVSO data and\nthe 2003 superoutburst using the data by VSNET Collaboration.\nThe superhump maxima are given in table \\ref{tab:akcncoc1999} and\n\\ref{tab:akcncoc2003}. The 1999 superoutburst was preceded by\na precursor outburst 9 d before.\nThe $O-C$ diagram during the 2003 superoutburst (figure \\ref{fig:octrans})\nshowed a feature characteristic to a short-$P_{\\rm orb}$ SU UMa-type\ndwarf nova:\nfollowing the stage B with a positive $P_{\\rm dot}$, the period\nswitched to a shorter one (stage C) before the termination of\nthe plateau phase.\nThe $P_{\\rm dot}$ for the first interval ($E < 101$) was\n$+4.8(3.2) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig72.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of AK Cnc between different\n superoutbursts. A period of 0.06736 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the superoutburst\n were used.\n }\n \\label{fig:akcnccomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of AK Cnc (1992).}\\label{tab:akcncoc1992}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48639.1631 & 0.0018 & 0.0006 & 34 \\\\\n1 & 48639.2302 & 0.0039 & 0.0003 & 29 \\\\\n2 & 48639.2933 & 0.0010 & $-$0.0040 & 45 \\\\\n13 & 48640.0374 & 0.0074 & $-$0.0008 & 59 \\\\\n14 & 48640.1063 & 0.0017 & 0.0007 & 101 \\\\\n15 & 48640.1715 & 0.0016 & $-$0.0014 & 89 \\\\\n16 & 48640.2380 & 0.0014 & $-$0.0023 & 86 \\\\\n17 & 48640.3154 & 0.0110 & 0.0078 & 89 \\\\\n72 & 48644.0112 & 0.0019 & $-$0.0011 & 54 \\\\\n73 & 48644.0772 & 0.0037 & $-$0.0024 & 58 \\\\\n74 & 48644.1450 & 0.0019 & $-$0.0020 & 64 \\\\\n75 & 48644.2189 & 0.0043 & 0.0045 & 56 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448639.1625 + 0.067358 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AK Cnc (1999).}\\label{tab:akcncoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51261.4195 & 0.0009 & 0.0001 & 30 \\\\\n1 & 51261.4838 & 0.0011 & $-$0.0030 & 36 \\\\\n2 & 51261.5572 & 0.0019 & 0.0030 & 21 \\\\\n88 & 51267.3485 & 0.0015 & $-$0.0000 & 36 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451261.4195 + 0.067376 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AK Cnc (2003).}\\label{tab:akcncoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52722.3924 & 0.0004 & $-$0.0035 & 65 \\\\\n1 & 52722.4644 & 0.0005 & 0.0011 & 52 \\\\\n14 & 52723.3417 & 0.0008 & 0.0025 & 31 \\\\\n15 & 52723.4135 & 0.0008 & 0.0069 & 66 \\\\\n16 & 52723.4714 & 0.0007 & $-$0.0025 & 70 \\\\\n38 & 52724.9547 & 0.0015 & $-$0.0015 & 118 \\\\\n39 & 52725.0188 & 0.0015 & $-$0.0048 & 108 \\\\\n40 & 52725.0851 & 0.0029 & $-$0.0058 & 115 \\\\\n56 & 52726.1683 & 0.0015 & $-$0.0006 & 144 \\\\\n59 & 52726.3712 & 0.0004 & 0.0001 & 67 \\\\\n83 & 52727.9958 & 0.0025 & 0.0077 & 70 \\\\\n98 & 52729.0003 & 0.0017 & 0.0016 & 71 \\\\\n99 & 52729.0689 & 0.0015 & 0.0028 & 90 \\\\\n100 & 52729.1413 & 0.0050 & 0.0078 & 74 \\\\\n104 & 52729.4044 & 0.0018 & 0.0014 & 32 \\\\\n105 & 52729.4722 & 0.0015 & 0.0018 & 57 \\\\\n119 & 52730.4068 & 0.0014 & $-$0.0068 & 45 \\\\\n120 & 52730.4728 & 0.0020 & $-$0.0082 & 34 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452722.3959 + 0.067375 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CC Cancri}\\label{obj:cccnc}\n\n \\citet{kat97cccnc} first reported the detection of superhumps in this\nobject. \\citet{kat02cccnc} further reported the result of a more extensive\ncampaign in 2001, yielding a strongly negative\n$P_{\\rm dot}$ = $-10.2(1.3) \\times 10^{-5}$.\nBased on our new knowledge, this period derivative can be better understood\nto represent the rapid period decrease (stage A to B) during\nthe early stage of a superoutburst. We thereby reexamined the 2001 data\nand obtained the times of maxima (table \\ref{tab:cccncoc}).\nThe $O-C$ diagram can be interpreted\nas a combination of stage A evolution with a long superhump period ($E < 20$),\nand the stage B with a more stabilized superhump period.\nThe $P_{\\rm dot}$ of the latter interval was $-7.3(2.5) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of CC Cnc (2001).}\\label{tab:cccncoc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52226.3217 & 0.0039 & $-$0.0107 & 70 \\\\\n11 & 52227.1401 & 0.0029 & $-$0.0232 & 79 \\\\\n12 & 52227.2344 & 0.0015 & $-$0.0044 & 93 \\\\\n13 & 52227.3099 & 0.0030 & $-$0.0044 & 75 \\\\\n24 & 52228.1482 & 0.0008 & 0.0031 & 145 \\\\\n25 & 52228.2212 & 0.0011 & 0.0006 & 147 \\\\\n26 & 52228.3014 & 0.0013 & 0.0053 & 147 \\\\\n27 & 52228.3780 & 0.0012 & 0.0064 & 77 \\\\\n37 & 52229.1273 & 0.0030 & 0.0003 & 55 \\\\\n38 & 52229.2072 & 0.0007 & 0.0047 & 147 \\\\\n39 & 52229.2823 & 0.0009 & 0.0043 & 146 \\\\\n40 & 52229.3592 & 0.0020 & 0.0057 & 19 \\\\\n50 & 52230.1126 & 0.0034 & 0.0038 & 53 \\\\\n51 & 52230.1918 & 0.0010 & 0.0074 & 100 \\\\\n52 & 52230.2637 & 0.0013 & 0.0038 & 103 \\\\\n53 & 52230.3439 & 0.0020 & 0.0085 & 82 \\\\\n64 & 52231.1685 & 0.0017 & 0.0023 & 89 \\\\\n65 & 52231.2473 & 0.0028 & 0.0055 & 20 \\\\\n79 & 52232.3036 & 0.0014 & 0.0044 & 120 \\\\\n80 & 52232.3756 & 0.0013 & 0.0009 & 89 \\\\\n90 & 52233.1340 & 0.0015 & 0.0041 & 145 \\\\\n91 & 52233.2064 & 0.0017 & 0.0009 & 146 \\\\\n92 & 52233.2818 & 0.0020 & 0.0008 & 146 \\\\\n93 & 52233.3532 & 0.0010 & $-$0.0033 & 82 \\\\\n104 & 52234.1860 & 0.0025 & $-$0.0013 & 147 \\\\\n105 & 52234.2532 & 0.0013 & $-$0.0097 & 147 \\\\\n106 & 52234.3374 & 0.0016 & $-$0.0010 & 124 \\\\\n116 & 52235.0789 & 0.0069 & $-$0.0147 & 115 \\\\\n119 & 52235.3201 & 0.0017 & $-$0.0001 & 146 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452226.3324 + 0.075528 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AL Comae Berenices}\\label{obj:alcom}\n\n We have reanalyzed the data in \\citet{nog97alcom} of this well-known\nWZ Sge-type dwarf nova. The combined list of superhump maxima from\n\\citet{how96alcom}, \\citet{pyc95alcom} and \\citet{pat96alcom} is presented\nin table \\ref{tab:alcomoc1995}.\nThe $O-C$ diagram clearly showed the same characteristics to that of another\nWZ Sge-type dwarf nova, HV Vir. The $P_{\\rm dot}$ of the middle segment\n(stage B) was $+1.9(0.5) \\times 10^{-5}$ ($24 \\le E \\le 229$). This value\nsupersedes the published period derivative in \\citet{nog97alcom}.\n\n The refined times of superhump maxima during the 2001 superoutburst\n\\citep{ish02wzsgeletter} are listed in table \\ref{tab:alcomoc2001}.\nThe $P_{\\rm dot}$ during the stage B was\n$-0.2(0.8) \\times 10^{-5}$ ($28 \\le E \\le 222$).\nA comparison of the $O-C$ diagrams is shown in figure \\ref{fig:alcomcomp}.\n\n The object underwent another superoutburst in 2007 \\citep{uem08alcom}.\nThis behavior of this superoutburst was different from those in\n1995 and 2001 in that the object showed separate rebrightenings\n(type-B). Although the observations was incomplete due to the poor\nseasonal location, a weak periodicity of 0.05717(1) d was detected\nduring this rebrightening stage. Since the object showed $P_{\\rm SH}$\nduring the type-A superoutburst in 1995, we adopted this period\nas the $P_{\\rm SH}$ of the 2007 superoutburst in table \\ref{tab:perlist}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig73.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of AL Com Cnc between different\n superoutbursts. A period of 0.05728 d was used to draw this figure.\n Approximate cycle counts ($E$) after the appearance of the ordinary\n superhumps were used.\n }\n \\label{fig:alcomcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of AL Com (1995).}\\label{tab:alcomoc1995}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49823.5693 & -- & $-$0.0139 & R3 \\\\\n1 & 49823.6311 & -- & $-$0.0094 & R5 \\\\\n24 & 49824.9629 & 0.0007 & 0.0053 & 25 \\\\\n25 & 49825.0190 & 0.0007 & 0.0042 & 29 \\\\\n26 & 49825.0757 & 0.0008 & 0.0035 & 29 \\\\\n27 & 49825.1332 & 0.0014 & 0.0038 & 29 \\\\\n37 & 49825.7069 & -- & 0.0048 & R5 \\\\\n38 & 49825.7631 & -- & 0.0037 & R5 \\\\\n41 & 49825.9355 & -- & 0.0043 & R5 \\\\\n70 & 49827.5925 & -- & 0.0006 & R3 \\\\\n71 & 49827.6525 & -- & 0.0033 & R3 \\\\\n76 & 49827.9313 & -- & $-$0.0042 & R5 \\\\\n81 & 49828.2210 & 0.0005 & $-$0.0008 & 38 \\\\\n83 & 49828.3345 & -- & $-$0.0019 & R4 \\\\\n84 & 49828.3931 & -- & $-$0.0005 & R4 \\\\\n89 & 49828.6784 & -- & $-$0.0016 & R5 \\\\\n101 & 49829.3636 & -- & $-$0.0036 & R4 \\\\\n102 & 49829.4200 & -- & $-$0.0044 & R4 \\\\\n103 & 49829.4778 & -- & $-$0.0039 & R4 \\\\\n105 & 49829.5928 & -- & $-$0.0034 & R5 \\\\\n105 & 49829.5961 & -- & $-$0.0001 & R3 \\\\\n106 & 49829.6491 & -- & $-$0.0044 & R5 \\\\\n106 & 49829.6562 & -- & 0.0027 & R3 \\\\\n107 & 49829.7064 & -- & $-$0.0044 & R5 \\\\\n108 & 49829.7623 & -- & $-$0.0057 & R5 \\\\\n120 & 49830.4536 & -- & $-$0.0016 & R4 \\\\\n121 & 49830.5084 & -- & $-$0.0041 & R4 \\\\\n122 & 49830.5677 & -- & $-$0.0021 & R4 \\\\\n123 & 49830.6275 & -- & 0.0005 & R5 \\\\\n132 & 49831.1424 & 0.0004 & $-$0.0001 & 34 \\\\\n133 & 49831.2004 & 0.0009 & 0.0006 & 38 \\\\\n134 & 49831.2593 & 0.0011 & 0.0023 & 25 \\\\\n137 & 49831.4293 & -- & 0.0005 & R4 \\\\\n138 & 49831.4850 & -- & $-$0.0011 & R4 \\\\\n139 & 49831.5422 & -- & $-$0.0011 & R4 \\\\\n141 & 49831.6564 & -- & $-$0.0015 & R5 \\\\\n154 & 49832.3995 & -- & $-$0.0028 & R4 \\\\\n155 & 49832.4580 & -- & $-$0.0016 & R4 \\\\\n159 & 49832.6870 & -- & $-$0.0017 & R5 \\\\\n160 & 49832.7450 & -- & $-$0.0009 & R5 \\\\\n161 & 49832.8020 & -- & $-$0.0012 & R5 \\\\\n162 & 49832.8610 & -- & 0.0005 & R5 \\\\\n172 & 49833.4360 & -- & 0.0029 & R4 \\\\\n173 & 49833.4915 & -- & 0.0011 & R4 \\\\\n174 & 49833.5489 & -- & 0.0012 & R4 \\\\\n175 & 49833.6065 & -- & 0.0016 & R3 \\\\\n176 & 49833.6630 & -- & 0.0008 & R5 \\\\\n177 & 49833.7220 & -- & 0.0025 & R5 \\\\\n178 & 49833.7770 & -- & 0.0003 & R5 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449823.5832 + 0.057267 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N = Rn (n=3--4)$ are references} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} as in \\citet{nog97alcom}} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N = R5$ refers to \\citet{pat96alcom}} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of AL Com (1995) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n179 & 49833.8330 & -- & $-$0.0010 & R5 \\\\\n192 & 49834.5843 & -- & 0.0058 & R3 \\\\\n194 & 49834.7000 & -- & 0.0070 & R5 \\\\\n219 & 49836.1319 & 0.0040 & 0.0073 & 24 \\\\\n220 & 49836.1928 & 0.0017 & 0.0109 & 22 \\\\\n227 & 49836.5970 & -- & 0.0142 & R3 \\\\\n229 & 49836.7100 & -- & 0.0127 & R5 \\\\\n264 & 49838.7050 & -- & 0.0033 & R5 \\\\\n349 & 49843.5732 & -- & 0.0038 & R3 \\\\\n360 & 49844.1662 & 0.0089 & $-$0.0331 & 21 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AL Com (2001).}\\label{tab:alcomoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52056.3598 & 0.0012 & $-$0.0124 & 142 \\\\\n1 & 52056.4151 & 0.0053 & $-$0.0144 & 142 \\\\\n2 & 52056.4830 & 0.0030 & $-$0.0038 & 85 \\\\\n28 & 52057.9826 & 0.0032 & 0.0062 & 67 \\\\\n29 & 52058.0470 & 0.0043 & 0.0134 & 89 \\\\\n30 & 52058.0944 & 0.0042 & 0.0035 & 78 \\\\\n31 & 52058.1538 & 0.0019 & 0.0056 & 77 \\\\\n105 & 52062.3912 & 0.0007 & 0.0036 & 51 \\\\\n106 & 52062.4477 & 0.0015 & 0.0027 & 42 \\\\\n116 & 52063.0199 & 0.0015 & 0.0021 & 104 \\\\\n117 & 52063.0779 & 0.0062 & 0.0028 & 101 \\\\\n221 & 52069.0316 & 0.0065 & $-$0.0017 & 55 \\\\\n222 & 52069.0830 & 0.0066 & $-$0.0076 & 69 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452056.3722 + 0.057290 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{GO Comae Berenices}\\label{obj:gocom}\n\n We reanalyzed the data used in \\citet{ima05gocom}, combined with\nCrimea (Pav) data, and new data for the 2005 and 2006 superoutbursts\n(tables \\ref{tab:gocomoc2003}, \\ref{tab:gocomoc2005}, \\ref{tab:gocomoc2006}).\nThe values of $P_{\\rm dot}$ were\n$+15.5(2.3) \\times 10^{-5}$ (2003, $16 \\le E \\le 115$),\n$+6.9(1.5) \\times 10^{-5}$ (2005, $13 \\le E \\le 142$).\n$+4.6(3.4) \\times 10^{-5}$ (2006, excluding $E=64$ and $E=136$).\nThe 2008 superoutburst was also observed (table \\ref{tab:gocomoc2008}).\nA marginally significant $P_{\\rm dot}$ = $+16(11) \\times 10^{-5}$\nwas recorded. The new observations in 2003 indicated that the stage C\nsuperhumps persisted even during the post-superoutburst stage ($E \\ge 230$).\nThe $O-C$ diagrams did not drastically vary between different\nsuperoutbursts (figure \\ref{fig:gocomcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig74.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of GO Com between different\n superoutbursts. A period of 0.063059 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:gocomcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of GO Com (2003).}\\label{tab:gocomoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52794.1340 & 0.0025 & $-$0.0141 & 225 \\\\\n2 & 52794.2734 & 0.0022 & $-$0.0007 & 65 \\\\\n3 & 52794.3329 & 0.0060 & $-$0.0042 & 72 \\\\\n4 & 52794.3981 & 0.0035 & $-$0.0020 & 39 \\\\\n16 & 52795.1538 & 0.0008 & $-$0.0024 & 109 \\\\\n17 & 52795.2207 & 0.0003 & 0.0015 & 36 \\\\\n18 & 52795.2839 & 0.0003 & 0.0016 & 37 \\\\\n19 & 52795.3474 & 0.0004 & 0.0022 & 60 \\\\\n25 & 52795.7248 & 0.0004 & 0.0015 & 89 \\\\\n26 & 52795.7887 & 0.0004 & 0.0023 & 88 \\\\\n29 & 52795.9767 & 0.0025 & 0.0013 & 107 \\\\\n30 & 52796.0411 & 0.0004 & 0.0027 & 767 \\\\\n31 & 52796.1025 & 0.0004 & 0.0011 & 455 \\\\\n32 & 52796.1636 & 0.0006 & $-$0.0008 & 364 \\\\\n33 & 52796.2274 & 0.0036 & 0.0000 & 96 \\\\\n35 & 52796.3561 & 0.0009 & 0.0027 & 32 \\\\\n36 & 52796.4175 & 0.0004 & 0.0011 & 90 \\\\\n37 & 52796.4788 & 0.0005 & $-$0.0007 & 82 \\\\\n38 & 52796.5405 & 0.0009 & $-$0.0020 & 50 \\\\\n39 & 52796.6020 & 0.0009 & $-$0.0035 & 26 \\\\\n40 & 52796.6683 & 0.0004 & $-$0.0002 & 37 \\\\\n41 & 52796.7329 & 0.0005 & 0.0014 & 97 \\\\\n42 & 52796.7939 & 0.0005 & $-$0.0006 & 85 \\\\\n43 & 52796.8587 & 0.0012 & 0.0011 & 49 \\\\\n45 & 52796.9806 & 0.0010 & $-$0.0029 & 39 \\\\\n46 & 52797.0447 & 0.0004 & $-$0.0019 & 342 \\\\\n52 & 52797.4209 & 0.0007 & $-$0.0037 & 103 \\\\\n51 & 52797.3602 & 0.0012 & $-$0.0014 & 30 \\\\\n52 & 52797.4210 & 0.0007 & $-$0.0036 & 105 \\\\\n53 & 52797.4843 & 0.0006 & $-$0.0033 & 116 \\\\\n58 & 52797.7990 & 0.0015 & $-$0.0037 & 29 \\\\\n64 & 52798.1784 & 0.0012 & $-$0.0023 & 21 \\\\\n65 & 52798.2394 & 0.0006 & $-$0.0043 & 30 \\\\\n66 & 52798.3004 & 0.0022 & $-$0.0063 & 49 \\\\\n67 & 52798.3741 & 0.0016 & 0.0043 & 70 \\\\\n68 & 52798.4291 & 0.0005 & $-$0.0036 & 151 \\\\\n69 & 52798.4920 & 0.0008 & $-$0.0038 & 131 \\\\\n71 & 52798.6201 & 0.0024 & $-$0.0017 & 25 \\\\\n72 & 52798.6781 & 0.0008 & $-$0.0067 & 50 \\\\\n77 & 52798.9999 & 0.0017 & 0.0001 & 306 \\\\\n78 & 52799.0580 & 0.0010 & $-$0.0048 & 453 \\\\\n79 & 52799.1206 & 0.0011 & $-$0.0052 & 333 \\\\\n80 & 52799.1799 & 0.0010 & $-$0.0089 & 254 \\\\\n81 & 52799.2498 & 0.0008 & $-$0.0020 & 34 \\\\\n82 & 52799.3149 & 0.0012 & 0.0001 & 53 \\\\\n83 & 52799.3773 & 0.0017 & $-$0.0005 & 39 \\\\\n84 & 52799.4435 & 0.0012 & 0.0026 & 81 \\\\\n88 & 52799.7010 & 0.0033 & 0.0080 & 66 \\\\\n89 & 52799.7535 & 0.0014 & $-$0.0025 & 61 \\\\\n93 & 52800.0115 & 0.0017 & 0.0036 & 175 \\\\\n94 & 52800.0673 & 0.0015 & $-$0.0036 & 127 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452794.1481 + 0.063009 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GO Com (2003) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n96 & 52800.1955 & 0.0010 & $-$0.0015 & 35 \\\\\n97 & 52800.2598 & 0.0024 & $-$0.0002 & 35 \\\\\n98 & 52800.3248 & 0.0014 & 0.0018 & 60 \\\\\n99 & 52800.3957 & 0.0027 & 0.0097 & 67 \\\\\n103 & 52800.6394 & 0.0014 & 0.0013 & 41 \\\\\n104 & 52800.7035 & 0.0017 & 0.0024 & 28 \\\\\n112 & 52801.2166 & 0.0018 & 0.0114 & 34 \\\\\n113 & 52801.2716 & 0.0018 & 0.0034 & 24 \\\\\n114 & 52801.3487 & 0.0015 & 0.0175 & 36 \\\\\n115 & 52801.4228 & 0.0035 & 0.0286 & 33 \\\\\n126 & 52802.0906 & 0.0033 & 0.0033 & 71 \\\\\n129 & 52802.2740 & 0.0023 & $-$0.0023 & 16 \\\\\n130 & 52802.3448 & 0.0030 & 0.0055 & 35 \\\\\n131 & 52802.4033 & 0.0007 & 0.0009 & 132 \\\\\n132 & 52802.4652 & 0.0014 & $-$0.0001 & 120 \\\\\n133 & 52802.5308 & 0.0022 & 0.0025 & 40 \\\\\n137 & 52802.7781 & 0.0043 & $-$0.0023 & 29 \\\\\n144 & 52803.2372 & 0.0088 & 0.0157 & 34 \\\\\n145 & 52803.2896 & 0.0020 & 0.0051 & 35 \\\\\n159 & 52804.1538 & 0.0197 & $-$0.0128 & 24 \\\\\n160 & 52804.2217 & 0.0015 & $-$0.0079 & 34 \\\\\n161 & 52804.2981 & 0.0025 & 0.0055 & 59 \\\\\n162 & 52804.3609 & 0.0028 & 0.0053 & 38 \\\\\n163 & 52804.4152 & 0.0026 & $-$0.0035 & 77 \\\\\n164 & 52804.4807 & 0.0019 & $-$0.0009 & 70 \\\\\n175 & 52805.1889 & 0.0014 & 0.0142 & 34 \\\\\n176 & 52805.2322 & 0.0039 & $-$0.0055 & 33 \\\\\n182 & 52805.6271 & 0.0026 & 0.0112 & 41 \\\\\n191 & 52806.1898 & 0.0024 & 0.0069 & 24 \\\\\n192 & 52806.2464 & 0.0013 & 0.0005 & 34 \\\\\n230 & 52808.6277 & 0.0072 & $-$0.0126 & 26 \\\\\n231 & 52808.6935 & 0.0036 & $-$0.0098 & 40 \\\\\n241 & 52809.3289 & 0.0016 & $-$0.0044 & 13 \\\\\n262 & 52810.6366 & 0.0017 & $-$0.0200 & 24 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GO Com (2005).}\\label{tab:gocomoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53482.1748 & 0.0015 & 0.0023 & 144 \\\\\n1 & 53482.2360 & 0.0009 & 0.0005 & 277 \\\\\n3 & 53482.3643 & 0.0002 & 0.0027 & 57 \\\\\n4 & 53482.4279 & 0.0003 & 0.0032 & 69 \\\\\n5 & 53482.4901 & 0.0002 & 0.0024 & 68 \\\\\n6 & 53482.5543 & 0.0002 & 0.0035 & 70 \\\\\n13 & 53482.9982 & 0.0019 & 0.0059 & 232 \\\\\n14 & 53483.0564 & 0.0009 & 0.0011 & 417 \\\\\n15 & 53483.1179 & 0.0007 & $-$0.0004 & 381 \\\\\n16 & 53483.1825 & 0.0010 & 0.0011 & 411 \\\\\n17 & 53483.2461 & 0.0012 & 0.0016 & 386 \\\\\n19 & 53483.3720 & 0.0008 & 0.0014 & 64 \\\\\n20 & 53483.4356 & 0.0006 & 0.0019 & 66 \\\\\n21 & 53483.4979 & 0.0008 & 0.0011 & 66 \\\\\n22 & 53483.5615 & 0.0007 & 0.0018 & 68 \\\\\n23 & 53483.6210 & 0.0007 & $-$0.0019 & 63 \\\\\n29 & 53484.0023 & 0.0010 & 0.0011 & 306 \\\\\n30 & 53484.0627 & 0.0009 & $-$0.0016 & 464 \\\\\n31 & 53484.1238 & 0.0007 & $-$0.0036 & 442 \\\\\n32 & 53484.1878 & 0.0015 & $-$0.0026 & 399 \\\\\n33 & 53484.2498 & 0.0004 & $-$0.0037 & 191 \\\\\n76 & 53486.9574 & 0.0040 & $-$0.0076 & 22 \\\\\n77 & 53487.0285 & 0.0042 & 0.0004 & 105 \\\\\n78 & 53487.0857 & 0.0008 & $-$0.0055 & 367 \\\\\n79 & 53487.1462 & 0.0012 & $-$0.0080 & 371 \\\\\n80 & 53487.2133 & 0.0028 & $-$0.0040 & 215 \\\\\n92 & 53487.9662 & 0.0035 & $-$0.0079 & 226 \\\\\n93 & 53488.0376 & 0.0015 & 0.0005 & 209 \\\\\n95 & 53488.1550 & 0.0020 & $-$0.0082 & 344 \\\\\n96 & 53488.2118 & 0.0021 & $-$0.0145 & 348 \\\\\n98 & 53488.3628 & 0.0020 & 0.0104 & 26 \\\\\n108 & 53488.9852 & 0.0090 & 0.0022 & 155 \\\\\n110 & 53489.1060 & 0.0032 & $-$0.0031 & 249 \\\\\n111 & 53489.1716 & 0.0037 & $-$0.0006 & 121 \\\\\n124 & 53490.0037 & 0.0024 & 0.0118 & 259 \\\\\n125 & 53490.0540 & 0.0021 & $-$0.0010 & 297 \\\\\n126 & 53490.1167 & 0.0015 & $-$0.0014 & 266 \\\\\n127 & 53490.1849 & 0.0051 & 0.0038 & 191 \\\\\n142 & 53491.1351 & 0.0068 & 0.0080 & 198 \\\\\n172 & 53493.0180 & 0.0020 & $-$0.0008 & 161 \\\\\n174 & 53493.1468 & 0.0047 & 0.0018 & 139 \\\\\n175 & 53493.2117 & 0.0036 & 0.0036 & 118 \\\\\n190 & 53494.1563 & 0.0006 & 0.0024 & 312 \\\\\n191 & 53494.2166 & 0.0013 & $-$0.0004 & 221 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453482.1725 + 0.063060 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GO Com (2006).}\\label{tab:gocomoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54084.6993 & 0.0012 & 0.0097 & 13 \\\\\n16 & 54085.7033 & 0.0011 & 0.0044 & 18 \\\\\n57 & 54088.2841 & 0.0010 & $-$0.0008 & 93 \\\\\n58 & 54088.3422 & 0.0023 & $-$0.0058 & 90 \\\\\n63 & 54088.6737 & 0.0075 & 0.0104 & 7 \\\\\n64 & 54088.7004 & 0.0021 & $-$0.0260 & 9 \\\\\n111 & 54091.6906 & 0.0018 & $-$0.0002 & 12 \\\\\n120 & 54092.2646 & 0.0041 & 0.0060 & 129 \\\\\n121 & 54092.3180 & 0.0024 & $-$0.0036 & 89 \\\\\n135 & 54093.2006 & 0.0020 & $-$0.0040 & 111 \\\\\n136 & 54093.2359 & 0.0023 & $-$0.0318 & 84 \\\\\n136 & 54093.2880 & 0.0014 & 0.0203 & 123 \\\\\n137 & 54093.3381 & 0.0026 & 0.0073 & 214 \\\\\n152 & 54094.2792 & 0.0023 & 0.0023 & 72 \\\\\n153 & 54094.3519 & 0.0020 & 0.0119 & 87 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454084.6897 + 0.063074 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of GO Com (2008).}\\label{tab:gocomoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54631.0857 & 0.0006 & 0.0016 & 195 \\\\\n21 & 54632.4071 & 0.0005 & $-$0.0010 & 94 \\\\\n22 & 54632.4693 & 0.0009 & $-$0.0018 & 88 \\\\\n47 & 54634.0458 & 0.0043 & $-$0.0015 & 195 \\\\\n48 & 54634.1132 & 0.0031 & 0.0028 & 118 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454631.0842 + 0.063047 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V728 Coronae Australis}\\label{obj:v728cra}\n\n This object was selected during the identification project of\nNSV objects against ROSAT X-ray source (Kato, vsnet-id-rosat 11).\nThe proximity of the ROSAT position to the position of NSV 9923\nsuggested that the object may be a dwarf nova, as we have seen in\nBB Ari (subsection \\ref{sec:bbari}) and DT Oct \\citep{kat02gzcncnsv10934}.\nFollowing this suggestion, the object was monitored for outbursts.\nAn outburst detection was announced on 2003 June 28\n(R. Stubbings, vsnet-alert 7787).\nThe mean superhump period with the PDM method was 0.082200(13) d\n(figure \\ref{fig:v728crashpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:v728craoc}.\nAlthough the original observations\nincluded later stage at $E > 50$, the superhump signal became weaker\nand irregular, sometimes with multiple peaks. We therefore restricted\nour $O-C$ analysis to $E \\leq 50$. The situation may be similar to\nanother long-period system SS UMi \\citep{ole06ssumi}.\nThe resultant $P_{\\rm dot}$ was $-2.3(3.4) \\times 10^{-5}$.\nUpon announcement of this observation, the variable has been given\na General Catalogue of Variable Stars (GCVS) designation V728 CrA\n\\citep{NameList78}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig75.eps}\n \\end{center}\n \\caption{Superhumps in V728 CrA (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v728crashpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V728 CrA (2003).}\\label{tab:v728craoc}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52820.3295 & 0.0006 & 0.0006 & 36 \\\\\n1 & 52820.4098 & 0.0003 & $-$0.0014 & 47 \\\\\n2 & 52820.4925 & 0.0003 & $-$0.0011 & 47 \\\\\n12 & 52821.3170 & 0.0010 & $-$0.0004 & 24 \\\\\n13 & 52821.4015 & 0.0010 & 0.0017 & 41 \\\\\n14 & 52821.4828 & 0.0006 & 0.0007 & 37 \\\\\n15 & 52821.5651 & 0.0004 & 0.0005 & 43 \\\\\n23 & 52822.2260 & 0.0005 & 0.0024 & 48 \\\\\n24 & 52822.3031 & 0.0005 & $-$0.0028 & 41 \\\\\n25 & 52822.3891 & 0.0007 & 0.0008 & 47 \\\\\n26 & 52822.4706 & 0.0004 & $-$0.0001 & 46 \\\\\n27 & 52822.5525 & 0.0005 & $-$0.0005 & 43 \\\\\n35 & 52823.2133 & 0.0010 & 0.0012 & 41 \\\\\n36 & 52823.2926 & 0.0005 & $-$0.0018 & 44 \\\\\n37 & 52823.3784 & 0.0005 & 0.0016 & 48 \\\\\n38 & 52823.4586 & 0.0006 & $-$0.0006 & 48 \\\\\n39 & 52823.5405 & 0.0014 & $-$0.0012 & 44 \\\\\n44 & 52823.9541 & 0.0005 & 0.0006 & 87 \\\\\n45 & 52824.0362 & 0.0005 & 0.0003 & 93 \\\\\n46 & 52824.1181 & 0.0007 & $-$0.0001 & 60 \\\\\n48 & 52824.2860 & 0.0009 & 0.0030 & 46 \\\\\n49 & 52824.3637 & 0.0007 & $-$0.0017 & 45 \\\\\n50 & 52824.4460 & 0.0008 & $-$0.0017 & 45 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452820.3288 + 0.082378 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{VW Coronae Borealis}\\label{obj:vwcrb}\n\n \\citet{nog04vwcrb} presented an analysis of 2003 superoutburst and\nother recorded superoutbursts. We reanalyzed the 2003 data and yielded\nrefined times of superhump maxima (table \\ref{tab:vwcrboc2003}).\nThe resultant $O-C$ diagram basically confirmed the finding\nin \\citet{nog04vwcrb}, giving\n$P_{\\rm dot}$ = $+7.7(0.8) \\times 10^{-5}$ for $E \\le 142$.\n\n As discussed in \\citet{nog04vwcrb}, positive period derivatives are\nrare in systems with long superhump periods ($P_{\\rm SH} > 0.07$ d).\nThis phenomenon may be analogous to the one observed in\nTT Boo \\citep{ole04ttboo}, another SU UMa-type dwarf nova with\na relatively long superhump period and long superoutbursts\n(see also FQ Mon, subsection \\ref{sec:fqmon}).\nFor objects with positive $P_{\\rm dot}$, also see subsections RU Hor\n(\\ref{sec:ruhor}) and QY Per (\\ref{sec:qyper}).\n\n We also included times of superhump maxima during the 2001 and 2006\nsuperoutbursts (tables \\ref{tab:vwcrboc2001}, \\ref{tab:vwcrboc2006}).\nAlthough the superhump signal was present, we did not use the 2001\nsuperoutburst to determine $P_{\\rm dot}$ because of the lower quality of\nthe data. This outburst was only observed for its late stage, and the\nobserved superhumps were likely stage C superhumps.\nThe 2006 superoutburst was observed for its early part.\nThe derived $P_{\\rm SH}$ = 0.07268(6) d, shorter than the mean $P_1$\nfor the 2003 superoutburst, also supports that the $P_{\\rm SH}$ was\nshorter (i.e. with a probable positive $P_{\\rm dot}$) near the start of\nthis superoutburst.\n\n A combined $O-C$ diagram is presented in figure \\ref{fig:vwcrbcomp}.\nThe stage C behavior may have been different between the 2001 and 2003\nsuperoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig76.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of VW CrB between different\n superoutbursts. A period of 0.07290 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:vwcrbcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of VW CrB (2003).}\\label{tab:vwcrboc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52847.0644 & 0.0005 & 0.0103 & 134 \\\\\n1 & 52847.1345 & 0.0006 & 0.0075 & 135 \\\\\n2 & 52847.2053 & 0.0013 & 0.0053 & 122 \\\\\n32 & 52849.3870 & 0.0010 & $-$0.0014 & 51 \\\\\n33 & 52849.4583 & 0.0009 & $-$0.0029 & 52 \\\\\n46 & 52850.4021 & 0.0009 & $-$0.0074 & 48 \\\\\n68 & 52852.0094 & 0.0008 & $-$0.0050 & 260 \\\\\n69 & 52852.0788 & 0.0009 & $-$0.0084 & 168 \\\\\n73 & 52852.3747 & 0.0008 & $-$0.0043 & 47 \\\\\n74 & 52852.4429 & 0.0016 & $-$0.0090 & 51 \\\\\n102 & 52854.4933 & 0.0056 & $-$0.0011 & 51 \\\\\n114 & 52855.3711 & 0.0035 & 0.0014 & 32 \\\\\nc128 & 52856.3927 & 0.0024 & 0.0017 & 26 \\\\\n142 & 52857.4183 & 0.0039 & 0.0060 & 32 \\\\\n155 & 52858.3643 & 0.0069 & 0.0038 & 24 \\\\\n156 & 52858.4372 & 0.0018 & 0.0038 & 40 \\\\\n169 & 52859.3825 & 0.0050 & 0.0008 & 30 \\\\\n170 & 52859.4521 & 0.0042 & $-$0.0025 & 27 \\\\\n197 & 52861.4221 & 0.0059 & $-$0.0021 & 34 \\\\\n211 & 52862.4495 & 0.0099 & 0.0041 & 29 \\\\\n238 & 52864.4146 & 0.0072 & $-$0.0003 & 40 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452847.0541 + 0.072945 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VW CrB (2001).}\\label{tab:vwcrboc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52087.1633 & 0.0034 & $-$0.0025 & 89 \\\\\n69 & 52092.1822 & 0.0047 & 0.0136 & 112 \\\\\n82 & 52093.1104 & 0.0040 & $-$0.0007 & 158 \\\\\n83 & 52093.1866 & 0.0051 & 0.0030 & 189 \\\\\n96 & 52094.1249 & 0.0039 & $-$0.0012 & 199 \\\\\n97 & 52094.1926 & 0.0031 & $-$0.0060 & 147 \\\\\n110 & 52095.1318 & 0.0027 & $-$0.0094 & 142 \\\\\n111 & 52095.2133 & 0.0041 & $-$0.0004 & 127 \\\\\n180 & 52100.2201 & 0.0016 & 0.0036 & 64 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452087.1658 + 0.072504 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VW CrB (2006).}\\label{tab:vwcrboc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53842.7528 & 0.0013 & 0.0001 & 10 \\\\\n1 & 53842.8246 & 0.0009 & $-$0.0008 & 27 \\\\\n27 & 53844.7189 & 0.0035 & 0.0038 & 11 \\\\\n28 & 53844.7860 & 0.0009 & $-$0.0018 & 27 \\\\\n41 & 53845.7309 & 0.0048 & $-$0.0017 & 19 \\\\\n42 & 53845.8056 & 0.0013 & 0.0004 & 27 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453842.7527 + 0.072679 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TU Crateris}\\label{obj:tucrt}\n\n TU Crt had long been suspected to be an SU UMa-type candidate since\nthe discovery (cf. \\cite{maz92tucrt}; \\cite{haz93tucrt}; \\cite{wen93tucrt}).\nIt was only in 1998 when its SU UMa-type nature was confirmed\n\\citep{men98tucrt}. \\citet{men98tucrt} reported an superhump period\nof 0.08535(5) d and $P_{\\rm dot}$ of $-7.2(0.9) \\times 10^{-5}$\n(the reference apparently had an error in conversion from coefficients\nto $P_{\\rm dot}$).\n\n We observed the 2001 and 2009 superoutbursts. The times of superhump\nmaxima are listed in tables \\ref{tab:tucrtoc2001} and \\ref{tab:tucrtoc2009}.\nThe mean superhump period of the 2001 superoutburst determined with\nPDM method was 0.08532(8) d.\nThe $P_{\\rm dot}$ was $-12.3(9.2) \\times 10^{-5}$.\n\n A combined $O-C$ diagram is presented in figure \\ref{fig:tucrtcomp}.\nThe early part of the 2001 superoutburst was likely missed and we shifted\nthe $O-C$ diagram to best fit the 1998 superoutburst. None of\nobservations yet recorded the epoch of stage A evolution.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig77.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of TU Crt between different\n superoutbursts. A period of 0.08550 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:tucrtcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of TU Crt (2001).}\\label{tab:tucrtoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52010.0402 & 0.0013 & $-$0.0070 & 101 \\\\\n1 & 52010.1329 & 0.0047 & 0.0005 & 69 \\\\\n24 & 52012.0955 & 0.0022 & 0.0040 & 109 \\\\\n35 & 52013.0235 & 0.0011 & $-$0.0050 & 57 \\\\\n36 & 52013.1230 & 0.0073 & 0.0094 & 59 \\\\\n48 & 52014.1427 & 0.0030 & 0.0068 & 18 \\\\\n58 & 52014.9852 & 0.0012 & $-$0.0024 & 158 \\\\\n71 & 52016.0886 & 0.0022 & $-$0.0063 & 141 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452010.0460 + 0.085175 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of TU Crt (2009).}\\label{tab:tucrtoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54881.1051 & 0.0001 & 0.0003 & 287 \\\\\n1 & 54881.1888 & 0.0002 & $-$0.0014 & 173 \\\\\n23 & 54883.0717 & 0.0005 & 0.0015 & 205 \\\\\n24 & 54883.1570 & 0.0003 & 0.0014 & 261 \\\\\n35 & 54884.0954 & 0.0004 & $-$0.0002 & 80 \\\\\n36 & 54884.1807 & 0.0005 & $-$0.0003 & 86 \\\\\n37 & 54884.2652 & 0.0008 & $-$0.0013 & 88 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454881.1048 + 0.085452 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TV Corvi}\\label{sec:tvcrv}\\label{obj:tvcrv}\n\n We reanalyzed the 2001, 2003 and 2004 data published in \\citet{uem05tvcrv}\n(tables \\ref{tab:tvcrvoc2001}, \\ref{tab:tvcrvoc2003} and\n\\ref{tab:tvcrvoc2004}).\nRegarding the 2001 superoutburst, we obtained a result similar to that\nin \\citet{uem05tvcrv}. The $P_{\\rm dot}$ was $+6.2(1.5) \\times 10^{-5}$\n($1 \\le E \\le 109$).\nWe, however, obtained a different result for the 2004 superoutburst\nThe $O-C$ diagram was similar to that of 2001 one, contrary to the analysis\nin \\citet{uem05tvcrv}\n(subsection \\ref{sec:different}; figure \\ref{fig:tvcrvcomp}).\nWe obtained $P_{\\rm dot}$ = $+9.5(3.1) \\times 10^{-5}$ ($16 \\le E \\le 103$),\nexcluding the initial stage of early evolution (stage A) and last segment\n(stage C) after a period decrease.\n\n\\begin{table}\n\\caption{Superhump maxima of TV Crv (2001).}\\label{tab:tvcrvoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51960.2263 & 0.0019 & $-$0.0148 & 55 \\\\\n1 & 51960.2923 & 0.0015 & $-$0.0138 & 157 \\\\\n13 & 51961.0918 & 0.0010 & 0.0055 & 40 \\\\\n14 & 51961.1568 & 0.0002 & 0.0054 & 105 \\\\\n15 & 51961.2211 & 0.0003 & 0.0047 & 103 \\\\\n16 & 51961.2854 & 0.0003 & 0.0041 & 109 \\\\\n17 & 51961.3505 & 0.0005 & 0.0041 & 74 \\\\\n32 & 51962.3235 & 0.0010 & 0.0018 & 67 \\\\\n46 & 51963.2321 & 0.0004 & 0.0002 & 145 \\\\\n47 & 51963.2971 & 0.0008 & 0.0002 & 107 \\\\\n90 & 51966.0944 & 0.0012 & 0.0018 & 26 \\\\\n91 & 51966.1609 & 0.0010 & 0.0032 & 33 \\\\\n108 & 51967.2694 & 0.0008 & 0.0064 & 140 \\\\\n109 & 51967.3295 & 0.0016 & 0.0015 & 71 \\\\\n168 & 51971.1537 & 0.0025 & $-$0.0103 & 88 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451960.2411 + 0.065017 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of TV Crv (2003).}\\label{tab:tvcrvoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52770.0238 & 0.0003 & $-$0.0007 & 66 \\\\\n1 & 52770.0885 & 0.0003 & $-$0.0009 & 66 \\\\\n2 & 52770.1534 & 0.0003 & $-$0.0009 & 66 \\\\\n3 & 52770.2204 & 0.0007 & 0.0011 & 34 \\\\\n93 & 52776.0758 & 0.0024 & 0.0111 & 19 \\\\\n107 & 52776.9741 & 0.0032 & 0.0002 & 69 \\\\\n121 & 52777.8773 & 0.0010 & $-$0.0059 & 152 \\\\\n122 & 52777.9413 & 0.0048 & $-$0.0068 & 56 \\\\\n170 & 52781.0686 & 0.0017 & 0.0029 & 58 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452770.0245 + 0.064948 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of TV Crv (2004).}\\label{tab:tvcrvoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53161.0000 & 0.0023 & 0.0153 & 118 \\\\\n1 & 53161.0532 & 0.0034 & 0.0036 & 120 \\\\\n16 & 53162.0201 & 0.0010 & $-$0.0045 & 81 \\\\\n23 & 53162.4772 & 0.0010 & $-$0.0023 & 40 \\\\\n25 & 53162.6056 & 0.0007 & $-$0.0039 & 59 \\\\\n26 & 53162.6715 & 0.0007 & $-$0.0030 & 67 \\\\\n40 & 53163.5796 & 0.0013 & $-$0.0048 & 71 \\\\\n41 & 53163.6465 & 0.0011 & $-$0.0029 & 59 \\\\\n42 & 53163.7117 & 0.0011 & $-$0.0026 & 44 \\\\\n62 & 53165.0089 & 0.0008 & $-$0.0053 & 34 \\\\\n86 & 53166.5737 & 0.0009 & $-$0.0003 & 73 \\\\\n87 & 53166.6360 & 0.0094 & $-$0.0030 & 39 \\\\\n88 & 53166.7068 & 0.0022 & 0.0028 & 36 \\\\\n102 & 53167.6177 & 0.0016 & 0.0038 & 70 \\\\\n103 & 53167.6882 & 0.0015 & 0.0094 & 63 \\\\\n117 & 53168.5850 & 0.0085 & $-$0.0037 & 48 \\\\\n118 & 53168.6551 & 0.0009 & 0.0013 & 80 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453160.9847 + 0.064992 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V337 Cygni}\\label{obj:v337cyg}\n\n Although V337 Cyg had long been registered as a dwarf nova,\nthe identification of the true object was made only recently\nby J. Manek based on archival Sonneberg plate (vsnet 775, 780\\footnote{\n $<$http:\/\/www.kusastro.kyoto-u.ac.jp\/vsnet\/DNe\/v337cyg.html$>$\n}; see also \\cite{boy07v337cyg}).\n\n We analyzed the AAVSO data of the 2006 superoutburst, the same\noutburst reported in \\citet{boy07v337cyg}. These observations\nwere performed during the late stage of the superoutburst, and the\nsuperhumps were most likely stage C superhumps.\nThe times of maxima are given in table \\ref{tab:v337cygoc2006}.\nThe mean $P_{\\rm SH}$ was determined with the PDM method\nto be 0.07013(3) d (figure \\ref{fig:v337cygshpdm}).\nThis outburst was followed by a rebrightening according to the\nAAVSO data. We might expect a positive $P_{\\rm dot}$ if observations\ncovered the earlier stage of this superoutburst.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig78.eps}\n \\end{center}\n \\caption{Superhumps in V337 Cyg (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v337cygshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V337 Cyg (2006).}\\label{tab:v337cygoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53886.4495 & 0.0010 & $-$0.0021 & 69 \\\\\n1 & 53886.5209 & 0.0014 & $-$0.0008 & 61 \\\\\n4 & 53886.7305 & 0.0009 & $-$0.0011 & 72 \\\\\n5 & 53886.8052 & 0.0010 & 0.0035 & 71 \\\\\n6 & 53886.8741 & 0.0009 & 0.0024 & 71 \\\\\n7 & 53886.9404 & 0.0012 & $-$0.0012 & 72 \\\\\n28 & 53888.4064 & 0.0081 & $-$0.0053 & 40 \\\\\n29 & 53888.4885 & 0.0014 & 0.0068 & 117 \\\\\n30 & 53888.5495 & 0.0009 & $-$0.0023 & 119 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453886.4516 + 0.070003 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V503 Cygni}\\label{obj:v503cyg}\n\n \\citet{har95v503cyg} established the SU UMa-type nature of this\nobject and reported a mean $P_{\\rm SH}$ of 0.08101(4) d.\n\n We observed the 2002 July superoutburst. The times of superhump\nmaxima are listed in table \\ref{tab:v503cygoc2002}.\nAlthough the coverage of the observation was not sufficient,\na likely stage B--C transition was recorded. The parameters are\nlisted in table \\ref{tab:perlist}.\nThe observation of the 2008 December superoutburst is given in\ntable \\ref{tab:v503cygoc2008}. There was an apparent break in the\n$O-C$ around $E=49$. Due to the limited phase coverage,\nwe determined superhump periods for the first (before BJD 2454824)\nand the second (after BJD 2454823) intervals with the PDM method.\nThe periods were 0.081767(45) d and 0.081022(18) d, respectively.\nThese periods were adopted in table \\ref{tab:perlist}.\n\n This object is of particular interest since its\nsupercycle is one of the next shortest to ER UMa stars and MN Dra\n(\\cite{har95v503cyg}; \\cite{kat02v503cyg}) and there appears to be\na hint of superhump evolution similar to ER UMa stars\n(\\cite{har95v503cyg}, figure 7).\nIt would be worth studying whether a phase reversal, or early\nemergence of stage C superhumps (cf. subsection \\ref{sec:erumastars}),\nalso takes place in this system.\n\n\\begin{table}\n\\caption{Superhump maxima of V503 Cyg (2002).}\\label{tab:v503cygoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52478.2155 & 0.0004 & $-$0.0110 & 312 \\\\\n13 & 52479.2861 & 0.0014 & 0.0047 & 196 \\\\\n17 & 52479.5975 & 0.0047 & $-$0.0085 & 28 \\\\\n18 & 52479.7013 & 0.0036 & 0.0142 & 28 \\\\\n25 & 52480.2501 & 0.0008 & $-$0.0051 & 309 \\\\\n30 & 52480.6656 & 0.0008 & 0.0047 & 44 \\\\\n31 & 52480.7429 & 0.0006 & 0.0009 & 55 \\\\\n37 & 52481.2303 & 0.0009 & 0.0014 & 324 \\\\\n38 & 52481.3145 & 0.0008 & 0.0044 & 180 \\\\\n49 & 52482.2026 & 0.0007 & $-$0.0000 & 238 \\\\\n76 & 52484.3913 & 0.0008 & $-$0.0023 & 50 \\\\\n77 & 52484.4713 & 0.0014 & $-$0.0034 & 65 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452478.2265 + 0.081145 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V503 Cyg (2008).}\\label{tab:v503cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54819.9455 & 0.0012 & $-$0.0035 & 81 \\\\\n36 & 54822.8735 & 0.0017 & 0.0029 & 78 \\\\\n49 & 54823.9288 & 0.0010 & 0.0033 & 100 \\\\\n98 & 54827.8995 & 0.0017 & $-$0.0027 & 64 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454819.9490 + 0.081155 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V550 Cygni}\\label{obj:v550cyg}\n\n Although V550 Cyg had long been known as a dwarf nova, the supposed\nidentification became available only in 1999 \\citep{ski99VSID}.\nTwo outbursts were detected in 2000 (vsnet-alert 3993, 5191).\nSuperhumps were detected during the August outburst (vsnet-alert 5196).\nH. Yamaoka provided astrometry from outburst images (vsnet-alert 5210),\nwhich slightly differed from the position in \\citet{ski99VSID}, making\nthe full amplitude of outbursts larger than five magnitudes.\n\n The mean superhump period with the PDM method was 0.06871(6) d\n(figure \\ref{fig:v550cygshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:v550cygoc2000}.\nThe outburst was apparently observed during its middle-to-late course,\nand a stage B--C transition was recorded.\nThe mean $P_{\\rm SH}$ for stages B and C were 0.06917(26) d and\n0.06848(6) d, respectively.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig79.eps}\n \\end{center}\n \\caption{Superhumps in V550 Cyg (2000). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v550cygshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V550 Cyg (2000).}\\label{tab:v550cygoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51777.0086 & 0.0018 & $-$0.0003 & 129 \\\\\n14 & 51777.9680 & 0.0011 & $-$0.0031 & 148 \\\\\n15 & 51778.0417 & 0.0016 & 0.0018 & 149 \\\\\n16 & 51778.0926 & 0.0011 & $-$0.0161 & 147 \\\\\n17 & 51778.1784 & 0.0040 & 0.0010 & 147 \\\\\n18 & 51778.2396 & 0.0018 & $-$0.0066 & 265 \\\\\n32 & 51779.2210 & 0.0088 & 0.0126 & 87 \\\\\n33 & 51779.2910 & 0.0094 & 0.0138 & 116 \\\\\n35 & 51779.4164 & 0.0011 & 0.0017 & 34 \\\\\n50 & 51780.4497 & 0.0009 & 0.0040 & 41 \\\\\n61 & 51781.2028 & 0.0015 & 0.0009 & 104 \\\\\n62 & 51781.2697 & 0.0044 & $-$0.0009 & 124 \\\\\n64 & 51781.4099 & 0.0016 & 0.0018 & 11 \\\\\n65 & 51781.4741 & 0.0014 & $-$0.0027 & 26 \\\\\n76 & 51782.2311 & 0.0088 & $-$0.0019 & 106 \\\\\n79 & 51782.4381 & 0.0012 & $-$0.0010 & 35 \\\\\n91 & 51783.2589 & 0.0143 & $-$0.0051 & 130 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451777.0088 + 0.068738 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V630 Cygni}\\label{obj:v630cyg}\n\n The SU UMa-type nature of this dwarf nova was established by\n\\citet{nog01v630cyg}. The times of superhump maxima during the 1996\nsuperoutburst measured from these data are listed in\ntable \\ref{tab:v630cygoc1996}.\n\n We further observed the 2008 superoutburst (table \\ref{tab:v630cygoc2008}).\nThe $O-C$'s apparently showed a stage B--C transition.\nThe mean $P_{\\rm SH}$ and $P_{\\rm dot}$ for the stage B were\n0.07918(7) d and $+27.4(7.7) \\times 10^{-5}$, respectively.\nSince the value was derived from a limited sample, the large positive\n$P_{\\rm dot}$ needs to be confirmed by further observations.\n\n\\begin{table}\n\\caption{Superhump maxima of V630 Cyg (1996).}\\label{tab:v630cygoc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50313.9866 & 0.0012 & 0.0007 & 52 \\\\\n1 & 50314.0667 & 0.0012 & 0.0014 & 45 \\\\\n16 & 50315.2506 & 0.0014 & $-$0.0045 & 55 \\\\\n29 & 50316.2887 & 0.0063 & 0.0024 & 34 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450313.9860 + 0.079320 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V630 Cyg (2008).}\\label{tab:v630cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54690.0683 & 0.0007 & $-$0.0053 & 129 \\\\\n12 & 54691.0151 & 0.0006 & $-$0.0040 & 81 \\\\\n25 & 54692.0444 & 0.0007 & 0.0010 & 112 \\\\\n26 & 54692.1213 & 0.0004 & $-$0.0009 & 167 \\\\\n39 & 54693.1564 & 0.0261 & 0.0099 & 10 \\\\\n40 & 54693.2342 & 0.0052 & 0.0088 & 70 \\\\\n51 & 54694.0912 & 0.0055 & $-$0.0009 & 51 \\\\\n76 & 54696.0586 & 0.0007 & $-$0.0034 & 165 \\\\\n77 & 54696.1350 & 0.0009 & $-$0.0057 & 118 \\\\\n103 & 54698.1900 & 0.0113 & 0.0005 & 115 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454690.0736 + 0.078795 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V632 Cygni}\\label{obj:v632cyg}\n\n The SU UMa-type nature of this dwarf nova had long been suggested\n(cf. \\cite{wen89v632cygv630cyg} for a historical record of bright\noutbursts). \\citet{she07CVspec} determined its orbital period\nto be 0.06377(8) d. The SU UMa-type nature was finally established\nduring the 2008 superoutburst.\n\n The global mean superhump period during the 2008 superoutburst was\n0.065695(6) d (PDM method, figure \\ref{fig:v632cygshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:v632cygoc2008}.\nAlthough the stage A--B and B--C transitions were observed,\na gap in the middle of the stage B makes determination of $P_{\\rm dot}$\nrather uncertain.\nThe value for $16 \\le E \\le 82$ was $+17.4(3.0) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig80.eps}\n \\end{center}\n \\caption{Superhumps in V632 Cyg (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v632cygshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V632 Cyg (2008).}\\label{tab:v632cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54782.3640 & 0.0079 & $-$0.0094 & 112 \\\\\n1 & 54782.4310 & 0.0048 & $-$0.0081 & 69 \\\\\n9 & 54782.9596 & 0.0014 & $-$0.0052 & 35 \\\\\n13 & 54783.2258 & 0.0003 & $-$0.0018 & 125 \\\\\n14 & 54783.2922 & 0.0005 & $-$0.0010 & 102 \\\\\n15 & 54783.3567 & 0.0007 & $-$0.0023 & 96 \\\\\n16 & 54783.4264 & 0.0018 & 0.0017 & 39 \\\\\n23 & 54783.8856 & 0.0003 & 0.0010 & 106 \\\\\n24 & 54783.9505 & 0.0003 & 0.0002 & 129 \\\\\n30 & 54784.3441 & 0.0005 & $-$0.0004 & 63 \\\\\n31 & 54784.4103 & 0.0005 & 0.0001 & 155 \\\\\n32 & 54784.4755 & 0.0008 & $-$0.0004 & 81 \\\\\n65 & 54786.6457 & 0.0008 & 0.0016 & 46 \\\\\n66 & 54786.7131 & 0.0008 & 0.0033 & 64 \\\\\n67 & 54786.7801 & 0.0007 & 0.0047 & 55 \\\\\n80 & 54787.6374 & 0.0005 & 0.0078 & 55 \\\\\n81 & 54787.7034 & 0.0006 & 0.0081 & 66 \\\\\n82 & 54787.7729 & 0.0016 & 0.0119 & 31 \\\\\n104 & 54789.2107 & 0.0004 & 0.0042 & 105 \\\\\n105 & 54789.2759 & 0.0008 & 0.0037 & 115 \\\\\n106 & 54789.3450 & 0.0020 & 0.0071 & 46 \\\\\n110 & 54789.6027 & 0.0006 & 0.0020 & 45 \\\\\n111 & 54789.6694 & 0.0006 & 0.0031 & 68 \\\\\n112 & 54789.7352 & 0.0007 & 0.0031 & 69 \\\\\n115 & 54789.9278 & 0.0011 & $-$0.0014 & 36 \\\\\n116 & 54789.9920 & 0.0009 & $-$0.0029 & 49 \\\\\n130 & 54790.9178 & 0.0013 & 0.0031 & 123 \\\\\n131 & 54790.9802 & 0.0013 & $-$0.0002 & 128 \\\\\n145 & 54791.8925 & 0.0013 & $-$0.0077 & 63 \\\\\n156 & 54792.6065 & 0.0014 & $-$0.0165 & 48 \\\\\n157 & 54792.6792 & 0.0020 & $-$0.0095 & 32 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454782.3734 + 0.065702 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1028 Cygni}\\label{sec:v1028cyg}\\label{obj:v1028cyg}\n\n \\citet{bab00v1028cyg} reported the detection of positive period\nderivative during the 1995 superoutburst. This outburst was indeed\none of the earliest with significantly positive $P_{\\rm dot}$'s.\nWe reanalyzed the data, combined with the AAVSO observations,\nfor an improvement of the parameters.\nThe results generally confirmed the conclusion by \\citet{bab00v1028cyg}\n(table \\ref{tab:v1028cygoc1995}).\nThe $P_{\\rm dot}$ for the interval $15 \\le E \\le 148$ (stage B) was\n$+8.2(1.2) \\times 10^{-5}$.\n\n We further analyzed the 1996, 1999, 2001, 2002, 2004 and 2008\nsuperoutbursts\n(tables \\ref{tab:v1028cygoc1996}, \\ref{tab:v1028cygoc1999},\n\\ref{tab:v1028cygoc2001}, \\ref{tab:v1028cygoc2002},\n\\ref{tab:v1028cygoc2004}, \\ref{tab:v1028cygoc2008}).\nThe observation in 2001 and 2002 covered\nthe middle-to-late portion of the superoutburst, and the $O-C$ diagram\ncommonly showed a transition to a shorter period (stage C).\nFor the 1999 and 2002 superoutbursts, we obtained $P_{\\rm dot}$\nbefore this transition as follows:\n$P_{\\rm dot}$ = $+12.2(3.1) \\times 10^{-5}$ (1999, $E \\le 148$) and\n$P_{\\rm dot}$ = $+14.7(5.5) \\times 10^{-5}$ (2002, $E \\le 55$).\nAlthough the 1996 and 2004 superoutbursts were preceded\nby a distinct precursor, only the late stage of the superoutburst was\nmeaningfully observed.\n\n A comparison of $O-C$ diagrams is shown in figure \\ref{fig:v1028cygcomp}.\nThere appears to be a slight variation in the $O-C$ behavior during the\nlate stage (stage B--C). This may have been caused by the difference\nin the extent between superoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig81.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V1028 Cyg between different\n superoutbursts. A period of 0.06180 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst (the start of the main superoutburst when preceded by\n a precursor) were used. The $E$ for the 2008 superoutburst was\n somewhat uncertain due to the lack of observations at the early stage.\n }\n \\label{fig:v1028cygcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (1995).}\\label{tab:v1028cygoc1995}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49929.0867 & 0.0014 & $-$0.0077 & 48 \\\\\n1 & 49929.1451 & 0.0023 & $-$0.0111 & 77 \\\\\n2 & 49929.2117 & 0.0007 & $-$0.0063 & 124 \\\\\n3 & 49929.2781 & 0.0010 & $-$0.0016 & 125 \\\\\n15 & 49930.0276 & 0.0004 & 0.0067 & 35 \\\\\n16 & 49930.0905 & 0.0002 & 0.0078 & 95 \\\\\n17 & 49930.1525 & 0.0002 & 0.0081 & 30 \\\\\n19 & 49930.2751 & 0.0011 & 0.0072 & 46 \\\\\n33 & 49931.1344 & 0.0006 & 0.0017 & 32 \\\\\n34 & 49931.1978 & 0.0004 & 0.0034 & 75 \\\\\n67 & 49933.2288 & 0.0006 & $-$0.0040 & 80 \\\\\n68 & 49933.2906 & 0.0008 & $-$0.0039 & 49 \\\\\n83 & 49934.2176 & 0.0006 & $-$0.0034 & 76 \\\\\n84 & 49934.2760 & 0.0009 & $-$0.0068 & 81 \\\\\n98 & 49935.1431 & 0.0009 & $-$0.0045 & 136 \\\\\n100 & 49935.2663 & 0.0009 & $-$0.0047 & 124 \\\\\n114 & 49936.1419 & 0.0016 & 0.0061 & 75 \\\\\n115 & 49936.1957 & 0.0026 & $-$0.0019 & 62 \\\\\n116 & 49936.2584 & 0.0034 & $-$0.0009 & 63 \\\\\n130 & 49937.1227 & 0.0053 & $-$0.0013 & 16 \\\\\n132 & 49937.2489 & 0.0023 & 0.0014 & 31 \\\\\n139 & 49937.6846 & 0.0030 & 0.0047 & 15 \\\\\n140 & 49937.7445 & 0.0024 & 0.0028 & 17 \\\\\n141 & 49937.8140 & 0.0032 & 0.0105 & 13 \\\\\n147 & 49938.1770 & 0.0025 & 0.0029 & 32 \\\\\n148 & 49938.2405 & 0.0017 & 0.0047 & 31 \\\\\n154 & 49938.6106 & 0.0016 & 0.0041 & 17 \\\\\n155 & 49938.6717 & 0.0031 & 0.0035 & 18 \\\\\n156 & 49938.7341 & 0.0030 & 0.0042 & 17 \\\\\n162 & 49939.1010 & 0.0014 & 0.0005 & 24 \\\\\n163 & 49939.1637 & 0.0016 & 0.0014 & 32 \\\\\n164 & 49939.2272 & 0.0051 & 0.0032 & 29 \\\\\n188 & 49940.6966 & 0.0041 & $-$0.0099 & 30 \\\\\n189 & 49940.7534 & 0.0132 & $-$0.0148 & 12 \\\\\n194 & 49941.0751 & 0.0021 & $-$0.0019 & 20 \\\\\n195 & 49941.1389 & 0.0080 & 0.0000 & 22 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449929.0944 + 0.061766 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (1996).}\\label{tab:v1028cygoc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50308.0425 & 0.0017 & $-$0.0049 & 33 \\\\\n90 & 50313.6069 & 0.0030 & 0.0015 & 17 \\\\\n91 & 50313.6768 & 0.0033 & 0.0097 & 19 \\\\\n92 & 50313.7308 & 0.0046 & 0.0019 & 16 \\\\\n93 & 50313.7886 & 0.0045 & $-$0.0020 & 14 \\\\\n99 & 50314.1640 & 0.0020 & 0.0029 & 59 \\\\\n100 & 50314.2237 & 0.0008 & 0.0008 & 59 \\\\\n106 & 50314.5908 & 0.0011 & $-$0.0027 & 19 \\\\\n107 & 50314.6538 & 0.0022 & $-$0.0014 & 19 \\\\\n108 & 50314.7151 & 0.0017 & $-$0.0018 & 15 \\\\\n109 & 50314.7754 & 0.0019 & $-$0.0033 & 19 \\\\\n110 & 50314.8474 & 0.0045 & 0.0069 & 18 \\\\\n115 & 50315.1574 & 0.0040 & 0.0081 & 49 \\\\\n131 & 50316.1275 & 0.0038 & $-$0.0098 & 42 \\\\\n132 & 50316.1929 & 0.0035 & $-$0.0062 & 47 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450308.0473 + 0.061755 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (1999).}\\label{tab:v1028cygoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51427.4199 & 0.0011 & 0.0277 & 110 \\\\\n45 & 51430.1621 & 0.0006 & $-$0.0079 & 121 \\\\\n46 & 51430.2243 & 0.0008 & $-$0.0074 & 122 \\\\\n61 & 51431.1503 & 0.0011 & $-$0.0074 & 120 \\\\\n66 & 51431.4520 & 0.0016 & $-$0.0143 & 109 \\\\\n67 & 51431.5234 & 0.0007 & $-$0.0047 & 83 \\\\\n91 & 51433.0147 & 0.0016 & 0.0051 & 61 \\\\\n92 & 51433.0675 & 0.0070 & $-$0.0038 & 79 \\\\\n108 & 51434.0616 & 0.0047 & 0.0026 & 99 \\\\\n109 & 51434.1162 & 0.0037 & $-$0.0046 & 122 \\\\\n126 & 51435.1755 & 0.0044 & 0.0054 & 121 \\\\\n128 & 51435.2889 & 0.0039 & $-$0.0047 & 94 \\\\\n147 & 51436.4702 & 0.0020 & 0.0038 & 82 \\\\\n148 & 51436.5309 & 0.0012 & 0.0026 & 94 \\\\\n190 & 51439.1197 & 0.0024 & $-$0.0012 & 98 \\\\\n192 & 51439.2451 & 0.0046 & 0.0008 & 38 \\\\\n193 & 51439.3112 & 0.0076 & 0.0052 & 32 \\\\\n194 & 51439.3626 & 0.0014 & $-$0.0052 & 61 \\\\\n195 & 51439.4376 & 0.0018 & 0.0081 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451427.3922 + 0.061730 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (2001).}\\label{tab:v1028cygoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52261.5987 & 0.0049 & $-$0.0077 & 17 \\\\\n1 & 52261.6697 & 0.0022 & 0.0015 & 11 \\\\\n66 & 52265.6900 & 0.0014 & 0.0048 & 15 \\\\\n67 & 52265.7537 & 0.0007 & 0.0067 & 14 \\\\\n81 & 52266.6128 & 0.0017 & 0.0005 & 15 \\\\\n82 & 52266.6774 & 0.0019 & 0.0034 & 16 \\\\\n83 & 52266.7372 & 0.0023 & 0.0014 & 13 \\\\\n114 & 52268.6410 & 0.0013 & $-$0.0106 & 14 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452261.6064 + 0.061800 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (2002).}\\label{tab:v1028cygoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52618.5958 & 0.0004 & 0.0016 & 27 \\\\\n1 & 52618.6564 & 0.0005 & 0.0004 & 31 \\\\\n2 & 52618.7181 & 0.0007 & 0.0004 & 22 \\\\\n5 & 52618.9038 & 0.0009 & 0.0008 & 159 \\\\\n6 & 52618.9644 & 0.0005 & $-$0.0004 & 233 \\\\\n7 & 52619.0259 & 0.0007 & $-$0.0007 & 116 \\\\\n17 & 52619.6431 & 0.0009 & $-$0.0011 & 25 \\\\\n21 & 52619.8896 & 0.0008 & $-$0.0017 & 112 \\\\\n22 & 52619.9558 & 0.0058 & 0.0028 & 86 \\\\\n37 & 52620.8782 & 0.0011 & $-$0.0012 & 116 \\\\\n38 & 52620.9376 & 0.0009 & $-$0.0036 & 218 \\\\\n39 & 52621.0007 & 0.0011 & $-$0.0023 & 105 \\\\\n54 & 52621.9314 & 0.0058 & 0.0020 & 153 \\\\\n55 & 52621.9953 & 0.0017 & 0.0041 & 107 \\\\\n70 & 52622.9168 & 0.0014 & $-$0.0009 & 121 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452618.5942 + 0.061763 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (2004).}\\label{tab:v1028cygoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53321.9325 & 0.0012 & 0.0014 & 87 \\\\\n12 & 53322.6703 & 0.0009 & $-$0.0020 & 60 \\\\\n37 & 53324.2157 & 0.0012 & $-$0.0009 & 39 \\\\\n38 & 53324.2798 & 0.0027 & 0.0015 & 48 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453321.9311 + 0.061770 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1028 Cyg (2008).}\\label{tab:v1028cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54828.3145 & 0.0003 & 0.0007 & 127 \\\\\n1 & 54828.3750 & 0.0002 & $-$0.0007 & 99 \\\\\n113 & 54835.3049 & 0.0056 & 0.0011 & 68 \\\\\n114 & 54835.3646 & 0.0090 & $-$0.0011 & 38 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454828.3138 + 0.061858 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1113 Cygni}\\label{obj:v1113cyg}\n\n We have reanalyzed the observation in \\citet{kat96v1113cyg}\nand obtained new observations during the 2008 superoutburst.\nBoth observations covered the relatively early stages of the\nsuperoutbursts.\nThe times of superhump maxima are listed in tables \\ref{tab:v1113cygoc1994}\nand \\ref{tab:v1113cygoc2008}, respectively.\nThe resultant global $P_{\\rm dot}$'s were $-19.2(6.8) \\times 10^{-5}$\nand $-5.2(4.7) \\times 10^{-5}$, respectively.\nThe former strongly negative value\ncan be interpreted as a result of a possible stage A--B transition.\n\n\\begin{table}\n\\caption{Superhump maxima of V1113 Cyg (1994).}\\label{tab:v1113cygoc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49598.0086 & 0.0022 & $-$0.0046 & 24 \\\\\n14 & 49599.1249 & 0.0007 & 0.0022 & 29 \\\\\n26 & 49600.0790 & 0.0005 & 0.0052 & 47 \\\\\n51 & 49602.0541 & 0.0005 & $-$0.0009 & 35 \\\\\n64 & 49603.0835 & 0.0005 & $-$0.0018 & 25 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449598.0132 + 0.079253 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1113 Cyg (2008).}\\label{tab:v1113cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54757.2763 & 0.0003 & $-$0.0012 & 109 \\\\\n1 & 54757.3568 & 0.0004 & 0.0002 & 139 \\\\\n2 & 54757.4356 & 0.0004 & $-$0.0001 & 135 \\\\\n8 & 54757.9108 & 0.0005 & 0.0009 & 143 \\\\\n9 & 54757.9866 & 0.0008 & $-$0.0024 & 81 \\\\\n13 & 54758.3069 & 0.0003 & 0.0017 & 156 \\\\\n14 & 54758.3849 & 0.0004 & 0.0007 & 159 \\\\\n21 & 54758.9386 & 0.0009 & 0.0010 & 118 \\\\\n34 & 54759.9650 & 0.0009 & $-$0.0002 & 155 \\\\\n46 & 54760.9125 & 0.0013 & $-$0.0014 & 73 \\\\\n47 & 54760.9936 & 0.0009 & 0.0007 & 68 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454757.2775 + 0.079051 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1251 Cygni}\\label{sec:v1251cyg}\\label{obj:v1251cyg}\n\n The history of V1251 Cyg was summarized in \\citet{kat95v1251cyg}.\nOnly five outbursts (1963, 1991, 1994--1995, 1997 and 2008) have been\nrecorded. All of these outbursts were superoutbursts, and were associated\nwith a rebrightening (1997, 2008). Despite the long $P_{\\rm SH}$,\n\\citet{kat01hvvir} included this object as a candidate WZ Sge-type\ndwarf nova based on the long recurrence time, the large outburst amplitude\nand the lack of normal outbursts.\n\n We observed the 1991 \\citep{kat95v1251cyg}, 1994--1995, and 2008\nsuperoutbursts. The 1995 observation was performed on single night,\nonly confirming the presence of a superhump. The times of superhump maxima\n(refined times for the 1991 superoutburst) are listed in tables\n\\ref{tab:v1251cygoc1991} and \\ref{tab:v1251cygoc2008}.\n\n The 2008 superoutburst was clearly composed of stages B and C.\nThe mean $P_{\\rm SH}$ and $P_{\\rm dot}$ for the stage B were\n0.07597(2) d and $+6.0(2.7) \\times 10^{-5}$, respectively.\n($0 \\le E \\le 62$). The last part of the stage C includes superhumps\nduring the rapid fading stage ($E=141$) and the post-superoutburst stage\n($E=153, 154$). A phase shift expected for traditional late superhumps\nwas not recorded.\nIt took five days ordinary superhumps (figure \\ref{fig:v1251shpdm}) to appear\nafter the onset of the outburst, which is unusually long for an SU UMa-type\ndwarf nova with this $P_{\\rm SH}$ (this anomaly was already addressed\nin \\cite{kat91v1251cygiauc}). During this stage, double-wave modulations\nsimilar to early superhumps in WZ Sge-type dwarf novae were observed\n(figure \\ref{fig:v1251eshpdm}).\nThe period (0.07433(6) d, vsnet-alert 10612; refined in this paper)\nis 2.2 \\% shorter than the above $P_{\\rm SH}$ and can be good candidate\nfor $P_{\\rm orb}$.\nDespite its long $P_{\\rm SH}$, V1251 Cyg is extremely analogous to\nWZ Sge-type dwarf novae. The implication for the presence of such\na long-$P_{\\rm SH}$ WZ Sge-like objects was discussed in \\citet{ish01rzleo},\n\\citet{kat02wzsgeESH}. Compared to the 2008 superoutburst, only later\nhalf of the stage B was likely recorded during the 1991 superoutburst\n(figure \\ref{fig:v1251cygcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig82.eps}\n \\end{center}\n \\caption{Ordinary superhumps in V1251 Cyg (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v1251shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig83.eps}\n \\end{center}\n \\caption{Early superhumps in V1251 Cyg (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v1251eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig84.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V1251 Cyg between different\n superoutbursts. A period of 0.06180 d was used to draw this figure.\n Approximate cycle counts ($E$, estimated ones for the 1991 superoutbursts)\n after the appearance of superhumps were used.\n }\n \\label{fig:v1251cygcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V1251 Cyg (1991).}\\label{tab:v1251cygoc1991}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48563.8754 & 0.0018 & $-$0.0029 & 33 \\\\\n1 & 48563.9532 & 0.0005 & $-$0.0012 & 75 \\\\\n2 & 48564.0291 & 0.0009 & $-$0.0013 & 68 \\\\\n3 & 48564.1075 & 0.0010 & 0.0010 & 65 \\\\\n14 & 48564.9435 & 0.0008 & 0.0004 & 71 \\\\\n15 & 48565.0205 & 0.0007 & 0.0014 & 75 \\\\\n16 & 48565.0986 & 0.0012 & 0.0034 & 72 \\\\\n27 & 48565.9335 & 0.0011 & 0.0017 & 67 \\\\\n28 & 48566.0085 & 0.0008 & 0.0007 & 74 \\\\\n29 & 48566.0845 & 0.0009 & 0.0006 & 54 \\\\\n40 & 48566.9188 & 0.0009 & $-$0.0016 & 50 \\\\\n41 & 48566.9998 & 0.0025 & 0.0032 & 46 \\\\\n42 & 48567.0671 & 0.0013 & $-$0.0055 & 43 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448563.8783 + 0.076054 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1251 Cyg (2008).}\\label{tab:v1251cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54764.3130 & 0.0003 & $-$0.0038 & 264 \\\\\n1 & 54764.3871 & 0.0004 & $-$0.0055 & 295 \\\\\n2 & 54764.4648 & 0.0002 & $-$0.0036 & 312 \\\\\n5 & 54764.6931 & 0.0002 & $-$0.0027 & 139 \\\\\n6 & 54764.7688 & 0.0002 & $-$0.0028 & 151 \\\\\n14 & 54765.3755 & 0.0004 & $-$0.0026 & 106 \\\\\n15 & 54765.4539 & 0.0003 & 0.0000 & 131 \\\\\n26 & 54766.2855 & 0.0004 & $-$0.0022 & 80 \\\\\n27 & 54766.3625 & 0.0005 & $-$0.0010 & 74 \\\\\n35 & 54766.9710 & 0.0009 & 0.0010 & 131 \\\\\n36 & 54767.0454 & 0.0012 & $-$0.0005 & 138 \\\\\n37 & 54767.1203 & 0.0007 & $-$0.0013 & 179 \\\\\n47 & 54767.8821 & 0.0031 & 0.0024 & 141 \\\\\n48 & 54767.9588 & 0.0009 & 0.0032 & 418 \\\\\n49 & 54768.0370 & 0.0012 & 0.0057 & 41 \\\\\n61 & 54768.9457 & 0.0017 & 0.0047 & 83 \\\\\n62 & 54769.0258 & 0.0013 & 0.0090 & 51 \\\\\n74 & 54769.9311 & 0.0007 & 0.0046 & 275 \\\\\n75 & 54770.0082 & 0.0006 & 0.0059 & 362 \\\\\n101 & 54771.9760 & 0.0015 & 0.0027 & 274 \\\\\n102 & 54772.0507 & 0.0003 & 0.0016 & 156 \\\\\n132 & 54774.3312 & 0.0008 & 0.0079 & 135 \\\\\n141 & 54775.0039 & 0.0023 & $-$0.0018 & 87 \\\\\n153 & 54775.9032 & 0.0013 & $-$0.0122 & 118 \\\\\n154 & 54775.9824 & 0.0036 & $-$0.0087 & 143 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454764.3168 + 0.075807 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1316 Cygni}\\label{obj:v1316cyg}\n\n Although V1316 Cyg was listed as an SU UMa-type dwarf nova in\nthe GCVS \\citep{GCVS}, the misidentification on the original discovery\npaper \\citep{rom69v1316cyg} led to a long-lasting confusion.\n\\citet{hen97sequence} suggested a nearby faint blue star to be\nthe genuine V1316 Cyg, whose variability in quiescence was confirmed\nin 2000 (B. Sumner, AAVSO discussion message).\nThis suggestion was confirmed by the later\ndetection of an outburst in 2002 (M. Moriyama, vsnet-campaign-dn 2910).\nSubsequent observations starting in 2003 recorded a number of outbursts.\nIt has now been established that the object a short cycle length\nof outbursts \\citep{she06v1316cyg} as originally reported\nby \\citet{rom69v1316cyg}.\n\n \\citet{boy08v1316cyg} observed the 2006 superoutburst of this object\nand reported a phase shift around $E=90$, which they interpreted\nas the appearance of (traditional) late superhumps. The phase shift\nwas so large that it is difficult to attribute it to the stage B period\nincrease. The relatively early appearance of late superhumps, or\nthe occurrence of a phase reversal, is somewhat reminiscent to\nER UMa (section \\ref{sec:erumastars}). Judging from the short\n($\\sim$ 10 d) outburst \\citep{she06v1316cyg}, this object appears to have\na high mass-transfer rate that could enable ER UMa-like evolution of\nsuperhumps. The other parameters, such as the duration of the superoutburst\nand $P_{\\rm SH}$ are, however, unlike those of ER UMa and resemble\nthose of a long $P_{\\rm SH}$-system BF Ara \\citep{kat03bfara}.\nSince \\citet{boy08v1316cyg} used a different method in extracting\nmaxima times, a reanalysis of their data and tracking maxima of the\noriginal superhumps as in ER UMa (section \\ref{sec:erumastars}) might be\nhelpful in better understanding this system and its relation to ER UMa.\nWe identified the period for $E \\ge 94$ as the stage C superhumps\nand listed in table \\ref{tab:perlist}.\n\n\\subsection{V1454 Cygni}\\label{obj:v1454cyg}\n\n V1454 Cyg is a poorly-known dwarf nova. Although discovery observations\nsuggested the existence of long and short outbursts resembling an SU UMa-type\ndwarf nova (\\cite{pin72v1454cyg}; \\cite{los79v1454cyg}),\nspectroscopic observation could not confirm the CV nature of the suggested\nquiescent counterpart (\\cite{liu99CVspec2}; this later turned out to be\na false identification).\n\n The object underwent a long, bright outburst in 1996 (vsnet-obs 4039).\nDuring the 2006 outburst, announced by J. Shears (November 23),\none of the authors (Njh) undertook\ntime-resolved CCD photometry, and detected superhumps.\nDuring the first seven days, the superhump signal was very weak.\nThe superhumps showed a remarkable growth on December 1 and were\nfollowed until December 6. On December 11, the object showed a\ntrend of rebrightening around the termination of the plateau\nstage (cf. \\cite{kat03hodel}). We used the data for December\n1--6 to determine the superhump period and its variation.\nA PDM analysis yielded a mean period of 0.06101(2) d\n(figure \\ref{fig:v1454cygshpdm}).\nOne-day aliases appear to be excluded from the December 1 data.\nThe times of maxima identified with this $P_{\\rm SH}$\nare listed in table \\ref{tab:v1454cygoc2006}, likely composed of\na stage B--C transition and a possible stage A observation at $E=0$.\nThe $P_{\\rm dot}$ for $113 \\le E \\le 196$ (stage B)\nwas $+15.0(4.3) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig85.eps}\n \\end{center}\n \\caption{Superhumps in V1454 Cyg (2006) for BJD 2454070.5--2454076.5.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v1454cygshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V1454 Cyg (2006).}\\label{tab:v1454cygoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54063.9562 & 0.0019 & $-$0.0274 & 83 \\\\\n113 & 54070.8827 & 0.0008 & 0.0113 & 88 \\\\\n114 & 54070.9395 & 0.0012 & 0.0071 & 87 \\\\\n135 & 54072.2185 & 0.0007 & 0.0061 & 23 \\\\\n163 & 54073.9221 & 0.0048 & 0.0029 & 84 \\\\\n179 & 54074.9054 & 0.0017 & 0.0110 & 88 \\\\\n195 & 54075.8850 & 0.0020 & 0.0153 & 66 \\\\\n196 & 54075.9445 & 0.0031 & 0.0138 & 66 \\\\\n234 & 54078.2569 & 0.0024 & 0.0100 & 34 \\\\\n261 & 54079.8787 & 0.0221 & $-$0.0140 & 49 \\\\\n262 & 54079.9336 & 0.0047 & $-$0.0201 & 73 \\\\\n278 & 54080.9128 & 0.0027 & $-$0.0161 & 89 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454063.9836 + 0.060955 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1504 Cygni}\\label{obj:v1504cyg}\n\n \\citet{raj87v1504cyg} suggested that this object is an SU UMa-type\ndwarf nova based on the presence of two types of outbursts.\n\\citet{nog97v1504cyg} indeed confirmed the presence of superhumps\nduring the 1994 outburst. \\citet{tho97uvpervyaqrv1504cyg} reported\nspectroscopic orbital period. Since the alias selection was incorrect\nin \\citet{nog97v1504cyg}, we (re)analyzed the 1994, 2008 and 2009\nsuperoutbursts (tables \\ref{tab:v1504cygoc2008}, \\ref{tab:v1504cygoc2009})\nto determine the superhump period. The results are summarized in\ntable \\ref{tab:perlist}. The 1994 and 2008 superoutbursts were probably\nobserved during the stage B, and the 2009 was probably observed during\nthe stage C. \\citet{pav02v1504cygproc} also reported correct period\nidentification.\n\n\\begin{table}\n\\caption{Superhump maxima of V1504 Cyg (2008).}\\label{tab:v1504cygoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54710.1735 & 0.0004 & $-$0.0001 & 143 \\\\\n13 & 54711.1116 & 0.0009 & 0.0016 & 189 \\\\\n14 & 54711.1805 & 0.0011 & $-$0.0015 & 134 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454710.1736 + 0.072028 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1504 Cyg (2009).}\\label{tab:v1504cygoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54950.2615 & 0.0011 & 0.0000 & 142 \\\\\n41 & 54953.2040 & 0.0019 & $-$0.0005 & 97 \\\\\n42 & 54953.2768 & 0.0015 & 0.0005 & 132 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454950.2615 + 0.071782 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V2176 Cygni}\\label{obj:v2176cyg}\n\n V2176 Cyg was discovered by \\citet{hu97v2176cygiauc}.\n\\citet{van97v2176cygiauc} reported the detection of superhumps\nwith a period of 0.0561(4) d. The object soon entered a 2-mag\n``dip'' characteristic to a WZ Sge-type outburst (type-A outburst)\nand exhibited a long-lasting second plateau stage following\na short precursor-like maximum \\citep{nov01v2176cyg}.\nSince only insufficient data were available before the dip,\nwe analyzed the second plateau stage. The data used for analysis\nwere from AAVSO database and ones extracted from electronic figures\nin \\citet{nov01v2176cyg} (the data for their figure 3 were not\nincluded for analysis). A PDM analysis after removing the overall\ntrend yielded a strong periodicity of 0.056239(12) d.\nThe period agrees with that by \\citet{van97v2176cygiauc} within\ntheir errors, and we regard it as a refined value of $P_{\\rm SH}$.\nThe times of superhump maxima are listed in table \\ref{tab:v2176cygoc1997b}.\n\n We also determined times of maxima during the initial superoutburst\nplateau using the data in \\citet{kwa98v2176cyg}\n(table \\ref{tab:v2176cygoc1997a}). These maxima could not be directly\nlinked by the above period. By assuming phase continuity,\nwe obtained a mean period of 0.05607(5) d between BJD 2450696 and\n2450703. Since early observations by \\citet{van97v2176cygiauc}\nare unavailable, the possibility remains open whether the $P_{\\rm SH}$\nincreased after the dip, or whether there was a phase discontinuity.\nBy allowing a 0.5 phase shift, the period from the combined data\nis 0.05630(4) d.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig86.eps}\n \\end{center}\n \\caption{Superhumps in V2176 Cyg after the dip (1997). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v2176shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V2176 Cyg after the dip (1997).}\\label{tab:v2176cygoc1997b}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50702.4013 & 0.0063 & 0.0121 & -- \\\\\n1 & 50702.4365 & 0.0018 & $-$0.0089 & -- \\\\\n3 & 50702.5537 & 0.0013 & $-$0.0043 & -- \\\\\n4 & 50702.5991 & 0.0020 & $-$0.0151 & -- \\\\\n19 & 50703.4775 & 0.0046 & 0.0197 & -- \\\\\n20 & 50703.5277 & 0.0031 & 0.0137 & -- \\\\\n52 & 50705.3081 & 0.0020 & $-$0.0055 & 21 \\\\\n53 & 50705.3589 & 0.0022 & $-$0.0110 & 22 \\\\\n123 & 50709.3007 & 0.0255 & $-$0.0058 & 34 \\\\\n124 & 50709.3531 & 0.0028 & $-$0.0097 & 34 \\\\\n125 & 50709.4246 & 0.0055 & 0.0056 & 30 \\\\\n141 & 50710.3297 & 0.0201 & 0.0109 & 29 \\\\\n142 & 50710.3605 & 0.0046 & $-$0.0145 & 28 \\\\\n143 & 50710.4327 & 0.0035 & 0.0015 & 22 \\\\\n152 & 50710.9360 & 0.0015 & $-$0.0014 & 53 \\\\\n153 & 50710.9964 & 0.0016 & 0.0028 & 54 \\\\\n154 & 50711.0464 & 0.0200 & $-$0.0035 & 33 \\\\\n159 & 50711.3335 & 0.0033 & 0.0025 & 30 \\\\\n160 & 50711.3982 & 0.0042 & 0.0109 & 25 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450702.3893 + 0.056238 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V2176 Cyg before the dip (1997).}\\label{tab:v2176cygoc1997a}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50696.3318 & 0.0008 & 0.0005 & 26 \\\\\n1 & 50696.3893 & 0.0011 & 0.0008 & 26 \\\\\n2 & 50696.4425 & 0.0013 & $-$0.0030 & 27 \\\\\n3 & 50696.5041 & 0.0012 & 0.0015 & 27 \\\\\n4 & 50696.5597 & 0.0017 & 0.0001 & 19 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450696.3314 + 0.057048 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{HO Delphini}\\label{obj:hodel}\n\n \\citet{kat03hodel} reported on three superoutbursts in 1994, 1996\nand 2001. \\citet{kat03hodel} did not attempt to determine $P_{\\rm dot}$\nbecause of the decaying signal of the superhumps. We present\ntimes of superhump maxima for the 1994 and 2001 superoutbursts\n(tables \\ref{tab:hodeloc1994}, \\ref{tab:hodeloc2001}).\n\n The 2008 superoutburst was well-observed. This outburst was preceded\nby a precursor outburst and followed by a rebrightening.\nThe times of superhump maxima are listed in table \\ref{tab:hodeloc2008}.\nThe $O-C$ diagram (figure \\ref{fig:octrans}) was clearly composed of\nthe stage A ($E \\le 2$), the stage B with a positive $P_{\\rm dot}$,\nand a transition to the stage C with a shorter period,\nassociated with the brightening near the termination of the superoutburst\n(cf. \\cite{kat03hodel}).\nThe $P_{\\rm dot}$ for the stage B was $+6.4(1.5) \\times 10^{-5}$.\n\n A comparison of $O-C$ diagrams between different superoutbursts\n(figure \\ref{fig:hodelcomp}) now clearly indicate that the 1994 observation\nrecorded the stage B--C transition, in good agreement with the presence\nof a terminal brightening, and the short $P_{\\rm SH}$ during the\n2001 superoutburst reflects the short $P_{\\rm SH}$ at the start of\nthe stage B.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig87.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of HO Del between different\n superoutbursts. A period of 0.06437 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst (the start of the main superoutburst when preceded by\n a precursor) were used.\n }\n \\label{fig:hodelcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of HO Del (1994).}\\label{tab:hodeloc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49591.0526 & 0.0008 & $-$0.0044 & 59 \\\\\n1 & 49591.1199 & 0.0008 & $-$0.0015 & 44 \\\\\n17 & 49592.1469 & 0.0011 & $-$0.0040 & 43 \\\\\n32 & 49593.1206 & 0.0014 & 0.0046 & 43 \\\\\n47 & 49594.0854 & 0.0027 & 0.0041 & 43 \\\\\n49 & 49594.2185 & 0.0035 & 0.0085 & 43 \\\\\n93 & 49597.0371 & 0.0025 & $-$0.0040 & 24 \\\\\n94 & 49597.1021 & 0.0016 & $-$0.0033 & 29 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449591.0570 + 0.064345 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of HO Del (2001).}\\label{tab:hodeloc2001}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $N^c$ \\\\\n\\hline\n0 & 52150.3235 & 0.0002 & 221 \\\\\n1 & 52150.3875 & 0.0001 & 220 \\\\\n2 & 52150.4516 & 0.0002 & 150 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of HO Del (2008).}\\label{tab:hodeloc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54682.9928 & 0.0009 & $-$0.0043 & 175 \\\\\n1 & 54683.0590 & 0.0004 & $-$0.0022 & 271 \\\\\n2 & 54683.1212 & 0.0008 & $-$0.0043 & 153 \\\\\n11 & 54683.7030 & 0.0011 & $-$0.0007 & 52 \\\\\n12 & 54683.7667 & 0.0005 & $-$0.0013 & 23 \\\\\n13 & 54683.8317 & 0.0005 & $-$0.0005 & 16 \\\\\n14 & 54683.8956 & 0.0006 & $-$0.0008 & 17 \\\\\n22 & 54684.4087 & 0.0003 & $-$0.0017 & 243 \\\\\n23 & 54684.4734 & 0.0004 & $-$0.0012 & 177 \\\\\n24 & 54684.5381 & 0.0004 & $-$0.0008 & 124 \\\\\n33 & 54685.1113 & 0.0003 & $-$0.0058 & 128 \\\\\n34 & 54685.1791 & 0.0005 & $-$0.0023 & 256 \\\\\n35 & 54685.2417 & 0.0005 & $-$0.0039 & 201 \\\\\n38 & 54685.4373 & 0.0005 & $-$0.0011 & 118 \\\\\n40 & 54685.5670 & 0.0008 & 0.0002 & 112 \\\\\n52 & 54686.3376 & 0.0004 & $-$0.0002 & 132 \\\\\n53 & 54686.4022 & 0.0007 & 0.0001 & 166 \\\\\n54 & 54686.4670 & 0.0006 & 0.0008 & 157 \\\\\n55 & 54686.5309 & 0.0010 & 0.0003 & 134 \\\\\n58 & 54686.7256 & 0.0007 & 0.0024 & 87 \\\\\n63 & 54687.0453 & 0.0010 & 0.0008 & 79 \\\\\n64 & 54687.1106 & 0.0012 & 0.0019 & 84 \\\\\n69 & 54687.4355 & 0.0012 & 0.0055 & 27 \\\\\n80 & 54688.1435 & 0.0008 & 0.0068 & 220 \\\\\n81 & 54688.2078 & 0.0007 & 0.0069 & 201 \\\\\n95 & 54689.1088 & 0.0012 & 0.0085 & 118 \\\\\n96 & 54689.1720 & 0.0005 & 0.0074 & 217 \\\\\n109 & 54690.0018 & 0.0118 & 0.0020 & 37 \\\\\n110 & 54690.0718 & 0.0007 & 0.0077 & 63 \\\\\n111 & 54690.1306 & 0.0005 & 0.0024 & 208 \\\\\n112 & 54690.1986 & 0.0007 & 0.0061 & 79 \\\\\n130 & 54691.3506 & 0.0014 & 0.0017 & 62 \\\\\n131 & 54691.4133 & 0.0012 & 0.0001 & 61 \\\\\n132 & 54691.4861 & 0.0062 & 0.0086 & 25 \\\\\n136 & 54691.7329 & 0.0005 & $-$0.0015 & 23 \\\\\n137 & 54691.7959 & 0.0013 & $-$0.0027 & 22 \\\\\n138 & 54691.8611 & 0.0008 & $-$0.0018 & 18 \\\\\n141 & 54692.0549 & 0.0011 & $-$0.0007 & 93 \\\\\n142 & 54692.1172 & 0.0016 & $-$0.0027 & 87 \\\\\n143 & 54692.1837 & 0.0014 & $-$0.0004 & 122 \\\\\n164 & 54693.5166 & 0.0010 & $-$0.0167 & 37 \\\\\n165 & 54693.5851 & 0.0016 & $-$0.0124 & 37 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454682.9970 + 0.064245 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BC Doradus}\\label{obj:bcdor}\n\n \\citet{kat04nsv10934mmscoabnorcal86} suggested the SU UMa-type\nclassification of BC Dor = CAL 86. This suggestion was confirmed\nby the detection of superhumps during the 2003 November superoutburst.\nThe times of superhump maxima are listed in table \\ref{tab:bcdoroc2003}.\nSince the superhumps were still growing on the first night and since\nthe object was already fading on the last night, we used the middle\ntwo nights and determined the mean superhump period of 0.06850(12) d.\nThe $O-C$'s were strongly negative on the first and last night,\nsuggesting that early (stage A to B) and late (stage B to C) evolution\ntook place. Although the global $P_{\\rm dot}$ of\n$-8.9(0.5) \\times 10^{-5}$ was obtained, this value should be treated\nwith caution since it was determined from presumably segments of different\ntypes of behavior.\n\n\\begin{table}\n\\caption{Superhump maxima of BC Dor (2003).}\\label{tab:bcdoroc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52958.0575 & 0.0005 & $-$0.0118 & 226 \\\\\n45 & 52961.1395 & 0.0005 & 0.0021 & 34 \\\\\n59 & 52962.0985 & 0.0006 & 0.0066 & 35 \\\\\n60 & 52962.1658 & 0.0005 & 0.0057 & 32 \\\\\n61 & 52962.2336 & 0.0006 & 0.0053 & 24 \\\\\n146 & 52968.0157 & 0.0012 & $-$0.0078 & 100 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452958.0693 + 0.068180 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CP Draconis}\\label{obj:cpdra}\n\n CP Dra was initially discovered as a suspect supernova in NGC 3147.\nSubsequent observations established the dwarf nova-type\nnature of the object (\\cite{kho72cpdra}; \\cite{kol79cpdraciuma}).\nThe object has been regularly monitored by visual observers.\nDuring the 2001 outburst, T. Vanmunster detected superhumps\nwith a period of 0.0687(7) d (vsnet-alert 5709). The period, however,\ndid not agree with later observations.\n\n During the 2003 superoutburst, we succeeded in identifying the\nsuperhump period from the high-quality observations on first two nights.\nThe best period determined from the entire outburst was 0.08348(10) d.\nThe times of superhump maxima are shown in table \\ref{tab:cpdraoc2003}.\nThe period decreased at $P_{\\rm dot}$ = $-22.6(4.6) \\times 10^{-5}$,\nprobably reflecting the stage B--C transition.\n\n The 2009 superoutburst was well-observed during its middle-to-late\nstage (table \\ref{tab:cpdraoc2009}). A clear stage B--C transition\nwas recorded. The mean $P_{\\rm SH}$ during the stage C was\n0.083323(11) d (PDM method). The other parameters are listed in\ntable \\ref{tab:perlist}.\n\n\\begin{table}\n\\caption{Superhump maxima of CP Dra (2003).}\\label{tab:cpdraoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52648.1234 & 0.0005 & $-$0.0022 & 156 \\\\\n1 & 52648.2076 & 0.0005 & $-$0.0015 & 158 \\\\\n14 & 52649.2950 & 0.0016 & 0.0015 & 134 \\\\\n15 & 52649.3794 & 0.0017 & 0.0024 & 101 \\\\\n36 & 52651.1326 & 0.0028 & 0.0036 & 82 \\\\\n48 & 52652.1296 & 0.0036 & $-$0.0005 & 146 \\\\\n49 & 52652.2103 & 0.0022 & $-$0.0033 & 149 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452648.1256 + 0.083427 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CP Dra (2009).}\\label{tab:cpdraoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54915.4402 & 0.0002 & $-$0.0044 & 79 \\\\\n1 & 54915.5231 & 0.0003 & $-$0.0049 & 109 \\\\\n2 & 54915.6080 & 0.0006 & $-$0.0035 & 87 \\\\\n24 & 54917.4506 & 0.0003 & 0.0036 & 374 \\\\\n25 & 54917.5330 & 0.0003 & 0.0025 & 386 \\\\\n26 & 54917.6226 & 0.0007 & 0.0087 & 154 \\\\\n34 & 54918.2832 & 0.0010 & 0.0018 & 155 \\\\\n45 & 54919.1955 & 0.0015 & $-$0.0036 & 133 \\\\\n46 & 54919.2869 & 0.0022 & 0.0044 & 118 \\\\\n48 & 54919.4502 & 0.0004 & 0.0007 & 94 \\\\\n49 & 54919.5330 & 0.0008 & 0.0002 & 256 \\\\\n50 & 54919.6164 & 0.0004 & 0.0002 & 168 \\\\\n59 & 54920.3640 & 0.0010 & $-$0.0032 & 144 \\\\\n60 & 54920.4507 & 0.0006 & 0.0001 & 149 \\\\\n61 & 54920.5339 & 0.0009 & $-$0.0002 & 61 \\\\\n68 & 54921.1155 & 0.0013 & $-$0.0026 & 180 \\\\\n69 & 54921.2052 & 0.0034 & 0.0037 & 62 \\\\\n72 & 54921.4542 & 0.0018 & 0.0024 & 37 \\\\\n83 & 54922.3702 & 0.0024 & 0.0006 & 76 \\\\\n84 & 54922.4540 & 0.0008 & 0.0010 & 76 \\\\\n95 & 54923.3656 & 0.0023 & $-$0.0052 & 131 \\\\\n96 & 54923.4515 & 0.0027 & $-$0.0028 & 97 \\\\\n97 & 54923.5383 & 0.0023 & 0.0006 & 14 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454915.4446 + 0.083434 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DM Draconis}\\label{obj:dmdra}\n\n DM Dra was discovered as a dwarf nova by \\citet{ste82dmdra}.\n\\citet{kat02dmdra} studied the 2001 outburst and reported superhumps\nwith a period of 0.07561(3) d. The coverage of this outburst was\ninsufficient to determine $P_{\\rm dot}$. We undertook a more extensive\ncampaign during the 2003 superoutburst. The times of superhump maxima\nare listed in table \\ref{tab:dmdraoc2003}. We obtained a global\n$P_{\\rm dot}$ = $-15.3(1.8) \\times 10^{-5}$. Excluding the first two\nmaxima, which may have been recorded during the stage A,\nwe obtained $P_{\\rm dot}$ = $-13.6(2.3) \\times 10^{-5}$\n(cf. figure \\ref{fig:octrans}).\n\n\\begin{table}\n\\caption{Superhump maxima of DM Dra (2003).}\\label{tab:dmdraoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52706.2096 & 0.0005 & $-$0.0086 & 182 \\\\\n1 & 52706.2893 & 0.0005 & $-$0.0045 & 245 \\\\\n12 & 52707.1236 & 0.0045 & $-$0.0008 & 80 \\\\\n13 & 52707.1984 & 0.0014 & $-$0.0015 & 80 \\\\\n14 & 52707.2737 & 0.0021 & $-$0.0017 & 79 \\\\\n15 & 52707.3546 & 0.0039 & 0.0037 & 49 \\\\\n25 & 52708.1070 & 0.0011 & 0.0010 & 176 \\\\\n26 & 52708.1834 & 0.0011 & 0.0018 & 185 \\\\\n27 & 52708.2588 & 0.0007 & 0.0017 & 185 \\\\\n28 & 52708.3360 & 0.0014 & 0.0035 & 163 \\\\\n38 & 52709.0884 & 0.0013 & 0.0007 & 81 \\\\\n39 & 52709.1661 & 0.0006 & 0.0029 & 176 \\\\\n40 & 52709.2405 & 0.0006 & 0.0018 & 236 \\\\\n41 & 52709.3206 & 0.0006 & 0.0064 & 239 \\\\\n51 & 52710.0709 & 0.0011 & 0.0016 & 79 \\\\\n52 & 52710.1467 & 0.0012 & 0.0019 & 81 \\\\\n53 & 52710.2205 & 0.0011 & 0.0001 & 81 \\\\\n54 & 52710.2987 & 0.0073 & 0.0028 & 77 \\\\\n80 & 52712.2539 & 0.0006 & $-$0.0052 & 96 \\\\\n81 & 52712.3270 & 0.0016 & $-$0.0076 & 73 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452706.2183 + 0.075510 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DV Draconis}\\label{obj:dvdra}\n\n DV Dra is a dwarf nova discovered by \\citet{pav85dvdra}. The object\nhad long been suspected to be a WZ Sge-type dwarf nova \\citep{wen91dvdra}.\n\\citet{iid95dvdra} claimed a detection of a new outburst,\nbut was later confirmed to be a false recognition of a field star\n(vsnet-id 182, 183).\nIn 2005 November, P. Schmeer detected an outburst at an unfiltered\nCCD magnitude of 15.0 (vsnet-alert 8749). T. Vanmunster reported\nthe detection of double-wave early superhumps (cvnet-outburst 790).\nWe observed the outburst between November 22 (just preceding Vanmunster's\nobservation) and December 6. Early superhumps with a mean period of\n0.05883(2) d were detected at least until November 27\n(figure \\ref{fig:dvdraeshpdm}).\nDue to the short visibility, we could not convincingly detect the appearance\nof ordinary superhumps.\nWe include this object for improving the statistics of WZ Sge-type\ndwarf novae.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig88.eps}\n \\end{center}\n \\caption{Early superhumps in DV Dra (2005). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:dvdraeshpdm}\n\\end{figure}\n\n\\subsection{KV Draconis}\\label{obj:kvdra}\n\n The 2000 superoutburst was observed by two teams, \\citet{nog00kvdra}\nand \\citet{van00kvdra}. Although \\citet{van00kvdra} reported a slight\nincrease of the superhump period from 0.0601 d to 0.0603 d, we could not\ncalculate $P_{\\rm dot}$ because they did not publish the times of maxima.\n\\citet{nog00kvdra} reported a candidate period of 0.06019(2) d based on\nobservations separated by seven days. The period by \\citet{nog00kvdra}\nwas severely suffered from an aliasing problem, particularly when\nthe period was changing, due to the large gap in observation.\nAlthough the SU UMa-type nature was well-established\nupon this superoutburst, we still needed a better coverage to determine\nthe superhump period and its derivative.\n\n The 2002 superoutburst was relatively well-observed during the\nmost of the course of the outburst (table \\ref{tab:kvdraoc2002}).\nAlthough we obtained $P_{\\rm dot}$ = $+11.4(3.9) \\times 10^{-5}$\nfor $E \\le 108$, the period variation appeared rather abrupt,\ngiving a relatively constant period of 0.06002(3) d for $E \\le 59$.\nThe similar pattern of period variation was also observed during\nthe 2008 superoutburst of AQ Eri (subsection \\ref{sec:aqeri}).\nA stage B--C transition was also recorded.\n\n The 2004 superoutburst was well-observed for the early stage\n(table \\ref{tab:kvdraoc2004}).\nThe $P_{\\rm dot}$ = $+43.4(8.5) \\times 10^{-5}$ for $E \\le 96$ appears\ntoo large. There might have been a phase shift between $E=70$ and\n$E=79$. The period for $E \\le 24$ was relatively constant at\n0.06001(8) d, a period very close to the 2002 one.\nThe rather anomalous $O-C$ behavior during the late course of\nthe superoutburst in this system requires further investigation.\n\n We also observed the 2005 superoutburst, covering the middle-to-later\nportion of the plateau phase. The estimated times of superhump\nmaxima are listed in table \\ref{tab:kvdraoc2005}. The data gave\na significantly longer mean period of 0.06034(3) d, which is in\nbetter agreement with the longer value in \\citet{van00kvdra}.\nThe $P_{\\rm dot}$ from these data was $+11.2(4.2) \\times 10^{-5}$.\n\n The 2009 superoutburst was observed during the stage A--B transition\nand a later stage (table \\ref{tab:kvdraoc2009}). The $P_1$ in\ntable \\ref{tab:perlist} refers to the mean period of the early part\nof the stage B, shorter than $P_1$'s of other superoutbursts.\nThe maximum of $E=100$ was not included in calculating the $P_2$.\nThis maximum may have been a final part of the stage B.\n\n A comparison of $O-C$ diagrams between different superoutbursts\nis given in figure \\ref{fig:kvdracomp}. The stage B in this system\nappears to be composed of two linear segments rather than a continuous\nperiod change. The behavior of the late stage B was different\nbetween 2002 and 2004 superoutbursts. The difference may be\na result of early appearance of stage C superhumps during the\n2002 superoutburst.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig89.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of KV Dra between different\n superoutbursts. A period of 0.06044 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:kvdracomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of KV Dra (2002).}\\label{tab:kvdraoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52517.9567 & 0.0017 & 0.0024 & 116 \\\\\n1 & 52518.0114 & 0.0009 & $-$0.0031 & 196 \\\\\n2 & 52518.0781 & 0.0005 & 0.0034 & 246 \\\\\n3 & 52518.1398 & 0.0008 & 0.0048 & 135 \\\\\n10 & 52518.5581 & 0.0007 & 0.0015 & 25 \\\\\n11 & 52518.6183 & 0.0005 & 0.0014 & 40 \\\\\n12 & 52518.6753 & 0.0009 & $-$0.0019 & 64 \\\\\n17 & 52518.9807 & 0.0005 & 0.0024 & 117 \\\\\n18 & 52519.0400 & 0.0006 & 0.0015 & 117 \\\\\n19 & 52519.0998 & 0.0012 & 0.0010 & 110 \\\\\n23 & 52519.3403 & 0.0005 & 0.0006 & 74 \\\\\n24 & 52519.4020 & 0.0005 & 0.0021 & 149 \\\\\n25 & 52519.4617 & 0.0005 & 0.0016 & 175 \\\\\n27 & 52519.5785 & 0.0014 & $-$0.0021 & 41 \\\\\n28 & 52519.6391 & 0.0013 & $-$0.0018 & 42 \\\\\n29 & 52519.7000 & 0.0007 & $-$0.0011 & 132 \\\\\n30 & 52519.7620 & 0.0009 & 0.0007 & 31 \\\\\n34 & 52520.0013 & 0.0006 & $-$0.0010 & 180 \\\\\n35 & 52520.0630 & 0.0006 & 0.0005 & 175 \\\\\n36 & 52520.1197 & 0.0013 & $-$0.0030 & 112 \\\\\n44 & 52520.5967 & 0.0012 & $-$0.0079 & 41 \\\\\n45 & 52520.6570 & 0.0016 & $-$0.0078 & 89 \\\\\n46 & 52520.7188 & 0.0029 & $-$0.0063 & 57 \\\\\n51 & 52521.0204 & 0.0029 & $-$0.0058 & 221 \\\\\n52 & 52521.0802 & 0.0023 & $-$0.0062 & 138 \\\\\n56 & 52521.3205 & 0.0007 & $-$0.0069 & 38 \\\\\n57 & 52521.3770 & 0.0009 & $-$0.0107 & 25 \\\\\n58 & 52521.4360 & 0.0016 & $-$0.0119 & 38 \\\\\n59 & 52521.4982 & 0.0005 & $-$0.0099 & 28 \\\\\n69 & 52522.1293 & 0.0037 & 0.0189 & 96 \\\\\n73 & 52522.3426 & 0.0015 & $-$0.0088 & 42 \\\\\n74 & 52522.4080 & 0.0029 & $-$0.0036 & 48 \\\\\n75 & 52522.4644 & 0.0010 & $-$0.0074 & 27 \\\\\n83 & 52522.9683 & 0.0033 & 0.0146 & 112 \\\\\n84 & 52523.0335 & 0.0045 & 0.0195 & 115 \\\\\n89 & 52523.3319 & 0.0021 & 0.0168 & 40 \\\\\n90 & 52523.3880 & 0.0109 & 0.0127 & 42 \\\\\n106 & 52524.3529 & 0.0048 & 0.0138 & 54 \\\\\n107 & 52524.4005 & 0.0013 & 0.0011 & 72 \\\\\n108 & 52524.4597 & 0.0013 & 0.0001 & 48 \\\\\n134 & 52526.0227 & 0.0017 & $-$0.0029 & 117 \\\\\n135 & 52526.0855 & 0.0064 & $-$0.0004 & 114 \\\\\n139 & 52526.3274 & 0.0039 & 0.0006 & 43 \\\\\n140 & 52526.3851 & 0.0024 & $-$0.0019 & 43 \\\\\n141 & 52526.4373 & 0.0015 & $-$0.0100 & 31 \\\\\n149 & 52526.9429 & 0.0024 & 0.0138 & 78 \\\\\n150 & 52526.9958 & 0.0030 & 0.0064 & 117 \\\\\n151 & 52527.0597 & 0.0018 & 0.0100 & 117 \\\\\n152 & 52527.1059 & 0.0032 & $-$0.0040 & 100 \\\\\n190 & 52529.3730 & 0.0030 & $-$0.0257 & 55 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452517.9543 + 0.060234 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KV Dra (2004).}\\label{tab:kvdraoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53120.0483 & 0.0005 & 0.0079 & 84 \\\\\n1 & 53120.1078 & 0.0004 & 0.0070 & 85 \\\\\n2 & 53120.1677 & 0.0004 & 0.0065 & 67 \\\\\n17 & 53121.0644 & 0.0043 & $-$0.0032 & 43 \\\\\n18 & 53121.1284 & 0.0009 & 0.0004 & 83 \\\\\n19 & 53121.1878 & 0.0006 & $-$0.0006 & 185 \\\\\n20 & 53121.2466 & 0.0008 & $-$0.0022 & 192 \\\\\n21 & 53121.3131 & 0.0015 & 0.0038 & 56 \\\\\n23 & 53121.4273 & 0.0009 & $-$0.0028 & 57 \\\\\n24 & 53121.4873 & 0.0009 & $-$0.0032 & 62 \\\\\n67 & 53124.0751 & 0.0013 & $-$0.0135 & 113 \\\\\n68 & 53124.1263 & 0.0027 & $-$0.0228 & 109 \\\\\n69 & 53124.1839 & 0.0011 & $-$0.0256 & 107 \\\\\n70 & 53124.2504 & 0.0041 & $-$0.0195 & 110 \\\\\n79 & 53124.8270 & 0.0024 & 0.0132 & 44 \\\\\n80 & 53124.8820 & 0.0029 & 0.0078 & 40 \\\\\n84 & 53125.1240 & 0.0015 & 0.0081 & 114 \\\\\n85 & 53125.1810 & 0.0024 & 0.0047 & 216 \\\\\n86 & 53125.2359 & 0.0047 & $-$0.0008 & 117 \\\\\n94 & 53125.7322 & 0.0045 & 0.0121 & 32 \\\\\n95 & 53125.7972 & 0.0020 & 0.0167 & 48 \\\\\n96 & 53125.8595 & 0.0021 & 0.0186 & 38 \\\\\n117 & 53127.0994 & 0.0038 & $-$0.0104 & 69 \\\\\n118 & 53127.1681 & 0.0024 & $-$0.0021 & 102 \\\\\n183 & 53131.0937 & 0.0035 & $-$0.0039 & 83 \\\\\n185 & 53131.2127 & 0.0046 & $-$0.0058 & 66 \\\\\n186 & 53131.2885 & 0.0032 & 0.0096 & 63 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453120.0404 + 0.060422 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KV Dra (2005).}\\label{tab:kvdraoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53465.1897 & 0.0005 & 0.0007 & 185 \\\\\n1 & 53465.2521 & 0.0005 & 0.0027 & 180 \\\\\n15 & 53466.0916 & 0.0016 & $-$0.0025 & 105 \\\\\n16 & 53466.1553 & 0.0014 & 0.0008 & 130 \\\\\n17 & 53466.2147 & 0.0011 & $-$0.0002 & 124 \\\\\n18 & 53466.2727 & 0.0017 & $-$0.0025 & 103 \\\\\n66 & 53469.1715 & 0.0023 & $-$0.0001 & 114 \\\\\n67 & 53469.2330 & 0.0013 & 0.0011 & 115 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453465.1890 + 0.060341 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KV Dra (2009).}\\label{tab:kvdraoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54971.0059 & 0.0010 & $-$0.0038 & 164 \\\\\n1 & 54971.0690 & 0.0013 & $-$0.0009 & 157 \\\\\n2 & 54971.1323 & 0.0011 & 0.0021 & 176 \\\\\n3 & 54971.1910 & 0.0005 & 0.0005 & 291 \\\\\n4 & 54971.2515 & 0.0005 & 0.0007 & 261 \\\\\n7 & 54971.4375 & 0.0012 & 0.0059 & 24 \\\\\n8 & 54971.4943 & 0.0004 & 0.0025 & 31 \\\\\n18 & 54972.0969 & 0.0088 & 0.0023 & 81 \\\\\n19 & 54972.1571 & 0.0017 & 0.0022 & 119 \\\\\n22 & 54972.3303 & 0.0027 & $-$0.0055 & 60 \\\\\n23 & 54972.3948 & 0.0003 & $-$0.0012 & 116 \\\\\n24 & 54972.4584 & 0.0004 & 0.0021 & 111 \\\\\n25 & 54972.5160 & 0.0004 & $-$0.0006 & 116 \\\\\n39 & 54973.3561 & 0.0006 & $-$0.0044 & 118 \\\\\n40 & 54973.4156 & 0.0005 & $-$0.0052 & 118 \\\\\n41 & 54973.4782 & 0.0006 & $-$0.0028 & 113 \\\\\n42 & 54973.5403 & 0.0016 & $-$0.0010 & 74 \\\\\n100 & 54977.0527 & 0.0061 & 0.0152 & 65 \\\\\n105 & 54977.3384 & 0.0035 & $-$0.0004 & 72 \\\\\n106 & 54977.4042 & 0.0018 & 0.0051 & 108 \\\\\n107 & 54977.4595 & 0.0015 & 0.0002 & 109 \\\\\n108 & 54977.5172 & 0.0013 & $-$0.0024 & 98 \\\\\n122 & 54978.3603 & 0.0011 & $-$0.0032 & 63 \\\\\n123 & 54978.4198 & 0.0012 & $-$0.0040 & 63 \\\\\n124 & 54978.4809 & 0.0013 & $-$0.0032 & 60 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454971.0097 + 0.060277 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{MN Draconis}\\label{obj:mndra}\n\n This object was discovered by \\citet{ant02var73dra}. \\citet{nog03var73dra}\npresented an extensive study of this object and established its unusual\nproperties: long $P_{\\rm SH}$ of 0.104--0.106 d and unusually short \n($\\sim$ 60 d) supercycle length. The difference of periods between\ntwo superoutbursts can be attributed to different stages observed:\nstage C in 2002 October and stage B--C transition in 2002 December\n(figure \\ref{fig:lp1}).\nWe present periods based on this interpretation in table \\ref{tab:perlist}.\n\n Since the photometric orbital period (0.10424 d) mentioned in\n\\citep{nog03var73dra} is extremely close to the $P_2$ in the present\nidentification, we analyzed the corresponding segment in our data\nand obtained a period a periodicity around 0.1042--0.1047 d.\nWe suspect that this period was not the true\norbital period, but persisting (or permanent) superhumps having\na period close to $P_2$. The presence of permanent superhumps,\nif confirmed, would strengthen the resemblance of MN Dra to\nER UMa stars (e.g. \\cite{gao99erumaSH}; \\cite{ole08rzlmi}).\nIf the true orbital period is shorter, the problem of an exceptionally\nsmall fractional superhump excess \\citet{nog03var73dra} will be solved.\n\n We further point out that the 2003 April outburst was a superoutburst\n(table \\ref{tab:mndraoc2003apr}). The derived superhump period\nof 0.10480(5) d with the PDM method is in good agreement with the mean\nperiod of the 2002 October superoutburst. This superoutburst occurred\n$\\sim$ 65 d after the 2003 February superoutburst mentioned in\n\\citet{nog03var73dra}, confirming the relatively stable, short\nsupercycle. A PDM analysis of the 2008 July superoutburst yielded\na mean period of 0.10514(14) d (table \\ref{tab:mndraoc2008jul}).\n\n\\begin{table}\n\\caption{Superhump maxima of MN Dra (2003 April).}\\label{tab:mndraoc2003apr}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52750.4325 & 0.0008 & $-$0.0017 & 91 \\\\\n9 & 52751.3812 & 0.0013 & 0.0039 & 51 \\\\\n10 & 52751.4814 & 0.0011 & $-$0.0007 & 43 \\\\\n19 & 52752.4238 & 0.0021 & $-$0.0015 & 43 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452750.4342 + 0.10479 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of MN Dra (2008 July).}\\label{tab:mndraoc2008jul}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54677.5447 & 0.0014 & $-$0.0001 & 60 \\\\\n9 & 54678.4928 & 0.0015 & 0.0009 & 60 \\\\\n10 & 54678.5963 & 0.0016 & $-$0.0008 & 41 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454677.5448 + 0.10524 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{XZ Eridani}\\label{obj:xzeri}\n\n XZ Eri is an eclipsing SU UMa-type dwarf nova with a short\norbital period (\\cite{uem04xzeri}; \\cite{wou01v359cenxzeriyytel}).\nWe reanalyzed the observations presented in \\citet{uem04xzeri}\nand determined the times of superhump maxima (table \\ref{tab:xzerioc2003a}).\nAlthough the scatter was rather large, we can see an earlier segment\nwith a positive $P_{\\rm dot}$ (stage B) followed by a transition to\na shorter period (stage C). The $P_{\\rm dot}$ for the stage B\n($E \\le 77$) was $+15.3(5.6) \\times 10^{-5}$, strengthening the\nsuggestion in \\citet{uem04xzeri}.\n\n We also observed two superoutbursts in 2003 December (table\n\\ref{tab:xzerioc2003b}), in 2007 (table \\ref{tab:xzerioc2007})\nand in 2008 (table \\ref{tab:xzerioc2008}, combined data with the AAVSO\nobservations).\nWe only recorded the transition to a shorter period during the first\nsuperoutburst, while we managed to mainly record the stages of early\nevolution (stage A to B) and a positive $P_{\\rm dot}$.\nThe $P_{\\rm dot}$ for the 2007\nsuperoutburst was $+7.6(1.0) \\times 10^{-5}$ ($15 \\le E \\le 138$).\nThe 2008 superoutburst showed all stages of A--C.\nThe $P_{\\rm dot}$ during the stage B was $+22.5(4.7) \\times 10^{-5}$\n($23 \\le E \\le 92$).\n\n A comparison of $O-C$ diagrams between different superoutbursts\nis presented in figure \\ref{fig:xzericomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig90.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of XZ Eri between different\n superoutbursts. A period of 0.06283 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:xzericomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of XZ Eri (2003a).}\\label{tab:xzerioc2003a}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52667.9769 & 0.0026 & 0.0027 & 41 \\\\\n1 & 52668.0372 & 0.0009 & 0.0002 & 135 \\\\\n2 & 52668.0946 & 0.0033 & $-$0.0052 & 132 \\\\\n15 & 52668.9163 & 0.0006 & 0.0002 & 240 \\\\\n16 & 52668.9735 & 0.0013 & $-$0.0054 & 247 \\\\\n17 & 52669.0383 & 0.0007 & $-$0.0034 & 343 \\\\\n18 & 52669.1071 & 0.0009 & 0.0027 & 161 \\\\\n19 & 52669.1642 & 0.0004 & $-$0.0030 & 28 \\\\\n21 & 52669.2896 & 0.0005 & $-$0.0033 & 59 \\\\\n22 & 52669.3520 & 0.0006 & $-$0.0036 & 62 \\\\\n23 & 52669.4133 & 0.0007 & $-$0.0051 & 57 \\\\\n25 & 52669.5366 & 0.0007 & $-$0.0074 & 54 \\\\\n26 & 52669.6004 & 0.0006 & $-$0.0064 & 56 \\\\\n27 & 52669.6594 & 0.0015 & $-$0.0102 & 38 \\\\\n32 & 52669.9768 & 0.0027 & $-$0.0067 & 105 \\\\\n33 & 52670.0420 & 0.0013 & $-$0.0043 & 282 \\\\\n34 & 52670.1116 & 0.0031 & 0.0025 & 125 \\\\\n35 & 52670.1708 & 0.0011 & $-$0.0011 & 28 \\\\\n47 & 52670.9329 & 0.0066 & 0.0075 & 62 \\\\\n48 & 52670.9761 & 0.0044 & $-$0.0121 & 188 \\\\\n49 & 52671.0540 & 0.0008 & 0.0031 & 36 \\\\\n50 & 52671.1147 & 0.0042 & 0.0009 & 37 \\\\\n53 & 52671.3022 & 0.0012 & 0.0001 & 31 \\\\\n54 & 52671.3676 & 0.0012 & 0.0027 & 63 \\\\\n55 & 52671.4387 & 0.0156 & 0.0110 & 28 \\\\\n62 & 52671.8791 & 0.0012 & 0.0118 & 56 \\\\\n63 & 52671.9351 & 0.0014 & 0.0050 & 79 \\\\\n70 & 52672.3741 & 0.0021 & 0.0045 & 44 \\\\\n76 & 52672.7552 & 0.0020 & 0.0089 & 80 \\\\\n77 & 52672.8185 & 0.0014 & 0.0094 & 85 \\\\\n84 & 52673.2557 & 0.0012 & 0.0071 & 51 \\\\\n85 & 52673.3190 & 0.0008 & 0.0076 & 54 \\\\\n86 & 52673.3788 & 0.0019 & 0.0046 & 31 \\\\\n92 & 52673.7574 & 0.0009 & 0.0065 & 86 \\\\\n93 & 52673.8231 & 0.0011 & 0.0093 & 61 \\\\\n96 & 52674.0098 & 0.0113 & 0.0076 & 46 \\\\\n97 & 52674.0687 & 0.0010 & 0.0038 & 26 \\\\\n98 & 52674.1292 & 0.0010 & 0.0015 & 35 \\\\\n100 & 52674.2511 & 0.0035 & $-$0.0022 & 34 \\\\\n101 & 52674.3226 & 0.0010 & 0.0066 & 42 \\\\\n102 & 52674.3838 & 0.0024 & 0.0049 & 33 \\\\\n109 & 52674.8192 & 0.0025 & 0.0008 & 83 \\\\\n113 & 52675.0693 & 0.0026 & $-$0.0003 & 53 \\\\\n114 & 52675.1317 & 0.0024 & $-$0.0006 & 53 \\\\\n126 & 52675.8678 & 0.0012 & $-$0.0180 & 84 \\\\\n129 & 52676.0704 & 0.0030 & $-$0.0038 & 46 \\\\\n142 & 52676.8983 & 0.0092 & 0.0078 & 33 \\\\\n143 & 52676.9527 & 0.0027 & $-$0.0006 & 169 \\\\\n144 & 52677.0053 & 0.0040 & $-$0.0108 & 191 \\\\\n145 & 52677.0698 & 0.0049 & $-$0.0091 & 142 \\\\\n148 & 52677.2633 & 0.0038 & $-$0.0040 & 59 \\\\\n149 & 52677.3236 & 0.0031 & $-$0.0064 & 59 \\\\\n150 & 52677.3845 & 0.0038 & $-$0.0083 & 60 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452667.9742 + 0.062791 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of XZ Eri (2003b).}\\label{tab:xzerioc2003b}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52988.1179 & 0.0007 & $-$0.0019 & 114 \\\\\n1 & 52988.1790 & 0.0010 & $-$0.0037 & 116 \\\\\n2 & 52988.2530 & 0.0037 & 0.0075 & 48 \\\\\n15 & 52989.0617 & 0.0012 & $-$0.0003 & 47 \\\\\n16 & 52989.1214 & 0.0024 & $-$0.0035 & 86 \\\\\n17 & 52989.1915 & 0.0036 & 0.0038 & 63 \\\\\n31 & 52990.0644 & 0.0015 & $-$0.0027 & 109 \\\\\n32 & 52990.1276 & 0.0017 & $-$0.0023 & 60 \\\\\n111 & 52995.1010 & 0.0024 & 0.0087 & 49 \\\\\n112 & 52995.1627 & 0.0060 & 0.0076 & 49 \\\\\n126 & 52996.0296 & 0.0041 & $-$0.0049 & 62 \\\\\n128 & 52996.1518 & 0.0037 & $-$0.0083 & 91 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452988.1199 + 0.062815 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of XZ Eri (2007).}\\label{tab:xzerioc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54440.1704 & 0.0004 & $-$0.0228 & 84 \\\\\n1 & 54440.2257 & 0.0015 & $-$0.0303 & 145 \\\\\n15 & 54441.1429 & 0.0004 & 0.0072 & 31 \\\\\n22 & 54441.5815 & 0.0001 & 0.0059 & 120 \\\\\n23 & 54441.6440 & 0.0001 & 0.0056 & 116 \\\\\n24 & 54441.7054 & 0.0001 & 0.0042 & 116 \\\\\n25 & 54441.7686 & 0.0001 & 0.0045 & 110 \\\\\n26 & 54441.8318 & 0.0002 & 0.0049 & 104 \\\\\n29 & 54442.0222 & 0.0015 & 0.0068 & 65 \\\\\n30 & 54442.0835 & 0.0031 & 0.0053 & 68 \\\\\n31 & 54442.1478 & 0.0010 & 0.0067 & 67 \\\\\n38 & 54442.5849 & 0.0004 & 0.0040 & 93 \\\\\n39 & 54442.6530 & 0.0022 & 0.0092 & 71 \\\\\n40 & 54442.7122 & 0.0004 & 0.0056 & 93 \\\\\n41 & 54442.7731 & 0.0004 & 0.0036 & 93 \\\\\n42 & 54442.8368 & 0.0017 & 0.0045 & 48 \\\\\n45 & 54443.0237 & 0.0012 & 0.0029 & 61 \\\\\n46 & 54443.0858 & 0.0020 & 0.0022 & 123 \\\\\n47 & 54443.1479 & 0.0015 & 0.0014 & 98 \\\\\n56 & 54443.7088 & 0.0002 & $-$0.0033 & 86 \\\\\n57 & 54443.7705 & 0.0003 & $-$0.0044 & 84 \\\\\n58 & 54443.8347 & 0.0003 & $-$0.0030 & 102 \\\\\n61 & 54444.0355 & 0.0009 & 0.0093 & 45 \\\\\n62 & 54444.0854 & 0.0004 & $-$0.0036 & 185 \\\\\n63 & 54444.1491 & 0.0007 & $-$0.0027 & 160 \\\\\n64 & 54444.2115 & 0.0007 & $-$0.0032 & 113 \\\\\n70 & 54444.5892 & 0.0003 & $-$0.0025 & 76 \\\\\n71 & 54444.6520 & 0.0005 & $-$0.0026 & 81 \\\\\n72 & 54444.7149 & 0.0005 & $-$0.0025 & 92 \\\\\n73 & 54444.7778 & 0.0004 & $-$0.0025 & 92 \\\\\n74 & 54444.8404 & 0.0005 & $-$0.0027 & 89 \\\\\n77 & 54445.0312 & 0.0010 & $-$0.0004 & 35 \\\\\n85 & 54445.5318 & 0.0005 & $-$0.0025 & 85 \\\\\n86 & 54445.5940 & 0.0005 & $-$0.0031 & 91 \\\\\n88 & 54445.7194 & 0.0003 & $-$0.0034 & 100 \\\\\n89 & 54445.7831 & 0.0003 & $-$0.0025 & 108 \\\\\n90 & 54445.8441 & 0.0003 & $-$0.0044 & 88 \\\\\n133 & 54448.5554 & 0.0006 & 0.0049 & 57 \\\\\n134 & 54448.6192 & 0.0008 & 0.0059 & 52 \\\\\n135 & 54448.6797 & 0.0004 & 0.0036 & 56 \\\\\n136 & 54448.7425 & 0.0005 & 0.0035 & 53 \\\\\n137 & 54448.8041 & 0.0004 & 0.0022 & 51 \\\\\n138 & 54448.8689 & 0.0015 & 0.0043 & 34 \\\\\n157 & 54450.0577 & 0.0046 & $-$0.0008 & 37 \\\\\n173 & 54451.0686 & 0.0048 & 0.0046 & 41 \\\\\n174 & 54451.1186 & 0.0022 & $-$0.0082 & 48 \\\\\n189 & 54452.0603 & 0.0033 & $-$0.0091 & 38 \\\\\n190 & 54452.1298 & 0.0190 & $-$0.0024 & 38 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454440.1931 + 0.062837 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of XZ Eri (2008).}\\label{tab:xzerioc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54796.9957 & 0.0072 & 0.0043 & 47 \\\\\n1 & 54797.0379 & 0.0017 & $-$0.0164 & 79 \\\\\n2 & 54797.1010 & 0.0012 & $-$0.0161 & 65 \\\\\n3 & 54797.1917 & 0.0022 & 0.0118 & 12 \\\\\n10 & 54797.6237 & 0.0010 & 0.0040 & 48 \\\\\n23 & 54798.4443 & 0.0007 & 0.0078 & 40 \\\\\n32 & 54799.0084 & 0.0010 & 0.0064 & 51 \\\\\n33 & 54799.0639 & 0.0004 & $-$0.0009 & 124 \\\\\n34 & 54799.1312 & 0.0008 & 0.0035 & 101 \\\\\n35 & 54799.1921 & 0.0006 & 0.0016 & 38 \\\\\n36 & 54799.2541 & 0.0006 & 0.0008 & 38 \\\\\n48 & 54800.0112 & 0.0098 & 0.0039 & 5 \\\\\n50 & 54800.1355 & 0.0021 & 0.0026 & 37 \\\\\n51 & 54800.1934 & 0.0046 & $-$0.0024 & 65 \\\\\n59 & 54800.6963 & 0.0009 & $-$0.0021 & 35 \\\\\n60 & 54800.7600 & 0.0007 & $-$0.0013 & 50 \\\\\n61 & 54800.8223 & 0.0007 & $-$0.0018 & 44 \\\\\n63 & 54800.9443 & 0.0068 & $-$0.0055 & 18 \\\\\n64 & 54801.0114 & 0.0016 & $-$0.0012 & 15 \\\\\n65 & 54801.0723 & 0.0022 & $-$0.0031 & 40 \\\\\n66 & 54801.1320 & 0.0011 & $-$0.0063 & 50 \\\\\n67 & 54801.1991 & 0.0073 & $-$0.0020 & 33 \\\\\n75 & 54801.7071 & 0.0010 & 0.0034 & 33 \\\\\n76 & 54801.7704 & 0.0008 & 0.0038 & 37 \\\\\n77 & 54801.8283 & 0.0015 & $-$0.0010 & 38 \\\\\n91 & 54802.7146 & 0.0009 & 0.0056 & 41 \\\\\n92 & 54802.7764 & 0.0010 & 0.0046 & 45 \\\\\n123 & 54804.7204 & 0.0011 & 0.0009 & 38 \\\\\n124 & 54804.7829 & 0.0013 & 0.0005 & 37 \\\\\n162 & 54807.1652 & 0.0058 & $-$0.0048 & 74 \\\\\n163 & 54807.2322 & 0.0065 & $-$0.0006 & 67 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454796.9914 + 0.062830 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AQ Eridani}\\label{sec:aqeri}\\label{obj:aqeri}\n\n \\citet{kat91aqeri} observed the 1991 superoutburst and reported\na period of 0.06225 d. \\citet{kat01aqeri} reported a single-night\nobservation of the 1992 superoutburst, and found an anomalously\nlong (0.0642(4) d) superhump period.\n\n Although the original data for the 1991 superoutburst is already\nunavailable, we reanalyzed the 1992 data together with unpublished\nobservations (table \\ref{tab:aqerioc1992}). The anomalously long\n$P_{\\rm SH}$ has been confirmed (0.0638(7) d for $0 \\le E \\le 3$).\nThe period, however, of the entire observation is 0.0616(2).\nThe observation likely caught the transition from the stage B to C.\n\n We further observed the 2006 superoutburst during its late plateau\nstage (table \\ref{tab:aqerioc2006}). Because the observation was\nperformed when the superhumps had small amplitudes and relatively\nirregular profiles, the quality of the $O-C$ analysis was not\nsatisfactory. The mean period (likely $P_2$) was 0.0617(1) d.\n\n The 2008 superoutburst was well observed (table \\ref{tab:aqerioc2008}),\nfirst clearly establishing the positive $P_{\\rm dot}$ of\n$+4.4(0.8) \\times 10^{-5}$ (figure \\ref{fig:aqeri2008oc}).\nThis superoutburst was preceded by a distinct precursor,\nstrengthening that the overall behavior of period derivatives are\nnot strongly affected by the presence of a precursor outburst.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig91.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps AQ Eri (2008).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($E \\le 163$, thin curve)\n (Lower): Light curve. Large dots are our CCD observations and small\n dots are visual and $V$ observation from the VSOLJ database and ASAS-3\n observations.}\n \\label{fig:aqeri2008oc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of AQ Eri (1992).}\\label{tab:aqerioc1992}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48626.0215 & 0.0006 & $-$0.0036 & 65 \\\\\n1 & 48626.0857 & 0.0002 & $-$0.0011 & 111 \\\\\n2 & 48626.1516 & 0.0003 & 0.0032 & 110 \\\\\n3 & 48626.2123 & 0.0006 & 0.0022 & 56 \\\\\n18 & 48627.1339 & 0.0012 & $-$0.0007 & 59 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448626.0252 + 0.061634 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AQ Eri (2006).}\\label{tab:aqerioc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n\\hline\n0 & 54070.1471 & 0.0046 & 0.0026 & 61 \\\\\n49 & 54073.1713 & 0.0037 & 0.0045 & 69 \\\\\n50 & 54073.2291 & 0.0011 & 0.0006 & 67 \\\\\n65 & 54074.1520 & 0.0043 & $-$0.0017 & 55 \\\\\n67 & 54074.2623 & 0.0012 & $-$0.0148 & 58 \\\\\n97 & 54076.1363 & 0.0021 & 0.0088 & 30 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454070.1445 + 0.061681 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AQ Eri (2008).}\\label{tab:aqerioc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54826.9930 & 0.0004 & 0.0040 & 208 \\\\\n1 & 54827.0601 & 0.0008 & 0.0087 & 233 \\\\\n2 & 54827.1204 & 0.0005 & 0.0066 & 233 \\\\\n3 & 54827.1822 & 0.0004 & 0.0061 & 271 \\\\\n4 & 54827.2403 & 0.0014 & 0.0018 & 50 \\\\\n16 & 54827.9912 & 0.0006 & 0.0043 & 183 \\\\\n17 & 54828.0507 & 0.0003 & 0.0014 & 316 \\\\\n18 & 54828.1153 & 0.0002 & 0.0037 & 300 \\\\\n19 & 54828.1766 & 0.0003 & 0.0026 & 173 \\\\\n22 & 54828.3645 & 0.0003 & 0.0034 & 75 \\\\\n23 & 54828.4258 & 0.0003 & 0.0023 & 87 \\\\\n24 & 54828.4877 & 0.0004 & 0.0019 & 77 \\\\\n32 & 54828.9859 & 0.0013 & 0.0011 & 44 \\\\\n34 & 54829.1101 & 0.0004 & 0.0006 & 93 \\\\\n35 & 54829.1718 & 0.0004 & $-$0.0001 & 87 \\\\\n49 & 54830.0419 & 0.0006 & $-$0.0031 & 88 \\\\\n50 & 54830.1041 & 0.0004 & $-$0.0032 & 92 \\\\\n51 & 54830.1690 & 0.0009 & $-$0.0008 & 126 \\\\\n52 & 54830.2248 & 0.0006 & $-$0.0073 & 82 \\\\\n54 & 54830.3552 & 0.0006 & $-$0.0016 & 81 \\\\\n55 & 54830.4174 & 0.0007 & $-$0.0018 & 78 \\\\\n56 & 54830.4773 & 0.0004 & $-$0.0042 & 83 \\\\\n65 & 54831.0347 & 0.0008 & $-$0.0081 & 123 \\\\\n66 & 54831.1010 & 0.0010 & $-$0.0042 & 174 \\\\\n67 & 54831.1616 & 0.0008 & $-$0.0060 & 90 \\\\\n68 & 54831.2194 & 0.0014 & $-$0.0105 & 82 \\\\\n69 & 54831.2907 & 0.0010 & $-$0.0016 & 61 \\\\\n70 & 54831.3520 & 0.0012 & $-$0.0027 & 77 \\\\\n80 & 54831.9782 & 0.0014 & $-$0.0001 & 91 \\\\\n81 & 54832.0353 & 0.0009 & $-$0.0054 & 92 \\\\\n82 & 54832.1002 & 0.0011 & $-$0.0029 & 105 \\\\\n83 & 54832.1603 & 0.0012 & $-$0.0052 & 85 \\\\\n84 & 54832.2182 & 0.0033 & $-$0.0096 & 90 \\\\\n96 & 54832.9808 & 0.0035 & 0.0046 & 109 \\\\\n97 & 54833.0278 & 0.0027 & $-$0.0108 & 47 \\\\\n98 & 54833.1018 & 0.0015 & 0.0009 & 83 \\\\\n111 & 54833.9120 & 0.0038 & 0.0003 & 38 \\\\\n115 & 54834.1606 & 0.0044 & $-$0.0005 & 88 \\\\\n127 & 54834.9150 & 0.0015 & 0.0055 & 76 \\\\\n128 & 54834.9747 & 0.0006 & 0.0028 & 205 \\\\\n129 & 54835.0370 & 0.0011 & 0.0028 & 74 \\\\\n130 & 54835.0989 & 0.0006 & 0.0023 & 44 \\\\\n131 & 54835.1609 & 0.0025 & 0.0020 & 24 \\\\\n144 & 54835.9775 & 0.0018 & 0.0078 & 124 \\\\\n145 & 54836.0295 & 0.0019 & $-$0.0026 & 92 \\\\\n146 & 54836.0873 & 0.0030 & $-$0.0072 & 26 \\\\\n160 & 54836.9728 & 0.0033 & 0.0052 & 89 \\\\\n161 & 54837.0418 & 0.0018 & 0.0119 & 93 \\\\\n162 & 54837.0929 & 0.0021 & 0.0006 & 60 \\\\\n163 & 54837.1505 & 0.0125 & $-$0.0042 & 47 \\\\\n176 & 54837.9701 & 0.0017 & 0.0047 & 31 \\\\\n177 & 54838.0272 & 0.0020 & $-$0.0006 & 81 \\\\\n178 & 54838.0946 & 0.0023 & 0.0045 & 34 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454826.9891 + 0.062366 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{UV Geminorum}\\label{sec:uvgem}\\label{obj:uvgem}\n\n UV Gem has long been known as a dwarf nova \\citep{GCVS}.\n\\citet{kat01uvgemfsandaspsc} suggested the SU UMa-type classification\nbased on the long-term light curve consisting of a likely superoutburst\nand short outbursts with a short cycle length.\nT. Vanmunster (vsnet-alert 3821) first reported the detection of\nsuperhumps with a period of 0.0902(6) d.\nDuring the 2003 superoutburst, we conducted an extensive campaign\nand obtained a high-quality set of superhump times\n(table \\ref{tab:uvgemoc2003}). The large variation in the $O-C$\ndiagram indicates a strong period decrease (figure \\ref{fig:lp1}).\nUsing all the data, the $P_{\\rm dot}$ was $-53.4(3.6) \\times 10^{-5}$.\nEven if we exclude the early part ($E \\le 5$), the $P_{\\rm dot}$ was\n$-33.5(2.0) \\times 10^{-5}$, still extreme.\nThe situation is particularly similar to a long-$P_{\\rm orb}$ system\nMN Dra \\citep{nog03var73dra}, who reported a global $P_{\\rm dot}$\nof $-170(20) \\times 10^{-5}$. The present data of UV Gem\nneither has cycle ambiguity nor a large gap in observation,\nthereby firmly demonstrating the existence of an exceptionally\nstrong decrease in the superhump period.\nLong-$P_{\\rm orb}$ systems appear to share this tendency of period\nvariation.\n\n The times of superhump maxima for the 2008 superoutburst are also\ngiven (table \\ref{tab:uvgemoc2008}). This superoutburst was probably\nobserved during its late stage.\n\n\\begin{table}\n\\caption{Superhump maxima of UV Gem (2003).}\\label{tab:uvgemoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52645.9759 & 0.0036 & $-$0.0276 & 106 \\\\\n1 & 52646.0681 & 0.0014 & $-$0.0285 & 179 \\\\\n2 & 52646.1590 & 0.0009 & $-$0.0307 & 238 \\\\\n3 & 52646.2522 & 0.0023 & $-$0.0305 & 202 \\\\\n4 & 52646.3538 & 0.0004 & $-$0.0221 & 48 \\\\\n5 & 52646.4534 & 0.0006 & $-$0.0156 & 57 \\\\\n10 & 52646.9352 & 0.0010 & 0.0007 & 178 \\\\\n11 & 52647.0290 & 0.0014 & 0.0013 & 177 \\\\\n12 & 52647.1271 & 0.0004 & 0.0063 & 292 \\\\\n13 & 52647.2200 & 0.0013 & 0.0061 & 264 \\\\\n15 & 52647.4116 & 0.0006 & 0.0116 & 49 \\\\\n16 & 52647.5019 & 0.0010 & 0.0087 & 56 \\\\\n21 & 52647.9717 & 0.0008 & 0.0130 & 178 \\\\\n22 & 52648.0660 & 0.0005 & 0.0142 & 180 \\\\\n23 & 52648.1589 & 0.0004 & 0.0140 & 178 \\\\\n24 & 52648.2520 & 0.0009 & 0.0140 & 178 \\\\\n25 & 52648.3414 & 0.0020 & 0.0102 & 170 \\\\\n26 & 52648.4389 & 0.0004 & 0.0147 & 127 \\\\\n27 & 52648.5332 & 0.0006 & 0.0158 & 90 \\\\\n33 & 52649.0914 & 0.0004 & 0.0154 & 165 \\\\\n34 & 52649.1860 & 0.0007 & 0.0170 & 98 \\\\\n35 & 52649.2759 & 0.0004 & 0.0137 & 163 \\\\\n36 & 52649.3691 & 0.0006 & 0.0139 & 114 \\\\\n37 & 52649.4626 & 0.0004 & 0.0142 & 168 \\\\\n38 & 52649.5537 & 0.0005 & 0.0122 & 75 \\\\\n54 & 52651.0392 & 0.0006 & 0.0080 & 160 \\\\\n55 & 52651.1297 & 0.0007 & 0.0054 & 146 \\\\\n56 & 52651.2254 & 0.0009 & 0.0080 & 122 \\\\\n57 & 52651.3171 & 0.0014 & 0.0065 & 72 \\\\\n58 & 52651.4055 & 0.0007 & 0.0019 & 130 \\\\\n59 & 52651.4966 & 0.0006 & $-$0.0001 & 124 \\\\\n60 & 52651.5953 & 0.0033 & 0.0055 & 37 \\\\\n65 & 52652.0533 & 0.0007 & $-$0.0021 & 189 \\\\\n66 & 52652.1459 & 0.0006 & $-$0.0025 & 185 \\\\\n67 & 52652.2365 & 0.0004 & $-$0.0051 & 188 \\\\\n75 & 52652.9728 & 0.0034 & $-$0.0136 & 105 \\\\\n76 & 52653.0668 & 0.0009 & $-$0.0127 & 187 \\\\\n77 & 52653.1607 & 0.0009 & $-$0.0119 & 163 \\\\\n78 & 52653.2514 & 0.0023 & $-$0.0144 & 74 \\\\\n80 & 52653.4345 & 0.0006 & $-$0.0174 & 76 \\\\\n81 & 52653.5275 & 0.0007 & $-$0.0176 & 74 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452646.0035 + 0.093106 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of UV Gem (2008).}\\label{tab:uvgemoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54806.1048 & 0.0108 & $-$0.0059 & 44 \\\\\n1 & 54806.2067 & 0.0014 & 0.0032 & 126 \\\\\n2 & 54806.2995 & 0.0036 & 0.0033 & 34 \\\\\n11 & 54807.1312 & 0.0019 & 0.0002 & 97 \\\\\n12 & 54807.2253 & 0.0016 & 0.0015 & 191 \\\\\n13 & 54807.3149 & 0.0007 & $-$0.0016 & 208 \\\\\n22 & 54808.1435 & 0.0048 & $-$0.0078 & 98 \\\\\n23 & 54808.2512 & 0.0021 & 0.0071 & 97 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454806.1107 + 0.092758 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AW Geminorum}\\label{obj:awgem}\n\n \\citet{kat96awgem} observed the 1995 superoutburst during its\nearly stage. The refined times of superhump maxima are listed in table\n\\ref{tab:awgemoc1995}. The $O-C$ diagram shows a similar trend to\nthose of V877 Ara and DT Oct (a period shift from a longer period\nduring the earliest stage). Excluding the early part (stage A, $E \\le 1$),\nwe obtained the mean $P_{\\rm SH}$ = 0.07935(9) d and\n$P_{\\rm dot}$ = $-3.2(1.5) \\times 10^{-5}$.\nWe also observed the 2008 superoutburst (table \\ref{tab:awgemoc2008})\nduring its early stage and the 2009 superoutburst\n(table \\ref{tab:awgemoc2009}).\nA strong period variation, as recorded in the 1995 superoutburst,\nwas recorded during the latter superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of AW Gem (1995).}\\label{tab:awgemoc1995}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50001.2611 & 0.0017 & $-$0.0133 & 74 \\\\\n1 & 50001.3368 & 0.0027 & $-$0.0176 & 43 \\\\\n12 & 50002.2511 & 0.0003 & 0.0155 & 75 \\\\\n13 & 50002.3325 & 0.0006 & 0.0169 & 61 \\\\\n25 & 50003.2896 & 0.0004 & 0.0126 & 58 \\\\\n38 & 50004.3172 & 0.0004 & $-$0.0011 & 75 \\\\\n51 & 50005.3468 & 0.0009 & $-$0.0129 & 54 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450001.2743 + 0.080106 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AW Gem (2008).}\\label{tab:awgemoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54567.9600 & 0.0009 & 0.0024 & 180 \\\\\n1 & 54568.0420 & 0.0009 & 0.0054 & 235 \\\\\n2 & 54568.1064 & 0.0150 & $-$0.0091 & 190 \\\\\n38 & 54570.9630 & 0.0017 & 0.0038 & 135 \\\\\n52 & 54572.0625 & 0.0014 & $-$0.0025 & 191 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454567.9576 + 0.078990 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AW Gem (2009).}\\label{tab:awgemoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54922.9682 & 0.0032 & $-$0.0156 & 95 \\\\\n1 & 54923.0417 & 0.0074 & $-$0.0215 & 147 \\\\\n12 & 54923.9486 & 0.0012 & 0.0132 & 137 \\\\\n13 & 54924.0267 & 0.0022 & 0.0121 & 119 \\\\\n63 & 54927.9950 & 0.0007 & 0.0156 & 144 \\\\\n64 & 54928.0751 & 0.0017 & 0.0164 & 95 \\\\\n88 & 54929.9653 & 0.0008 & 0.0035 & 82 \\\\\n89 & 54930.0420 & 0.0015 & 0.0009 & 81 \\\\\n101 & 54930.9870 & 0.0010 & $-$0.0056 & 81 \\\\\n102 & 54931.0698 & 0.0025 & $-$0.0021 & 53 \\\\\n114 & 54932.0064 & 0.0016 & $-$0.0170 & 81 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454922.9838 + 0.079295 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CI Geminorum}\\label{obj:cigem}\n\n \\citet{wen90cigem} suggested the SU UMa-type classification of this\nobject based on the existence of long and short outbursts.\nThe large rate of decline of a short outburst in 1999 was consistent\nwith that of a normal outburst of an SU UMa-type dwarf nova\n\\citep{kat99cigem}, although \\citet{sch99cigem} favored the SS Cyg-type\nclassification.\nThe object underwent a long outburst in 2005 April, consisting of\na precursor and a long plateau (figure \\ref{fig:cigemlc}).\n\n Although the presence of superhumps with a period about $\\sim$0.1 d\nis apparent in the sparse raw data, a PDM analysis of the entire set of\ndata did not yield a significant period. The situation appears similar to \nCTCV J0549 with a long $P_{\\rm SH}$ and large period variation.\nWe therefore analyzed the data in separate segments, measured superhump\nmaxima (table \\ref{tab:cigemoc2005}) and searched for a likely period.\nThe period of $\\sim$0.117 d with a significant period decrease only can\nnaturally express the available observations (figure \\ref{fig:cigemshpdm}).\nAlthough the exact identification of the period should await further\nobservations, the present analysis suggests that CI Gem is an excellent\ncandidate for a dwarf nova in the period gap.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig92.eps}\n \\end{center}\n \\caption{Superoutburst of CI Gem in 2005. The data are a combination\n of the AAVSO data and our observations. The fading around BJD\n 2453473--2453474 is a precursor outburst.}\n \\label{fig:cigemlc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig93.eps}\n \\end{center}\n \\caption{Superhumps in CI Gem for the early stage the plateau\n (BJD 2453474.5 -- 2453476). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:cigemshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CI Gem (2005).}\\label{tab:cigemoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53474.6646 & 0.0077 & $-$0.0206 & 55 \\\\\n6 & 53475.3707 & 0.0017 & $-$0.0072 & 16 \\\\\n9 & 53475.7219 & 0.0048 & $-$0.0023 & 91 \\\\\n16 & 53476.5655 & 0.0144 & 0.0333 & 21 \\\\\n17 & 53476.6938 & 0.0011 & 0.0461 & 25 \\\\\n25 & 53477.5421 & 0.0059 & $-$0.0290 & 7 \\\\\n26 & 53477.6663 & 0.0023 & $-$0.0203 & 19 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453474.6853 + 0.115433 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{IR Geminorum}\\label{obj:irgem}\n\n We measured times of superhump maxima (table \\ref{tab:irgemoc1991})\nfrom observations reported in \\citet{kat01irgem}.\nWe also observed the 2009 superoutburst (table \\ref{tab:irgemoc2009}).\nAlthough the data were limited, we can see a likely stage B--C\ntransition (the presence of a phase shift between $E=27$ and $E=86$\nis not completely excluded).\nBecause the profile of the superhumps was rather irregular, we determined\nthe mean period for stage B with the PDM method as 0.07093(3) d.\n\n\\begin{table}\n\\caption{Superhump maxima of IR Gem (1991).}\\label{tab:irgemoc1991}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48333.9835 & 0.0006 & 0.0018 & 268 \\\\\n1 & 48334.0507 & 0.0006 & $-$0.0019 & 260 \\\\\n14 & 48334.9742 & 0.0009 & 0.0009 & 269 \\\\\n15 & 48335.0434 & 0.0010 & $-$0.0007 & 261 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448333.9818 + 0.070821 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IR Gem (2009).}\\label{tab:irgemoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54838.0172 & 0.0003 & $-$0.0048 & 196 \\\\\n2 & 54838.1611 & 0.0007 & $-$0.0018 & 73 \\\\\n3 & 54838.2338 & 0.0006 & 0.0005 & 74 \\\\\n4 & 54838.3022 & 0.0008 & $-$0.0016 & 63 \\\\\n27 & 54839.9357 & 0.0007 & 0.0117 & 63 \\\\\n86 & 54844.0724 & 0.0019 & $-$0.0080 & 61 \\\\\n87 & 54844.1521 & 0.0036 & 0.0013 & 24 \\\\\n100 & 54845.0674 & 0.0010 & 0.0007 & 193 \\\\\n101 & 54845.1414 & 0.0009 & 0.0043 & 185 \\\\\n102 & 54845.2089 & 0.0015 & 0.0014 & 145 \\\\\n103 & 54845.2744 & 0.0019 & $-$0.0036 & 53 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454838.0220 + 0.070447 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CI Gruis}\\label{obj:cigru}\n\n CI Gru was discovered as an outbursting CV \\citep{haw83cegruchgrucigru}.\n\\citet{hae95cfgrucigru} reported semi-periodic variations with a period\nof 0.056 d during the possible fading stage of an outburst.\nB. Monard detected an outburst on 2004 June 4 at a CCD magnitude of 16.2.\nThe outburst lasted at least for five days, accompanied by a rapid fading.\nThe overall behavior suggests that the object underwent a superoutburst.\nBased on a single-night observation covering for 7.7 hours, likely\nsuperhumps were detected\n(figure \\ref{fig:cigrushpdm}, table \\ref{tab:cigruoc2004}).\nThe best period was 0.05402(14) d. Although this value needs to be\nconfirmed by future observations, this object would be a candidate for\na very short-$P_{\\rm orb}$ SU UMa-type dwarf nova.\nThe object underwent another outburst (possibly a superoutburst)\nin 2006 September at a visual magnitude of 15.4 (Stubbings,\nvsnet-alert 9023).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig94.eps}\n \\end{center}\n \\caption{Superhumps in CI Gru (2004). (Upper): PDM analysis.\n (Lower): Phase-average profile.}\n \\label{fig:cigrushpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CI Gru (2004).}\\label{tab:cigruoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53162.3545 & 0.0036 & 0.0008 & 35 \\\\\n1 & 53162.3994 & 0.0050 & $-$0.0078 & 62 \\\\\n2 & 53162.4689 & 0.0199 & 0.0081 & 62 \\\\\n3 & 53162.5175 & 0.0091 & 0.0032 & 62 \\\\\n4 & 53162.5642 & 0.0083 & $-$0.0037 & 62 \\\\\n5 & 53162.6208 & 0.0030 & $-$0.0007 & 59 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453162.3537 + 0.053553 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V844 Herculis}\\label{sec:v844her}\\label{obj:v844her}\n\n \\citet{oiz07v844her} summarized the analysis of past outbursts.\nWe present observation of the 2008 superoutburst, an analysis the\nAAVSO data for the 1997 superoutburst and a reanalysis of\nthe 1999 superoutburst \\citep{kat00v844her}.\nThe times of superhumps maxima are listed in\ntables \\ref{tab:v844heroc1997}, \\ref{tab:v844heroc1999},\n\\ref{tab:v844heroc2008}.\n\n During the 1999 superoutburst, we obtained\n$P_{\\rm dot}$ = $+4.5(2.8) \\times 10^{-5}$.\nNo significant period variation was recorded during the 1997 superoutburst.\nThis was probably due to the limited sampling near the end of the\nstage B.\n\n A comparison of $O-C$ diagrams between different superoutburst\nis given in figure \\ref{fig:v844hercomp}. While $P_{\\rm dot}$'s were\nrelatively similar, the start of the stage B was different between\ndifferent superoutbursts:\nthe stage B started earlier during a faint (maximum 12.4 mag)\nsuperoutburst in 2002 and later during a bright (12.1 mag)\nsuperoutburst in 2006.\nThis result further supports the earlier claim \\citep{kat08wzsgelateSH}\nthat the duration before the start of the stage B (or the appearance of\nsuperhumps) depends on the extent of the superoutburst\n(see also \\cite{soe09swuma}).\n\n During the 2008 superoutburst we obtained\n$P_{\\rm dot}$ = $+7.1(0.4) \\times 10^{-5}$ for $E \\le 149$ (stage B).\nThere was, however, a phase reversal (associated with\nsecondary maxima) on BJD 2454584. These maxima were omitted for\ncalculating the $P_{\\rm dot}$. This phenomenon may have been similar\nto the one observed in OT J055718$+$683226 \\citep{uem09j0557}.\n\n A full description of the outburst will be discussed in Ohshima et al.,\nin preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig95.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V844 Her between different\n superoutbursts. A period of 0.05590 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n The evolution of superhumps apparently started earlier during\n a faint (maximum 12.4 mag) superoutburst in 2002 and later\n during a bright (12.1 mag) superoutburst in 2006.\n }\n \\label{fig:v844hercomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V844 Her (1997).}\\label{tab:v844heroc1997}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50593.4682 & 0.0014 & 0.0008 & 30 \\\\\n1 & 50593.5235 & 0.0010 & $-$0.0000 & 33 \\\\\n71 & 50597.4434 & 0.0033 & $-$0.0006 & 17 \\\\\n107 & 50599.4633 & 0.0021 & 0.0031 & 26 \\\\\n108 & 50599.5157 & 0.0015 & $-$0.0005 & 20 \\\\\n125 & 50600.4675 & 0.0015 & $-$0.0009 & 32 \\\\\n126 & 50600.5161 & 0.0013 & $-$0.0082 & 22 \\\\\n142 & 50601.4278 & 0.0024 & 0.0073 & 20 \\\\\n143 & 50601.4753 & 0.0018 & $-$0.0011 & 32 \\\\\n160 & 50602.4288 & 0.0014 & 0.0002 & 18 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450593.4675 + 0.056007 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V844 Her (1999).}\\label{tab:v844heroc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51454.9147 & 0.0006 & 0.0026 & 91 \\\\\n1 & 51454.9704 & 0.0007 & 0.0024 & 100 \\\\\n18 & 51455.9176 & 0.0004 & $-$0.0008 & 111 \\\\\n19 & 51455.9724 & 0.0007 & $-$0.0019 & 107 \\\\\n36 & 51456.9235 & 0.0010 & $-$0.0012 & 91 \\\\\n37 & 51456.9781 & 0.0022 & $-$0.0025 & 67 \\\\\n125 & 51461.9053 & 0.0033 & 0.0050 & 64 \\\\\n126 & 51461.9528 & 0.0058 & $-$0.0034 & 48 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451454.9121 + 0.055906 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V844 Her (2008).}\\label{tab:v844heroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54577.1964 & 0.0003 & 0.0078 & 104 \\\\\n1 & 54577.2533 & 0.0003 & 0.0088 & 78 \\\\\n34 & 54579.0924 & 0.0007 & 0.0015 & 73 \\\\\n35 & 54579.1468 & 0.0004 & $-$0.0001 & 102 \\\\\n36 & 54579.2026 & 0.0004 & $-$0.0003 & 99 \\\\\n37 & 54579.2601 & 0.0007 & 0.0013 & 74 \\\\\n71 & 54581.1563 & 0.0003 & $-$0.0049 & 171 \\\\\n74 & 54581.3250 & 0.0005 & $-$0.0040 & 67 \\\\\n75 & 54581.3801 & 0.0002 & $-$0.0048 & 116 \\\\\n76 & 54581.4371 & 0.0003 & $-$0.0039 & 108 \\\\\n77 & 54581.4922 & 0.0002 & $-$0.0047 & 113 \\\\\n92 & 54582.3337 & 0.0003 & $-$0.0025 & 113 \\\\\n93 & 54582.3894 & 0.0005 & $-$0.0027 & 91 \\\\\n94 & 54582.4429 & 0.0005 & $-$0.0051 & 50 \\\\\n95 & 54582.5009 & 0.0003 & $-$0.0031 & 113 \\\\\n111 & 54583.3950 & 0.0006 & $-$0.0043 & 112 \\\\\n112 & 54583.4539 & 0.0005 & $-$0.0013 & 116 \\\\\n113 & 54583.5108 & 0.0006 & $-$0.0003 & 99 \\\\\n147 & 54585.4184 & 0.0003 & 0.0049 & 115 \\\\\n148 & 54585.4749 & 0.0005 & 0.0054 & 114 \\\\\n149 & 54585.5305 & 0.0004 & 0.0051 & 91 \\\\\n160 & 54586.1445 & 0.0004 & 0.0036 & 171 \\\\\n161 & 54586.1985 & 0.0005 & 0.0016 & 172 \\\\\n178 & 54587.1483 & 0.0012 & 0.0003 & 173 \\\\\n179 & 54587.2057 & 0.0010 & 0.0017 & 163 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454577.1886 + 0.055952 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1108 Herculis}\\label{obj:v1108her}\n\n V1108 Her was discovered by Y. Nakamura on 2004 June 16\n\\citep{nak04v1108her}. The earliest positive detection of the\noutburst was on 2004 Jun 12 (unfiltered CCD magnitude of 12.0)\nby A. Takao (vsnet-alert 8190).\nDue to the delayed announcement of the discovery, only the late part\nof the superoutburst (11 d after the initial detection) was observed.\nWe used a combined data set of ours and from the AAVSO data,\nwhich were used in \\citet{pri04v1108her}.\nThe times of superhump maxima are listed in table \\ref{tab:v1108heroc2004}.\nAs in WZ Sge, a strong hump feature appeared and surpassed in amplitude\nin the late stage of the outburst. For the interval $E \\ge 79$,\nwe used a fit to a smaller width $\\pm$0.1 $P_{\\rm SH}$ around the\npeaks whose phases can be smoothly linked to earlier peaks,\nas in V455 And and WZ Sge. The resultant data clearly showed\na transition from a longer period to a shorter one around $E = 29$.\nThe mean period for $E \\le 29$ was 0.05880(18) d, while the period\nfor $E \\ge 29$ was 0.05748(3) d. \nThe maxima of secondary (but stronger in the final\nfading stage) peaks are listed in table \\ref{tab:v1108heroc2004sec}.\nFor the interval $81 \\le E \\le 108$, they had a relatively stable\nperiodicity of 0.05703(8) d. By analogy with WZ Sge, this periodicity\nmight be considered to be the orbital period.\\footnote{\n This period, though, might refer to a variety of superhumps.\n \\citet{pri04v1108her} reported another candidate periodicity\n of 0.05686(7) d marginally detected in post-superoutburst stage.\n The exact identification of the periodicities should await\n future observations.\n}\nUsing this period, we\nobtained the fractional superhump excesses for the two segments\n($E \\le 29$ and $E \\ge 29$) of 3.1(3) \\% and 0.8(1) \\%, respectively.\nThese period excesses might be attributed to stage B and C superhumps.\nThe unusually large fractional superhump excess (3.1 \\%) might be\na result of lengthening in the $P_{\\rm SH}$ during the stage B\n(see an example of AQ Eri, subsection \\ref{sec:aqeri}). This value\nmight not be used to derive system parameters such as $q$.\nThis object, with relatively frequent historical outbursts\n\\citep{pri04v1108her}, appears more analogous to positive-$P_{\\rm dot}$\nsystems such as HV Vir and AL Com rather than extreme WZ Sge-type\ndwarf novae with little variation in the superhump period (e.g. WZ Sge\nand V455 And).\n\n\\begin{table}\n\\caption{Superhump maxima of V1108 Her (2004).}\\label{tab:v1108heroc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53179.8955 & 0.0006 & $-$0.0106 & 107 \\\\\n1 & 53179.9527 & 0.0010 & $-$0.0112 & 89 \\\\\n4 & 53180.1292 & 0.0063 & $-$0.0079 & 63 \\\\\n5 & 53180.1739 & 0.0011 & $-$0.0210 & 82 \\\\\n12 & 53180.5920 & 0.0011 & $-$0.0072 & 94 \\\\\n13 & 53180.6493 & 0.0027 & $-$0.0077 & 37 \\\\\n14 & 53180.7084 & 0.0012 & $-$0.0063 & 55 \\\\\n15 & 53180.7684 & 0.0010 & $-$0.0041 & 62 \\\\\n16 & 53180.8246 & 0.0014 & $-$0.0056 & 44 \\\\\n26 & 53181.4212 & 0.0006 & 0.0134 & 53 \\\\\n27 & 53181.4733 & 0.0015 & 0.0078 & 70 \\\\\n29 & 53181.6027 & 0.0030 & 0.0216 & 49 \\\\\n30 & 53181.6487 & 0.0013 & 0.0098 & 14 \\\\\n31 & 53181.7095 & 0.0019 & 0.0129 & 23 \\\\\n32 & 53181.7693 & 0.0014 & 0.0149 & 92 \\\\\n33 & 53181.8174 & 0.0008 & 0.0053 & 136 \\\\\n34 & 53181.8762 & 0.0012 & 0.0063 & 106 \\\\\n35 & 53181.9293 & 0.0018 & 0.0017 & 168 \\\\\n36 & 53181.9847 & 0.0009 & $-$0.0007 & 26 \\\\\n44 & 53182.4512 & 0.0007 & 0.0038 & 52 \\\\\n45 & 53182.5083 & 0.0005 & 0.0031 & 66 \\\\\n46 & 53182.5654 & 0.0005 & 0.0025 & 67 \\\\\n47 & 53182.6209 & 0.0011 & 0.0002 & 41 \\\\\n48 & 53182.6816 & 0.0005 & 0.0032 & 143 \\\\\n49 & 53182.7392 & 0.0003 & 0.0029 & 143 \\\\\n50 & 53182.7979 & 0.0004 & 0.0039 & 163 \\\\\n51 & 53182.8555 & 0.0003 & 0.0037 & 65 \\\\\n52 & 53182.9132 & 0.0007 & 0.0037 & 34 \\\\\n54 & 53183.0264 & 0.0010 & 0.0014 & 159 \\\\\n64 & 53183.6029 & 0.0004 & 0.0003 & 148 \\\\\n65 & 53183.6631 & 0.0003 & 0.0028 & 233 \\\\\n66 & 53183.7192 & 0.0002 & 0.0011 & 264 \\\\\n67 & 53183.7757 & 0.0003 & $-$0.0001 & 219 \\\\\n68 & 53183.8349 & 0.0006 & 0.0013 & 67 \\\\\n71 & 53184.0055 & 0.0009 & $-$0.0013 & 129 \\\\\n72 & 53184.0635 & 0.0007 & $-$0.0011 & 107 \\\\\n73 & 53184.1268 & 0.0045 & 0.0045 & 82 \\\\\n79 & 53184.4642 & 0.0002 & $-$0.0047 & 33 \\\\\n80 & 53184.5229 & 0.0006 & $-$0.0037 & 62 \\\\\n83 & 53184.6956 & 0.0019 & $-$0.0044 & 47 \\\\\n84 & 53184.7495 & 0.0007 & $-$0.0082 & 47 \\\\\n85 & 53184.8085 & 0.0008 & $-$0.0070 & 53 \\\\\n87 & 53184.9224 & 0.0013 & $-$0.0085 & 7 \\\\\n97 & 53185.4979 & 0.0004 & $-$0.0106 & 17 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453179.9061 + 0.057757 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Secondary Superhump of V1108 Her (2004).}\\label{tab:v1108heroc2004sec}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n81 & 53184.5950 & 0.0011 & 0.0250 & 72 \\\\\n82 & 53184.6526 & 0.0020 & 0.0251 & 32 \\\\\n83 & 53184.7130 & 0.0010 & 0.0281 & 46 \\\\\n84 & 53184.7696 & 0.0004 & 0.0272 & 50 \\\\\n85 & 53184.8292 & 0.0019 & 0.0292 & 54 \\\\\n87 & 53184.9434 & 0.0026 & 0.0285 & 7 \\\\\n89 & 53185.0577 & 0.0007 & 0.0277 & 39 \\\\\n90 & 53185.1140 & 0.0004 & 0.0266 & 53 \\\\\n96 & 53185.4575 & 0.0006 & 0.0252 & 18 \\\\\n97 & 53185.5162 & 0.0005 & 0.0264 & 17 \\\\\n98 & 53185.5715 & 0.0005 & 0.0242 & 17 \\\\\n100 & 53185.6789 & 0.0010 & 0.0166 & 30 \\\\\n101 & 53185.7386 & 0.0027 & 0.0188 & 26 \\\\\n102 & 53185.7916 & 0.0044 & 0.0143 & 31 \\\\\n103 & 53185.8525 & 0.0009 & 0.0178 & 43 \\\\\n107 & 53186.0817 & 0.0025 & 0.0170 & 18 \\\\\n108 & 53186.1389 & 0.0011 & 0.0167 & 23 \\\\\n116 & 53186.5952 & 0.0014 & 0.0131 & 38 \\\\\n117 & 53186.6528 & 0.0030 & 0.0132 & 49 \\\\\n118 & 53186.7174 & 0.0015 & 0.0203 & 45 \\\\\n119 & 53186.7712 & 0.0027 & 0.0166 & 33 \\\\\n120 & 53186.8319 & 0.0025 & 0.0198 & 37 \\\\\n121 & 53186.8899 & 0.0033 & 0.0203 & 11 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against }the same ephemeris in table \\ref{tab:v1108heroc2004}. \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RU Horologii}\\label{sec:ruhor}\\label{obj:ruhor}\n\n The times of superhump maxima obtained during the 2003 superoutburst are\nlisted in table \\ref{tab:ruhoroc2003}. The object clearly showed\nbrightening near the termination of a superoutburst (cf. \\cite{kat03hodel}\nand discussion in subsection \\ref{sec:lland}), after which ($E > 80$)\nthe superhump period remarkably decreased\n(cf. figure \\ref{fig:octrans}).\nUsing the timings for the interval $0 \\le E \\le 76$, we obtained\n$P_{\\rm dot}$ = $+7.5(1.1) \\times 10^{-5}$ and a mean superhump\nperiod of 0.07095(2) d.\n\n The 2008 superoutburst (table \\ref{tab:ruhoroc2008}) was observed\nduring the middle-to-late stage of the plateau phase. There is\na clear signature of a transition to a shorter period (stage B to C).\nThe $P_{\\rm dot}$ before this transition, disregarding the slightly\ndiscrepant point $E = 0$, was $+6.5(3.2) \\times 10^{-5}$\n($1 \\le E \\le 44$).\n\n A comparison of $O-C$ diagrams of RU Hor between different\nsuperoutbursts is given in figure \\ref{fig:ruhorcomp}.\nAlthough the actual start of the outburst was not well constrained,\nthe $O-C$ diagram of the 2008 superoutburst almost perfectly fits\nthe 2003 one by assuming a 50-cycle difference in $E$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig96.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of RU Hor between different\n superoutbursts. A period of 0.07087 d was used to draw this figure.\n Although the actual start of the outburst was not well constrained,\n the $O-C$ diagram of the 2008 superoutburst almost perfectly fits\n the 2003 one by assuming a 50-cycle difference in $E$.\n }\n \\label{fig:ruhorcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of RU Hor (2003).}\\label{tab:ruhoroc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52910.1929 & 0.0003 & $-$0.0023 & 123 \\\\\n1 & 52910.2657 & 0.0003 & $-$0.0004 & 132 \\\\\n2 & 52910.3368 & 0.0003 & $-$0.0002 & 124 \\\\\n32 & 52912.4611 & 0.0006 & $-$0.0019 & 71 \\\\\n33 & 52912.5312 & 0.0004 & $-$0.0026 & 75 \\\\\n34 & 52912.6013 & 0.0015 & $-$0.0033 & 42 \\\\\n46 & 52913.4539 & 0.0008 & $-$0.0011 & 81 \\\\\n47 & 52913.5268 & 0.0006 & 0.0009 & 81 \\\\\n58 & 52914.3075 & 0.0011 & 0.0020 & 110 \\\\\n59 & 52914.3764 & 0.0008 & 0.0001 & 102 \\\\\n60 & 52914.4485 & 0.0009 & 0.0013 & 107 \\\\\n61 & 52914.5205 & 0.0006 & 0.0025 & 110 \\\\\n72 & 52915.3021 & 0.0011 & 0.0045 & 82 \\\\\n73 & 52915.3726 & 0.0008 & 0.0041 & 82 \\\\\n74 & 52915.4442 & 0.0007 & 0.0049 & 74 \\\\\n75 & 52915.5151 & 0.0006 & 0.0049 & 81 \\\\\n76 & 52915.5857 & 0.0010 & 0.0047 & 62 \\\\\n98 & 52917.1357 & 0.0008 & $-$0.0044 & 132 \\\\\n99 & 52917.2060 & 0.0008 & $-$0.0050 & 134 \\\\\n100 & 52917.2790 & 0.0013 & $-$0.0028 & 134 \\\\\n101 & 52917.3470 & 0.0010 & $-$0.0057 & 129 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452910.1952 + 0.070866 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of RU Hor (2008).}\\label{tab:ruhoroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54686.4831 & 0.0020 & $-$0.0089 & 82 \\\\\n1 & 54686.5571 & 0.0003 & $-$0.0056 & 164 \\\\\n2 & 54686.6285 & 0.0003 & $-$0.0049 & 164 \\\\\n11 & 54687.2661 & 0.0006 & $-$0.0037 & 133 \\\\\n15 & 54687.5503 & 0.0005 & $-$0.0023 & 164 \\\\\n16 & 54687.6216 & 0.0004 & $-$0.0017 & 163 \\\\\n29 & 54688.5447 & 0.0005 & 0.0021 & 162 \\\\\n30 & 54688.6172 & 0.0005 & 0.0038 & 162 \\\\\n43 & 54689.5408 & 0.0004 & 0.0082 & 163 \\\\\n44 & 54689.6108 & 0.0003 & 0.0075 & 163 \\\\\n56 & 54690.4564 & 0.0004 & 0.0046 & 146 \\\\\n57 & 54690.5292 & 0.0004 & 0.0067 & 164 \\\\\n58 & 54690.5983 & 0.0004 & 0.0051 & 164 \\\\\n70 & 54691.4436 & 0.0007 & 0.0019 & 146 \\\\\n71 & 54691.5154 & 0.0007 & 0.0029 & 164 \\\\\n72 & 54691.5854 & 0.0006 & 0.0023 & 164 \\\\\n73 & 54691.6569 & 0.0009 & 0.0031 & 96 \\\\\n86 & 54692.5741 & 0.0008 & 0.0010 & 163 \\\\\n87 & 54692.6428 & 0.0005 & $-$0.0010 & 138 \\\\\n99 & 54693.4920 & 0.0018 & $-$0.0004 & 164 \\\\\n100 & 54693.5645 & 0.0010 & 0.0014 & 164 \\\\\n101 & 54693.6329 & 0.0010 & $-$0.0008 & 163 \\\\\n113 & 54694.4770 & 0.0019 & $-$0.0053 & 164 \\\\\n114 & 54694.5441 & 0.0014 & $-$0.0089 & 163 \\\\\n115 & 54694.6167 & 0.0013 & $-$0.0070 & 164 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454686.4920 + 0.070711 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CT Hydrae}\\label{obj:cthya}\n\n Superhumps during two superoutbursts (1995 and 1999) were reported\nin the past literature (\\cite{nog96cthya}; \\cite{kat99cthya}).\nWe reanalyzed the 1999 observations in view of\nthe modern knowledge. The times of superhump maxima are listed in table\n\\ref{tab:cthyaoc1999}. The Brno data were removed before the\nanalysis because of the yet unsolved phase problem (cf. \\cite{kat99cthya}).\nAlthough \\citet{kat99cthya} stated that the change in the superhump\nperiod was negligible, the present analysis seems to show a tendency\nof a period increase. The negative $O-C$ of the last ($E = 105$)\nbeing likely a result of the period decrease associated with\na stage B--C transition, we excluded this point and obtained\n$P_{\\rm dot}$ = $+7.0(4.3) \\times 10^{-5}$.\nIf we include this point, the resultant $P_{\\rm dot}$ is almost zero\n($-1.0(8.7) \\times 10^{-5}$), confirming the analysis in\n\\citet{kat99cthya}. We further present the superoutbursts in 2000,\n2002 February, 2002 November and 2009 January.\n(tables \\ref{tab:cthyaoc2000}, \\ref{tab:cthyaoc2002a},\n\\ref{tab:cthyaoc2002b}, \\ref{tab:cthyaoc2009}).\nThe resultant values of $P_{\\rm dot}$ for the stage B\nwere $+9.6(5.2) \\times 10^{-5}$ (2000, $E \\le 78$),\n$+11.6(3.8) \\times 10^{-5}$ (2002 February, $E \\ge 14$)\nand $+13.2(3.1) \\times 10^{-5}$ (2002 November, $E \\le 90$), respectively.\n\n A comparison of $O-C$ diagrams between different superoutbursts\nis given in figure \\ref{fig:cthyacomp}. The relatively large error in\n$O-C$'s in this system makes a comparison rather difficult.\nThe behavior (and diversity) of the late stage B is somewhat reminiscent\nto KV Dra.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig97.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of CT Hya between different\n superoutbursts. A period of 0.06640 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:cthyacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CT Hya (1999).}\\label{tab:cthyaoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51225.0000 & 0.0018 & 0.0064 & 79 \\\\\n14 & 51225.9200 & 0.0021 & $-$0.0030 & 91 \\\\\n15 & 51225.9947 & 0.0021 & 0.0052 & 110 \\\\\n16 & 51226.0575 & 0.0026 & 0.0017 & 28 \\\\\n17 & 51226.1177 & 0.0014 & $-$0.0045 & 68 \\\\\n18 & 51226.1872 & 0.0031 & $-$0.0015 & 71 \\\\\n29 & 51226.9176 & 0.0039 & $-$0.0014 & 92 \\\\\n30 & 51226.9847 & 0.0026 & $-$0.0006 & 130 \\\\\n31 & 51227.0527 & 0.0044 & 0.0010 & 73 \\\\\n32 & 51227.1137 & 0.0062 & $-$0.0044 & 61 \\\\\n33 & 51227.1775 & 0.0070 & $-$0.0070 & 23 \\\\\n63 & 51229.1813 & 0.0011 & 0.0049 & 115 \\\\\n75 & 51229.9773 & 0.0021 & 0.0043 & 96 \\\\\n90 & 51230.9692 & 0.0040 & 0.0002 & 68 \\\\\n91 & 51231.0382 & 0.0031 & 0.0028 & 17 \\\\\n92 & 51231.1035 & 0.0051 & 0.0018 & 23 \\\\\n105 & 51231.9588 & 0.0082 & $-$0.0060 & 71 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451224.9935 + 0.066394 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CT Hya (2000).}\\label{tab:cthyaoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51880.1597 & 0.0005 & $-$0.0003 & 57 \\\\\n1 & 51880.2290 & 0.0006 & 0.0025 & 148 \\\\\n2 & 51880.2945 & 0.0016 & 0.0016 & 184 \\\\\n3 & 51880.3667 & 0.0041 & 0.0074 & 82 \\\\\n17 & 51881.2863 & 0.0017 & $-$0.0031 & 93 \\\\\n45 & 51883.1482 & 0.0010 & $-$0.0013 & 51 \\\\\n46 & 51883.2086 & 0.0012 & $-$0.0074 & 63 \\\\\n47 & 51883.2816 & 0.0012 & $-$0.0008 & 131 \\\\\n48 & 51883.3471 & 0.0012 & $-$0.0018 & 140 \\\\\n60 & 51884.1412 & 0.0099 & $-$0.0049 & 32 \\\\\n61 & 51884.2125 & 0.0010 & 0.0000 & 63 \\\\\n62 & 51884.2814 & 0.0017 & 0.0025 & 131 \\\\\n63 & 51884.3472 & 0.0017 & 0.0018 & 97 \\\\\n78 & 51885.3417 & 0.0023 & $-$0.0002 & 99 \\\\\n153 & 51890.3283 & 0.0118 & 0.0038 & 10 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451880.1600 + 0.066434 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CT Hya (2002a).}\\label{tab:cthyaoc2002a}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52317.1711 & 0.0087 & $-$0.0016 & 81 \\\\\n1 & 52317.2400 & 0.0058 & 0.0010 & 81 \\\\\n2 & 52317.3020 & 0.0022 & $-$0.0035 & 94 \\\\\n14 & 52318.1060 & 0.0012 & 0.0037 & 126 \\\\\n15 & 52318.1702 & 0.0023 & 0.0016 & 129 \\\\\n16 & 52318.2469 & 0.0078 & 0.0118 & 117 \\\\\n29 & 52319.1048 & 0.0014 & 0.0066 & 128 \\\\\n58 & 52321.0290 & 0.0027 & 0.0052 & 63 \\\\\n59 & 52321.0779 & 0.0025 & $-$0.0124 & 124 \\\\\n60 & 52321.1509 & 0.0012 & $-$0.0057 & 129 \\\\\n61 & 52321.2155 & 0.0015 & $-$0.0076 & 127 \\\\\n62 & 52321.2806 & 0.0040 & $-$0.0089 & 81 \\\\\n136 & 52326.2130 & 0.0074 & 0.0099 & 17 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452317.1726 + 0.066401 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CT Hya (2002b).}\\label{tab:cthyaoc2002b}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52591.1998 & 0.0052 & 0.0017 & 26 \\\\\n15 & 52592.1926 & 0.0010 & $-$0.0011 & 126 \\\\\n16 & 52592.2597 & 0.0013 & $-$0.0003 & 213 \\\\\n17 & 52592.3244 & 0.0003 & $-$0.0020 & 221 \\\\\n60 & 52595.1773 & 0.0016 & $-$0.0030 & 126 \\\\\n75 & 52596.1780 & 0.0029 & 0.0022 & 114 \\\\\n76 & 52596.2405 & 0.0019 & $-$0.0017 & 122 \\\\\n90 & 52597.1790 & 0.0019 & 0.0076 & 89 \\\\\n105 & 52598.1646 & 0.0181 & $-$0.0023 & 92 \\\\\n106 & 52598.2349 & 0.0017 & 0.0017 & 126 \\\\\n150 & 52601.1485 & 0.0031 & $-$0.0049 & 125 \\\\\n151 & 52601.2219 & 0.0019 & 0.0020 & 200 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452591.1981 + 0.066369 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CT Hya (2009).}\\label{tab:cthyaoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54847.0839 & 0.0004 & 0.0012 & 72 \\\\\n1 & 54847.1493 & 0.0007 & $-$0.0000 & 54 \\\\\n2 & 54847.2178 & 0.0005 & 0.0018 & 83 \\\\\n3 & 54847.2850 & 0.0006 & 0.0024 & 48 \\\\\n15 & 54848.0805 & 0.0004 & $-$0.0016 & 132 \\\\\n16 & 54848.1482 & 0.0008 & $-$0.0006 & 100 \\\\\n17 & 54848.2150 & 0.0008 & $-$0.0004 & 117 \\\\\n32 & 54849.2079 & 0.0016 & $-$0.0069 & 76 \\\\\n59 & 54851.0083 & 0.0034 & $-$0.0056 & 63 \\\\\n60 & 54851.0922 & 0.0062 & 0.0117 & 138 \\\\\n61 & 54851.1452 & 0.0133 & $-$0.0019 & 73 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454847.0827 + 0.066630 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{MM Hydrae}\\label{obj:mmhya}\n\n MM Hya, selected by the Palomer-Green survey \\citep{gre82PGsurveyCV},\nhad long been suspected to be a WZ Sge-like object based on the\nshort orbital period \\citep{mis95PGCV}. The object was soon confirmed\nto undergo long outbursts approximately once per year, indicating\na more usual SU UMa-type dwarf nova rather than a WZ Wge-like object.\n\\citet{pat03suumas} reported a mean $P_{\\rm SH}$ of 0.05868 d during the\n1998 superoutburst without giving the details.\nWe analyzed the AAVSO observations of the 1998 superoutburst and obtained\ntimes of superhump maxima (table \\ref{tab:mmhyaoc1998}).\nThe mean $P_{\\rm SH}$ determined with the PDM method was 0.05894(3) d.\nThis period is significantly longer than that by \\citet{pat03suumas}.\nThe present observation was probably obtained near the end of the stage B.\nA possible decrease in $O-C$, although the uncertainty is large, in\n$E=65-66$ may be a result of a transition to the stage C.\n\n We also observed the 2001 superoutburst during its earliest stage\n(table \\ref{tab:mmhyaoc2001}). The observations corresponded to\nthe stage A--B transition. The mean periods during the stage A was\n0.0603(3) d. The observed length of the stage B was too short to\ndetermine the period. On the first night of the observation\n(2001 May 15), double-wave modulations similar to early superhumps\nin WZ Sge-type dwarf novae were observed (figure \\ref{fig:mmhyaearly}).\nAlthough the length of observations was insufficient to discriminate\nbetween $P_{\\rm SH}$ and $P_{\\rm orb}$, the profile strongly suggests\nthe presence of early superhumps. The object is similar to\nBC UMa (\\cite{pat03suumas}; \\cite{mae07bcuma}) and RZ Leo\n(\\cite{ish01rzleo}; \\cite{pat03suumas}) that showed early superhumps\nduring the earliest stage of their superoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig98.eps}\n \\end{center}\n \\caption{Double-wave humps in MM Hya (2001) (Upper): Light curve.\n (Lower): Phase-averaged profile referring to the orbital period.}\n \\label{fig:mmhyaearly}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of MM Hya (1998).}\\label{tab:mmhyaoc1998}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50882.2853 & 0.0076 & $-$0.0050 & 17 \\\\\n1 & 50882.3503 & 0.0023 & 0.0011 & 33 \\\\\n2 & 50882.4123 & 0.0021 & 0.0042 & 34 \\\\\n3 & 50882.4671 & 0.0012 & 0.0001 & 29 \\\\\n15 & 50883.1732 & 0.0026 & $-$0.0011 & 58 \\\\\n51 & 50885.3016 & 0.0030 & 0.0058 & 23 \\\\\n52 & 50885.3517 & 0.0016 & $-$0.0031 & 34 \\\\\n65 & 50886.1191 & 0.0058 & $-$0.0018 & 48 \\\\\n66 & 50886.1796 & 0.0029 & $-$0.0002 & 48 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450882.2903 + 0.058931 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of MM Hya (2001).}\\label{tab:mmhyaoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52045.9826 & 0.0025 & $-$0.0000 & 89 \\\\\n4 & 52046.2195 & 0.0007 & $-$0.0022 & 615 \\\\\n17 & 52047.0068 & 0.0021 & 0.0082 & 71 \\\\\n21 & 52047.2359 & 0.0003 & $-$0.0017 & 707 \\\\\n22 & 52047.2931 & 0.0001 & $-$0.0043 & 703 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452045.9826 + 0.059762 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{VW Hydri}\\label{obj:vwhyi}\n\n We analyzed the 2000 May superoutburst (table \\ref{tab:vwhyioc2002}).\nThe observation covered the early stage of the superoutburst and\nwe obtained a mean $P_{\\rm SH}$ of 0.07699(6) d.\nThe observations were slightly insufficient\nto estimate a $P_{\\rm dot}$.\nThe $O-C$ variation in \\citet{vog74vwhyi} confirmed the presence\nof the stage B--C transition.\n\\citet{lil96vwhyi} reported little evidence for period variation\nof superhumps during the 1995 November superoutburst. We did not,\nhowever, include this observation because the periods were\nnot based on an $O-C$ analysis nor times of superhumps were given.\nThe reported period of 0.076646(3) d with the Fourier analysis\nwas between $P_1$ and $P_2$ of the 2000 superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of VW Hyi (2000).}\\label{tab:vwhyioc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51680.9054 & 0.0022 & $-$0.0014 & 6 \\\\\n8 & 51681.5219 & 0.0020 & $-$0.0007 & 7 \\\\\n13 & 51681.9050 & 0.0074 & $-$0.0026 & 7 \\\\\n33 & 51683.4515 & 0.0032 & 0.0042 & 6 \\\\\n34 & 51683.5298 & 0.0059 & 0.0056 & 7 \\\\\n46 & 51684.4467 & 0.0045 & $-$0.0014 & 5 \\\\\n47 & 51684.5265 & 0.0024 & 0.0014 & 7 \\\\\n52 & 51684.9081 & 0.0099 & $-$0.0019 & 7 \\\\\n60 & 51685.5228 & 0.0022 & $-$0.0031 & 9 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451680.9067 + 0.076986 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RZ Leonis}\\label{obj:rzleo}\n\n We reanalyzed a combination of \\citet{ish01rzleo} and the AAVSO data.\nThe times of superhump maxima are given in table \\ref{tab:rzleooc2000}.\nAlthough \\citet{ish01rzleo}\nidentified earlier maxima ($E \\le 6$) as being early superhumps, we examined\nwhether these maxima can be tracked back as in the stage A\nof other SU UMa-type dwarf novae. Although we could track back\nthe maxima with a slightly longer period for $\\sim$ 1 d, as in the stage A\nof other SU UMa-type dwarf novae, this attempt failed to express earlier\n($E < 0$) epochs.\nThis analysis also supports the identification of these humps as being\nearly superhumps, rather than a smooth extension of ordinary superhumps.\nThe $O-C$ diagram showed a transition to the stage C after $E = 100$.\nFor the interval $13 \\le E \\le 100$ (stage B), we obtained\n$P_{\\rm dot}$ = $+4.9(1.7) \\times 10^{-5}$.\nThe value is in good agreement with \\citet{ish01rzleo}.\n\n The object underwent another superoutburst in 2006.\nAlthough the seasonal condition was poor, we obtained several superhump\nmaxima (table \\ref{tab:rzleooc2006}). The $O-C$'s against the mean period\nof 2000 suggest that the observation caught the increasing period\nduring the first two nights, and last observation with a strongly negative\n$O-C$ should have caught the late transition from the stage B to C\n(see figure \\ref{fig:rzleocomp}).\nWe did not attempt to derive a global $P_{\\rm dot}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig99.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of RZ Leo between different\n superoutbursts. A period of 0.07865 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:rzleocomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of RZ Leo (2000--2001).}\\label{tab:rzleooc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51901.1571 & 0.0009 & $-$0.0189 & 106 \\\\\n1 & 51901.2283 & 0.0012 & $-$0.0262 & 145 \\\\\n2 & 51901.3069 & 0.0011 & $-$0.0261 & 146 \\\\\n3 & 51901.3948 & 0.0019 & $-$0.0168 & 76 \\\\\n5 & 51901.5460 & 0.0010 & $-$0.0227 & 173 \\\\\n6 & 51901.6273 & 0.0009 & $-$0.0199 & 183 \\\\\n13 & 51902.1998 & 0.0004 & 0.0027 & 214 \\\\\n14 & 51902.2781 & 0.0004 & 0.0025 & 203 \\\\\n15 & 51902.3578 & 0.0004 & 0.0036 & 165 \\\\\n18 & 51902.5934 & 0.0006 & 0.0037 & 134 \\\\\n19 & 51902.6728 & 0.0010 & 0.0045 & 46 \\\\\n23 & 51902.9858 & 0.0005 & 0.0034 & 42 \\\\\n24 & 51903.0655 & 0.0004 & 0.0045 & 41 \\\\\n25 & 51903.1444 & 0.0007 & 0.0048 & 114 \\\\\n26 & 51903.2226 & 0.0003 & 0.0045 & 174 \\\\\n27 & 51903.2995 & 0.0003 & 0.0029 & 207 \\\\\n28 & 51903.3784 & 0.0008 & 0.0032 & 105 \\\\\n39 & 51904.2464 & 0.0007 & 0.0072 & 83 \\\\\n40 & 51904.3232 & 0.0004 & 0.0055 & 114 \\\\\n51 & 51905.1834 & 0.0004 & 0.0017 & 181 \\\\\n52 & 51905.2602 & 0.0003 & $-$0.0000 & 176 \\\\\n53 & 51905.3394 & 0.0005 & 0.0006 & 146 \\\\\n63 & 51906.1347 & 0.0017 & 0.0105 & 102 \\\\\n64 & 51906.2083 & 0.0006 & 0.0056 & 150 \\\\\n65 & 51906.2875 & 0.0004 & 0.0062 & 218 \\\\\n66 & 51906.3645 & 0.0010 & 0.0046 & 118 \\\\\n76 & 51907.1554 & 0.0005 & 0.0101 & 147 \\\\\n77 & 51907.2315 & 0.0007 & 0.0077 & 105 \\\\\n78 & 51907.3128 & 0.0020 & 0.0104 & 39 \\\\\n79 & 51907.3922 & 0.0039 & 0.0112 & 29 \\\\\n84 & 51907.7850 & 0.0010 & 0.0113 & 35 \\\\\n85 & 51907.8651 & 0.0017 & 0.0129 & 17 \\\\\n86 & 51907.9440 & 0.0009 & 0.0132 & 17 \\\\\n89 & 51908.1775 & 0.0005 & 0.0111 & 149 \\\\\n90 & 51908.2559 & 0.0005 & 0.0110 & 289 \\\\\n91 & 51908.3334 & 0.0004 & 0.0099 & 260 \\\\\n99 & 51908.9665 & 0.0006 & 0.0147 & 40 \\\\\n100 & 51909.0413 & 0.0006 & 0.0110 & 40 \\\\\n111 & 51909.9018 & 0.0010 & 0.0074 & 33 \\\\\n112 & 51909.9747 & 0.0010 & 0.0018 & 40 \\\\\n113 & 51910.0563 & 0.0006 & 0.0049 & 41 \\\\\n128 & 51911.2287 & 0.0014 & $-$0.0008 & 224 \\\\\n129 & 51911.3083 & 0.0013 & 0.0001 & 220 \\\\\n142 & 51912.3223 & 0.0032 & $-$0.0069 & 27 \\\\\n148 & 51912.7917 & 0.0009 & $-$0.0088 & 36 \\\\\n149 & 51912.8688 & 0.0027 & $-$0.0102 & 20 \\\\\n153 & 51913.1855 & 0.0009 & $-$0.0077 & 206 \\\\\n154 & 51913.2635 & 0.0007 & $-$0.0082 & 222 \\\\\n155 & 51913.3409 & 0.0008 & $-$0.0094 & 226 \\\\\n166 & 51914.2029 & 0.0045 & $-$0.0114 & 74 \\\\\n167 & 51914.2867 & 0.0026 & $-$0.0061 & 63 \\\\\n168 & 51914.3601 & 0.0024 & $-$0.0112 & 91 \\\\\n179 & 51915.2156 & 0.0127 & $-$0.0197 & 26 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451901.1760 + 0.078544 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of RZ Leo (2006).}\\label{tab:rzleooc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53886.0103 & 0.0002 & $-$0.0038 & 195 \\\\\n13 & 53887.0380 & 0.0006 & 0.0043 & 314 \\\\\n127 & 53895.9741 & 0.0013 & $-$0.0004 & 81 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453886.0142 + 0.078428 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{GW Librae}\\label{sec:gwlib}\\label{obj:gwlib}\n\n GW Lib, originally reported as a nova in 1983 \\citep{maz83gwlibiauc},\nand long suspected to be a WZ Sge-type dwarf nova, underwent a spectacular\noutburst in 2007 (R. Stubbings, vsnet-alert 9279; \\cite{waa07gwlibiauc}).\nThe object initially showed only very low-amplitude modulations similar to\nearly superhumps, whose period was not well determined. After $\\sim$ 11\ndays, ordinary superhumps emerged (vsnet-alert 9315, 9316).\n\n The maxima times of ordinary superhumps are listed\nin table \\ref{tab:gwliboc2007}.\nThe $O-C$ diagram (figure \\ref{fig:gwlibhumpall}) very clearly\nconsisted of the stage A with a long superhump period\n($E \\le 39$), the stage B with a definitely positive $P_{\\rm dot}$,\nand later stage ($E \\ge 289$) with noticeably negative $O-C$'s.\nFor the stage B ($51 \\le E \\le 278$), we obtained $P_{\\rm dot}$ =\n$+4.0(0.1) \\times 10^{-5}$. It seems that the phase was discontinuous\nbetween the middle and the last segments. This may be attributed\nto the appearance of the orbital humps (figure \\ref{fig:gwporb}).\nAt an estimated orbital inclination of 11$^{\\circ}$\n\\citep{tho02gwlibv844herdiuma}, the appearance of orbital humps\nis surprising. The orbital inclination is either higher or\nthere is a special mechanism for manifesting orbital humps during\nthe late stage of the plateau phase of WZ Sge-type dwarf novae\n(see also V455 And and WZ Sge, subsections \\ref{sec:v455and} amd\n\\ref{sec:wzsge}. The double-wave profile in GW Lib might suggest\nthat a sort of the 2:1 resonance, as in early superhumps, is somehow\nexcited, or persists, during the last stage of the superoutburst\nplateau of WZ Sge-type dwarf novae.\n\n More detailed analysis of the outburst will be presented by\nImada et al., in preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig100.eps}\n \\end{center}\n \\caption{Orbital humps in GW Lib (2007) during the late stage\n (BJD 2454227--2454230) of the superoutburst plateau.\n (Upper): PDM analysis. The tick mark is given at the\n orbital period.\n (Lower): Phase-averaged profile.}\n \\label{fig:gwporb}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007).}\\label{tab:gwliboc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54212.3805 & 0.0011 & $-$0.0274 & 249 \\\\\n2 & 54212.4933 & 0.0008 & $-$0.0227 & 206 \\\\\n11 & 54212.9948 & 0.0026 & $-$0.0081 & 148 \\\\\n12 & 54213.0405 & 0.0015 & $-$0.0165 & 168 \\\\\n31 & 54214.0785 & 0.0007 & $-$0.0063 & 416 \\\\\n32 & 54214.1357 & 0.0003 & $-$0.0032 & 1040 \\\\\n35 & 54214.3004 & 0.0002 & $-$0.0007 & 249 \\\\\n36 & 54214.3542 & 0.0002 & $-$0.0010 & 249 \\\\\n37 & 54214.4098 & 0.0001 & 0.0005 & 249 \\\\\n38 & 54214.4639 & 0.0001 & 0.0005 & 245 \\\\\n39 & 54214.5198 & 0.0001 & 0.0023 & 249 \\\\\n51 & 54215.1758 & 0.0001 & 0.0092 & 171 \\\\\n53 & 54215.2834 & 0.0003 & 0.0086 & 112 \\\\\n54 & 54215.3385 & 0.0002 & 0.0096 & 97 \\\\\n55 & 54215.3920 & 0.0001 & 0.0090 & 209 \\\\\n56 & 54215.4457 & 0.0001 & 0.0086 & 250 \\\\\n57 & 54215.4996 & 0.0001 & 0.0085 & 250 \\\\\n58 & 54215.5529 & 0.0001 & 0.0076 & 248 \\\\\n66 & 54215.9851 & 0.0002 & 0.0071 & 158 \\\\\n67 & 54216.0385 & 0.0001 & 0.0064 & 158 \\\\\n68 & 54216.0943 & 0.0004 & 0.0082 & 341 \\\\\n69 & 54216.1450 & 0.0002 & 0.0047 & 1099 \\\\\n70 & 54216.2006 & 0.0001 & 0.0062 & 1245 \\\\\n71 & 54216.2548 & 0.0002 & 0.0064 & 689 \\\\\n72 & 54216.3075 & 0.0002 & 0.0050 & 499 \\\\\n73 & 54216.3621 & 0.0001 & 0.0055 & 250 \\\\\n74 & 54216.4164 & 0.0001 & 0.0057 & 213 \\\\\n87 & 54217.1173 & 0.0002 & 0.0034 & 1105 \\\\\n88 & 54217.1708 & 0.0002 & 0.0028 & 1433 \\\\\n89 & 54217.2248 & 0.0002 & 0.0027 & 1250 \\\\\n105 & 54218.0873 & 0.0005 & $-$0.0002 & 356 \\\\\n106 & 54218.1422 & 0.0005 & 0.0006 & 386 \\\\\n107 & 54218.1956 & 0.0003 & $-$0.0001 & 293 \\\\\n108 & 54218.2486 & 0.0009 & $-$0.0012 & 117 \\\\\n123 & 54219.0616 & 0.0005 & 0.0004 & 137 \\\\\n124 & 54219.1147 & 0.0002 & $-$0.0006 & 468 \\\\\n125 & 54219.1687 & 0.0004 & $-$0.0007 & 729 \\\\\n126 & 54219.2193 & 0.0007 & $-$0.0042 & 341 \\\\\n128 & 54219.3305 & 0.0001 & $-$0.0012 & 246 \\\\\n129 & 54219.3836 & 0.0001 & $-$0.0022 & 250 \\\\\n130 & 54219.4389 & 0.0001 & $-$0.0010 & 246 \\\\\n131 & 54219.4920 & 0.0001 & $-$0.0019 & 250 \\\\\n132 & 54219.5464 & 0.0001 & $-$0.0016 & 250 \\\\\n141 & 54220.0311 & 0.0007 & $-$0.0037 & 238 \\\\\n142 & 54220.0890 & 0.0005 & 0.0001 & 379 \\\\\n143 & 54220.1430 & 0.0003 & $-$0.0001 & 720 \\\\\n144 & 54220.1959 & 0.0003 & $-$0.0013 & 782 \\\\\n145 & 54220.2491 & 0.0008 & $-$0.0022 & 404 \\\\\n146 & 54220.3034 & 0.0002 & $-$0.0020 & 260 \\\\\n147 & 54220.3567 & 0.0002 & $-$0.0028 & 249 \\\\\n148 & 54220.4114 & 0.0001 & $-$0.0021 & 249 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454212.4079 + 0.054092 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n149 & 54220.4655 & 0.0002 & $-$0.0022 & 249 \\\\\n150 & 54220.5172 & 0.0002 & $-$0.0045 & 249 \\\\\n151 & 54220.5735 & 0.0001 & $-$0.0023 & 249 \\\\\n160 & 54221.0578 & 0.0010 & $-$0.0048 & 175 \\\\\n161 & 54221.1148 & 0.0010 & $-$0.0019 & 192 \\\\\n165 & 54221.3302 & 0.0002 & $-$0.0028 & 249 \\\\\n166 & 54221.3832 & 0.0002 & $-$0.0040 & 250 \\\\\n167 & 54221.4385 & 0.0001 & $-$0.0028 & 249 \\\\\n183 & 54222.3044 & 0.0002 & $-$0.0024 & 250 \\\\\n184 & 54222.3584 & 0.0002 & $-$0.0024 & 250 \\\\\n198 & 54223.1158 & 0.0006 & $-$0.0023 & 263 \\\\\n199 & 54223.1741 & 0.0009 & 0.0019 & 358 \\\\\n234 & 54225.0653 & 0.0041 & $-$0.0002 & 31 \\\\\n236 & 54225.1755 & 0.0007 & 0.0019 & 87 \\\\\n258 & 54226.3718 & 0.0002 & 0.0082 & 247 \\\\\n259 & 54226.4270 & 0.0003 & 0.0093 & 241 \\\\\n260 & 54226.4808 & 0.0003 & 0.0089 & 197 \\\\\n261 & 54226.5352 & 0.0006 & 0.0093 & 217 \\\\\n262 & 54226.5898 & 0.0003 & 0.0098 & 237 \\\\\n276 & 54227.3504 & 0.0004 & 0.0131 & 249 \\\\\n277 & 54227.4035 & 0.0005 & 0.0121 & 190 \\\\\n278 & 54227.4580 & 0.0002 & 0.0125 & 249 \\\\\n289 & 54228.0378 & 0.0008 & $-$0.0026 & 383 \\\\\n290 & 54228.0884 & 0.0019 & $-$0.0062 & 859 \\\\\n291 & 54228.1374 & 0.0030 & $-$0.0113 & 1258 \\\\\n292 & 54228.1995 & 0.0008 & $-$0.0033 & 1160 \\\\\n295 & 54228.3558 & 0.0008 & $-$0.0092 & 191 \\\\\n296 & 54228.4130 & 0.0007 & $-$0.0061 & 249 \\\\\n297 & 54228.4633 & 0.0009 & $-$0.0099 & 249 \\\\\n298 & 54228.5190 & 0.0008 & $-$0.0084 & 249 \\\\\n299 & 54228.5694 & 0.0012 & $-$0.0120 & 248 \\\\\n300 & 54228.6274 & 0.0015 & $-$0.0081 & 228 \\\\\n308 & 54229.0510 & 0.0028 & $-$0.0173 & 261 \\\\\n309 & 54229.1079 & 0.0006 & $-$0.0144 & 703 \\\\\n310 & 54229.1603 & 0.0006 & $-$0.0162 & 719 \\\\\n311 & 54229.2126 & 0.0012 & $-$0.0180 & 619 \\\\\n312 & 54229.2724 & 0.0028 & $-$0.0122 & 154 \\\\\n314 & 54229.3783 & 0.0006 & $-$0.0145 & 181 \\\\\n315 & 54229.4318 & 0.0018 & $-$0.0151 & 187 \\\\\n316 & 54229.4832 & 0.0004 & $-$0.0177 & 187 \\\\\n317 & 54229.5330 & 0.0012 & $-$0.0220 & 188 \\\\\n318 & 54229.5928 & 0.0008 & $-$0.0164 & 187 \\\\\n333 & 54230.4039 & 0.0003 & $-$0.0166 & 186 \\\\\n334 & 54230.4600 & 0.0004 & $-$0.0146 & 187 \\\\\n335 & 54230.5093 & 0.0007 & $-$0.0194 & 188 \\\\\n336 & 54230.5510 & 0.0008 & $-$0.0318 & 187 \\\\\n337 & 54230.6164 & 0.0006 & $-$0.0205 & 134 \\\\\n345 & 54231.0452 & 0.0033 & $-$0.0244 & 44 \\\\\n346 & 54231.1132 & 0.0013 & $-$0.0105 & 79 \\\\\n347 & 54231.1661 & 0.0114 & $-$0.0118 & 46 \\\\\n348 & 54231.2181 & 0.0015 & $-$0.0138 & 63 \\\\\n349 & 54231.2782 & 0.0009 & $-$0.0078 & 179 \\\\\n350 & 54231.3294 & 0.0002 & $-$0.0107 & 188 \\\\\n351 & 54231.3828 & 0.0003 & $-$0.0114 & 179 \\\\\n363 & 54232.0410 & 0.0013 & $-$0.0023 & 175 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n364 & 54232.0870 & 0.0010 & $-$0.0104 & 211 \\\\\n365 & 54232.1444 & 0.0009 & $-$0.0071 & 308 \\\\\n366 & 54232.2039 & 0.0014 & $-$0.0016 & 82 \\\\\n367 & 54232.2558 & 0.0009 & $-$0.0038 & 172 \\\\\n368 & 54232.3072 & 0.0004 & $-$0.0065 & 186 \\\\\n369 & 54232.3615 & 0.0004 & $-$0.0064 & 188 \\\\\n373 & 54232.5795 & 0.0006 & $-$0.0047 & 188 \\\\\n374 & 54232.6272 & 0.0005 & $-$0.0111 & 140 \\\\\n380 & 54232.9630 & 0.0003 & 0.0001 & 67 \\\\\n381 & 54233.0126 & 0.0008 & $-$0.0044 & 111 \\\\\n382 & 54233.0704 & 0.0008 & $-$0.0006 & 60 \\\\\n383 & 54233.1273 & 0.0014 & 0.0022 & 27 \\\\\n386 & 54233.2860 & 0.0010 & $-$0.0014 & 188 \\\\\n387 & 54233.3378 & 0.0004 & $-$0.0037 & 188 \\\\\n400 & 54234.0426 & 0.0007 & $-$0.0021 & 120 \\\\\n401 & 54234.0968 & 0.0004 & $-$0.0020 & 245 \\\\\n402 & 54234.1487 & 0.0005 & $-$0.0042 & 194 \\\\\n404 & 54234.2590 & 0.0003 & $-$0.0021 & 249 \\\\\n405 & 54234.3111 & 0.0003 & $-$0.0041 & 249 \\\\\n406 & 54234.3647 & 0.0003 & $-$0.0046 & 248 \\\\\n407 & 54234.4171 & 0.0002 & $-$0.0063 & 249 \\\\\n408 & 54234.4719 & 0.0003 & $-$0.0056 & 249 \\\\\n409 & 54234.5251 & 0.0003 & $-$0.0064 & 234 \\\\\n416 & 54234.9092 & 0.0006 & $-$0.0010 & 33 \\\\\n417 & 54234.9560 & 0.0003 & $-$0.0082 & 50 \\\\\n418 & 54235.0106 & 0.0003 & $-$0.0077 & 46 \\\\\n419 & 54235.0664 & 0.0008 & $-$0.0060 & 206 \\\\\n420 & 54235.1207 & 0.0007 & $-$0.0059 & 244 \\\\\n421 & 54235.1740 & 0.0011 & $-$0.0066 & 144 \\\\\n423 & 54235.2839 & 0.0005 & $-$0.0049 & 173 \\\\\n424 & 54235.3367 & 0.0003 & $-$0.0062 & 248 \\\\\n425 & 54235.3907 & 0.0003 & $-$0.0063 & 249 \\\\\n426 & 54235.4449 & 0.0003 & $-$0.0062 & 241 \\\\\n427 & 54235.4996 & 0.0003 & $-$0.0056 & 235 \\\\\n436 & 54235.9875 & 0.0037 & $-$0.0046 & 95 \\\\\n438 & 54236.1028 & 0.0009 & 0.0026 & 142 \\\\\n439 & 54236.1486 & 0.0011 & $-$0.0057 & 171 \\\\\n442 & 54236.3177 & 0.0005 & 0.0011 & 249 \\\\\n443 & 54236.3699 & 0.0004 & $-$0.0007 & 250 \\\\\n444 & 54236.4239 & 0.0003 & $-$0.0008 & 250 \\\\\n445 & 54236.4778 & 0.0004 & $-$0.0010 & 250 \\\\\n446 & 54236.5319 & 0.0005 & $-$0.0011 & 236 \\\\\n447 & 54236.5842 & 0.0006 & $-$0.0028 & 222 \\\\\n454 & 54236.9644 & 0.0005 & $-$0.0013 & 27 \\\\\n460 & 54237.2908 & 0.0004 & 0.0006 & 189 \\\\\n461 & 54237.3439 & 0.0003 & $-$0.0005 & 249 \\\\\n462 & 54237.3968 & 0.0003 & $-$0.0016 & 250 \\\\\n463 & 54237.4520 & 0.0006 & $-$0.0005 & 249 \\\\\n474 & 54238.0450 & 0.0013 & $-$0.0025 & 179 \\\\\n475 & 54238.1042 & 0.0013 & 0.0026 & 200 \\\\\n476 & 54238.1554 & 0.0004 & $-$0.0003 & 355 \\\\\n477 & 54238.2095 & 0.0013 & $-$0.0003 & 205 \\\\\n478 & 54238.2610 & 0.0013 & $-$0.0029 & 187 \\\\\n479 & 54238.3187 & 0.0003 & 0.0008 & 125 \\\\\n480 & 54238.3694 & 0.0004 & $-$0.0027 & 124 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n481 & 54238.4256 & 0.0003 & $-$0.0006 & 125 \\\\\n482 & 54238.4791 & 0.0004 & $-$0.0011 & 125 \\\\\n483 & 54238.5267 & 0.0003 & $-$0.0076 & 125 \\\\\n484 & 54238.5870 & 0.0004 & $-$0.0014 & 124 \\\\\n496 & 54239.2343 & 0.0020 & $-$0.0032 & 63 \\\\\n498 & 54239.3458 & 0.0006 & 0.0001 & 101 \\\\\n499 & 54239.3992 & 0.0005 & $-$0.0006 & 124 \\\\\n500 & 54239.4545 & 0.0003 & 0.0006 & 125 \\\\\n501 & 54239.5040 & 0.0005 & $-$0.0040 & 125 \\\\\n502 & 54239.5607 & 0.0004 & $-$0.0013 & 123 \\\\\n511 & 54240.0517 & 0.0008 & 0.0028 & 78 \\\\\n512 & 54240.1068 & 0.0011 & 0.0038 & 131 \\\\\n513 & 54240.1596 & 0.0015 & 0.0025 & 111 \\\\\n520 & 54240.5337 & 0.0004 & $-$0.0020 & 116 \\\\\n521 & 54240.5896 & 0.0006 & $-$0.0003 & 85 \\\\\n528 & 54240.9714 & 0.0005 & 0.0030 & 110 \\\\\n529 & 54241.0260 & 0.0009 & 0.0034 & 164 \\\\\n530 & 54241.0807 & 0.0007 & 0.0041 & 338 \\\\\n531 & 54241.1330 & 0.0007 & 0.0023 & 324 \\\\\n532 & 54241.1850 & 0.0014 & 0.0001 & 255 \\\\\n547 & 54241.9971 & 0.0026 & 0.0009 & 54 \\\\\n548 & 54242.0569 & 0.0011 & 0.0066 & 58 \\\\\n549 & 54242.1070 & 0.0078 & 0.0026 & 17 \\\\\n551 & 54242.2148 & 0.0010 & 0.0022 & 82 \\\\\n552 & 54242.2678 & 0.0005 & 0.0012 & 123 \\\\\n553 & 54242.3221 & 0.0005 & 0.0014 & 124 \\\\\n554 & 54242.3767 & 0.0003 & 0.0019 & 125 \\\\\n555 & 54242.4340 & 0.0003 & 0.0050 & 124 \\\\\n556 & 54242.4842 & 0.0003 & 0.0011 & 125 \\\\\n568 & 54243.1438 & 0.0042 & 0.0116 & 43 \\\\\n571 & 54243.2970 & 0.0005 & 0.0026 & 117 \\\\\n572 & 54243.3516 & 0.0004 & 0.0031 & 125 \\\\\n573 & 54243.4070 & 0.0003 & 0.0044 & 125 \\\\\n574 & 54243.4585 & 0.0007 & 0.0018 & 125 \\\\\n575 & 54243.5147 & 0.0005 & 0.0039 & 108 \\\\\n590 & 54244.3233 & 0.0005 & 0.0011 & 122 \\\\\n591 & 54244.3826 & 0.0004 & 0.0064 & 121 \\\\\n592 & 54244.4364 & 0.0003 & 0.0061 & 125 \\\\\n593 & 54244.4891 & 0.0006 & 0.0046 & 124 \\\\\n594 & 54244.5412 & 0.0004 & 0.0027 & 124 \\\\\n595 & 54244.5964 & 0.0010 & 0.0037 & 89 \\\\\n601 & 54244.9234 & 0.0005 & 0.0062 & 26 \\\\\n607 & 54245.2449 & 0.0007 & 0.0032 & 93 \\\\\n608 & 54245.3034 & 0.0004 & 0.0076 & 125 \\\\\n609 & 54245.3567 & 0.0010 & 0.0068 & 123 \\\\\n610 & 54245.4091 & 0.0005 & 0.0051 & 125 \\\\\n611 & 54245.4635 & 0.0005 & 0.0054 & 125 \\\\\n612 & 54245.5180 & 0.0005 & 0.0058 & 124 \\\\\n613 & 54245.5708 & 0.0006 & 0.0045 & 123 \\\\\n638 & 54246.9264 & 0.0020 & 0.0078 & 26 \\\\\n639 & 54246.9785 & 0.0007 & 0.0058 & 26 \\\\\n640 & 54247.0368 & 0.0018 & 0.0101 & 66 \\\\\n641 & 54247.0893 & 0.0015 & 0.0084 & 29 \\\\\n642 & 54247.1478 & 0.0026 & 0.0128 & 44 \\\\\n643 & 54247.2046 & 0.0021 & 0.0155 & 22 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n645 & 54247.3087 & 0.0016 & 0.0114 & 77 \\\\\n646 & 54247.3640 & 0.0010 & 0.0127 & 125 \\\\\n647 & 54247.4150 & 0.0013 & 0.0095 & 124 \\\\\n648 & 54247.4637 & 0.0007 & 0.0042 & 125 \\\\\n649 & 54247.5234 & 0.0012 & 0.0098 & 105 \\\\\n660 & 54248.1203 & 0.0023 & 0.0117 & 87 \\\\\n663 & 54248.2812 & 0.0010 & 0.0103 & 125 \\\\\n664 & 54248.3428 & 0.0018 & 0.0178 & 98 \\\\\n681 & 54249.2501 & 0.0008 & 0.0055 & 125 \\\\\n682 & 54249.3066 & 0.0012 & 0.0080 & 125 \\\\\n700 & 54250.2883 & 0.0010 & 0.0160 & 124 \\\\\n786 & 54254.9363 & 0.0032 & 0.0120 & 23 \\\\\n787 & 54254.9872 & 0.0113 & 0.0089 & 29 \\\\\n788 & 54255.0486 & 0.0051 & 0.0162 & 27 \\\\\n803 & 54255.8694 & 0.0026 & 0.0256 & 18 \\\\\n804 & 54255.9161 & 0.0017 & 0.0182 & 27 \\\\\n805 & 54255.9636 & 0.0020 & 0.0116 & 21 \\\\\n806 & 54256.0321 & 0.0036 & 0.0260 & 149 \\\\\n808 & 54256.1247 & 0.0023 & 0.0105 & 162 \\\\\n811 & 54256.2919 & 0.0012 & 0.0153 & 78 \\\\\n812 & 54256.3486 & 0.0008 & 0.0180 & 124 \\\\\n813 & 54256.4028 & 0.0007 & 0.0181 & 125 \\\\\n814 & 54256.4543 & 0.0016 & 0.0155 & 124 \\\\\n815 & 54256.5201 & 0.0028 & 0.0272 & 65 \\\\\n824 & 54256.9931 & 0.0020 & 0.0134 & 25 \\\\\n843 & 54258.0189 & 0.0041 & 0.0114 & 47 \\\\\n848 & 54258.3031 & 0.0011 & 0.0251 & 80 \\\\\n849 & 54258.3520 & 0.0008 & 0.0200 & 125 \\\\\n850 & 54258.4050 & 0.0010 & 0.0189 & 124 \\\\\n851 & 54258.4584 & 0.0024 & 0.0182 & 125 \\\\\n852 & 54258.5101 & 0.0007 & 0.0159 & 125 \\\\\n867 & 54259.3271 & 0.0004 & 0.0214 & 92 \\\\\n868 & 54259.3804 & 0.0007 & 0.0206 & 125 \\\\\n869 & 54259.4341 & 0.0006 & 0.0202 & 114 \\\\\n870 & 54259.4858 & 0.0007 & 0.0178 & 125 \\\\\n871 & 54259.5441 & 0.0011 & 0.0220 & 97 \\\\\n885 & 54260.3031 & 0.0010 & 0.0238 & 74 \\\\\n886 & 54260.3568 & 0.0013 & 0.0233 & 124 \\\\\n887 & 54260.4135 & 0.0008 & 0.0260 & 125 \\\\\n888 & 54260.4696 & 0.0008 & 0.0280 & 125 \\\\\n889 & 54260.5205 & 0.0016 & 0.0248 & 125 \\\\\n903 & 54261.2805 & 0.0006 & 0.0276 & 124 \\\\\n904 & 54261.3323 & 0.0011 & 0.0252 & 125 \\\\\n905 & 54261.3852 & 0.0008 & 0.0240 & 125 \\\\\n906 & 54261.4387 & 0.0006 & 0.0234 & 125 \\\\\n907 & 54261.4962 & 0.0009 & 0.0268 & 125 \\\\\n908 & 54261.5452 & 0.0008 & 0.0218 & 87 \\\\\n921 & 54262.2493 & 0.0015 & 0.0227 & 82 \\\\\n922 & 54262.3090 & 0.0009 & 0.0283 & 125 \\\\\n923 & 54262.3623 & 0.0007 & 0.0275 & 125 \\\\\n924 & 54262.4129 & 0.0010 & 0.0240 & 125 \\\\\n925 & 54262.4693 & 0.0013 & 0.0263 & 125 \\\\\n926 & 54262.5283 & 0.0019 & 0.0313 & 78 \\\\\n935 & 54263.0107 & 0.0031 & 0.0268 & 154 \\\\\n941 & 54263.3320 & 0.0006 & 0.0235 & 125 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of GW Lib (2007) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n942 & 54263.3911 & 0.0012 & 0.0286 & 125 \\\\\n943 & 54263.4410 & 0.0012 & 0.0243 & 125 \\\\\n944 & 54263.4987 & 0.0016 & 0.0280 & 124 \\\\\n957 & 54264.1973 & 0.0025 & 0.0233 & 101 \\\\\n958 & 54264.2567 & 0.0014 & 0.0286 & 125 \\\\\n959 & 54264.3110 & 0.0007 & 0.0289 & 125 \\\\\n960 & 54264.3613 & 0.0008 & 0.0251 & 125 \\\\\n961 & 54264.4171 & 0.0010 & 0.0268 & 125 \\\\\n976 & 54265.2351 & 0.0009 & 0.0334 & 94 \\\\\n979 & 54265.3911 & 0.0016 & 0.0271 & 115 \\\\\n980 & 54265.4543 & 0.0013 & 0.0362 & 30 \\\\\n994 & 54266.2096 & 0.0011 & 0.0343 & 124 \\\\\n995 & 54266.2578 & 0.0010 & 0.0284 & 125 \\\\\n1013 & 54267.2442 & 0.0009 & 0.0411 & 123 \\\\\n1014 & 54267.2956 & 0.0010 & 0.0384 & 125 \\\\\n1015 & 54267.3467 & 0.0014 & 0.0355 & 125 \\\\\n1016 & 54267.3968 & 0.0008 & 0.0314 & 124 \\\\\n1017 & 54267.4585 & 0.0032 & 0.0391 & 124 \\\\\n1032 & 54268.2646 & 0.0009 & 0.0337 & 89 \\\\\n1033 & 54268.3162 & 0.0014 & 0.0313 & 125 \\\\\n1034 & 54268.3724 & 0.0009 & 0.0333 & 125 \\\\\n1035 & 54268.4318 & 0.0013 & 0.0387 & 124 \\\\\n1036 & 54268.4857 & 0.0014 & 0.0385 & 125 \\\\\n1051 & 54269.2956 & 0.0013 & 0.0370 & 124 \\\\\n1052 & 54269.3583 & 0.0021 & 0.0456 & 124 \\\\\n1053 & 54269.4015 & 0.0031 & 0.0347 & 125 \\\\\n1062 & 54269.8804 & 0.0180 & 0.0268 & 15 \\\\\n1063 & 54269.9413 & 0.0015 & 0.0336 & 25 \\\\\n1069 & 54270.2699 & 0.0009 & 0.0376 & 125 \\\\\n1070 & 54270.3211 & 0.0021 & 0.0348 & 125 \\\\\n1071 & 54270.3763 & 0.0011 & 0.0358 & 125 \\\\\n1072 & 54270.4264 & 0.0008 & 0.0318 & 125 \\\\\n1073 & 54270.4997 & 0.0048 & 0.0511 & 68 \\\\\n1087 & 54271.2444 & 0.0009 & 0.0385 & 112 \\\\\n1089 & 54271.3526 & 0.0010 & 0.0385 & 124 \\\\\n1090 & 54271.4057 & 0.0045 & 0.0376 & 125 \\\\\n1102 & 54272.0533 & 0.0020 & 0.0360 & 44 \\\\\n1106 & 54272.2758 & 0.0024 & 0.0422 & 125 \\\\\n1107 & 54272.3208 & 0.0011 & 0.0330 & 125 \\\\\n1108 & 54272.3812 & 0.0008 & 0.0394 & 125 \\\\\n1109 & 54272.4337 & 0.0025 & 0.0378 & 125 \\\\\n1110 & 54272.4930 & 0.0074 & 0.0430 & 66 \\\\\n1125 & 54273.3001 & 0.0013 & 0.0387 & 124 \\\\\n1127 & 54273.3981 & 0.0037 & 0.0285 & 125 \\\\\n1144 & 54274.3323 & 0.0018 & 0.0432 & 124 \\\\\n1145 & 54274.3925 & 0.0022 & 0.0492 & 125 \\\\\n1147 & 54274.4879 & 0.0015 & 0.0365 & 105 \\\\\n1161 & 54275.2535 & 0.0011 & 0.0447 & 125 \\\\\n1162 & 54275.3018 & 0.0017 & 0.0390 & 125 \\\\\n1163 & 54275.3605 & 0.0020 & 0.0436 & 125 \\\\\n1164 & 54275.4108 & 0.0012 & 0.0398 & 124 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RZ Leonis Minoris}\\label{sec:rzlmi}\\label{obj:rzlmi}\n\n We analyzed the 2005 April superoutburst of RZ LMi\n(table \\ref{tab:rzlmioc2005}). This superoutburst had a marginally\npositive $P_{\\rm dot}$ of $+2.3(1.1) \\times 10^{-5}$, as in the 2004\nsuperoutburst \\citet{ole08rzlmi}. The maxima for $E \\ge 118$\n(during the rapid fading stage) were either phase 0.5 offset\n(traditional late superhumps), stage C superhumps with a period\nof 0.05875(8) d ($E \\ge 84$), or even a candidate for orbital humps.\nSince none of these kinds of phenomena have not yet been reported\nin RZ LMi \\citep{ole08rzlmi}, further detailed observations during\nthe rapid fading stage might provide crucial information.\n\n\\begin{table}\n\\caption{Superhump maxima of RZ LMi (2005).}\\label{tab:rzlmioc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53473.7101 & 0.0004 & $-$0.0054 & 40 \\\\\n1 & 53473.7688 & 0.0004 & $-$0.0058 & 36 \\\\\n2 & 53473.8282 & 0.0003 & $-$0.0057 & 36 \\\\\n33 & 53475.6684 & 0.0005 & $-$0.0003 & 45 \\\\\n34 & 53475.7284 & 0.0006 & 0.0005 & 36 \\\\\n35 & 53475.7862 & 0.0006 & $-$0.0009 & 35 \\\\\n36 & 53475.8467 & 0.0009 & 0.0004 & 30 \\\\\n50 & 53476.6803 & 0.0008 & 0.0053 & 37 \\\\\n51 & 53476.7379 & 0.0006 & 0.0037 & 40 \\\\\n52 & 53476.7962 & 0.0005 & 0.0028 & 38 \\\\\n53 & 53476.8563 & 0.0006 & 0.0037 & 37 \\\\\n84 & 53478.7001 & 0.0008 & 0.0126 & 40 \\\\\n86 & 53478.8169 & 0.0017 & 0.0111 & 41 \\\\\n118 & 53480.7007 & 0.0079 & 0.0007 & 20 \\\\\n119 & 53480.7497 & 0.0025 & $-$0.0094 & 20 \\\\\n120 & 53480.8145 & 0.0017 & $-$0.0038 & 20 \\\\\n136 & 53481.7560 & 0.0069 & $-$0.0094 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453473.7154 + 0.059191 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SS Leonis Minoris}\\label{obj:sslmi}\n\n SS LMi was discovered as an extragalactic nova or an unusual\ndwarf nova \\citep{alk80sslmi}. Although \\citet{har91sslmiiauc} reported\na ``red'' outburst in 1991, the nature of this outburst remained\nunclear.\\footnote{\n See also \\citet{how91sslmiiauc}; the unusual color in these\n observations could have been a combination with a nearby field star\n \\citet{she08sslmi}.\n}\n \\citet{she08sslmi} reported the 2006 superoutburst.\nBased on their times of superhump maxima, we obtained\n$P_{\\rm dot}$ = $+0.3(0.4) \\times 10^{-5}$ ($E \\le 128$).\nSince these superhumps were detected during the initial stage of\na likely WZ Sge-type outburst, they can be interpreted as\nearly superhumps rather than ordinary superhumps. The lack of\nperiod variation and a hint of double-wave modulations\n\\citep{she08sslmi} may support this interpretation.\nWe listed the period in table \\ref{tab:perlist} based on this\nidentification.\n\n\\subsection{SX Leonis Minoris}\\label{obj:sxlmi}\n\n \\citet{nog97sxlmi} reported on the 1994 superoutburst. We reanalyzed\nthe data during this superoutburst. The resultant times of superhump maxima\nare listed in table \\ref{tab:sxlmioc1994}.\nThe overall $P_{\\rm dot}$ was $-8.2(1.1) \\times 10^{-5}$, in good\nagreement with \\citet{nog97sxlmi}.\n\n We also observed the 2001 and 2002 superoutbursts\n(tables \\ref{tab:sxlmioc2001}, \\ref{tab:sxlmioc2002}).\nThe resultant values of $P_{\\rm dot}$ were $-3.3(3.0) \\times 10^{-5}$\nand $-4.1(1.5) \\times 10^{-5}$ (excluding $E = 0$), respectively.\nThe 2002 result might be interpreted as a sudden shift to a shorter\nsuperhump period (stage B to C) between $E = 116$ and $E = 130$.\nUsing the interval of $14 \\le E \\le 115$, the resultant period\nchange was almost zero, $P_{\\rm dot}$ = $-0.7(0.5) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of SX LMi (1994).}\\label{tab:sxlmioc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49702.1736 & 0.0010 & $-$0.0031 & 14 \\\\\n1 & 49702.2438 & 0.0006 & $-$0.0022 & 27 \\\\\n2 & 49702.3122 & 0.0003 & $-$0.0030 & 36 \\\\\n16 & 49703.2854 & 0.0005 & 0.0007 & 66 \\\\\n17 & 49703.3543 & 0.0004 & 0.0004 & 63 \\\\\n29 & 49704.1875 & 0.0009 & 0.0026 & 30 \\\\\n45 & 49705.3009 & 0.0007 & 0.0081 & 42 \\\\\n89 & 49708.3412 & 0.0007 & 0.0015 & 46 \\\\\n103 & 49709.3076 & 0.0007 & $-$0.0016 & 46 \\\\\n104 & 49709.3794 & 0.0008 & 0.0010 & 29 \\\\\n118 & 49710.3435 & 0.0011 & $-$0.0044 & 44 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449702.1767 + 0.069248 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SX LMi (2001).}\\label{tab:sxlmioc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51938.3604 & 0.0111 & 0.0013 & 70 \\\\\n12 & 51939.1870 & 0.0011 & $-$0.0017 & 121 \\\\\n13 & 51939.2539 & 0.0014 & $-$0.0039 & 119 \\\\\n14 & 51939.3245 & 0.0016 & $-$0.0023 & 133 \\\\\n26 & 51940.1626 & 0.0019 & 0.0063 & 113 \\\\\n70 & 51943.1962 & 0.0008 & $-$0.0014 & 120 \\\\\n71 & 51943.2680 & 0.0010 & 0.0012 & 132 \\\\\n72 & 51943.3358 & 0.0022 & $-$0.0001 & 68 \\\\\n84 & 51944.1640 & 0.0036 & $-$0.0014 & 112 \\\\\n85 & 51944.2400 & 0.0057 & 0.0055 & 105 \\\\\n113 & 51946.1665 & 0.0021 & $-$0.0034 & 56 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451938.3592 + 0.069122 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SX LMi (2002).}\\label{tab:sxlmioc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52297.3399 & 0.0036 & $-$0.0077 & 110 \\\\\n14 & 52298.3214 & 0.0003 & 0.0029 & 100 \\\\\n29 & 52299.3616 & 0.0010 & 0.0029 & 115 \\\\\n43 & 52300.3326 & 0.0009 & 0.0030 & 101 \\\\\n101 & 52304.3547 & 0.0020 & 0.0029 & 77 \\\\\n115 & 52305.3246 & 0.0011 & 0.0020 & 130 \\\\\n129 & 52306.2904 & 0.0021 & $-$0.0031 & 101 \\\\\n130 & 52306.3599 & 0.0010 & $-$0.0029 & 97 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452297.3477 + 0.069347 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BR Lupi}\\label{obj:brlup}\n\n We observed the 2003 and 2004 superoutbursts. The times of\nsuperhump maxima are listed in tables \\ref{tab:brlupoc2003} and\n\\ref{tab:brlupoc2004}.\nThe both observations covered the relatively late stages of the\nsuperoutbursts (figure \\ref{fig:brlupcomp}).\nA stage B--C transition was probably caught during the 2003 superoutburst\nand the only the stage C was likely recorded during the 2004 superoutburst.\nWe give parameters in table \\ref{tab:perlist} based on this interpretation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig101.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of BR Lup between different\n superoutbursts. A period of 0.08228 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:brlupcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of BR Lup (2003).}\\label{tab:brlupoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52737.2349 & 0.0005 & $-$0.0023 & 83 \\\\\n1 & 52737.3172 & 0.0004 & $-$0.0020 & 83 \\\\\n2 & 52737.4008 & 0.0006 & $-$0.0006 & 59 \\\\\n11 & 52738.1398 & 0.0005 & $-$0.0007 & 66 \\\\\n12 & 52738.2236 & 0.0004 & 0.0010 & 83 \\\\\n13 & 52738.3041 & 0.0005 & $-$0.0006 & 82 \\\\\n15 & 52738.4706 & 0.0006 & 0.0016 & 89 \\\\\n16 & 52738.5520 & 0.0005 & 0.0009 & 94 \\\\\n17 & 52738.6335 & 0.0006 & 0.0002 & 78 \\\\\n50 & 52741.3457 & 0.0008 & 0.0025 & 69 \\\\\n51 & 52741.4272 & 0.0006 & 0.0019 & 88 \\\\\n52 & 52741.5088 & 0.0008 & 0.0013 & 79 \\\\\n53 & 52741.5901 & 0.0009 & 0.0005 & 58 \\\\\n95 & 52745.0350 & 0.0146 & $-$0.0037 & 18 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452737.2372 + 0.082121 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of BR Lup (2004).}\\label{tab:brlupoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53139.6291 & 0.0003 & 0.0077 & 176 \\\\\n5 & 53140.0364 & 0.0006 & 0.0041 & 44 \\\\\n6 & 53140.1124 & 0.0008 & $-$0.0022 & 40 \\\\\n7 & 53140.1900 & 0.0006 & $-$0.0067 & 38 \\\\\n60 & 53144.5527 & 0.0005 & $-$0.0002 & 186 \\\\\n61 & 53144.6273 & 0.0013 & $-$0.0079 & 186 \\\\\n70 & 53145.3763 & 0.0006 & 0.0014 & 186 \\\\\n71 & 53145.4563 & 0.0005 & $-$0.0008 & 186 \\\\\n72 & 53145.5367 & 0.0006 & $-$0.0026 & 186 \\\\\n94 & 53147.3479 & 0.0084 & 0.0003 & 167 \\\\\n95 & 53147.4352 & 0.0017 & 0.0055 & 181 \\\\\n96 & 53147.5132 & 0.0022 & 0.0013 & 141 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453139.6214 + 0.082193 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AY Lyrae}\\label{obj:aylyr}\n\n Although AY Lyr has long been known a representative SU UMa-type\ndwarf nova, little is known about the variation of the superhump period\nexcept for the classical study by \\citet{uda88aylyr}.\nWe observed the 2008 and 2009 superoutbursts\n(tables \\ref{tab:aylyroc2008}, \\ref{tab:aylyroc2009}).\nAlthough we only observed five consecutive nights during the 2008\nsuperoutburst, a transition from stage B to C was apparently recorded.\nThe early stage of the 2009 superoutburst was likely missed.\nThe period variation probably reflects a stage B--C transition.\nA comparison of $O-C$ diagrams of between different superoutbursts\nis given in figure \\ref{fig:aylyrcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig102.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of AY Lyr between different\n superoutbursts. A period of 0.07597 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n Since the start of the 2009 superoutburst was not well constrained,\n we shifted the $O-C$ diagrams to best fit the others.\n }\n \\label{fig:aylyrcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of AY Lyr (2008).}\\label{tab:aylyroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54754.9197 & 0.0022 & $-$0.0031 & 87 \\\\\n1 & 54754.9970 & 0.0011 & $-$0.0016 & 140 \\\\\n13 & 54755.9057 & 0.0014 & $-$0.0034 & 77 \\\\\n14 & 54755.9870 & 0.0009 & 0.0020 & 243 \\\\\n15 & 54756.0593 & 0.0025 & $-$0.0017 & 119 \\\\\n27 & 54756.9789 & 0.0014 & 0.0075 & 82 \\\\\n28 & 54757.0542 & 0.0020 & 0.0069 & 67 \\\\\n40 & 54757.9561 & 0.0015 & $-$0.0017 & 58 \\\\\n41 & 54758.0359 & 0.0017 & 0.0022 & 75 \\\\\n53 & 54758.9396 & 0.0012 & $-$0.0046 & 141 \\\\\n54 & 54759.0177 & 0.0008 & $-$0.0024 & 105 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454754.9228 + 0.075876 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AY Lyr (2009).}\\label{tab:aylyroc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54963.1200 & 0.0006 & $-$0.0038 & 151 \\\\\n1 & 54963.1944 & 0.0005 & $-$0.0052 & 269 \\\\\n2 & 54963.2698 & 0.0008 & $-$0.0056 & 139 \\\\\n26 & 54965.1018 & 0.0005 & 0.0071 & 190 \\\\\n27 & 54965.1748 & 0.0004 & 0.0043 & 256 \\\\\n28 & 54965.2488 & 0.0004 & 0.0026 & 266 \\\\\n40 & 54966.1607 & 0.0004 & 0.0048 & 125 \\\\\n41 & 54966.2346 & 0.0017 & 0.0029 & 75 \\\\\n92 & 54970.0989 & 0.0017 & 0.0013 & 99 \\\\\n93 & 54970.1674 & 0.0010 & $-$0.0060 & 114 \\\\\n94 & 54970.2467 & 0.0041 & $-$0.0025 & 99 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454963.1238 + 0.075802 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DM Lyrae}\\label{obj:dmlyr}\n\n \\citet{nog03dmlyr} studied the 1996 and 1997 outbursts and confirmed\nthe SU UMa-type nature of this object (the times of superhump maxima\nmeasured from the 1997 data are listed in table \\ref{tab:dmlyroc1997}).\nWe further observed the 2002 superoutburst (table \\ref{tab:dmlyroc2002}).\nAs in 1996 and 1997 ones, the 2002 superoutburst was observed during its\nlater stage. Although we could not determine $P_{\\rm dot}$ for the stage B,\nother parameters are given in table \\ref{tab:perlist}.\n\n\\begin{table}\n\\caption{Superhump maxima of DM Lyr (1997).}\\label{tab:dmlyroc1997}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50509.2862 & 0.0015 & $-$0.0001 & 61 \\\\\n45 & 50512.3171 & 0.0011 & 0.0066 & 63 \\\\\n46 & 50512.3713 & 0.0014 & $-$0.0065 & 33 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450509.2863 + 0.067205 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DM Lyr (2002).}\\label{tab:dmlyroc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52580.0178 & 0.0073 & $-$0.0019 & 100 \\\\\n58 & 52583.9153 & 0.0027 & $-$0.0001 & 101 \\\\\n59 & 52583.9862 & 0.0010 & 0.0037 & 103 \\\\\n104 & 52587.0065 & 0.0097 & 0.0015 & 41 \\\\\n119 & 52588.0084 & 0.0108 & $-$0.0041 & 58 \\\\\n134 & 52589.0209 & 0.0068 & 0.0009 & 60 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452580.0197 + 0.067166 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V344 Lyrae}\\label{obj:v344lyr}\n\n \\citet{kat93v344lyr} reported on the 1993 superoutburst.\nWe determined superhump maxima from these observations\n(table \\ref{tab:v344lyroc1993}). The resultant $P_{\\rm dot}$ was\n$-7.1(4.3) \\times 10^{-5}$. Since this object has one of the longest\n$P_{\\rm orb}$, more complicated period variation may be expected\nas in MN Dra and UV Gem. Future better observations are needed\nto test this possibility.\n\n\\begin{table}\n\\caption{Superhump maxima of V344 Lyr (1993).}\\label{tab:v344lyroc1993}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49133.1065 & 0.0014 & $-$0.0042 & 49 \\\\\n1 & 49133.2004 & 0.0011 & $-$0.0015 & 48 \\\\\n2 & 49133.2949 & 0.0019 & 0.0016 & 29 \\\\\n12 & 49134.2104 & 0.0024 & 0.0035 & 34 \\\\\n34 & 49136.2187 & 0.0016 & 0.0020 & 47 \\\\\n78 & 49140.2348 & 0.0046 & $-$0.0014 & 23 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449133.1106 + 0.091354 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V358 Lyrae}\\label{obj:v358lyr}\n\n Although the object was originally discovered as a nova\n\\citep{hof67an289205}, \\citet{ric86v358lyr} suggested that it is\na WZ Sge-type dwarf nova based on its faintness and the similarity\nin the light curve with that of WZ Sge. \\citet{ant04v358lyr}\npointed out that the reported maximum in \\citet{ric86v358lyr} referred\nto a plate defect and presented the correct identification.\nThe maximum recorded photographic magnitude was 16.42.\n\n J. Shears detected a new outburst on 2008 November 22 at an unfiltered\nCCD magnitude of 16.26 (vsnet-outburst 9714). The object experienced\na ``dip''-like fading characteristic to (type-A) WZ Sge-type superoutbursts\nand exhibited a long-lasting second plateau stage.\n\n Due to the low amplitudes of variations and faintness of the object,\nwe mainly focus on the variation before the dip. Using the best segments\nof observations, we obtained a $P_{\\rm SH}$ of 0.05563(3) with the\nPDM method (figure \\ref{fig:v358lyrshpdm}). The profile of variation\nappeared doubly humped. Although the profile resembles those of\nearly superhumps, we identified these variations as ordinary superhumps\nbecause these variations were observed $\\sim$ 10 d before the dip,\nat an epoch when all well-observed WZ Sge-type dwarf novae exhibited\nordinary superhumps. The low-amplitude, double-wave modulations may\nhave been a result of temporary reduction of amplitudes of superhumps\nfrequently seen in many systems in the middle-to-late stage of\na superoutburst plateau (see e.g. \\cite{kat03hodel}).\nAlthough we measured times of superhump maxima \n(table \\ref{tab:v358lyroc2008}), the quality was not sufficient\nbecause of this complexity in the profile.\n\\citet{she09v358lyr} reported possible detection of small-scale periodic\nsignals including a candidate period of 0.05556(32) d.\n\n The overall light curve of the superoutburst bears strong similarity\nto that of AL Com in 1995 (figure \\ref{fig:v358lyrlc}). The earlier\nstage of the outburst, potentially with early superhumps, may have\nbeen unfortunately missed below the detection limit of visual observations.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,130mm){fig103.eps}\n \\end{center}\n \\caption{Superhumps in V358 Lyr (2008). (Upper): PDM analysis of the\n interval BJD 2454793.8--2454794.3. (Middle): PDM analysis of the\n interval BJD 2454793.8--2454797.0. (Lower): Phase-averaged profile.}\n \\label{fig:v358lyrshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig104.eps}\n \\end{center}\n \\caption{Comparison of light curves of AL Com and V358 Lyr.\n (Upper) AL Com in 1995. The data are from \\citet{kat96alcom}.\n (Lower) V358 Lyr. The ``v'' marks indicate upper limits.}\n \\label{fig:v358lyrlc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V358 Lyr (2008).}\\label{tab:v358lyroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54793.8615 & 0.0049 & 0.0039 & 55 \\\\\n1 & 54793.9053 & 0.0226 & $-$0.0080 & 130 \\\\\n13 & 54794.5960 & 0.0030 & 0.0133 & 13 \\\\\n26 & 54795.3027 & 0.0036 & $-$0.0051 & 48 \\\\\n27 & 54795.3578 & 0.0030 & $-$0.0057 & 47 \\\\\n48 & 54796.5339 & 0.0014 & $-$0.0010 & 14 \\\\\n55 & 54796.9275 & 0.0043 & 0.0022 & 44 \\\\\n109 & 54799.9377 & 0.0043 & 0.0004 & 30 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454793.8576 + 0.055777 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V419 Lyrae}\\label{obj:v419lyr}\n\n \\citet{nog98gxcasv419lyr} reported the detection of superhumps in\nthis object and proposed candidate periods. Although their observations\nwere not long enough to discriminate the possibilities, the long superhump\nperiod already made V419 Lyr an outstanding object.\nWe observed the 1999 superoutburst, and obtained the following superhump\nmaxima and first identified the correct superhump period (table\n\\ref{tab:v419lyroc1999}). The superhump period apparently largely\nvaried between $E = 0$ and $E = 3$. Excluding the point of $E = 11$\n(observation of the maximum somewhat affected by thin clouds),\nand $E \\le 3$ epochs, we obtained $P_{\\rm dot}$ of\n$-32.4(2.4) \\times 10^{-5}$.\n\n \\citet{rut07v419lyr} obtained\n$P_{\\rm dot}$ = $-24.8(2.2) \\times 10^{-5}$ during the 2006 superoutburst.\nWe analyzed the available data (from the AAVSO database and Dubovsky's data)\nand combined with \\citet{rut07v419lyr} after adding a systematic correction\nof 0.0026 d to \\citet{rut07v419lyr} and removing maxima of Boyd's\nobservations, which were included in our own analysis\n(table \\ref{tab:v419lyroc2006})\n\n A comparison of $O-C$ diagrams between different superoutbursts\nis given in figure \\ref{fig:v419lyrcomp}.\n\n This long-period system resembles UV Gem, MN Dra and NY Ser in its strongly\nnegative superhump derivative. It would be notable that V419 Lyr\nshows frequent normal outbursts (intervals 9--12 d), which is also\nreminiscent of the behavior in UV Gem \\citep{kat01uvgemfsandaspsc}\nand NY Ser \\citep{iid95nyser}. Very long-$P_{\\rm SH}$ systems with\nfrequent normal outbursts may be associated with strongly negative\n$P_{\\rm dot}$ (see subsection \\ref{sec:longp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig105.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V419 Lyr between different\n superoutbursts. A period of 0.09005 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v419lyrcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V419 Lyr (1999).}\\label{tab:v419lyroc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51415.0770 & 0.0018 & $-$0.0270 & 96 \\\\\n3 & 51415.3722 & 0.0011 & $-$0.0010 & 89 \\\\\n4 & 51415.4646 & 0.0012 & 0.0016 & 90 \\\\\n11 & 51416.0808 & 0.0029 & $-$0.0106 & 66 \\\\\n14 & 51416.3683 & 0.0010 & 0.0077 & 89 \\\\\n15 & 51416.4583 & 0.0013 & 0.0080 & 82 \\\\\n16 & 51416.5456 & 0.0023 & 0.0056 & 56 \\\\\n36 & 51418.3474 & 0.0020 & 0.0122 & 82 \\\\\n37 & 51418.4342 & 0.0038 & 0.0092 & 86 \\\\\n38 & 51418.5284 & 0.0047 & 0.0137 & 38 \\\\\n78 & 51422.0858 & 0.0033 & $-$0.0192 & 71 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451415.1040 + 0.089758 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V419 Lyr (2006).}\\label{tab:v419lyroc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53934.4226 & 0.0015 & $-$0.0179 & 0 \\\\\n11 & 53935.4264 & 0.0004 & $-$0.0026 & 64 \\\\\n12 & 53935.5188 & 0.0004 & $-$0.0000 & 77 \\\\\n22 & 53936.4226 & 0.0016 & 0.0051 & 0 \\\\\n33 & 53937.4106 & 0.0014 & 0.0046 & 0 \\\\\n34 & 53937.5000 & 0.0005 & 0.0042 & 114 \\\\\n45 & 53938.4903 & 0.0005 & 0.0060 & 100 \\\\\n47 & 53938.6716 & 0.0022 & 0.0076 & 0 \\\\\n48 & 53938.7596 & 0.0025 & 0.0057 & 0 \\\\\n55 & 53939.3856 & 0.0044 & 0.0027 & 0 \\\\\n57 & 53939.5617 & 0.0006 & $-$0.0010 & 85 \\\\\n58 & 53939.6526 & 0.0034 & 0.0001 & 0 \\\\\n59 & 53939.7436 & 0.0029 & 0.0012 & 0 \\\\\n60 & 53939.8336 & 0.0033 & 0.0014 & 0 \\\\\n61 & 53939.9226 & 0.0033 & 0.0005 & 0 \\\\\n66 & 53940.3723 & 0.0014 & 0.0009 & 62 \\\\\n67 & 53940.4595 & 0.0004 & $-$0.0018 & 202 \\\\\n78 & 53941.4466 & 0.0007 & $-$0.0031 & 118 \\\\\n79 & 53941.5356 & 0.0030 & $-$0.0040 & 0 \\\\\n88 & 53942.3466 & 0.0015 & $-$0.0018 & 0 \\\\\n89 & 53942.4346 & 0.0033 & $-$0.0037 & 0 \\\\\n103 & 53943.6986 & 0.0047 & 0.0023 & 0 \\\\\n104 & 53943.7856 & 0.0044 & $-$0.0006 & 0 \\\\\n111 & 53944.4096 & 0.0022 & $-$0.0056 & 0 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453934.4405 + 0.089862 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N=0$ refers to \\citet{rut07v419lyr}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V585 Lyrae}\\label{obj:v585lyr}\n\n V585 Lyr was discovered by \\citet{kry01v585lyrv587lyr}.\nAn extensive photometric campaign was undertaken during the 2003\nsuperoutburst. The times of superhump maxima during this superoutburst\nare listed in table \\ref{tab:v585lyroc2003}.\nThe interval $32 \\le E \\le 150$ (stage B) showed\na positive $P_{\\rm dot}$ of $+10.7(1.2) \\times 10^{-5}$, then followed\nby the emergence of a shorter period (stage C) and a regrowth\nof superhumps, typical behavior for a short-period system\n(cf. figure \\ref{fig:ocsamp}).\n\n\\begin{table}\n\\caption{Superhump maxima of V585 Lyr (2003).}\\label{tab:v585lyroc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52898.3727 & 0.0027 & $-$0.0155 & 67 \\\\\n9 & 52898.9215 & 0.0085 & $-$0.0106 & 68 \\\\\n12 & 52899.1050 & 0.0024 & $-$0.0085 & 149 \\\\\n13 & 52899.1703 & 0.0033 & $-$0.0036 & 28 \\\\\n18 & 52899.4708 & 0.0129 & $-$0.0053 & 52 \\\\\n19 & 52899.5337 & 0.0031 & $-$0.0028 & 58 \\\\\n28 & 52900.0831 & 0.0018 & 0.0027 & 74 \\\\\n29 & 52900.1338 & 0.0083 & $-$0.0072 & 44 \\\\\n32 & 52900.3316 & 0.0005 & 0.0094 & 54 \\\\\n33 & 52900.3949 & 0.0004 & 0.0122 & 61 \\\\\n34 & 52900.4514 & 0.0007 & 0.0083 & 63 \\\\\n35 & 52900.5124 & 0.0016 & 0.0088 & 62 \\\\\n36 & 52900.5742 & 0.0010 & 0.0102 & 40 \\\\\n37 & 52900.6346 & 0.0002 & 0.0102 & 58 \\\\\n43 & 52900.9988 & 0.0016 & 0.0118 & 80 \\\\\n44 & 52901.0575 & 0.0020 & 0.0100 & 60 \\\\\n45 & 52901.1120 & 0.0018 & 0.0040 & 38 \\\\\n49 & 52901.3559 & 0.0007 & 0.0062 & 63 \\\\\n50 & 52901.4149 & 0.0006 & 0.0048 & 63 \\\\\n51 & 52901.4759 & 0.0008 & 0.0053 & 61 \\\\\n52 & 52901.5340 & 0.0008 & 0.0030 & 57 \\\\\n62 & 52902.1375 & 0.0004 & 0.0021 & 33 \\\\\n63 & 52902.1968 & 0.0006 & 0.0010 & 33 \\\\\n64 & 52902.2578 & 0.0006 & 0.0014 & 33 \\\\\n65 & 52902.3176 & 0.0008 & 0.0008 & 71 \\\\\n66 & 52902.3843 & 0.0011 & 0.0071 & 43 \\\\\n67 & 52902.4358 & 0.0007 & $-$0.0018 & 54 \\\\\n68 & 52902.4959 & 0.0008 & $-$0.0022 & 59 \\\\\n69 & 52902.5576 & 0.0024 & $-$0.0009 & 26 \\\\\n72 & 52902.7388 & 0.0011 & $-$0.0010 & 74 \\\\\n73 & 52902.8007 & 0.0007 & 0.0004 & 99 \\\\\n81 & 52903.2806 & 0.0014 & $-$0.0032 & 21 \\\\\n82 & 52903.3423 & 0.0019 & $-$0.0019 & 272 \\\\\n83 & 52903.4017 & 0.0010 & $-$0.0030 & 291 \\\\\n84 & 52903.4641 & 0.0015 & $-$0.0010 & 273 \\\\\n85 & 52903.5191 & 0.0025 & $-$0.0065 & 123 \\\\\n88 & 52903.7031 & 0.0009 & $-$0.0038 & 118 \\\\\n90 & 52903.8223 & 0.0008 & $-$0.0054 & 118 \\\\\n96 & 52904.1860 & 0.0011 & $-$0.0044 & 29 \\\\\n97 & 52904.2454 & 0.0012 & $-$0.0054 & 28 \\\\\n98 & 52904.3065 & 0.0010 & $-$0.0048 & 91 \\\\\n99 & 52904.3683 & 0.0011 & $-$0.0034 & 99 \\\\\n100 & 52904.4262 & 0.0014 & $-$0.0059 & 125 \\\\\n101 & 52904.4913 & 0.0017 & $-$0.0013 & 105 \\\\\n104 & 52904.6723 & 0.0010 & $-$0.0016 & 111 \\\\\n105 & 52904.7299 & 0.0008 & $-$0.0045 & 104 \\\\\n106 & 52904.7915 & 0.0007 & $-$0.0032 & 112 \\\\\n107 & 52904.8530 & 0.0020 & $-$0.0023 & 77 \\\\\n110 & 52905.0369 & 0.0012 & 0.0004 & 113 \\\\\n111 & 52905.0860 & 0.0020 & $-$0.0110 & 115 \\\\\n114 & 52905.2735 & 0.0018 & $-$0.0048 & 53 \\\\\n115 & 52905.3363 & 0.0017 & $-$0.0025 & 59 \\\\\n116 & 52905.3994 & 0.0012 & 0.0002 & 61 \\\\\n117 & 52905.4517 & 0.0017 & $-$0.0080 & 61 \\\\\n118 & 52905.5241 & 0.0049 & 0.0040 & 60 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452898.3882 + 0.060440 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of V585 Lyr (2003) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n120 & 52905.6324 & 0.0045 & $-$0.0085 & 16 \\\\\n122 & 52905.7636 & 0.0012 & 0.0018 & 22 \\\\\n123 & 52905.8222 & 0.0021 & $-$0.0001 & 18 \\\\\n128 & 52906.1229 & 0.0021 & $-$0.0016 & 33 \\\\\n129 & 52906.1848 & 0.0028 & $-$0.0001 & 32 \\\\\n130 & 52906.2455 & 0.0020 & 0.0002 & 33 \\\\\n137 & 52906.6630 & 0.0046 & $-$0.0055 & 22 \\\\\n138 & 52906.7280 & 0.0020 & $-$0.0009 & 25 \\\\\n139 & 52906.7790 & 0.0074 & $-$0.0103 & 21 \\\\\n145 & 52907.1628 & 0.0047 & 0.0108 & 17 \\\\\n149 & 52907.3974 & 0.0008 & 0.0038 & 102 \\\\\n148 & 52907.3366 & 0.0009 & 0.0033 & 109 \\\\\n149 & 52907.3971 & 0.0008 & 0.0034 & 100 \\\\\n150 & 52907.4603 & 0.0014 & 0.0062 & 47 \\\\\n164 & 52908.3061 & 0.0018 & 0.0058 & 38 \\\\\n166 & 52908.4220 & 0.0017 & 0.0008 & 33 \\\\\n166 & 52908.4220 & 0.0019 & 0.0009 & 37 \\\\\n167 & 52908.4865 & 0.0030 & 0.0049 & 17 \\\\\n178 & 52909.1489 & 0.0014 & 0.0025 & 17 \\\\\n179 & 52909.2107 & 0.0006 & 0.0038 & 17 \\\\\n180 & 52909.2680 & 0.0017 & 0.0007 & 17 \\\\\n181 & 52909.3286 & 0.0029 & 0.0009 & 32 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AD Mensae}\\label{obj:admen}\n\n AD Men was discovered as a variable star in the region of the\nLarge Magellanic Cloud. The GCVS \\citep{GCVS} listed the object\nas an SS Cyg-type dwarf nova with an outburst cycle length of $\\sim$ 30 d.\n\n The object underwent a bright outburst in 2003 March at a visual\nmagnitude of 14.0. The existence of superhumps was inconclusive\nduring this outburst.\\footnote{\n $<$http:\/\/vsnet.kusastro.kyoto-u.ac.jp\/vsnet\/DNe\/admen.html$>$.\n}\n\n The object underwent another bright outburst in 2004 March.\nThe existence of superhumps was confirmed during this outburst,\nestablishing the SU UMa-type nature of this object.\nAlthough a single superhump maximum of BJD 2453090.3137(7) was\nobtained, a PDM analysis and the examination of the single-night\nobservation yielded the most likely period of 0.0966(2) d\n(figure \\ref{fig:admenshpdm}). The object is an SU UMa-type dwarf nova\nlikely in the period gap. The present $P_{\\rm SH}$ is consistent\nwith a photometric measurement of $P_{\\rm orb}$ = 0.0917(10) d\n\\citep{sch06admen}. The fractional superhump excess is $\\sim$ 5 \\%.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig106.eps}\n \\end{center}\n \\caption{Superhumps in AD Men (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:admenshpdm}\n\\end{figure}\n\n\\subsection{FQ Monocerotis}\\label{sec:fqmon}\\label{obj:fqmon}\n\n FQ Mon, originally classified as a possible Mira-type variable\n\\citep{GCVS}, was suspected to be a CV (vsnet-chat 3063,3066).\nThe first known outburst since the discovery was recorded in 2004\n(vsnet-alert 8048).\nWe observed the 2004, 2006, 2007--2008 superoutbursts.\n\n The 2004 superoutburst was relatively well observed\n(table \\ref{tab:fqmonoc2004}). The $O-C$ diagram was composed of\na typical stage B--C transition. The $P_{\\rm dot}$ for the\nstage B was $+9.2(2.4) \\times 10^{-5}$ ($E \\le 111$).\n\nThe later part of the 2006 superoutburst was observed\n(table \\ref{tab:fqmonoc2006}). Compared to other superoutbursts,\nthe fairly constant period after $E=51$ likely corresponds to $P_2$.\n\n A photometric campaign was undertaken during the 2007--2008\nsuperoutburst. The times of superhump maxima are listed in table\n\\ref{tab:fqmonoc2007}. The object reached the maximum\nlight around $E = 40$. Although superhumps were still prominent\nbefore this epoch, the period was significantly shorter than in the\nlater epoch. The combined $O-C$ diagram (figure \\ref{fig:fqmoncomp})\nsuggests that stages B and C were recorded during this superoutburst.\nThe $P_{\\rm dot}$ for the stage B was $+5.4(1.3) \\times 10^{-5}$\n($E \\le 124$).\n\n The overall behavior resembles the $O-C$ variation in TT Boo\n\\citep{ole04ttboo}. These two objects have common\nproperties of a relatively long superhump period (0.07--0.08 d),\nunusually long superoutburst ($\\ge$ 15 d) and relatively few normal\noutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig107.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of FQ Mon between different\n superoutbursts. A period of 0.07335 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:fqmoncomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of FQ Mon (2004).}\\label{tab:fqmonoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53068.9790 & 0.0013 & 0.0023 & 107 \\\\\n1 & 53069.0595 & 0.0021 & 0.0096 & 84 \\\\\n6 & 53069.4104 & 0.0012 & $-$0.0056 & 78 \\\\\n7 & 53069.4832 & 0.0058 & $-$0.0061 & 25 \\\\\n8 & 53069.5592 & 0.0002 & $-$0.0033 & 53 \\\\\n9 & 53069.6336 & 0.0003 & $-$0.0021 & 55 \\\\\n10 & 53069.7062 & 0.0003 & $-$0.0027 & 55 \\\\\n14 & 53069.9988 & 0.0024 & $-$0.0031 & 184 \\\\\n22 & 53070.5856 & 0.0003 & $-$0.0021 & 60 \\\\\n23 & 53070.6586 & 0.0005 & $-$0.0024 & 41 \\\\\n41 & 53071.9707 & 0.0027 & $-$0.0083 & 113 \\\\\n42 & 53072.0476 & 0.0011 & $-$0.0047 & 209 \\\\\n50 & 53072.6327 & 0.0006 & $-$0.0055 & 60 \\\\\n51 & 53072.7086 & 0.0007 & $-$0.0028 & 57 \\\\\n60 & 53073.3676 & 0.0014 & $-$0.0029 & 57 \\\\\n69 & 53074.0333 & 0.0027 & 0.0038 & 133 \\\\\n73 & 53074.3311 & 0.0009 & 0.0086 & 101 \\\\\n76 & 53074.5419 & 0.0008 & $-$0.0002 & 33 \\\\\n77 & 53074.6187 & 0.0019 & 0.0034 & 44 \\\\\n78 & 53074.6902 & 0.0010 & 0.0016 & 28 \\\\\n109 & 53076.9701 & 0.0048 & 0.0114 & 95 \\\\\n110 & 53077.0566 & 0.0022 & 0.0246 & 136 \\\\\n111 & 53077.1115 & 0.0066 & 0.0063 & 129 \\\\\n122 & 53077.9152 & 0.0091 & 0.0045 & 130 \\\\\n123 & 53077.9858 & 0.0015 & 0.0018 & 188 \\\\\n124 & 53078.0558 & 0.0057 & $-$0.0013 & 178 \\\\\n136 & 53078.9388 & 0.0024 & 0.0029 & 171 \\\\\n137 & 53079.0161 & 0.0016 & 0.0070 & 243 \\\\\n138 & 53079.0856 & 0.0036 & 0.0032 & 86 \\\\\n150 & 53079.9599 & 0.0022 & $-$0.0012 & 216 \\\\\n151 & 53080.0308 & 0.0026 & $-$0.0036 & 188 \\\\\n152 & 53080.1030 & 0.0098 & $-$0.0046 & 68 \\\\\n164 & 53080.9786 & 0.0032 & $-$0.0078 & 94 \\\\\n165 & 53081.0578 & 0.0035 & $-$0.0018 & 37 \\\\\n205 & 53083.9697 & 0.0036 & $-$0.0191 & 31 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453068.9766 + 0.073230 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of FQ Mon (2006).}\\label{tab:fqmonoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53754.1730 & 0.0062 & $-$0.0151 & 256 \\\\\n1 & 53754.2529 & 0.0022 & $-$0.0084 & 134 \\\\\n51 & 53757.9460 & 0.0125 & 0.0224 & 78 \\\\\n67 & 53759.1050 & 0.0011 & 0.0094 & 214 \\\\\n68 & 53759.1778 & 0.0051 & 0.0090 & 194 \\\\\n81 & 53760.1268 & 0.0013 & 0.0057 & 132 \\\\\n82 & 53760.1930 & 0.0017 & $-$0.0012 & 131 \\\\\n95 & 53761.1506 & 0.0028 & 0.0041 & 132 \\\\\n96 & 53761.2109 & 0.0019 & $-$0.0088 & 132 \\\\\n134 & 53763.9860 & 0.0015 & $-$0.0171 & 100 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453754.1881 + 0.073246 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of FQ Mon (2007--2008).}\\label{tab:fqmonoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54463.1149 & 0.0005 & 0.0007 & 53 \\\\\n1 & 54463.1908 & 0.0004 & 0.0033 & 76 \\\\\n2 & 54463.2629 & 0.0003 & 0.0022 & 76 \\\\\n3 & 54463.3347 & 0.0003 & 0.0005 & 55 \\\\\n14 & 54464.1450 & 0.0018 & 0.0044 & 41 \\\\\n15 & 54464.2158 & 0.0004 & 0.0018 & 76 \\\\\n16 & 54464.2883 & 0.0004 & 0.0010 & 77 \\\\\n41 & 54466.1144 & 0.0010 & $-$0.0060 & 77 \\\\\n42 & 54466.1907 & 0.0012 & $-$0.0030 & 125 \\\\\n43 & 54466.2643 & 0.0010 & $-$0.0027 & 83 \\\\\n54 & 54467.0738 & 0.0010 & 0.0002 & 97 \\\\\n55 & 54467.1465 & 0.0014 & $-$0.0003 & 138 \\\\\n56 & 54467.2189 & 0.0009 & $-$0.0013 & 136 \\\\\n57 & 54467.2803 & 0.0016 & $-$0.0132 & 114 \\\\\n69 & 54468.1643 & 0.0046 & $-$0.0091 & 81 \\\\\n70 & 54468.2454 & 0.0017 & $-$0.0013 & 138 \\\\\n95 & 54470.0834 & 0.0030 & 0.0037 & 152 \\\\\n96 & 54470.1571 & 0.0030 & 0.0041 & 152 \\\\\n97 & 54470.2309 & 0.0021 & 0.0046 & 64 \\\\\n108 & 54471.0324 & 0.0024 & $-$0.0005 & 123 \\\\\n109 & 54471.1110 & 0.0009 & 0.0048 & 221 \\\\\n110 & 54471.1821 & 0.0013 & 0.0025 & 157 \\\\\n122 & 54472.0645 & 0.0015 & 0.0051 & 158 \\\\\n123 & 54472.1372 & 0.0014 & 0.0045 & 211 \\\\\n124 & 54472.2110 & 0.0019 & 0.0050 & 138 \\\\\n163 & 54475.0557 & 0.0084 & $-$0.0099 & 141 \\\\\n164 & 54475.1377 & 0.0044 & $-$0.0012 & 198 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454463.1142 + 0.073322 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AB Normae}\\label{obj:abnor}\n\n \\citet{kat04nsv10934mmscoabnorcal86} reported the detection of\nsuperhumps in AB Nor during its 2002 superoutburst. Due to the\nobservational gap and apparent period variation, the identification\nof the correct $P_{\\rm SH}$ was rather ambiguous. Based on the\nimproved knowledge of period variations in long-$P_{\\rm SH}$ systems,\nwe succeeded in identifying a more likely $P_{\\rm SH}$\n(table \\ref{tab:abnoroc2002}). For $E \\le 16$, the system showed\nthe stage A period evolution associated with the growth of\nsuperhumps. The mean period and $P_{\\rm dot}$'s were\n0.07962(3) d and $-8.1(2.7) \\times 10^{-5}$, respectively\n($15 \\le E \\le 142$) or 0.07955(3) d and $-6.1(5.2) \\times 10^{-5}$,\nrespectively ($37 \\le E \\le 142$).\n\n\\begin{table}\n\\caption{Superhump maxima of AB Nor (2002).}\\label{tab:abnoroc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52518.9807 & 0.0013 & $-$0.0189 & 36 \\\\\n4 & 52519.3045 & 0.0020 & $-$0.0141 & 86 \\\\\n15 & 52520.2092 & 0.0007 & 0.0134 & 41 \\\\\n16 & 52520.2844 & 0.0015 & 0.0089 & 31 \\\\\n37 & 52521.9670 & 0.0003 & 0.0167 & 40 \\\\\n124 & 52528.8911 & 0.0022 & 0.0027 & 18 \\\\\n141 & 52530.2420 & 0.0019 & $-$0.0022 & 87 \\\\\n142 & 52530.3175 & 0.0061 & $-$0.0065 & 49 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452518.9996 + 0.079749 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DT Octantis}\\label{sec:dtoct}\\label{obj:dtoct}\n\n \\citet{kat04nsv10934mmscoabnorcal86} reported the detection of\nsuperhumps in DT Oct = NSV 10934 during its 2003 January superoutburst.\nTable \\ref{tab:dtoctoc2003a} gives an upgraded list of superhump maxima.\nThe epochs $156 \\le E \\le 158$ correspond to the post-superoutburst\nstage. There was a hint of double-wave modulation at this stage\nand was possibly from classical ``late superhumps''.\nDisregarding this stage and the stage A ($E \\le 9$), the global\n$P_{\\rm dot}$ corresponds to $-9.0(1.1) \\times 10^{-5}$.\nThe times of superhump maxima during the 2003 November superoutburst\nand the 2008 superoutburst are also given for a supplementary purpose\n(tables \\ref{tab:dtoctoc2003b}, \\ref{tab:dtoctoc2008}). The latter\nsuperoutburst probably recorded the stage C superhumps\n(see figure \\ref{fig:dtoctcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig108.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of DT Oct between different\n superoutbursts. A period of 0.07485 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:dtoctcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of DT Oct (2003a).}\\label{tab:dtoctoc2003a}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52643.3689 & 0.0010 & $-$0.0387 & 195 \\\\\n8 & 52643.9890 & 0.0003 & $-$0.0167 & 82 \\\\\n9 & 52644.0657 & 0.0005 & $-$0.0146 & 104 \\\\\n21 & 52644.9791 & 0.0002 & 0.0017 & 197 \\\\\n22 & 52645.0560 & 0.0002 & 0.0037 & 254 \\\\\n23 & 52645.1312 & 0.0004 & 0.0042 & 60 \\\\\n34 & 52645.9559 & 0.0013 & 0.0065 & 90 \\\\\n35 & 52646.0318 & 0.0002 & 0.0077 & 392 \\\\\n36 & 52646.1063 & 0.0002 & 0.0075 & 383 \\\\\n37 & 52646.1832 & 0.0003 & 0.0095 & 211 \\\\\n61 & 52647.9799 & 0.0002 & 0.0121 & 128 \\\\\n88 & 52649.9957 & 0.0002 & 0.0094 & 319 \\\\\n89 & 52650.0702 & 0.0003 & 0.0092 & 347 \\\\\n90 & 52650.1467 & 0.0004 & 0.0109 & 269 \\\\\n91 & 52650.2201 & 0.0004 & 0.0095 & 191 \\\\\n101 & 52650.9625 & 0.0008 & 0.0043 & 85 \\\\\n102 & 52651.0394 & 0.0006 & 0.0064 & 199 \\\\\n103 & 52651.1139 & 0.0004 & 0.0062 & 130 \\\\\n104 & 52651.1875 & 0.0005 & 0.0051 & 108 \\\\\n115 & 52652.0081 & 0.0005 & 0.0033 & 270 \\\\\n116 & 52652.0827 & 0.0004 & 0.0031 & 329 \\\\\n117 & 52652.1601 & 0.0007 & 0.0058 & 237 \\\\\n118 & 52652.2326 & 0.0006 & 0.0036 & 149 \\\\\n156 & 52655.0686 & 0.0023 & $-$0.0013 & 26 \\\\\n157 & 52655.1075 & 0.0010 & $-$0.0372 & 25 \\\\\n158 & 52655.1983 & 0.0012 & $-$0.0211 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452643.4076 + 0.074759 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DT Oct (2003b).}\\label{tab:dtoctoc2003b}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52970.0252 & 0.0004 & $-$0.0000 & 282 \\\\\n13 & 52970.9995 & 0.0004 & 0.0006 & 243 \\\\\n14 & 52971.0732 & 0.0006 & $-$0.0006 & 152 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452970.0253 + 0.074893 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DT Oct (2008).}\\label{tab:dtoctoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54526.0354 & 0.0008 & $-$0.0014 & 34 \\\\\n1 & 54526.1124 & 0.0008 & 0.0010 & 33 \\\\\n2 & 54526.1860 & 0.0007 & 0.0001 & 34 \\\\\n14 & 54527.0821 & 0.0012 & 0.0015 & 16 \\\\\n15 & 54527.1530 & 0.0012 & $-$0.0021 & 17 \\\\\n16 & 54527.2307 & 0.0009 & 0.0010 & 17 \\\\\n40 & 54529.0188 & 0.0021 & $-$0.0002 & 34 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454526.0368 + 0.074554 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V699 Ophiuchi}\\label{sec:v699oph}\\label{obj:v699oph}\n\n Until very recently, the nature of V699 Oph remained controversial.\nThe object was originally discovered as a possible dwarf nova.\n\\citet{wal58CVchart} presented a finding chart, but later spectroscopic\nstudies have shown that the marked object is a normal star\n(\\cite{zwi96CVspec}; \\cite{liu99CVspec2}; Kato et al., unpublished).\n\n On 1999 April 16, A. Pearce discovered an outburst of this object\n(vsnet-alert 2877). Astrometry and photometry of the outbursting object\nindicated that the true V699 Oph is an unresolved companion to a 16-th\nmagnitude star (vsnet-alert 2878, vsnet-chat 1810, 1868).\n\n The 2003 superoutburst was noteworthy in that it was preceded by\na precursor outburst (vsnet-alert 7768, 7795) 11 d before the onset\nof the superoutburst and followed by a rebrightening\n(figure \\ref{fig:v699oph2003oc}). The mean superhump period\nwith the PDM method was 0.070242(12) d (figure \\ref{fig:v699ophshpdm}).\nThe superhump maxima during the plateau stage are listed in table\n\\ref{tab:v699ophoc2003}. There was likely a stage B--C transition around\n$E=43$. The $P_{\\rm dot}$ during the stage B was $+14.2(7.7) \\times 10^{-5}$.\nThere was marginal evidence for $\\sim$ 0.02 mag modulation with\na period of 0.0689(2) d during the first two days of the precursor,\nwhich might be related to orbital modulations.\n\n The 2008 superoutburst (table \\ref{tab:v699ophoc2008}) lacked good\ncoverage in the middle of the superoutburst. The maxima with $E \\ge 87$\nwere obtained during the late-stage decline of the superoutburst and\nmost likely correspond to the stage C.\nUsing all the superhump maxima, we obtained a global\n$P_{\\rm dot}$ of $-6.9(1.4) \\times 10^{-5}$. The $P_{\\rm dot}$ before\nthe supposed stage B--C transition should have been closer to\nzero than this global value.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig109.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps V699 Oph (2003).\n (Upper): $O-C$ diagram.\n (Lower): Light curve. The superoutburst was preceded by a precursor\n and followed by a rebrightening. The flat bottom at magnitude\n $\\sim$ 16.1 was a result of an unresolved companion.\n }\n \\label{fig:v699oph2003oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig110.eps}\n \\end{center}\n \\caption{Superhumps in V699 Oph (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v699ophshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V699 Oph (2003).}\\label{tab:v699ophoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52824.2510 & 0.0011 & 0.0003 & 38 \\\\\n11 & 52825.0233 & 0.0007 & $-$0.0005 & 389 \\\\\n13 & 52825.1616 & 0.0035 & $-$0.0027 & 20 \\\\\n14 & 52825.2354 & 0.0009 & 0.0008 & 39 \\\\\n15 & 52825.3058 & 0.0015 & 0.0010 & 27 \\\\\n26 & 52826.0753 & 0.0005 & $-$0.0026 & 121 \\\\\n28 & 52826.2183 & 0.0009 & $-$0.0001 & 39 \\\\\n29 & 52826.2887 & 0.0014 & $-$0.0000 & 39 \\\\\n39 & 52826.9913 & 0.0021 & $-$0.0002 & 93 \\\\\n42 & 52827.2056 & 0.0011 & 0.0034 & 39 \\\\\n43 & 52827.2746 & 0.0011 & 0.0021 & 38 \\\\\n54 & 52828.0453 & 0.0015 & $-$0.0002 & 220 \\\\\n56 & 52828.1884 & 0.0010 & 0.0023 & 37 \\\\\n57 & 52828.2579 & 0.0014 & 0.0016 & 38 \\\\\n66 & 52828.8891 & 0.0008 & 0.0002 & 150 \\\\\n67 & 52828.9581 & 0.0013 & $-$0.0010 & 192 \\\\\n68 & 52829.0250 & 0.0009 & $-$0.0043 & 291 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452824.2508 + 0.070274 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V699 Oph (2008).}\\label{tab:v699ophoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54618.1103 & 0.0026 & $-$0.0063 & 72 \\\\\n1 & 54618.1851 & 0.0006 & $-$0.0017 & 141 \\\\\n14 & 54619.1009 & 0.0007 & 0.0030 & 131 \\\\\n15 & 54619.1697 & 0.0008 & 0.0017 & 121 \\\\\n16 & 54619.2392 & 0.0007 & 0.0011 & 115 \\\\\n17 & 54619.3097 & 0.0010 & 0.0015 & 128 \\\\\n87 & 54624.2193 & 0.0019 & 0.0047 & 100 \\\\\n128 & 54627.0849 & 0.0039 & $-$0.0034 & 144 \\\\\n129 & 54627.1577 & 0.0063 & $-$0.0007 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454618.1166 + 0.070091 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V2051 Ophiuchi}\\label{obj:v2051oph}\n\n V2051 Oph is an eclipsing dwarf nova whose SU UMa-type nature was\nestablished by \\citet{kiy1998v2051oph}. \\citet{pat03suumas}\nobserved the 1999 superoutburst and reported a representative superhump\nperiod.\n\n We observed the 1999, 2003 and 2009 superoutburst.\nThe times of superhump maxima\n(tables \\ref{tab:v2051ophoc1999}, \\ref{tab:v2051ophoc2003},\n\\ref{tab:v2051ophoc2009}) were obtained after removing observations\nwithin 0.07 $P_{\\rm orb}$ of eclipses.\nThe 1999 observation covered the later part of a superoutburst\nand 2003 mostly covered the earlier part.\nWe could not reliably determine superhump maxima during the\nlater course of the 2003 superoutburst because of the complex superhump\nprofile and the presence of eclipses and the orbital signature.\nThe 1999 $O-C$ diagram clearly showed a shift to a shorter superhump\nperiod (stage B to C) associated with a regrowth of superhumps.\nUsing the $0 \\le E \\le 113$ segment,\nwe obtained $P_{\\rm dot}$ = $+2.9(2.9) \\times 10^{-5}$.\nUsing the entire data ($0 \\le E \\le 48$) of the 2003 superoutburst,\nwe obtained $P_{\\rm dot}$ = $-44.8(15.1) \\times 10^{-5}$.\nSuch a large decrease in the period\nwas most likely due to the early development of the superhump period\nfrom a longer period (stage A to B).\nUsing the interval of $E \\le 16$, we obtained a mean superhump period\nof 0.06380(8) d and $P_{\\rm dot}$ of $+14.0(26.8) \\times 10^{-5}$.\n\\citet{pat03suumas} reported a possible period decrease from 0.0641 d\nto 0.0637 d during the 1998 superoutburst, which may have been a similar\nphenomenon as seen in the 2003 superoutburst.\nCombining the 1999 and 2003 results, the behavior of the period change\nwas not dramatically different from those of other SU UMa-type dwarf\nnovae with similar superhump periods.\nMore comprehensive observations covering the entire superoutburst are\nneeded to clearly identify the superhump period and its evolution.\n\n A comparison of $O-C$ diagrams of V2051 Oph between different\nsuperoutbursts is shown in figure \\ref{fig:v2051ophcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig111.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V2051 Oph between different\n superoutbursts. A period of 0.06430 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v2051ophcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V2051 Oph (1999).}\\label{tab:v2051ophoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51387.8383 & 0.0008 & $-$0.0027 & 80 \\\\\n1 & 51387.9018 & 0.0006 & $-$0.0035 & 83 \\\\\n47 & 51390.8609 & 0.0014 & 0.0001 & 94 \\\\\n48 & 51390.9289 & 0.0018 & 0.0039 & 102 \\\\\n50 & 51391.0504 & 0.0018 & $-$0.0030 & 108 \\\\\n97 & 51394.0747 & 0.0013 & 0.0015 & 82 \\\\\n110 & 51394.9246 & 0.0010 & 0.0162 & 85 \\\\\n111 & 51394.9810 & 0.0011 & 0.0084 & 78 \\\\\n112 & 51395.0465 & 0.0007 & 0.0096 & 80 \\\\\n113 & 51395.1088 & 0.0007 & 0.0076 & 83 \\\\\n126 & 51395.9254 & 0.0004 & $-$0.0109 & 83 \\\\\n127 & 51395.9881 & 0.0005 & $-$0.0125 & 84 \\\\\n128 & 51396.0503 & 0.0008 & $-$0.0146 & 80 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451387.8411 + 0.064248 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V2051 Oph (2003).}\\label{tab:v2051ophoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52749.0260 & 0.0006 & $-$0.0048 & 69 \\\\\n1 & 52749.0901 & 0.0003 & $-$0.0048 & 312 \\\\\n16 & 52750.0619 & 0.0004 & 0.0054 & 260 \\\\\n17 & 52750.1293 & 0.0003 & 0.0087 & 268 \\\\\n32 & 52751.0846 & 0.0004 & 0.0024 & 171 \\\\\n33 & 52751.1470 & 0.0009 & 0.0007 & 395 \\\\\n34 & 52751.2080 & 0.0007 & $-$0.0024 & 352 \\\\\n39 & 52751.5277 & 0.0004 & $-$0.0033 & 280 \\\\\n40 & 52751.5989 & 0.0003 & 0.0038 & 239 \\\\\n47 & 52752.0418 & 0.0003 & $-$0.0020 & 244 \\\\\n48 & 52752.1044 & 0.0003 & $-$0.0036 & 384 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452749.0308 + 0.064108 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V2051 Oph (2009).}\\label{tab:v2051ophoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54974.0782 & 0.0006 & 0.0000 & 66 \\\\\n47 & 54977.0944 & 0.0006 & $-$0.0002 & 167 \\\\\n48 & 54977.1590 & 0.0010 & 0.0002 & 115 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454974.0782 + 0.064178 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V2527 Ophiuchi}\\label{obj:v2527oph}\n\n V2527 Oph was an X-ray selected CV, 1E1719.1$-$1946\n\\citep{her90XrayCVs}. The low absolute magnitude in quiescence inferred\nfrom spectroscopy was already suggestive of a short-period SU UMa-type\ndwarf nova.\nThe first detection of an outburst was reported in 1999 October\n(P. Schmeer).\n\n The 2004 superoutburst was very well observed.\nThe mean superhump period during the entire outburst was 0.071919(5) d\n(PDM method, figure \\ref{fig:v2527ophshpdm}).\nThis superoutburst had a distinct precursor outburst,\nduring which superhumps already started emerging.\nThe times of superhump maxima are listed in\ntable \\ref{tab:v2527ophoc2004}. The portion $E \\le 7$ corresponds to\nthe precursor, and $20 \\le E \\le 22$ rising stage from the minimum\nfollowing the precursor.\nThe superhump period showed stage A ($E \\le 29$),\nstage B with a positive period derivative,\nand a transition to the stage C with a shorter period ($E \\ge 103$).\nUsing the stage B, we obtained $P_{\\rm dot}$ = $+6.0(1.7) \\times 10^{-5}$\n($29 \\le E \\le 103$).\nThe times of superhump maxima and period analyses of two other\nsuperoutbursts in 2006 and 2008 are also given\n(tables \\ref{tab:v2527ophoc2006} and\n\\ref{tab:v2527ophoc2008}). A comparison of $O-C$ diagrams between\ndifferent superoutbursts is given in figure \\ref{fig:v2527ophcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig112.eps}\n \\end{center}\n \\caption{Superhumps in V2527 Oph (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v2527ophshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig113.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps V2527 Oph (2004).\n (Upper): $O-C$ diagram. The curve represents a quadratic fit to\n $29 \\le E \\le 103$.\n (Lower): Light curve. The superoutburst was preceded by a precursor.\n Large dots represent CCD observations. Small dots and a ``V'' mark\n represent visual observations and a upper limit, respectively.\n }\n \\label{fig:v2527oph2004oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig114.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V2527 Oph between different\n superoutbursts. A period of 0.07200 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v2527ophcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V2527 Oph (2004).}\\label{tab:v2527ophoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53209.3317 & 0.0019 & $-$0.0003 & 163 \\\\\n1 & 53209.3892 & 0.0007 & $-$0.0148 & 163 \\\\\n2 & 53209.4688 & 0.0013 & $-$0.0071 & 163 \\\\\n10 & 53210.0466 & 0.0005 & $-$0.0047 & 73 \\\\\n11 & 53210.1183 & 0.0004 & $-$0.0050 & 74 \\\\\n12 & 53210.1915 & 0.0003 & $-$0.0037 & 164 \\\\\n13 & 53210.2648 & 0.0002 & $-$0.0023 & 188 \\\\\n14 & 53210.3364 & 0.0001 & $-$0.0027 & 163 \\\\\n15 & 53210.4090 & 0.0002 & $-$0.0020 & 163 \\\\\n16 & 53210.4803 & 0.0002 & $-$0.0026 & 162 \\\\\n24 & 53211.0574 & 0.0008 & $-$0.0011 & 130 \\\\\n25 & 53211.1315 & 0.0026 & 0.0012 & 66 \\\\\n27 & 53211.2759 & 0.0002 & 0.0017 & 163 \\\\\n28 & 53211.3480 & 0.0002 & 0.0018 & 162 \\\\\n29 & 53211.4197 & 0.0002 & 0.0016 & 163 \\\\\n30 & 53211.4917 & 0.0004 & 0.0017 & 113 \\\\\n37 & 53211.9940 & 0.0004 & 0.0004 & 68 \\\\\n38 & 53212.0680 & 0.0003 & 0.0025 & 70 \\\\\n39 & 53212.1383 & 0.0004 & 0.0008 & 74 \\\\\n40 & 53212.2103 & 0.0003 & 0.0009 & 182 \\\\\n41 & 53212.2832 & 0.0003 & 0.0019 & 162 \\\\\n42 & 53212.3541 & 0.0003 & 0.0008 & 160 \\\\\n43 & 53212.4263 & 0.0003 & 0.0011 & 132 \\\\\n51 & 53213.0025 & 0.0003 & 0.0019 & 70 \\\\\n52 & 53213.0732 & 0.0004 & 0.0006 & 87 \\\\\n53 & 53213.1450 & 0.0004 & 0.0004 & 75 \\\\\n54 & 53213.2173 & 0.0007 & 0.0008 & 47 \\\\\n65 & 53214.0090 & 0.0010 & 0.0012 & 155 \\\\\n66 & 53214.0828 & 0.0006 & 0.0031 & 250 \\\\\n67 & 53214.1541 & 0.0007 & 0.0025 & 77 \\\\\n68 & 53214.2279 & 0.0005 & 0.0043 & 183 \\\\\n69 & 53214.2985 & 0.0007 & 0.0030 & 157 \\\\\n93 & 53216.0294 & 0.0003 & 0.0074 & 157 \\\\\n94 & 53216.1046 & 0.0012 & 0.0107 & 115 \\\\\n100 & 53216.5360 & 0.0007 & 0.0105 & 98 \\\\\n103 & 53216.7477 & 0.0009 & 0.0064 & 108 \\\\\n110 & 53217.2495 & 0.0006 & 0.0046 & 160 \\\\\n111 & 53217.3226 & 0.0005 & 0.0058 & 159 \\\\\n112 & 53217.3929 & 0.0004 & 0.0042 & 158 \\\\\n113 & 53217.4637 & 0.0009 & 0.0030 & 116 \\\\\n124 & 53218.2519 & 0.0008 & $-$0.0000 & 153 \\\\\n125 & 53218.3253 & 0.0006 & 0.0014 & 152 \\\\\n126 & 53218.3968 & 0.0008 & 0.0010 & 150 \\\\\n135 & 53219.0388 & 0.0014 & $-$0.0045 & 122 \\\\\n167 & 53221.3264 & 0.0011 & $-$0.0187 & 161 \\\\\n168 & 53221.3975 & 0.0014 & $-$0.0196 & 140 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453209.3320 + 0.071935 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V2527 Oph (2006).}\\label{tab:v2527ophoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53938.0839 & 0.0003 & 0.0000 & 190 \\\\\n96 & 53944.9892 & 0.0012 & $-$0.0011 & 99 \\\\\n97 & 53945.0633 & 0.0029 & 0.0011 & 97 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453938.0838 + 0.071942 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V2527 Oph (2008).}\\label{tab:v2527ophoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54709.9750 & 0.0006 & $-$0.0028 & 115 \\\\\n14 & 54710.9839 & 0.0007 & $-$0.0011 & 175 \\\\\n15 & 54711.0641 & 0.0014 & 0.0072 & 124 \\\\\n28 & 54711.9877 & 0.0007 & $-$0.0045 & 139 \\\\\n97 & 54716.9637 & 0.0089 & 0.0074 & 86 \\\\\n111 & 54717.9573 & 0.0010 & $-$0.0062 & 174 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454709.9778 + 0.071943 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1159 Orionis}\\label{obj:v1159ori}\n\n V1159 Ori is a member of ER UMa stars (\\cite{nog95v1159ori};\n\\cite{rob95eruma}; \\cite{pat95v1159ori}), having outburst characteristics\nsimilar to those of the prototype ER UMa itself.\nWe analyzed the 2002 November--December superoutburst\n(table \\ref{tab:v1159orioc2002}). Since the waveform of superhumps\nin ER UMa stars are relatively complex and sometimes show double peaks\n(cf. \\cite{kat03erumaSH}; \\cite{pat95v1159ori}), we only deal with\nprominent maxima and do not discuss on secondary maxima.\\footnote{\n In table \\ref{tab:v1159orioc2002}, two maxima are given for $E = 110$.\n These maxima, with nearly equal amplitudes, were probably a result\n of manifestation of the secondary maximum. We only used the latter\n maximum, which fits the trend of the rest of superhump maxima,\n in the analysis.\n}\nThere appears to be a $\\sim$0.5 phase shift before $E = 93$ as reported\nin ER UMa \\citep{kat03erumaSH}. The nominal $P_{\\rm dot}$ for the\nsegment $E \\le 63$ was $+14.9(5.4) \\times 10^{-5}$.\nAfter $E = 93$, the object showed a fairly constant $P_{\\rm SH}$\nof 0.06409(5) d, which likely corresponds to $P_2$ in ordinary\nSU UMa-type dwarf novae. The overall feature is similar to\nthat reported by \\citet{pat95v1159ori}. The times of superhump\nminima listed in \\citet{pat95v1159ori} can be expressed\nby a segment with a positive $P_{\\rm dot}$, followed by a transition\n(without a phase shift) to a shorter period which was very close to ours.\nNote, however, the difference may have been caused by different methods\n(\\cite{pat95v1159ori} used superhump minima rather than maxima)\nin determining period variation.\n\n\\begin{table}\n\\caption{Superhump maxima of V1159 Ori (2002).}\\label{tab:v1159orioc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52604.1949 & 0.0006 & 0.0004 & 67 \\\\\n16 & 52605.2186 & 0.0008 & $-$0.0035 & 86 \\\\\n30 & 52606.1185 & 0.0012 & $-$0.0027 & 98 \\\\\n31 & 52606.1800 & 0.0026 & $-$0.0055 & 81 \\\\\n32 & 52606.2399 & 0.0011 & $-$0.0098 & 118 \\\\\n45 & 52607.0753 & 0.0009 & $-$0.0093 & 85 \\\\\n46 & 52607.1406 & 0.0010 & $-$0.0082 & 64 \\\\\n48 & 52607.2707 & 0.0009 & $-$0.0066 & 190 \\\\\n62 & 52608.1717 & 0.0024 & $-$0.0047 & 88 \\\\\n63 & 52608.2363 & 0.0023 & $-$0.0043 & 284 \\\\\n93 & 52610.1934 & 0.0015 & 0.0262 & 97 \\\\\n94 & 52610.2460 & 0.0011 & 0.0145 & 130 \\\\\n109 & 52611.2102 & 0.0046 & 0.0153 & 148 \\\\\n110 & 52611.2447 & 0.0028 & $-$0.0143 & 196 \\\\\n110 & 52611.2762 & 0.0028 & 0.0171 & 187 \\\\\n138 & 52613.0700 & 0.0056 & 0.0127 & 85 \\\\\n139 & 52613.1316 & 0.0057 & 0.0101 & 74 \\\\\n233 & 52619.1500 & 0.0034 & $-$0.0084 & 53 \\\\\n234 & 52619.2248 & 0.0023 & 0.0022 & 82 \\\\\n235 & 52619.2805 & 0.0009 & $-$0.0064 & 85 \\\\\n248 & 52620.1199 & 0.0023 & $-$0.0019 & 58 \\\\\n249 & 52620.1730 & 0.0008 & $-$0.0130 & 70 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452604.1946 + 0.064222 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V344 Pavonis}\\label{obj:v344pav}\n\n We analyzed the data in \\citet{uem04v344pav} and obtained the times\nof superhump maxima (table \\ref{tab:v344pavoc2004}).\nSince the observation started during the late stage of the superoutburst,\nwe did not attempt to determine a $P_{\\rm dot}$.\nIt would be noteworthy that no phase reversal, expected\nfor traditional late superhumps, was recorded even after the rapid\nfading.\n\n\\begin{table}\n\\caption{Superhump maxima of V344 Pav (2004).}\\label{tab:v344pavoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53235.5965 & 0.0009 & 0.0029 & 158 \\\\\n13 & 53236.6301 & 0.0009 & 0.0007 & 168 \\\\\n14 & 53236.7121 & 0.0014 & 0.0031 & 169 \\\\\n15 & 53236.7940 & 0.0022 & 0.0053 & 169 \\\\\n25 & 53237.5816 & 0.0014 & $-$0.0037 & 166 \\\\\n26 & 53237.6655 & 0.0045 & 0.0005 & 170 \\\\\n27 & 53237.7345 & 0.0077 & $-$0.0102 & 169 \\\\\n37 & 53238.5451 & 0.0083 & 0.0038 & 120 \\\\\n38 & 53238.6052 & 0.0154 & $-$0.0158 & 165 \\\\\n50 & 53239.5808 & 0.0046 & 0.0038 & 153 \\\\\n51 & 53239.6663 & 0.0066 & 0.0097 & 111 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453235.5937 + 0.079667 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{EF Pegasi}\\label{obj:efpeg}\n\n \\citet{how93efpeg} and \\citet{kat02efpeg} reported on the 1991\nsuperoutburst. \\citet{kat02efpeg} reported a period decrease\nat $P_{\\rm dot}$ = $-5.1(0.7) \\times 10^{-5}$ after combination\nwith the times of maxima in \\citet{how93efpeg}.\nWe further observed this object during the 1997\nsuperoutburst. The times of superhump maxima are listed in table\n\\ref{tab:efpegoc1997}. The $P_{\\rm dot}$ determined from these data,\nexcluding the last two maxima, corresponds to\n$-4.2(2.1) \\times 10^{-5}$, similar to the one in 1991.\nThere was an indication that the earliest superhump maxima of\nthe 1991 were obtained during the evolutionary stage of superhumps.\nAn exclusion of these maxima has only yielded an insignificant $P_{\\rm dot}$\ndue to the fragmentary observational coverage.\nWe thus regard the 1997 result more reliable based on\nhomogeneous set of observations.\nThis result supersedes the preliminary argument on period changes\nin \\citet{kat02efpeg}. A comparison of 1991 and 1997 $O-C$ variations\nis presented in figure \\ref{fig:efpegcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig115.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of EF Peg between different\n superoutbursts. A period of 0.08705 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:efpegcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of EF Peg (1997).}\\label{tab:efpegoc1997}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50757.0034 & 0.0005 & $-$0.0073 & 152 \\\\\n11 & 50757.9621 & 0.0013 & $-$0.0049 & 117 \\\\\n12 & 50758.0528 & 0.0006 & $-$0.0011 & 126 \\\\\n22 & 50758.9216 & 0.0003 & $-$0.0017 & 193 \\\\\n23 & 50759.0123 & 0.0020 & 0.0021 & 145 \\\\\n34 & 50759.9642 & 0.0008 & $-$0.0023 & 162 \\\\\n35 & 50760.0541 & 0.0048 & 0.0007 & 56 \\\\\n45 & 50760.9232 & 0.0004 & 0.0004 & 165 \\\\\n46 & 50761.0162 & 0.0007 & 0.0064 & 126 \\\\\n56 & 50761.8829 & 0.0031 & 0.0038 & 100 \\\\\n57 & 50761.9685 & 0.0016 & 0.0025 & 160 \\\\\n58 & 50762.0597 & 0.0019 & 0.0067 & 143 \\\\\n68 & 50762.9273 & 0.0009 & 0.0050 & 186 \\\\\n69 & 50763.0103 & 0.0013 & 0.0011 & 163 \\\\\n79 & 50763.8807 & 0.0008 & 0.0021 & 115 \\\\\n80 & 50763.9665 & 0.0011 & 0.0010 & 151 \\\\\n81 & 50764.0546 & 0.0020 & 0.0022 & 62 \\\\\n91 & 50764.9292 & 0.0013 & 0.0075 & 23 \\\\\n102 & 50765.8572 & 0.0017 & $-$0.0208 & 44 \\\\\n103 & 50765.9616 & 0.0020 & $-$0.0034 & 132 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450757.0107 + 0.086934 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V364 Pegasi}\\label{obj:v364peg}\n\n V364 Peg is a dwarf nova discovered during the supernova survey\n\\citep{qiu97v364pegiauc6746}. \\citet{kat99v364peg} reported, based on\ntime-resolved photometry during the 1997 November outburst, that this\nobject is a likely SU UMa-type dwarf nova with a long superhump period.\nThis suggestion has been confirmed during the 2004 outburst\n(T. Vanmunster, aavso-photometry message), reporting a superhump\nperiod of 0.0882(70) d.\nWe have refined the period to 0.08556(5) d with the PDM method\n(figure \\ref{fig:v364pegshpdm}). The times of superhump maxima\nare listed in table \\ref{tab:v364pegoc2004}.\nIf there was a stage B--C transition as in many SU UMa-type dwarf novae,\nthis period likely represents $P_2$.\nThe inferred orbital period lies close to the lower edge of the\nperiod gap. The object appears to show rather frequent outbursts\n(cf. \\cite{qiu97v364pegiauc6772}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig116.eps}\n \\end{center}\n \\caption{Superhumps in V364 Peg (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v364pegshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V364 Peg (2004).}\\label{tab:v364pegoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53329.2263 & 0.0007 & 0.0008 & 57 \\\\\n1 & 53329.3101 & 0.0007 & $-$0.0007 & 70 \\\\\n2 & 53329.3967 & 0.0024 & 0.0006 & 30 \\\\\n4 & 53329.5654 & 0.0024 & $-$0.0015 & 48 \\\\\n5 & 53329.6529 & 0.0012 & 0.0008 & 60 \\\\\n27 & 53331.5302 & 0.0364 & 0.0006 & 29 \\\\\n28 & 53331.6144 & 0.0032 & $-$0.0005 & 46 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453329.2255 + 0.085338 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V368 Pegasi}\\label{obj:v368peg}\n\n V368 Peg is a dwarf nova discovered by\n\\citet{ant99v368pegftcamv367pegv2209cyg}.\nThe SU UMa-type nature of this object was established by J. Pietz\nduring the 1999 superoutburst (vsnet-alert 3317).\nWe observed the 2000 superoutburst.\nThe mean superhump period with the PDM method was 0.070253(17) d\n(figure \\ref{fig:v368pegshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:v368pegoc2000}.\nThere was a clear transition in the superhump period around $E = 86$.\nThe mean $P_{\\rm SH}$ and $P_{\\rm dot}$ for $E \\le 86$ were\n0.070380(8) d and $+0.5(1.2) \\times 10^{-5}$, respectively.\nWe also observed the 2005 superoutburst (table \\ref{tab:v368pegoc2005})\nduring the growing stage of superhumps. A likely stage A--B transition\nwas recorded ($E \\le 14$). Combined with the AAVSO\nobservations, we obtained $P_{\\rm SH}$ = 0.07038(3) d for $70 \\le E \\le 97$.\nThe 2006 superoutburst was observed during its late stage\n(table \\ref{tab:v368pegoc2006}), yielding $P_2$ = 0.069945(18) d with\nthe PDM method.\nA comparison of $O-C$ diagrams between different superoutbursts\nis shown in figure \\ref{fig:v368pegcomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig117.eps}\n \\end{center}\n \\caption{Superhumps in V368 Peg (2000). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v368pegshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig118.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V368 Peg between different\n superoutbursts. A period of 0.07039 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v368pegcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V368 Peg (2000).}\\label{tab:v368pegoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51785.2531 & 0.0005 & $-$0.0017 & 145 \\\\\n1 & 51785.3229 & 0.0011 & $-$0.0023 & 95 \\\\\n11 & 51786.0278 & 0.0006 & $-$0.0002 & 51 \\\\\n12 & 51786.0966 & 0.0007 & $-$0.0017 & 50 \\\\\n13 & 51786.1680 & 0.0009 & $-$0.0005 & 42 \\\\\n14 & 51786.2390 & 0.0004 & 0.0002 & 144 \\\\\n15 & 51786.3085 & 0.0011 & $-$0.0006 & 102 \\\\\n25 & 51787.0106 & 0.0012 & $-$0.0013 & 45 \\\\\n26 & 51787.0819 & 0.0012 & $-$0.0003 & 42 \\\\\n28 & 51787.2236 & 0.0022 & 0.0008 & 59 \\\\\n71 & 51790.2509 & 0.0034 & 0.0060 & 19 \\\\\n85 & 51791.2349 & 0.0006 & 0.0060 & 140 \\\\\n86 & 51791.3049 & 0.0013 & 0.0057 & 96 \\\\\n99 & 51792.2142 & 0.0016 & 0.0012 & 142 \\\\\n100 & 51792.2836 & 0.0069 & 0.0004 & 118 \\\\\n113 & 51793.1981 & 0.0016 & 0.0013 & 126 \\\\\n114 & 51793.2611 & 0.0013 & $-$0.0060 & 136 \\\\\n142 & 51795.2282 & 0.0032 & $-$0.0069 & 125 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451785.2548 + 0.070284 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V368 Peg (2005).}\\label{tab:v368pegoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53621.1701 & 0.0017 & $-$0.0073 & 191 \\\\\n14 & 53622.1728 & 0.0020 & 0.0044 & 163 \\\\\n70 & 53626.1372 & 0.0003 & 0.0048 & 201 \\\\\n71 & 53626.2065 & 0.0003 & 0.0033 & 212 \\\\\n72 & 53626.2779 & 0.0008 & 0.0039 & 139 \\\\\n74 & 53626.4181 & 0.0003 & 0.0026 & 49 \\\\\n75 & 53626.4880 & 0.0004 & 0.0017 & 71 \\\\\n88 & 53627.4024 & 0.0004 & $-$0.0041 & 53 \\\\\n89 & 53627.4747 & 0.0009 & $-$0.0026 & 57 \\\\\n97 & 53628.0371 & 0.0009 & $-$0.0065 & 96 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453621.1774 + 0.070785 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V368 Peg (2006).}\\label{tab:v368pegoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53993.2190 & 0.0006 & 0.0001 & 78 \\\\\n54 & 53996.9972 & 0.0017 & $-$0.0006 & 75 \\\\\n60 & 53997.4132 & 0.0009 & $-$0.0045 & 103 \\\\\n61 & 53997.4927 & 0.0219 & 0.0050 & 52 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453993.2189 + 0.069981 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V369 Pegasi}\\label{obj:v369peg}\n\n The SU UMa-type nature of V369 Peg (=KUV 23012$+$1702) was established\nduring the 1999 superoutburst \\citep{kat01v369peg}.\nWe reanalyzed the data in \\citet{kat01v369peg} and AAVSO observations.\nThe times of superhump maxima are listed in table \\ref{tab:v369pegoc1999}.\nThe $O-C$ diagram shows a stage B--C transition.\n\n\\begin{table}\n\\caption{Superhump maxima of V369 Peg (1999).}\\label{tab:v369pegoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51490.0631 & 0.0057 & $-$0.0153 & 53 \\\\\n12 & 51491.1040 & 0.0040 & 0.0055 & 90 \\\\\n24 & 51492.1264 & 0.0042 & 0.0079 & 166 \\\\\n26 & 51492.2963 & 0.0025 & 0.0078 & 56 \\\\\n27 & 51492.3757 & 0.0012 & 0.0022 & 92 \\\\\n35 & 51493.0500 & 0.0035 & $-$0.0035 & 155 \\\\\n36 & 51493.1412 & 0.0047 & 0.0027 & 168 \\\\\n71 & 51496.1034 & 0.0180 & $-$0.0101 & 170 \\\\\n82 & 51497.0513 & 0.0031 & 0.0027 & 111 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451490.0785 + 0.085001 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{UV Persei}\\label{sec:uvper}\\label{obj:uvper}\n\n UV Per is a well-known SU UMa-type dwarf nova with a relatively long\nrecurrence time and a large outburst amplitude.\n\\citet{uda92uvper} detected superhumps during the 1989 superoutburst.\n\\citet{uda92uvper} reported that they did not detect a significant\nquadratic term ($P_{\\rm dot}$), probably due to the short ($\\sim 3$ d)\ncoverage.\n\n We observed four superoutbursts in 1991--1992, 2000, 2003 and 2007\n(tables \\ref{tab:uvperoc1991}, \\ref{tab:uvperoc2000}, \\ref{tab:uvperoc2003},\n\\ref{tab:uvperoc2007}).\nThe 2000 observation covered the entire superoutburst, including the\ngrowing stage of superhumps and the rapid fading stage, but with\nlower signal statistics. The 2003 observation covered the\nsuperoutburst with higher statistics. The $O-C$ diagrams of these\noutbursts can be interpreted as a well-demonstrated sequence of\nstages A--C.\nThe $P_{\\rm dot}$'s of the stage B corresponded to\n$+9.5(6.0) \\times 10^{-5}$ ($14 \\le E \\le 62$)\nfor the 2000 superoutburst, and $+5.1(1.0) \\times 10^{-5}$\n($20 \\le E \\le 109$) for the 2003 superoutburst, respectively.\nThe 1991--1992 and 2007 superoutbursts were observed during the\n(middle-to-)final stage\nof the plateau and clearly showed a transition to a shorter period\n(stage B to C).\nAlthough the $P_{\\rm dot}$ of the entire 2007 data was\n$-7.0(0.9) \\times 10^{-5}$, this value should be used carefully since\nthe measured segment of the $O-C$ diagram was different from those\nin the 2000 and 2003 superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of UV Per (1991--1992).}\\label{tab:uvperoc1991}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48615.0640 & 0.0021 & $-$0.0118 & 63 \\\\\n58 & 48618.9295 & 0.0006 & 0.0044 & 107 \\\\\n73 & 48619.9247 & 0.0007 & 0.0042 & 62 \\\\\n88 & 48620.9195 & 0.0019 & 0.0035 & 45 \\\\\n91 & 48621.1213 & 0.0016 & 0.0062 & 68 \\\\\n92 & 48621.1855 & 0.0008 & 0.0040 & 128 \\\\\n103 & 48621.9170 & 0.0007 & 0.0055 & 143 \\\\\n104 & 48621.9773 & 0.0006 & $-$0.0005 & 7 \\\\\n105 & 48622.0463 & 0.0062 & 0.0021 & 70 \\\\\n106 & 48622.1199 & 0.0030 & 0.0093 & 51 \\\\\n120 & 48623.0287 & 0.0024 & $-$0.0110 & 80 \\\\\n121 & 48623.1109 & 0.0017 & 0.0048 & 154 \\\\\n134 & 48623.9528 & 0.0017 & $-$0.0161 & 117 \\\\\n135 & 48624.0368 & 0.0012 & 0.0016 & 116 \\\\\n136 & 48624.0954 & 0.0019 & $-$0.0062 & 116 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448615.0758 + 0.066366 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of UV Per (2000).}\\label{tab:uvperoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51904.0426 & 0.0006 & $-$0.0098 & 129 \\\\\n1 & 51904.1035 & 0.0037 & $-$0.0154 & 73 \\\\\n2 & 51904.1784 & 0.0018 & $-$0.0070 & 85 \\\\\n14 & 51904.9789 & 0.0011 & $-$0.0046 & 77 \\\\\n15 & 51905.0530 & 0.0023 & 0.0030 & 51 \\\\\n16 & 51905.1145 & 0.0026 & $-$0.0020 & 30 \\\\\n19 & 51905.3151 & 0.0002 & $-$0.0010 & 130 \\\\\n20 & 51905.3821 & 0.0004 & $-$0.0004 & 76 \\\\\n29 & 51905.9802 & 0.0005 & $-$0.0009 & 79 \\\\\n31 & 51906.1163 & 0.0006 & 0.0022 & 69 \\\\\n44 & 51906.9772 & 0.0003 & $-$0.0015 & 106 \\\\\n45 & 51907.0468 & 0.0005 & 0.0017 & 84 \\\\\n51 & 51907.4439 & 0.0006 & $-$0.0003 & 56 \\\\\n53 & 51907.5815 & 0.0006 & 0.0043 & 32 \\\\\n54 & 51907.6477 & 0.0006 & 0.0040 & 32 \\\\\n55 & 51907.7161 & 0.0006 & 0.0059 & 31 \\\\\n58 & 51907.9119 & 0.0006 & 0.0022 & 91 \\\\\n59 & 51907.9784 & 0.0004 & 0.0022 & 212 \\\\\n60 & 51908.0444 & 0.0004 & 0.0017 & 246 \\\\\n61 & 51908.1145 & 0.0004 & 0.0052 & 167 \\\\\n62 & 51908.1849 & 0.0008 & 0.0091 & 88 \\\\\n75 & 51909.0494 & 0.0021 & 0.0091 & 113 \\\\\n105 & 51911.0415 & 0.0007 & 0.0061 & 105 \\\\\n119 & 51911.9732 & 0.0005 & 0.0067 & 111 \\\\\n120 & 51912.0354 & 0.0008 & 0.0024 & 123 \\\\\n121 & 51912.1057 & 0.0009 & 0.0062 & 86 \\\\\n134 & 51912.9633 & 0.0008 & $-$0.0008 & 82 \\\\\n135 & 51913.0334 & 0.0007 & 0.0029 & 129 \\\\\n136 & 51913.0953 & 0.0030 & $-$0.0018 & 91 \\\\\n164 & 51914.9453 & 0.0033 & $-$0.0139 & 91 \\\\\n185 & 51916.3404 & 0.0029 & $-$0.0154 & 72 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451904.0524 + 0.066505 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of UV Per (2003).}\\label{tab:uvperoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52950.0550 & 0.0007 & $-$0.0130 & 77 \\\\\n2 & 52950.1920 & 0.0006 & $-$0.0091 & 103 \\\\\n3 & 52950.2599 & 0.0010 & $-$0.0077 & 127 \\\\\n4 & 52950.3278 & 0.0012 & $-$0.0063 & 185 \\\\\n5 & 52950.3964 & 0.0005 & $-$0.0043 & 192 \\\\\n6 & 52950.4647 & 0.0004 & $-$0.0024 & 101 \\\\\n7 & 52950.5315 & 0.0009 & $-$0.0022 & 38 \\\\\n20 & 52951.3978 & 0.0003 & $-$0.0008 & 329 \\\\\n21 & 52951.4634 & 0.0004 & $-$0.0018 & 264 \\\\\n22 & 52951.5311 & 0.0004 & $-$0.0005 & 182 \\\\\n23 & 52951.5976 & 0.0006 & $-$0.0006 & 16 \\\\\n24 & 52951.6646 & 0.0003 & $-$0.0001 & 98 \\\\\n25 & 52951.7286 & 0.0002 & $-$0.0027 & 216 \\\\\n26 & 52951.7941 & 0.0002 & $-$0.0037 & 207 \\\\\n27 & 52951.8612 & 0.0005 & $-$0.0031 & 222 \\\\\n28 & 52951.9292 & 0.0005 & $-$0.0016 & 172 \\\\\n29 & 52951.9944 & 0.0006 & $-$0.0030 & 76 \\\\\n34 & 52952.3283 & 0.0002 & $-$0.0017 & 226 \\\\\n35 & 52952.3948 & 0.0003 & $-$0.0017 & 149 \\\\\n37 & 52952.5287 & 0.0011 & $-$0.0009 & 71 \\\\\n38 & 52952.5936 & 0.0002 & $-$0.0026 & 184 \\\\\n39 & 52952.6606 & 0.0002 & $-$0.0021 & 193 \\\\\n42 & 52952.8608 & 0.0005 & $-$0.0015 & 15 \\\\\n43 & 52952.9263 & 0.0008 & $-$0.0025 & 18 \\\\\n44 & 52952.9930 & 0.0011 & $-$0.0023 & 18 \\\\\n45 & 52953.0573 & 0.0006 & $-$0.0045 & 16 \\\\\n48 & 52953.2590 & 0.0005 & $-$0.0024 & 64 \\\\\n49 & 52953.3266 & 0.0006 & $-$0.0014 & 70 \\\\\n50 & 52953.3921 & 0.0006 & $-$0.0024 & 64 \\\\\n51 & 52953.4559 & 0.0004 & $-$0.0051 & 121 \\\\\n52 & 52953.5254 & 0.0003 & $-$0.0021 & 190 \\\\\n53 & 52953.5921 & 0.0002 & $-$0.0019 & 157 \\\\\n54 & 52953.6584 & 0.0003 & $-$0.0022 & 175 \\\\\n55 & 52953.7251 & 0.0003 & $-$0.0020 & 169 \\\\\n56 & 52953.7919 & 0.0004 & $-$0.0017 & 163 \\\\\n57 & 52953.8597 & 0.0004 & $-$0.0005 & 170 \\\\\n58 & 52953.9250 & 0.0003 & $-$0.0017 & 159 \\\\\n64 & 52954.3231 & 0.0007 & $-$0.0027 & 118 \\\\\n65 & 52954.3926 & 0.0005 & 0.0002 & 283 \\\\\n66 & 52954.4596 & 0.0004 & 0.0006 & 340 \\\\\n67 & 52954.5264 & 0.0004 & 0.0009 & 455 \\\\\n68 & 52954.5937 & 0.0005 & 0.0017 & 343 \\\\\n69 & 52954.6597 & 0.0003 & 0.0012 & 498 \\\\\n70 & 52954.7265 & 0.0002 & 0.0014 & 622 \\\\\n71 & 52954.7927 & 0.0002 & 0.0011 & 550 \\\\\n72 & 52954.8618 & 0.0002 & 0.0037 & 274 \\\\\n73 & 52954.9228 & 0.0014 & $-$0.0018 & 154 \\\\\n78 & 52955.2640 & 0.0004 & 0.0067 & 160 \\\\\n79 & 52955.3286 & 0.0005 & 0.0048 & 172 \\\\\n80 & 52955.3939 & 0.0004 & 0.0036 & 172 \\\\\n81 & 52955.4611 & 0.0004 & 0.0042 & 152 \\\\\n82 & 52955.5280 & 0.0004 & 0.0046 & 192 \\\\\n82 & 52955.5280 & 0.0004 & 0.0046 & 192 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452950.0680 + 0.066529 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of UV Per (2003). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n83 & 52955.5956 & 0.0004 & 0.0056 & 246 \\\\\n84 & 52955.6634 & 0.0002 & 0.0069 & 562 \\\\\n85 & 52955.7302 & 0.0003 & 0.0073 & 510 \\\\\n86 & 52955.7967 & 0.0003 & 0.0072 & 382 \\\\\n87 & 52955.8631 & 0.0003 & 0.0070 & 286 \\\\\n95 & 52956.3966 & 0.0005 & 0.0083 & 116 \\\\\n96 & 52956.4639 & 0.0004 & 0.0090 & 111 \\\\\n99 & 52956.6633 & 0.0002 & 0.0089 & 382 \\\\\n100 & 52956.7295 & 0.0002 & 0.0086 & 380 \\\\\n101 & 52956.7965 & 0.0002 & 0.0090 & 375 \\\\\n102 & 52956.8630 & 0.0002 & 0.0090 & 360 \\\\\n103 & 52956.9256 & 0.0004 & 0.0051 & 234 \\\\\n104 & 52956.9959 & 0.0002 & 0.0088 & 365 \\\\\n105 & 52957.0619 & 0.0002 & 0.0083 & 361 \\\\\n106 & 52957.1274 & 0.0003 & 0.0073 & 271 \\\\\n107 & 52957.1934 & 0.0003 & 0.0067 & 355 \\\\\n108 & 52957.2601 & 0.0002 & 0.0069 & 354 \\\\\n109 & 52957.3271 & 0.0002 & 0.0074 & 406 \\\\\n112 & 52957.5248 & 0.0010 & 0.0055 & 16 \\\\\n113 & 52957.5921 & 0.0008 & 0.0063 & 41 \\\\\n114 & 52957.6581 & 0.0009 & 0.0057 & 41 \\\\\n115 & 52957.7237 & 0.0012 & 0.0048 & 33 \\\\\n116 & 52957.7910 & 0.0009 & 0.0056 & 16 \\\\\n117 & 52957.8570 & 0.0006 & 0.0050 & 18 \\\\\n118 & 52957.9229 & 0.0007 & 0.0044 & 17 \\\\\n119 & 52957.9894 & 0.0004 & 0.0044 & 110 \\\\\n120 & 52958.0600 & 0.0003 & 0.0084 & 91 \\\\\n124 & 52958.3199 & 0.0004 & 0.0023 & 86 \\\\\n125 & 52958.3864 & 0.0004 & 0.0022 & 87 \\\\\n126 & 52958.4529 & 0.0004 & 0.0022 & 85 \\\\\n127 & 52958.5193 & 0.0004 & 0.0021 & 82 \\\\\n128 & 52958.5862 & 0.0003 & 0.0024 & 90 \\\\\n131 & 52958.7848 & 0.0016 & 0.0014 & 12 \\\\\n132 & 52958.8508 & 0.0007 & 0.0009 & 18 \\\\\n133 & 52958.9182 & 0.0007 & 0.0018 & 18 \\\\\n140 & 52959.3808 & 0.0005 & $-$0.0013 & 62 \\\\\n141 & 52959.4451 & 0.0014 & $-$0.0036 & 50 \\\\\n142 & 52959.5085 & 0.0019 & $-$0.0067 & 156 \\\\\n143 & 52959.5820 & 0.0005 & 0.0003 & 164 \\\\\n144 & 52959.6470 & 0.0004 & $-$0.0012 & 177 \\\\\n145 & 52959.7134 & 0.0003 & $-$0.0014 & 152 \\\\\n146 & 52959.7794 & 0.0003 & $-$0.0019 & 152 \\\\\n147 & 52959.8464 & 0.0004 & $-$0.0015 & 152 \\\\\n148 & 52959.9128 & 0.0003 & $-$0.0015 & 421 \\\\\n149 & 52959.9769 & 0.0004 & $-$0.0039 & 385 \\\\\n150 & 52960.0445 & 0.0003 & $-$0.0029 & 360 \\\\\n151 & 52960.1105 & 0.0004 & $-$0.0034 & 285 \\\\\n152 & 52960.1774 & 0.0003 & $-$0.0031 & 359 \\\\\n153 & 52960.2430 & 0.0004 & $-$0.0040 & 354 \\\\\n154 & 52960.3119 & 0.0006 & $-$0.0016 & 408 \\\\\n155 & 52960.3791 & 0.0007 & $-$0.0009 & 208 \\\\\n156 & 52960.4431 & 0.0007 & $-$0.0034 & 120 \\\\\n159 & 52960.6431 & 0.0010 & $-$0.0031 & 30 \\\\\n164 & 52960.9715 & 0.0004 & $-$0.0073 & 361 \\\\\n165 & 52961.0392 & 0.0004 & $-$0.0062 & 360 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of UV Per (2003). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n166 & 52961.1021 & 0.0004 & $-$0.0097 & 318 \\\\\n167 & 52961.1677 & 0.0005 & $-$0.0107 & 357 \\\\\n168 & 52961.2337 & 0.0006 & $-$0.0112 & 307 \\\\\n169 & 52961.2962 & 0.0009 & $-$0.0153 & 337 \\\\\n175 & 52961.6975 & 0.0007 & $-$0.0132 & 341 \\\\\n176 & 52961.7642 & 0.0005 & $-$0.0130 & 360 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of UV Per (2007).}\\label{tab:uvperoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54379.0219 & 0.0003 & $-$0.0039 & 366 \\\\\n1 & 54379.0890 & 0.0004 & $-$0.0031 & 359 \\\\\n2 & 54379.1550 & 0.0003 & $-$0.0035 & 358 \\\\\n9 & 54379.6212 & 0.0006 & $-$0.0015 & 103 \\\\\n20 & 54380.3538 & 0.0005 & 0.0014 & 66 \\\\\n21 & 54380.4187 & 0.0009 & 0.0001 & 76 \\\\\n22 & 54380.4869 & 0.0005 & 0.0019 & 75 \\\\\n23 & 54380.5522 & 0.0007 & 0.0008 & 67 \\\\\n24 & 54380.6204 & 0.0004 & 0.0027 & 76 \\\\\n25 & 54380.6851 & 0.0027 & 0.0011 & 72 \\\\\n36 & 54381.4147 & 0.0003 & 0.0011 & 136 \\\\\n37 & 54381.4817 & 0.0002 & 0.0018 & 134 \\\\\n38 & 54381.5484 & 0.0003 & 0.0021 & 141 \\\\\n39 & 54381.6143 & 0.0003 & 0.0016 & 101 \\\\\n67 & 54383.4704 & 0.0003 & 0.0006 & 138 \\\\\n68 & 54383.5371 & 0.0003 & 0.0010 & 124 \\\\\n69 & 54383.6032 & 0.0003 & 0.0007 & 138 \\\\\n75 & 54384.0013 & 0.0005 & 0.0009 & 296 \\\\\n76 & 54384.0666 & 0.0009 & $-$0.0002 & 178 \\\\\n82 & 54384.4653 & 0.0003 & 0.0005 & 110 \\\\\n83 & 54384.5320 & 0.0005 & 0.0009 & 136 \\\\\n84 & 54384.5973 & 0.0004 & $-$0.0000 & 137 \\\\\n85 & 54384.6670 & 0.0011 & 0.0033 & 82 \\\\\n97 & 54385.4584 & 0.0006 & $-$0.0012 & 140 \\\\\n98 & 54385.5215 & 0.0010 & $-$0.0045 & 123 \\\\\n99 & 54385.5877 & 0.0008 & $-$0.0046 & 58 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454379.0258 + 0.066328 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{PU Persei}\\label{obj:puper}\n\n PU Per was discovered as a dwarf nova by \\citet{hof67an29043}.\nThe object has a relatively long outburst recurrence time and\na large outburst amplitude (cf. \\cite{rom76DN}; \\cite{bus79VS17};\n\\cite{kat95puper}).\nAlthough the detection of superhumps in this object was reported in\n\\citet{kat99puper}, the identification of the period had awaited further\nobservation. We observed the object during the 2009 superoutburst\nand identified the superhump period as 0.06811(3) d\n(figure \\ref{fig:pupershpdm}), a one-day alias to \\citet{kat99puper}.\n\n The times of superhump maxima are listed in table \\ref{tab:puperoc2009}.\nSince the object faded shortly after the last observation, it was most\nlikely that we observed the later part of the superoutburst, corresponding\nto the stage B--C transition. We presented the measured periods based on\nthis interpretation in table \\ref{tab:perlist}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig119.eps}\n \\end{center}\n \\caption{Superhumps in PU Per (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:pupershpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of PU Per (2009).}\\label{tab:puperoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54837.8888 & 0.0021 & 0.0026 & 42 \\\\\n1 & 54837.9477 & 0.0025 & $-$0.0067 & 70 \\\\\n2 & 54838.0191 & 0.0038 & $-$0.0034 & 69 \\\\\n3 & 54838.0902 & 0.0050 & $-$0.0004 & 38 \\\\\n18 & 54839.1206 & 0.0031 & 0.0082 & 139 \\\\\n60 & 54841.9793 & 0.0014 & 0.0060 & 132 \\\\\n61 & 54842.0340 & 0.0021 & $-$0.0073 & 133 \\\\\n75 & 54843.0002 & 0.0039 & 0.0053 & 58 \\\\\n76 & 54843.0678 & 0.0086 & 0.0048 & 72 \\\\\n89 & 54843.9468 & 0.0013 & $-$0.0018 & 142 \\\\\n90 & 54844.0095 & 0.0018 & $-$0.0072 & 125 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454837.8863 + 0.068116 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{PV Persei}\\label{obj:pvper}\n\n In contrast to PU Per, discovered at the same time \\citep{hof67an29043},\nPV Per shows frequent outbursts (\\cite{rom76DN}; \\cite{bus79VS17}).\nThe SU UMa-type nature of PV Per was established by \\citet{van97pvper},\nwho reported a period of 0.0805(1) d.\nWe further observed the 2008 superoutburst.\nThe mean superhump period with the PDM method was 0.08031(4) d\n(figure \\ref{fig:pvpershpdm}).\nThe times of superhump maxima during the 2008 superoutburst\nare listed in table \\ref{tab:pvperoc2008}. The observation mainly\ncovered the later stage of the superoutburst. Although the global\n$P_{\\rm dot}$ was $-4.4(2.1) \\times 10^{-5}$, this change can be\ninterpreted as a result of a stage B--C transition\n(see also table \\ref{tab:perlist}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig120.eps}\n \\end{center}\n \\caption{Superhumps in PV Per (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:pvpershpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of PV Per (2008).}\\label{tab:pvperoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54745.3856 & 0.0006 & $-$0.0074 & 60 \\\\\n1 & 54745.4668 & 0.0008 & $-$0.0066 & 86 \\\\\n35 & 54748.2132 & 0.0007 & 0.0057 & 150 \\\\\n36 & 54748.2952 & 0.0011 & 0.0073 & 136 \\\\\n73 & 54751.2686 & 0.0005 & 0.0054 & 170 \\\\\n74 & 54751.3372 & 0.0036 & $-$0.0064 & 89 \\\\\n121 & 54755.1253 & 0.0011 & 0.0022 & 151 \\\\\n122 & 54755.2073 & 0.0033 & 0.0038 & 132 \\\\\n123 & 54755.2909 & 0.0048 & 0.0070 & 127 \\\\\n135 & 54756.2568 & 0.0068 & 0.0079 & 153 \\\\\n146 & 54757.1335 & 0.0027 & 0.0000 & 149 \\\\\n147 & 54757.2170 & 0.0046 & 0.0032 & 151 \\\\\n159 & 54758.1612 & 0.0033 & $-$0.0177 & 168 \\\\\n160 & 54758.2475 & 0.0055 & $-$0.0118 & 149 \\\\\n161 & 54758.3471 & 0.0075 & 0.0074 & 78 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454745.3930 + 0.080414 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{QY Persei}\\label{sec:qyper}\\label{obj:qyper}\n\n QY Per is a dwarf nova discovered by \\citet{hof66an289139}.\nThe object had long been suspected to be an excellent candidate\nfor a WZ Sge-like object based on the large outburst amplitude\nand long recurrence time.\n\n We observed two superoutbursts in 1999 (\\cite{mat99qyperiauc};\n\\cite{kat00qyperiauc}) and 2005.\nThe 1999 superoutburst (table \\ref{tab:qyperoc1999}) was\none of the the best sampled superoutbursts among all SU UMa-type\ndwarf novae. The $O-C$ diagram consisted of all stages A--C\n(cf. figure \\ref{fig:ocsamp}).\nThe $P_{\\rm dot}$ during the stage B corresponds to\n$+7.8(3.1) \\times 10^{-5}$ ($5 \\le E \\le 69$).\nThis example demonstrates that a positive $P_{\\rm dot}$ system\nis present among systems with longer superhump periods.\nA stage B--C transition was recorded\nduring the 2005 superoutburst (table \\ref{tab:qyperoc2005}).\nA comparison of $O-C$ diagrams between different superoutbursts\nis shown in figure \\ref{fig:qypercomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig121.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of QY Per between different\n superoutbursts. A period of 0.07862 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:qypercomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of QY Per (1999).}\\label{tab:qyperoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51542.3954 & 0.0007 & $-$0.0115 & 204 \\\\\n1 & 51542.4781 & 0.0013 & $-$0.0073 & 108 \\\\\n3 & 51542.6392 & 0.0006 & $-$0.0032 & 231 \\\\\n4 & 51542.7174 & 0.0007 & $-$0.0034 & 194 \\\\\n5 & 51542.7981 & 0.0011 & $-$0.0012 & 106 \\\\\n6 & 51542.8775 & 0.0011 & $-$0.0003 & 120 \\\\\n7 & 51542.9541 & 0.0006 & $-$0.0022 & 143 \\\\\n8 & 51543.0314 & 0.0006 & $-$0.0033 & 150 \\\\\n9 & 51543.1126 & 0.0005 & $-$0.0006 & 159 \\\\\n10 & 51543.1879 & 0.0008 & $-$0.0038 & 150 \\\\\n12 & 51543.3486 & 0.0007 & $-$0.0001 & 74 \\\\\n13 & 51543.4267 & 0.0004 & $-$0.0004 & 92 \\\\\n14 & 51543.5063 & 0.0005 & 0.0007 & 114 \\\\\n16 & 51543.6605 & 0.0006 & $-$0.0020 & 233 \\\\\n17 & 51543.7392 & 0.0007 & $-$0.0018 & 200 \\\\\n18 & 51543.8169 & 0.0008 & $-$0.0026 & 148 \\\\\n19 & 51543.8967 & 0.0006 & $-$0.0012 & 157 \\\\\n20 & 51543.9743 & 0.0008 & $-$0.0022 & 114 \\\\\n21 & 51544.0562 & 0.0009 & 0.0013 & 153 \\\\\n22 & 51544.1316 & 0.0016 & $-$0.0017 & 138 \\\\\n26 & 51544.4438 & 0.0020 & $-$0.0035 & 17 \\\\\n27 & 51544.5266 & 0.0008 & 0.0009 & 20 \\\\\n28 & 51544.6042 & 0.0009 & 0.0000 & 21 \\\\\n29 & 51544.6825 & 0.0007 & $-$0.0001 & 19 \\\\\n31 & 51544.8394 & 0.0013 & $-$0.0002 & 15 \\\\\n35 & 51545.1533 & 0.0019 & $-$0.0002 & 144 \\\\\n36 & 51545.2362 & 0.0017 & 0.0042 & 161 \\\\\n37 & 51545.3084 & 0.0024 & $-$0.0020 & 36 \\\\\n38 & 51545.3887 & 0.0005 & $-$0.0003 & 144 \\\\\n39 & 51545.4687 & 0.0007 & 0.0013 & 101 \\\\\n40 & 51545.5506 & 0.0018 & 0.0047 & 37 \\\\\n42 & 51545.7019 & 0.0007 & $-$0.0009 & 166 \\\\\n43 & 51545.7805 & 0.0007 & $-$0.0008 & 213 \\\\\n44 & 51545.8586 & 0.0009 & $-$0.0012 & 204 \\\\\n45 & 51545.9397 & 0.0026 & 0.0014 & 64 \\\\\n47 & 51546.0938 & 0.0019 & $-$0.0013 & 110 \\\\\n48 & 51546.1844 & 0.0061 & 0.0108 & 39 \\\\\n49 & 51546.2563 & 0.0010 & 0.0042 & 111 \\\\\n50 & 51546.3336 & 0.0011 & 0.0030 & 109 \\\\\n51 & 51546.4089 & 0.0016 & $-$0.0002 & 24 \\\\\n54 & 51546.6459 & 0.0009 & 0.0014 & 227 \\\\\n55 & 51546.7255 & 0.0012 & 0.0026 & 207 \\\\\n56 & 51546.8068 & 0.0014 & 0.0053 & 183 \\\\\n57 & 51546.8854 & 0.0009 & 0.0055 & 248 \\\\\n58 & 51546.9671 & 0.0021 & 0.0087 & 113 \\\\\n59 & 51547.0380 & 0.0016 & 0.0011 & 155 \\\\\n67 & 51547.6685 & 0.0009 & 0.0039 & 158 \\\\\n68 & 51547.7499 & 0.0011 & 0.0068 & 113 \\\\\n69 & 51547.8355 & 0.0023 & 0.0140 & 33 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451542.4070 + 0.078473 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of QY Per (1999) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n72 & 51548.0578 & 0.0015 & 0.0008 & 80 \\\\\n75 & 51548.2983 & 0.0009 & 0.0059 & 128 \\\\\n76 & 51548.3796 & 0.0011 & 0.0088 & 87 \\\\\n78 & 51548.5334 & 0.0007 & 0.0055 & 55 \\\\\n87 & 51549.2335 & 0.0015 & $-$0.0006 & 62 \\\\\n88 & 51549.3144 & 0.0005 & 0.0019 & 102 \\\\\n89 & 51549.3939 & 0.0005 & 0.0029 & 99 \\\\\n90 & 51549.4721 & 0.0005 & 0.0026 & 97 \\\\\n91 & 51549.5497 & 0.0005 & 0.0018 & 91 \\\\\n92 & 51549.6256 & 0.0009 & $-$0.0009 & 201 \\\\\n93 & 51549.7033 & 0.0009 & $-$0.0016 & 157 \\\\\n94 & 51549.7867 & 0.0020 & 0.0033 & 82 \\\\\n103 & 51550.4868 & 0.0025 & $-$0.0029 & 39 \\\\\n104 & 51550.5619 & 0.0019 & $-$0.0063 & 40 \\\\\n109 & 51550.9634 & 0.0036 & 0.0029 & 35 \\\\\n110 & 51551.0354 & 0.0017 & $-$0.0035 & 145 \\\\\n111 & 51551.1114 & 0.0018 & $-$0.0061 & 157 \\\\\n121 & 51551.8962 & 0.0028 & $-$0.0060 & 152 \\\\\n122 & 51551.9583 & 0.0054 & $-$0.0223 & 123 \\\\\n123 & 51552.0504 & 0.0150 & $-$0.0087 & 158 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of QY Per (2005).}\\label{tab:qyperoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53667.0498 & 0.0003 & $-$0.0047 & 306 \\\\\n1 & 53667.1278 & 0.0005 & $-$0.0052 & 361 \\\\\n2 & 53667.2079 & 0.0005 & $-$0.0034 & 315 \\\\\n3 & 53667.2860 & 0.0003 & $-$0.0039 & 362 \\\\\n12 & 53667.9933 & 0.0005 & $-$0.0023 & 134 \\\\\n13 & 53668.0748 & 0.0003 & 0.0007 & 212 \\\\\n14 & 53668.1536 & 0.0003 & 0.0011 & 281 \\\\\n15 & 53668.2318 & 0.0003 & 0.0010 & 409 \\\\\n16 & 53668.3095 & 0.0004 & 0.0002 & 309 \\\\\n27 & 53669.1726 & 0.0005 & 0.0007 & 159 \\\\\n28 & 53669.2494 & 0.0005 & $-$0.0009 & 158 \\\\\n29 & 53669.3286 & 0.0008 & $-$0.0002 & 126 \\\\\n50 & 53670.9929 & 0.0012 & 0.0173 & 138 \\\\\n51 & 53671.0476 & 0.0028 & $-$0.0065 & 131 \\\\\n52 & 53671.1366 & 0.0012 & 0.0042 & 280 \\\\\n53 & 53671.2170 & 0.0005 & 0.0061 & 226 \\\\\n54 & 53671.2986 & 0.0005 & 0.0093 & 224 \\\\\n104 & 53675.2095 & 0.0007 & $-$0.0008 & 154 \\\\\n105 & 53675.2868 & 0.0011 & $-$0.0019 & 109 \\\\\n116 & 53676.1462 & 0.0013 & $-$0.0052 & 151 \\\\\n117 & 53676.2239 & 0.0015 & $-$0.0058 & 164 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453667.0545 + 0.078421 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V518 Persei}\\label{sec:v518per}\\label{obj:v518per}\n\n This object (=GRO J0422+32) is a BHXT (see subsection \\ref{sec:BHXT}).\nWe present reanalysis of observations in \\citet{kat95v518per}.\nA new analysis has yielded a slightly longer superhump period of 0.2159(3) d.\n(table \\ref{tab:v518peroc1992}).\nThe fractional superhump excess is 1.8(1) \\%. Using the relation in\nsubsection \\ref{tab:v518peroc1992}), we can expect $q =$ 0.096(7),\nreasonably consistent with the determination from radial-velocity studies\n($q =$ 0.116(8), \\cite{har99v518per}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig122.eps}\n \\end{center}\n \\caption{Superhumps in V518 Per (1992). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v518pershpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V518 Per (1992).}\\label{tab:v518peroc1992}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48948.0905 & 0.0061 & $-$0.0064 & 249 \\\\\n1 & 48948.3060 & 0.0051 & $-$0.0099 & 228 \\\\\n4 & 48948.9895 & 0.0052 & 0.0168 & 247 \\\\\n5 & 48949.1934 & 0.0033 & 0.0017 & 254 \\\\\n9 & 48950.0745 & 0.0027 & 0.0069 & 265 \\\\\n13 & 48950.9336 & 0.0195 & $-$0.0099 & 174 \\\\\n14 & 48951.1657 & 0.0029 & 0.0033 & 293 \\\\\n18 & 48952.0357 & 0.0023 & $-$0.0026 & 260 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448948.0969 + 0.21897 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TY Piscis Austrini}\\label{obj:typsa}\n\n Although TY PsA is among the SU UMa-type dwarf novae earliest\ndiscovered \\citep{bar82typsa}, the only published $P_{\\rm SH}$ was\n0.08765 d, determined from the relatively limited data taken during\nthe 1984 superoutburst \\citep{war89typsa}.\n\n We observed the 2008 superoutburst starting 2 d after the initial\ndetection of the outburst.\nThe times of superhump maxima are listed in table \\ref{tab:typsaoc2008}.\nAlthough a stage B--C transition was likely present around $E = 40$,\nthe times of maxima were not very well determined because the durations\nof each observations were comparable to the superhump period and the maxima\noften fell close to start or end of the observation. We therefore\ndetermined periods for the stage B ($E \\le 34$) and the stage C ($E \\ge 46$)\nusing the PDM method. The values were 0.087990(17) d and 0.087730(30) d,\nrespectively, and these values are adopted in table \\ref{tab:perlist}.\nThe latter period is close to one reported by \\citet{war89typsa}, suggesting\nthat \\citet{war89typsa} recorded the stage C superhumps.\n\n\\begin{table}\n\\caption{Superhump maxima of TY PsA (2008).}\\label{tab:typsaoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54798.9021 & 0.0003 & $-$0.0043 & 148 \\\\\n11 & 54799.8674 & 0.0019 & $-$0.0044 & 89 \\\\\n12 & 54799.9677 & 0.0005 & 0.0081 & 99 \\\\\n23 & 54800.9228 & 0.0004 & $-$0.0021 & 156 \\\\\n34 & 54801.8976 & 0.0007 & 0.0074 & 74 \\\\\nx46 & 54802.9482 & 0.0010 & 0.0048 & 86 \\\\\n57 & 54803.9093 & 0.0006 & 0.0006 & 163 \\\\\n68 & 54804.8764 & 0.0012 & 0.0024 & 128 \\\\\n69 & 54804.9378 & 0.0028 & $-$0.0240 & 98 \\\\\n80 & 54805.9325 & 0.0020 & 0.0053 & 75 \\\\\n91 & 54806.8987 & 0.0009 & 0.0062 & 197 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454798.9064 + 0.087759 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TY Piscium}\\label{obj:typsc}\n\n TY Psc has long been known as an SU UMa-type dwarf nova\n(cf. \\cite{szk88DNnovaIR}), though accurate determination of\nthe superhump period has not yet been published. Although\n\\citet{kun01typsc} reported observations of the 2000 superoutburst,\nthe resultant period had a large uncertainty.\n\n We observed the 2005 and 2008 superoutbursts\n(tables \\ref{tab:typscoc2005}, \\ref{tab:typscoc2008}).\nThe global $P_{\\rm dot}$ during the 2005 superoutburst was\n$+1.5(3.0) \\times 10^{-5}$. A stage B--C transition\nwas observed during the 2008 superoutburst, although this outburst\nmay have had a prolonged state with stage A superhumps\n(figure \\ref{fig:typsccomp}).\nThe nominal global superhump period and derivative were 0.07045(2) d and\n$P_{\\rm dot}$ = $-9.2(0.8) \\times 10^{-5}$, respectively.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig123.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of TY Psc between different\n superoutbursts. A period of 0.07035 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:typsccomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of TY Psc (2005).}\\label{tab:typscoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53614.2326 & 0.0004 & 0.0001 & 129 \\\\\n13 & 53615.1465 & 0.0006 & $-$0.0003 & 100 \\\\\n14 & 53615.2168 & 0.0005 & $-$0.0003 & 104 \\\\\n15 & 53615.2882 & 0.0004 & 0.0007 & 97 \\\\\n28 & 53616.2016 & 0.0003 & $-$0.0003 & 145 \\\\\n43 & 53617.2571 & 0.0002 & 0.0002 & 205 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453614.2324 + 0.070338 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of TY Psc (2008).}\\label{tab:typscoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54752.2907 & 0.0008 & $-$0.0092 & 67 \\\\\n1 & 54752.3614 & 0.0005 & $-$0.0089 & 114 \\\\\n2 & 54752.4319 & 0.0004 & $-$0.0088 & 115 \\\\\n38 & 54754.9773 & 0.0005 & 0.0005 & 138 \\\\\n39 & 54755.0482 & 0.0004 & 0.0010 & 137 \\\\\n40 & 54755.1176 & 0.0007 & $-$0.0000 & 222 \\\\\n41 & 54755.1929 & 0.0013 & 0.0049 & 152 \\\\\n69 & 54757.1654 & 0.0012 & 0.0048 & 79 \\\\\n70 & 54757.2382 & 0.0010 & 0.0072 & 74 \\\\\n82 & 54758.0833 & 0.0009 & 0.0070 & 101 \\\\\n83 & 54758.1495 & 0.0008 & 0.0028 & 115 \\\\\n84 & 54758.2233 & 0.0012 & 0.0061 & 64 \\\\\n86 & 54758.3629 & 0.0003 & 0.0048 & 127 \\\\\n87 & 54758.4332 & 0.0003 & 0.0046 & 128 \\\\\n88 & 54758.5032 & 0.0003 & 0.0042 & 128 \\\\\n89 & 54758.5747 & 0.0008 & 0.0053 & 90 \\\\\n90 & 54758.6440 & 0.0009 & 0.0042 & 68 \\\\\n98 & 54759.2054 & 0.0008 & 0.0020 & 124 \\\\\n100 & 54759.3470 & 0.0005 & 0.0026 & 145 \\\\\n101 & 54759.4159 & 0.0006 & 0.0012 & 138 \\\\\n102 & 54759.4837 & 0.0005 & $-$0.0015 & 139 \\\\\n111 & 54760.1216 & 0.0022 & 0.0023 & 93 \\\\\n112 & 54760.1937 & 0.0023 & 0.0040 & 222 \\\\\n113 & 54760.2643 & 0.0006 & 0.0042 & 353 \\\\\n114 & 54760.3322 & 0.0005 & 0.0017 & 225 \\\\\n115 & 54760.4040 & 0.0006 & 0.0031 & 223 \\\\\n116 & 54760.4690 & 0.0007 & $-$0.0024 & 214 \\\\\n117 & 54760.5451 & 0.0009 & 0.0032 & 84 \\\\\n118 & 54760.6152 & 0.0008 & 0.0029 & 86 \\\\\n125 & 54761.1022 & 0.0011 & $-$0.0032 & 83 \\\\\n127 & 54761.2433 & 0.0009 & $-$0.0030 & 96 \\\\\n128 & 54761.3103 & 0.0005 & $-$0.0064 & 248 \\\\\n129 & 54761.3783 & 0.0008 & $-$0.0090 & 235 \\\\\n130 & 54761.4533 & 0.0005 & $-$0.0043 & 128 \\\\\n131 & 54761.5203 & 0.0008 & $-$0.0078 & 125 \\\\\n132 & 54761.5921 & 0.0010 & $-$0.0064 & 125 \\\\\n133 & 54761.6555 & 0.0027 & $-$0.0135 & 118 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454752.2998 + 0.070445 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{EI Piscium}\\label{obj:eipsc}\n\n EI Psc (=1RXS J232953.9$+$062814) is one of two (the other being\nV485 Cen) unusually short-$P_{\\rm SH}$ SU UMa-type dwarf novae with\nevolved secondaries (\\cite{uem02j2329letter}; \\cite{ski02j2329}).\nSince the orbital variation, arising from the ellipsoidal variation of\nthe secondary star, is strong, we subtracted the mean orbital variation\nfrom the raw data in \\citet{uem02j2329}. The resultant times of superhump\nmaxima are listed in table \\ref{tab:eipscoc2001}.\nA combination of the times of reported superhumps in \\citet{ski02j2329}\nyielded a slightly discontinuous $O-C$ variation, although the transition\nto a shorter period was recorded in both sets of observations\n(figure \\ref{fig:eipscoc2001}).\nThe discrepancy between these analyses was largest between the fading stage\nof the main superoutburst and the rebrightening, suggesting that the\ntimes of maxima in \\citet{ski02j2329} were more affected by orbital variations.\nWe therefore used times in \\citet{uem02j2329}, updated here, and obtained\n$P_{\\rm dot}$ = $+0.3(0.8) \\times 10^{-5}$ ($E \\le 141$).\nThe period then experienced a transition to a shorter one 0.046090(12) d.\nWe regard this transition as a stage B--C transition based on the\n$O-C$ characteristics. Since this transition is usually observed during\nthe superoutburst plateau in most SU UMa-type dwarf novae, the existence\nof a transition around the rebrightening looks peculiar to EI Psc.\n\n We also analyzed the 2005 superoutburst and obtained the times of\nsuperhump maxima (table \\ref{tab:eipscoc2005}). The global $P_{\\rm dot}$\nwas $-2.8(2.0) \\times 10^{-5}$, although there may have been a break\nin the $O-C$ diagram around $E=9$. This possible break may be a stage\nA--B transition (cf. figure \\ref{fig:eipsccomp}).\nThis superoutburst exhibited a rebrightening in a similar way as in\nthe 2001 one.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig124.eps}\n \\end{center}\n \\caption{$O-C$ diagram of EI Psc during the superoutburst in 2001.\n (Upper) $O-C$ diagram. The filled circles and open squares represent\n maxima presented here and maxima reported in \\citet{ski02j2329}.\n We used only the former set of maxima in order to avoid a systematic\n error potentially caused by superimposed orbital modulations.\n The dashed curve corresponds to $P_{\\rm dot}$ = $+0.3 \\times 10^{-5}$.\n (Lower) light curve.\n }\n \\label{fig:eipscoc2001}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig125.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of EI Psc between different\n superoutbursts. A period of 0.04634 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n Since the start of the 2001 superoutburst was unknown, the $E$ was\n shifted assuming that the two superoutbursts have the same duration\n of the plateau phase.\n }\n \\label{fig:eipsccomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of EI Psc (2001).}\\label{tab:eipscoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52218.0208 & 0.0003 & $-$0.0120 & 84 \\\\\n1 & 52218.0664 & 0.0004 & $-$0.0126 & 76 \\\\\n2 & 52218.1119 & 0.0002 & $-$0.0133 & 80 \\\\\n3 & 52218.1583 & 0.0002 & $-$0.0130 & 84 \\\\\n30 & 52219.4076 & 0.0005 & $-$0.0106 & 94 \\\\\n31 & 52219.4551 & 0.0007 & $-$0.0093 & 64 \\\\\n32 & 52219.4980 & 0.0005 & $-$0.0125 & 45 \\\\\n34 & 52219.5958 & 0.0010 & $-$0.0071 & 35 \\\\\n35 & 52219.6432 & 0.0010 & $-$0.0059 & 36 \\\\\n43 & 52220.0109 & 0.0008 & $-$0.0077 & 47 \\\\\n44 & 52220.0554 & 0.0007 & $-$0.0093 & 51 \\\\\n45 & 52220.1063 & 0.0006 & $-$0.0046 & 66 \\\\\n46 & 52220.1520 & 0.0008 & $-$0.0051 & 28 \\\\\n56 & 52220.6112 & 0.0036 & $-$0.0077 & 30 \\\\\n57 & 52220.6622 & 0.0009 & $-$0.0028 & 53 \\\\\n58 & 52220.7048 & 0.0010 & $-$0.0064 & 108 \\\\\n63 & 52220.9419 & 0.0005 & $-$0.0002 & 124 \\\\\n64 & 52220.9886 & 0.0005 & 0.0003 & 132 \\\\\n65 & 52221.0335 & 0.0004 & $-$0.0010 & 132 \\\\\n66 & 52221.0787 & 0.0010 & $-$0.0020 & 101 \\\\\n77 & 52221.5895 & 0.0007 & 0.0008 & 38 \\\\\n78 & 52221.6359 & 0.0011 & 0.0011 & 37 \\\\\n118 & 52223.4867 & 0.0012 & 0.0047 & 82 \\\\\n123 & 52223.7170 & 0.0008 & 0.0042 & 200 \\\\\n124 & 52223.7661 & 0.0030 & 0.0071 & 170 \\\\\n128 & 52223.9510 & 0.0004 & 0.0072 & 148 \\\\\n129 & 52223.9979 & 0.0005 & 0.0080 & 148 \\\\\n130 & 52224.0405 & 0.0003 & 0.0044 & 314 \\\\\n131 & 52224.0908 & 0.0004 & 0.0085 & 316 \\\\\n132 & 52224.1361 & 0.0005 & 0.0076 & 238 \\\\\n135 & 52224.2786 & 0.0009 & 0.0116 & 88 \\\\\n136 & 52224.3219 & 0.0006 & 0.0087 & 88 \\\\\n137 & 52224.3715 & 0.0006 & 0.0121 & 150 \\\\\n138 & 52224.4156 & 0.0006 & 0.0100 & 160 \\\\\n139 & 52224.4630 & 0.0006 & 0.0112 & 148 \\\\\n140 & 52224.5082 & 0.0007 & 0.0103 & 56 \\\\\n141 & 52224.5565 & 0.0005 & 0.0124 & 68 \\\\\n162 & 52225.5238 & 0.0008 & 0.0100 & 22 \\\\\n163 & 52225.5717 & 0.0015 & 0.0117 & 25 \\\\\n171 & 52225.9405 & 0.0007 & 0.0111 & 106 \\\\\n173 & 52226.0344 & 0.0003 & 0.0125 & 93 \\\\\n184 & 52226.5370 & 0.0025 & 0.0072 & 16 \\\\\n185 & 52226.5842 & 0.0010 & 0.0082 & 25 \\\\\n186 & 52226.6285 & 0.0012 & 0.0064 & 24 \\\\\n205 & 52227.5013 & 0.0017 & 0.0017 & 17 \\\\\n206 & 52227.5481 & 0.0017 & 0.0024 & 25 \\\\\n208 & 52227.6397 & 0.0011 & 0.0016 & 25 \\\\\n209 & 52227.6905 & 0.0014 & 0.0062 & 17 \\\\\n214 & 52227.9154 & 0.0043 & 0.0003 & 80 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452218.0328 + 0.046179 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of EI Psc (2001). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n215 & 52227.9671 & 0.0034 & 0.0057 & 76 \\\\\n216 & 52228.0103 & 0.0017 & 0.0028 & 85 \\\\\n217 & 52228.0526 & 0.0021 & $-$0.0011 & 85 \\\\\n288 & 52231.3368 & 0.0005 & 0.0044 & 76 \\\\\n289 & 52231.3841 & 0.0008 & 0.0055 & 94 \\\\\n293 & 52231.5676 & 0.0017 & 0.0042 & 52 \\\\\n296 & 52231.7127 & 0.0011 & 0.0108 & 48 \\\\\n304 & 52232.0732 & 0.0017 & 0.0019 & 180 \\\\\n305 & 52232.1214 & 0.0049 & 0.0039 & 146 \\\\\n315 & 52232.5795 & 0.0016 & 0.0002 & 52 \\\\\n316 & 52232.6280 & 0.0008 & 0.0026 & 50 \\\\\n317 & 52232.6719 & 0.0023 & 0.0003 & 50 \\\\\n337 & 52233.5880 & 0.0009 & $-$0.0072 & 80 \\\\\n338 & 52233.6371 & 0.0006 & $-$0.0044 & 104 \\\\\n339 & 52233.6798 & 0.0009 & $-$0.0078 & 78 \\\\\n345 & 52233.9607 & 0.0014 & $-$0.0040 & 170 \\\\\n346 & 52234.0082 & 0.0012 & $-$0.0026 & 172 \\\\\n360 & 52234.6386 & 0.0009 & $-$0.0188 & 52 \\\\\n361 & 52234.6981 & 0.0015 & $-$0.0054 & 50 \\\\\n368 & 52235.0119 & 0.0014 & $-$0.0149 & 254 \\\\\n379 & 52235.5270 & 0.0006 & $-$0.0078 & 54 \\\\\n381 & 52235.6090 & 0.0009 & $-$0.0181 & 76 \\\\\n382 & 52235.6570 & 0.0011 & $-$0.0163 & 52 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of EI Psc (2005).}\\label{tab:eipscoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53592.8642 & 0.0001 & $-$0.0014 & 112 \\\\\n1 & 53592.9108 & 0.0002 & $-$0.0011 & 104 \\\\\n2 & 53592.9581 & 0.0002 & $-$0.0001 & 60 \\\\\n6 & 53593.1441 & 0.0003 & 0.0006 & 68 \\\\\n7 & 53593.1903 & 0.0003 & 0.0005 & 68 \\\\\n8 & 53593.2364 & 0.0002 & 0.0003 & 143 \\\\\n9 & 53593.2838 & 0.0003 & 0.0014 & 165 \\\\\n21 & 53593.8374 & 0.0003 & $-$0.0009 & 98 \\\\\n22 & 53593.8850 & 0.0001 & 0.0004 & 147 \\\\\n23 & 53593.9315 & 0.0001 & 0.0006 & 146 \\\\\n24 & 53593.9776 & 0.0001 & 0.0004 & 65 \\\\\n69 & 53596.0612 & 0.0008 & $-$0.0003 & 68 \\\\\n70 & 53596.1078 & 0.0005 & 0.0000 & 68 \\\\\n71 & 53596.1543 & 0.0006 & 0.0002 & 68 \\\\\n72 & 53596.1997 & 0.0005 & $-$0.0008 & 67 \\\\\n73 & 53596.2472 & 0.0005 & 0.0004 & 68 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453592.8656 + 0.046317 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{VZ Pyxidis}\\label{obj:vzpyx}\n\n VZ Pyx was identified as an SU UMa-type dwarf nova by \\citet{kat97vzpyx}.\nWe observed the 2008 superoutburst (table \\ref{tab:vzpyxoc2008}).\nSince multiple maxima apparently appeared around and after the rapid\nfading stage ($E \\ge 120$), we restricted our analysis to $E < 120$.\nAlthough a global $P_{\\rm dot}$ = $-16.3(1.3) \\times 10^{-5}$\n($E \\le 80$) was obtained, there was apparently a break in the period\nbetween $E=27$ and $E=54$. In table \\ref{tab:perlist}, we presented\nthe periods based in this interpretation.\nWe also included a reanalysis of \\citet{kat97vzpyx}\n(table \\ref{tab:vzpyxoc1996})\nand the times of superhump maxima during the 2002 and 2004 superoutbursts\n(tables \\ref{tab:vzpyxoc2000}, \\ref{tab:vzpyxoc2004}).\nThe 2000 superoutburst was observed during the terminal stage and\nthe 2004 superoutburst was observed between 5 and 9 d from the onset of\nthe outburst. The period for the 2000 superoutburst could be considered\nas a typical period for stage C superhumps in this object.\n\n\\begin{table}\n\\caption{Superhump maxima of VZ Pyx (1996).}\\label{tab:vzpyxoc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50161.0287 & 0.0005 & $-$0.0002 & 119 \\\\\n1 & 50161.1048 & 0.0007 & 0.0002 & 57 \\\\\n27 & 50163.0742 & 0.0005 & $-$0.0000 & 107 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450161.0289 + 0.075754 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VZ Pyx (2000).}\\label{tab:vzpyxoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51888.2125 & 0.0014 & $-$0.0006 & 48 \\\\\n27 & 51890.2523 & 0.0006 & 0.0009 & 38 \\\\\n94 & 51895.3091 & 0.0018 & $-$0.0002 & 40 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451888.2132 + 0.075492 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VZ Pyx (2004).}\\label{tab:vzpyxoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53047.1835 & 0.0012 & 0.0000 & 133 \\\\\n51 & 53051.0513 & 0.0004 & $-$0.0018 & 134 \\\\\n52 & 53051.1308 & 0.0011 & 0.0018 & 120 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453047.1835 + 0.075875 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of VZ Pyx (2008).}\\label{tab:vzpyxoc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54790.2587 & 0.0004 & $-$0.0087 & 253 \\\\\n1 & 54790.3343 & 0.0005 & $-$0.0086 & 181 \\\\\n13 & 54791.2463 & 0.0006 & $-$0.0026 & 147 \\\\\n14 & 54791.3223 & 0.0004 & $-$0.0022 & 210 \\\\\n26 & 54792.2360 & 0.0007 & 0.0056 & 213 \\\\\n27 & 54792.3113 & 0.0004 & 0.0054 & 265 \\\\\n54 & 54794.3546 & 0.0008 & 0.0100 & 88 \\\\\n79 & 54796.2390 & 0.0005 & 0.0068 & 147 \\\\\n80 & 54796.3145 & 0.0007 & 0.0069 & 148 \\\\\n120 & 54799.3427 & 0.0011 & 0.0149 & 97 \\\\\n132 & 54800.2288 & 0.0008 & $-$0.0050 & 224 \\\\\n133 & 54800.2869 & 0.0015 & $-$0.0224 & 255 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454790.2674 + 0.075503 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DV Scorpii}\\label{obj:dvsco}\n\n DV Sco was recently reclassified as a likely dwarf nova \\citep{pas03dvsco}.\nThe SU UMa-type nature of this dwarf nova was established by B. Monard\n(cf. vsnet-alert 8321, 8322) during its 2004 outburst.\nThis object is a dwarf nova in the period gap (vsnet-alert 8325).\nWe analyzed this superoutburst (table \\ref{tab:dvscooc2004})\nand another in 2008 (table \\ref{tab:dvscooc2008}).\nThe mean superhump period with the PDM method was 0.09970(7) d\nfor the 2004 superoutburst (figure \\ref{fig:dvscoshpdm}).\nThe resultant global $P_{\\rm dot}$ for the 2004 superoutburst\nwas $-15.1(5.5) \\times 10^{-5}$. The 2008 superoutburst was observed\nduring its late course to its final decline. Due to relatively large\nerror in maxima times and the short coverage, we did not attempt to\ndetermine $P_{\\rm dot}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig126.eps}\n \\end{center}\n \\caption{Superhumps in DV Sco (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:dvscoshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of DV Sco (2004).}\\label{tab:dvscooc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53274.2954 & 0.0011 & $-$0.0027 & 211 \\\\\n7 & 53274.9935 & 0.0007 & $-$0.0004 & 84 \\\\\n10 & 53275.2893 & 0.0012 & $-$0.0028 & 225 \\\\\n17 & 53275.9922 & 0.0010 & 0.0044 & 61 \\\\\n20 & 53276.2884 & 0.0013 & 0.0024 & 214 \\\\\n30 & 53277.2821 & 0.0025 & 0.0021 & 220 \\\\\n50 & 53279.2655 & 0.0068 & $-$0.0023 & 103 \\\\\n53 & 53279.5652 & 0.0037 & $-$0.0008 & 149 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453274.2982 + 0.099393 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DV Sco (2008).}\\label{tab:dvscooc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54713.2375 & 0.0010 & $-$0.0058 & 240 \\\\\n1 & 54713.3385 & 0.0022 & $-$0.0040 & 278 \\\\\n20 & 54715.2247 & 0.0021 & $-$0.0054 & 127 \\\\\n21 & 54715.3316 & 0.0009 & 0.0021 & 140 \\\\\n28 & 54716.0314 & 0.0013 & 0.0065 & 186 \\\\\n50 & 54718.2417 & 0.0066 & 0.0313 & 181 \\\\\n51 & 54718.3210 & 0.0351 & 0.0112 & 213 \\\\\n61 & 54719.2735 & 0.0032 & $-$0.0297 & 212 \\\\\n70 & 54720.1956 & 0.0107 & $-$0.0017 & 119 \\\\\n71 & 54720.2922 & 0.0132 & $-$0.0044 & 142 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454713.2432 + 0.099344 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{MM Scorpii}\\label{obj:mmsco}\n\n The updated times of superhump maxima from the 2002 data\n\\citep{kat04nsv10934mmscoabnorcal86} are listed in table \\ref{tab:mmscooc2002}.\nThe observation was likely performed in the middle of the stage B,\nafter 5 d of the visual maximum \\citep{kat04nsv10934mmscoabnorcal86}.\n\n\\begin{table}\n\\caption{Superhump maxima of MM Sco (2002).}\\label{tab:mmscooc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52528.2351 & 0.0008 & $-$0.0002 & 51 \\\\\n1 & 52528.2954 & 0.0011 & $-$0.0012 & 66 \\\\\n2 & 52528.3599 & 0.0013 & 0.0020 & 61 \\\\\n16 & 52529.2160 & 0.0010 & $-$0.0005 & 59 \\\\\n17 & 52529.2793 & 0.0009 & 0.0015 & 67 \\\\\n18 & 52529.3379 & 0.0009 & $-$0.0013 & 68 \\\\\n19 & 52529.3990 & 0.0016 & $-$0.0015 & 65 \\\\\n25 & 52529.7697 & 0.0008 & 0.0013 & 143 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452528.2353 + 0.061323 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{NY Serpentis}\\label{obj:nyser}\n\n We used the data in \\citet{nog98nyser} to determine the refined times\nof superhump maxima (table \\ref{tab:nyseroc1996}).\nAlthough the initial maximum was recorded during the developmental stage\nof superhumps, we adopted $P_{\\rm dot}$ = $-144(8) \\times 10^{-5}$\nusing all maxima times because the effect of the evolutionary stage is\nrelatively small in systems with strongly negative $P_{\\rm dot}$'s\n(cf. UV Gem: subsection \\ref{sec:uvgem}).\nExcluding the initial maximum, the $P_{\\rm dot}$ amounted to\n$-117(27) \\times 10^{-5}$.\nMore observations are needed to see if such an extreme period variation\nis indeed present during the entire superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of NY Ser (1996).}\\label{tab:nyseroc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50195.2477 & 0.0029 & $-$0.0103 & 69 \\\\\n18 & 50197.2027 & 0.0006 & 0.0145 & 71 \\\\\n27 & 50198.1604 & 0.0007 & 0.0071 & 75 \\\\\n28 & 50198.2642 & 0.0008 & 0.0037 & 59 \\\\\n37 & 50199.2107 & 0.0014 & $-$0.0150 & 31 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450195.2580 + 0.107235 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RZ Sagittae}\\label{obj:rzsge}\n\n \\citet{kat96rzsge} reported on the 1994 superoutburst, giving\n$P_{\\rm dot}$ = $-10(2) \\times 10^{-5}$. Table \\ref{tab:rzsgeoc1994}\ngives refined and newly measured times of superhump maxima from the\ndata used in \\citet{kat96rzsge}.\nThe refined global $P_{\\rm dot}$ corresponds to $-11.0(2.2) \\times 10^{-5}$.\nThe 1996 superoutburst was observed by us and by \\citet{sem97rzsge}.\nA combined list of superhump maxima is given in table \\ref{tab:rzsgeoc1996}.\nThe global $P_{\\rm dot}$ corresponds to $-6.9(1.6) \\times 10^{-5}$.\nThe difference in $P_{\\rm dot}$ from \\citet{sem97rzsge} was probably\nbecause they only observed the late stage of the superoutburst.\nThere is an indication of a transition from a longer to a shorter\nperiod (already somewhat evident on the figure 4 in \\cite{sem97rzsge}),\ncorresponding to a stage B--C transition.\nIf we restrict the fit to $E < 100$, we obtain $P_{\\rm dot}$ =\n$+0.6(5.1) \\times 10^{-5}$ indicating a relatively constant superhump\nperiod. This phenomenon may be analogous to the one observed in\nTT Boo \\citep{ole04ttboo}, another SU UMa-type dwarf nova with\na relatively long superhump period and long superoutbursts\n(see also FQ Mon, subsection \\ref{sec:fqmon}).\nWe also observed the 2002 superoutburst (table \\ref{tab:rzsgeoc2002}).\nAlthough the coverage was not sufficient (our observation covered the\nearly to middle stage of the superoutburst), we obtained the global\n$P_{\\rm dot}$ = $-4.9(3.0) \\times 10^{-5}$.\nA comparison of $O-C$ diagrams between different superoutbursts\nis shown in figure \\ref{fig:rzsgecomp}. The 1994 superoutburst may have\nhad a shorter stage B than in other superoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig127.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of RZ Sge between different\n superoutbursts. A period of 0.07045 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n The 1994 superoutburst probably had a shorter stage B.\n }\n \\label{fig:rzsgecomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of RZ Sge (1994).}\\label{tab:rzsgeoc1994}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49576.0726 & 0.0008 & $-$0.0029 & 42 \\\\\n1 & 49576.1401 & 0.0014 & $-$0.0057 & 30 \\\\\n13 & 49576.9896 & 0.0008 & $-$0.0001 & 58 \\\\\n15 & 49577.1303 & 0.0008 & $-$0.0000 & 50 \\\\\n41 & 49578.9652 & 0.0005 & 0.0065 & 91 \\\\\n42 & 49579.0351 & 0.0004 & 0.0061 & 90 \\\\\n55 & 49579.9430 & 0.0023 & $-$0.0001 & 52 \\\\\n56 & 49580.0165 & 0.0005 & 0.0030 & 77 \\\\\n100 & 49583.1009 & 0.0015 & $-$0.0067 & 29 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449576.0755 + 0.070322 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of RZ Sge (1996).}\\label{tab:rzsgeoc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50302.2160 & 0.0012 & $-$0.0158 & 143 \\\\\n41 & 50305.1164 & 0.0004 & $-$0.0012 & 102 \\\\\n45 & 50305.3974 & -- & $-$0.0018 & S \\\\\n46 & 50305.4671 & -- & $-$0.0025 & S \\\\\n47 & 50305.5375 & -- & $-$0.0024 & S \\\\\n56 & 50306.1692 & 0.0064 & $-$0.0042 & 37 \\\\\n57 & 50306.2462 & 0.0008 & 0.0024 & 53 \\\\\n59 & 50306.3829 & -- & $-$0.0017 & S \\\\\n69 & 50307.0932 & 0.0005 & 0.0047 & 102 \\\\\n74 & 50307.4413 & -- & 0.0009 & S \\\\\n85 & 50308.2244 & 0.0009 & 0.0098 & 109 \\\\\n87 & 50308.3618 & -- & 0.0064 & S \\\\\n88 & 50308.4345 & -- & 0.0087 & S \\\\\n103 & 50309.4890 & -- & 0.0074 & S \\\\\n116 & 50310.4030 & -- & 0.0064 & S \\\\\n117 & 50310.4726 & -- & 0.0056 & S \\\\\n118 & 50310.5431 & -- & 0.0058 & S \\\\\n130 & 50311.3829 & -- & 0.0009 & S \\\\\n132 & 50311.5233 & -- & 0.0006 & S \\\\\n153 & 50312.9980 & 0.0011 & $-$0.0029 & 101 \\\\\n160 & 50313.4833 & -- & $-$0.0103 & S \\\\\n173 & 50314.3914 & -- & $-$0.0172 & S \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450302.2318 + 0.070386 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} S refers to \\citet{sem97rzsge}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of RZ Sge (2002).}\\label{tab:rzsgeoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52549.0368 & 0.0019 & $-$0.0114 & 48 \\\\\n13 & 52549.9604 & 0.0011 & $-$0.0031 & 131 \\\\\n15 & 52550.1033 & 0.0022 & $-$0.0010 & 110 \\\\\n27 & 52550.9573 & 0.0024 & 0.0080 & 65 \\\\\n29 & 52551.0921 & 0.0065 & 0.0020 & 107 \\\\\n126 & 52557.9277 & 0.0007 & 0.0077 & 111 \\\\\n127 & 52557.9983 & 0.0008 & 0.0079 & 125 \\\\\n128 & 52558.0690 & 0.0010 & 0.0082 & 96 \\\\\n141 & 52558.9787 & 0.0023 & 0.0026 & 106 \\\\\n142 & 52559.0503 & 0.0042 & 0.0037 & 84 \\\\\n156 & 52560.0275 & 0.0021 & $-$0.0047 & 133 \\\\\n170 & 52561.0060 & 0.0066 & $-$0.0120 & 28 \\\\\n171 & 52561.0804 & 0.0104 & $-$0.0081 & 11 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452549.0482 + 0.070411 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{WZ Sagittae}\\label{sec:wzsge}\\label{obj:wzsge}\n\n Several authors reported on the 2001 superoutburst of WZ Sge\n(\\cite{pat02wzsge}; \\cite{ish02wzsgeletter}). We used the data\nused in \\citet{ish02wzsgeletter} to determine superhump maxima.\nWe deal with ordinary superhumps and give only a representative\nfigure of early superhumps (figure \\ref{fig:wzsgeeshpdm}).\n\n We extracted times of superhump maxima after subtracting the\ngeneral trend of the outburst and subtracting averaged orbital\nvariation as in V455 And. The interval for averaging the orbital\nvariation was 4--6 d during the superoutburst plateau and 1 d\nfor the final stage of early superhumps and the final stage of\nthe superoutburst plateau.\n\n The tables of maxima are separately given for the earlier half\nbefore double humps became apparent (table \\ref{tab:wzsgeoc2001}) and\nthe final stage when newly arising humps became apparent\n(table \\ref{tab:wzsgeoc2001b}) because different base periods were\nused for calculating the $O-C$'s. The humps having orbital phases\n$0.6 < {\\rm phase} < 1.0$ in the latter table can be attributed to\norbital humps. The situation can be clearly seen on the combined\n$O-C$ diagram during this stage and the early part the subsequent\nrebrightening phase (figure \\ref{fig:wzsgemainoc}).\nIt is evident from the $O-C$ diagram that our method is less affected\nby the orbital (eclipse) feature than in \\citet{pat02wzsge}, enabling\na firmer estimate of the period variation.\nThe interval $E \\le 27$ showed an early-stage transition with a\nlonger period (stage A). Since the orbital phases of these humps\ndo not coincide either of two maxima of early superhumps, we regard\nthem as genuine superhumps. The mean period was 0.05839(6) d.\n\n The mean $P_{\\rm SH}$ and $P_{\\rm dot}$ for $27 \\le E \\le 177$\\footnote{\n The epochs $E > 165$ in this paragraph denotes maxima in table\n \\ref{tab:wzsgeoc2001b}. The epoch $E=0$ in table \\ref{tab:wzsgeoc2001b}\n corresponds to $E=169$.\n}\n(stage B) was 0.057204(5) d and $P_{\\rm dot}$ = $+2.0(0.4) \\times 10^{-5}$.\nDuring the last stage of the superoutburst plateau, rapid fading\nand the dip, the orbital humps dominated (see figure \\ref{fig:wzsgemainoc}).\nA new series of superhumps with a longer period emerged\n(filled circles in figure \\ref{fig:wzsgemainoc} for $E>200$)\nduring the rapid fading and smoothly evolved into superhumps\nduring the rebrightening phase. The mean period and period derivative\nof these superhumps for $200 \\le E \\le 400$ were 0.057488(14) d\nand $P_{\\rm dot}$ = $+5.0(0.7) \\times 10^{-5}$.\n\n We also analyzed the rebrightening phase. The analysis follows\nthe similar manner as in SDSS J0804 \\citep{kat09j0804}.\nThe phase-averaged light curve (figure \\ref{fig:wzsgerebph}) closely\nresembles that of SDSS J0804 and is in good agreement with\nthe analysis by \\citet{pat02wzsge}. After subtracting orbital light\ncurves averaged over three days, we extracted the times of measured\nmaxima (table \\ref{tab:wzsgeoc2001reb}).\nThe $P_{\\rm SH}$ was 0.057501(12) d for $E \\le 199$ and was\n0.057305(11) d for $E \\ge 200$ (see figure \\ref{fig:wzsgereboc}).\nThese periods are 0.52(2) \\% and 0.18(2) \\% longer than the\nmean $P_{\\rm SH}$ during the main superoutburst, respectively.\nThese long-period superhumps correspond to long-period\nlate(-stage) superhumps reported in \\citet{kat08wzsgelateSH}.\n\nDuring the post-superoutburst stage, although eclipses and orbital humps\nwere prominent (figure \\ref{fig:wzsgelateph}), overlapping superhumps\npersisted at least for $\\sim$ 600 cycles ($\\sim$ 30 d).\nThe times of maxima, determined after subtracting the orbital modulations,\nduring the post-superoutburst stage are listed in\ntable \\ref{tab:wzsgeoc2001late}.\nThe interval for averaging the orbital variation was 10 d.\nFor $E \\le 598$, the mean $P_{\\rm SH}$ and $P_{\\rm dot}$ were\n0.057351(3) d and $+0.5(0.1) \\times 10^{-5}$.\nThis period is 0.25(1) \\% longer than the mean $P_{\\rm SH}$ during\nthe main superoutburst.\nThere was some indication of the persisting superhumps after $E = 848$\nwith a different period before $E=598$.\n\nThe overall $O-C$ behavior during the entire course of the superoutburst\nis shown in figure \\ref{fig:wzsgehumpall}. The behavior is remarkably\nsimilar to GW Lib (subsection \\ref{sec:latestage}).\nIn WZ Sge, a disturbance in the $O-C$ diagram also appeared during the rapid\nfading stage and subsequent ``dip'' phase. During the rebrightening\nand post-superoutburst stages, the superhump period lengthened in\na similar way to GW Lib. The $O-C$ diagram showed a slightly positive\ndeviation from this overall trend during the rebrightening phase.\nThe $O-C$ behavior after the rebrightening phase appears to be a natural\nextension of the stage B superhumps, as in GW Lib.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig128.eps}\n \\end{center}\n \\caption{Early superhumps in WZ Sge (2001). (Upper): PDM analysis.\n (Lower): Phase-averaged profile. The phase zero corresponds\n to eclipses in quiescence.}\n \\label{fig:wzsgeeshpdm}\n\\end{figure}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(150mm,30mm){fig129.eps}\n \\end{center}\n \\caption{Transition from early superhumps to ordinary superhumps\n in WZ Sge (2001). The open circles represent minima of early\n superhumps. The stage A superhumps (ticks) smoothly developed\n from one of two peaks of early superhumps.}\n \\label{fig:wzsgeeshtrans}\n\\end{figure*}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(140mm,140mm){fig130.eps}\n \\end{center}\n \\caption{$O-C$ variation in WZ Sge (2001). (Upper) $O-C$.\n Open squares indicate humps coinciding with the phase of orbital humps.\n Filled circles are humps outside the phase of orbital humps.\n We used a period of 0.057244 d for calculating the $O-C$'s.\n The evolution of the $O-C$ diagram is remarkably similar\n to that of GW Lib (figure \\ref{fig:gwlibhumpall}).\n (Lower) Light curve.\n }\n \\label{fig:wzsgemainoc}\n\\end{figure*}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig131.eps}\n \\end{center}\n \\caption{Orbital light curve of WZ Sge during the rebrightening\n phase of the 2001 superoutburst (BJD 2452141--2452167)}\n \\label{fig:wzsgerebph}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig132.eps}\n \\end{center}\n \\caption{$O-C$ of humps during the rebrightening phase of WZ Sge (2001).\n (Upper): $O-C$ diagram. Filled squares and open squares represent\n superhumps and humps coinciding with orbital humps, respectively.\n Two dashes represent the superhump periods of 0.057501(12) d and\n 0.057305(11) d. (Lower): Light curve.}\n \\label{fig:wzsgereboc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig133.eps}\n \\end{center}\n \\caption{Orbital light curve of WZ Sge during the post-superoutburst\n stage (BJD 2452167--2452267)}\n \\label{fig:wzsgelateph}\n\\end{figure}\n\n\\begin{figure*}\n \\begin{center}\n \\FigureFile(160mm,160mm){fig134.eps}\n \\end{center}\n \\caption{$O-C$ variation in WZ Sge (2001). (Upper) $O-C$.\n Open squares and filled circles represent superhumps\n and humps coinciding with orbital humps, respectively.\n We used a period of 0.057244 d for calculating the $O-C$'s.\n The global evolution of the $O-C$ diagram is remarkably similar\n to that of GW Lib (figure \\ref{fig:gwlibhumpall}).\n (Lower) Light curve.\n }\n \\label{fig:wzsgehumpall}\n\\end{figure*}\n\nThe times of superhump maxima during the 1978 superoutburst are\nlisted in table \\ref{tab:wzsgeoc1978}. The times were taken from\nliterature except for \\citet{hei79wzsge}, for which we measured\nthe maxima from individual observations. We obtained\n$P_{\\rm dot}$ = $+0.4(0.8) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge (2001).}\\label{tab:wzsgeoc2001}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 52126.3302 & 0.0013 & $-$0.0163 & 0.32 & 361 \\\\\n1 & 52126.3881 & 0.0009 & $-$0.0157 & 0.34 & 245 \\\\\n2 & 52126.4412 & 0.0011 & $-$0.0199 & 0.27 & 245 \\\\\n3 & 52126.5074 & 0.0009 & $-$0.0109 & 0.44 & 245 \\\\\n4 & 52126.5646 & 0.0004 & $-$0.0110 & 0.45 & 300 \\\\\n5 & 52126.6194 & 0.0007 & $-$0.0134 & 0.42 & 109 \\\\\n6 & 52126.6775 & 0.0005 & $-$0.0127 & 0.44 & 164 \\\\\n7 & 52126.7346 & 0.0005 & $-$0.0128 & 0.45 & 315 \\\\\n9 & 52126.8504 & 0.0003 & $-$0.0116 & 0.49 & 337 \\\\\n11 & 52126.9692 & 0.0003 & $-$0.0073 & 0.59 & 523 \\\\\n11 & 52126.9687 & 0.0002 & $-$0.0078 & 0.58 & 536 \\\\\n12 & 52127.0248 & 0.0002 & $-$0.0090 & 0.57 & 460 \\\\\n13 & 52127.0840 & 0.0003 & $-$0.0071 & 0.61 & 463 \\\\\n14 & 52127.1437 & 0.0002 & $-$0.0046 & 0.67 & 465 \\\\\n15 & 52127.2005 & 0.0003 & $-$0.0051 & 0.67 & 361 \\\\\n16 & 52127.2589 & 0.0010 & $-$0.0040 & 0.70 & 208 \\\\\n17 & 52127.3203 & 0.0005 & 0.0002 & 0.78 & 304 \\\\\n18 & 52127.3809 & 0.0003 & 0.0035 & 0.85 & 311 \\\\\n19 & 52127.4385 & 0.0002 & 0.0038 & 0.87 & 312 \\\\\n20 & 52127.4988 & 0.0002 & 0.0068 & 0.93 & 261 \\\\\n21 & 52127.5557 & 0.0003 & 0.0065 & 0.94 & 298 \\\\\n22 & 52127.6149 & 0.0004 & 0.0083 & 0.98 & 185 \\\\\n23 & 52127.6710 & 0.0004 & 0.0072 & 0.97 & 214 \\\\\n24 & 52127.7298 & 0.0002 & 0.0087 & 0.01 & 273 \\\\\n25 & 52127.7868 & 0.0002 & 0.0084 & 0.01 & 262 \\\\\n26 & 52127.8449 & 0.0003 & 0.0093 & 0.04 & 256 \\\\\n27 & 52127.9022 & 0.0009 & 0.0093 & 0.05 & 71 \\\\\n34 & 52128.3021 & 0.0002 & 0.0083 & 0.10 & 183 \\\\\n35 & 52128.3608 & 0.0002 & 0.0097 & 0.14 & 237 \\\\\n36 & 52128.4183 & 0.0003 & 0.0099 & 0.15 & 236 \\\\\n37 & 52128.4740 & 0.0003 & 0.0083 & 0.13 & 236 \\\\\n38 & 52128.5290 & 0.0005 & 0.0060 & 0.10 & 237 \\\\\n40 & 52128.6398 & 0.0010 & 0.0024 & 0.06 & 59 \\\\\n41 & 52128.7018 & 0.0004 & 0.0070 & 0.15 & 298 \\\\\n42 & 52128.7558 & 0.0004 & 0.0038 & 0.11 & 257 \\\\\n43 & 52128.8132 & 0.0007 & 0.0039 & 0.12 & 116 \\\\\n45 & 52128.9294 & 0.0003 & 0.0056 & 0.17 & 153 \\\\\n53 & 52129.3892 & 0.0002 & 0.0071 & 0.28 & 224 \\\\\n54 & 52129.4457 & 0.0002 & 0.0064 & 0.28 & 224 \\\\\n55 & 52129.5019 & 0.0003 & 0.0053 & 0.27 & 224 \\\\\n56 & 52129.5609 & 0.0002 & 0.0070 & 0.31 & 292 \\\\\n57 & 52129.6181 & 0.0005 & 0.0070 & 0.32 & 106 \\\\\n58 & 52129.6746 & 0.0003 & 0.0062 & 0.31 & 219 \\\\\n59 & 52129.7312 & 0.0002 & 0.0055 & 0.31 & 222 \\\\\n60 & 52129.7877 & 0.0003 & 0.0047 & 0.31 & 213 \\\\\n61 & 52129.8432 & 0.0003 & 0.0029 & 0.29 & 138 \\\\\n68 & 52130.2441 & 0.0002 & 0.0029 & 0.36 & 377 \\\\\n69 & 52130.2982 & 0.0005 & $-$0.0002 & 0.31 & 187 \\\\\n70 & 52130.3587 & 0.0002 & 0.0030 & 0.38 & 238 \\\\\n71 & 52130.4165 & 0.0003 & 0.0035 & 0.40 & 238 \\\\\n72 & 52130.4743 & 0.0002 & 0.0041 & 0.42 & 238 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2452126.3465 + 0.057274 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n73 & 52130.5303 & 0.0002 & 0.0027 & 0.41 & 238 \\\\\n74 & 52130.5866 & 0.0004 & 0.0019 & 0.40 & 180 \\\\\n85 & 52131.2154 & 0.0005 & 0.0006 & 0.49 & 209 \\\\\n87 & 52131.3318 & 0.0004 & 0.0025 & 0.55 & 230 \\\\\n88 & 52131.3890 & 0.0004 & 0.0024 & 0.56 & 245 \\\\\n89 & 52131.4459 & 0.0004 & 0.0020 & 0.56 & 361 \\\\\n90 & 52131.5034 & 0.0004 & 0.0022 & 0.57 & 320 \\\\\n91 & 52131.5582 & 0.0003 & $-$0.0003 & 0.54 & 174 \\\\\n93 & 52131.6833 & 0.0004 & 0.0103 & 0.75 & 99 \\\\\n94 & 52131.7323 & 0.0007 & 0.0020 & 0.61 & 153 \\\\\n95 & 52131.7894 & 0.0005 & 0.0018 & 0.62 & 154 \\\\\n96 & 52131.8460 & 0.0004 & 0.0012 & 0.62 & 152 \\\\\n97 & 52131.9049 & 0.0005 & 0.0028 & 0.66 & 153 \\\\\n99 & 52132.0263 & 0.0005 & 0.0097 & 0.80 & 184 \\\\\n100 & 52132.0708 & 0.0010 & $-$0.0031 & 0.58 & 100 \\\\\n105 & 52132.3610 & 0.0003 & 0.0007 & 0.70 & 241 \\\\\n106 & 52132.4177 & 0.0002 & 0.0002 & 0.70 & 332 \\\\\n107 & 52132.4749 & 0.0003 & 0.0001 & 0.71 & 296 \\\\\n108 & 52132.5321 & 0.0002 & 0.0000 & 0.72 & 344 \\\\\n109 & 52132.5889 & 0.0002 & $-$0.0005 & 0.72 & 520 \\\\\n110 & 52132.6468 & 0.0003 & 0.0001 & 0.74 & 268 \\\\\n111 & 52132.7043 & 0.0002 & 0.0004 & 0.76 & 345 \\\\\n112 & 52132.7605 & 0.0002 & $-$0.0007 & 0.75 & 378 \\\\\n113 & 52132.8185 & 0.0003 & 0.0000 & 0.77 & 355 \\\\\n114 & 52132.8738 & 0.0004 & $-$0.0020 & 0.75 & 197 \\\\\n115 & 52132.9341 & 0.0005 & 0.0010 & 0.81 & 248 \\\\\n116 & 52132.9913 & 0.0002 & 0.0009 & 0.82 & 505 \\\\\n117 & 52133.0479 & 0.0002 & 0.0004 & 0.82 & 496 \\\\\n118 & 52133.1040 & 0.0006 & $-$0.0009 & 0.81 & 303 \\\\\n119 & 52133.1621 & 0.0002 & $-$0.0000 & 0.83 & 510 \\\\\n120 & 52133.2179 & 0.0002 & $-$0.0015 & 0.82 & 516 \\\\\n121 & 52133.2764 & 0.0005 & $-$0.0003 & 0.85 & 576 \\\\\n122 & 52133.3333 & 0.0005 & $-$0.0007 & 0.85 & 465 \\\\\n123 & 52133.3897 & 0.0003 & $-$0.0015 & 0.85 & 369 \\\\\n124 & 52133.4473 & 0.0002 & $-$0.0012 & 0.87 & 370 \\\\\n125 & 52133.5036 & 0.0003 & $-$0.0022 & 0.86 & 171 \\\\\n126 & 52133.5607 & 0.0002 & $-$0.0023 & 0.87 & 327 \\\\\n127 & 52133.6182 & 0.0003 & $-$0.0022 & 0.88 & 209 \\\\\n129 & 52133.7339 & 0.0003 & $-$0.0010 & 0.92 & 150 \\\\\n130 & 52133.7897 & 0.0003 & $-$0.0025 & 0.91 & 151 \\\\\n131 & 52133.8477 & 0.0003 & $-$0.0017 & 0.93 & 152 \\\\\n132 & 52133.9044 & 0.0003 & $-$0.0023 & 0.93 & 152 \\\\\n133 & 52133.9674 & 0.0008 & 0.0034 & 0.04 & 90 \\\\\n136 & 52134.1351 & 0.0004 & $-$0.0007 & 1.00 & 306 \\\\\n139 & 52134.3064 & 0.0008 & $-$0.0012 & 0.02 & 253 \\\\\n140 & 52134.3625 & 0.0003 & $-$0.0024 & 0.01 & 242 \\\\\n141 & 52134.4203 & 0.0002 & $-$0.0019 & 0.03 & 242 \\\\\n142 & 52134.4780 & 0.0002 & $-$0.0014 & 0.05 & 242 \\\\\n143 & 52134.5351 & 0.0001 & $-$0.0017 & 0.05 & 226 \\\\\n144 & 52134.5912 & 0.0003 & $-$0.0028 & 0.04 & 317 \\\\\n145 & 52134.6517 & 0.0008 & 0.0004 & 0.11 & 127 \\\\\n146 & 52134.7063 & 0.0004 & $-$0.0022 & 0.08 & 205 \\\\\n147 & 52134.7631 & 0.0005 & $-$0.0028 & 0.08 & 229 \\\\\n148 & 52134.8200 & 0.0005 & $-$0.0031 & 0.08 & 172 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n149 & 52134.8793 & 0.0006 & $-$0.0011 & 0.13 & 111 \\\\\n150 & 52134.9348 & 0.0004 & $-$0.0028 & 0.11 & 143 \\\\\n151 & 52134.9936 & 0.0008 & $-$0.0013 & 0.14 & 373 \\\\\n152 & 52135.0518 & 0.0005 & $-$0.0004 & 0.17 & 397 \\\\\n153 & 52135.1071 & 0.0004 & $-$0.0024 & 0.15 & 372 \\\\\n154 & 52135.1638 & 0.0003 & $-$0.0030 & 0.15 & 407 \\\\\n155 & 52135.2215 & 0.0003 & $-$0.0025 & 0.16 & 386 \\\\\n156 & 52135.2788 & 0.0005 & $-$0.0025 & 0.17 & 427 \\\\\n157 & 52135.3377 & 0.0005 & $-$0.0009 & 0.21 & 392 \\\\\n158 & 52135.3938 & 0.0003 & $-$0.0020 & 0.20 & 321 \\\\\n159 & 52135.4504 & 0.0003 & $-$0.0028 & 0.20 & 300 \\\\\n160 & 52135.5078 & 0.0003 & $-$0.0026 & 0.21 & 278 \\\\\n162 & 52135.6216 & 0.0011 & $-$0.0034 & 0.22 & 76 \\\\\n163 & 52135.6803 & 0.0008 & $-$0.0019 & 0.26 & 69 \\\\\n164 & 52135.7364 & 0.0007 & $-$0.0031 & 0.25 & 76 \\\\\n165 & 52135.7937 & 0.0007 & $-$0.0031 & 0.26 & 75 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Hump Maxima of WZ Sge during the end stage of the superoutburst plateau (2001).}\\label{tab:wzsgeoc2001b}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 52136.0213 & 0.0002 & $-$0.0144 & 0.27 & 235 \\\\\n1 & 52136.0784 & 0.0002 & $-$0.0142 & 0.28 & 241 \\\\\n2 & 52136.1382 & 0.0010 & $-$0.0113 & 0.33 & 203 \\\\\n4 & 52136.2558 & 0.0017 & $-$0.0073 & 0.41 & 48 \\\\\n5 & 52136.3100 & 0.0009 & $-$0.0099 & 0.37 & 230 \\\\\n6 & 52136.3651 & 0.0005 & $-$0.0116 & 0.34 & 164 \\\\\n7 & 52136.4236 & 0.0003 & $-$0.0100 & 0.37 & 176 \\\\\n7 & 52136.4440 & 0.0003 & 0.0104 & 0.73 & 174 \\\\\n8 & 52136.4794 & 0.0003 & $-$0.0110 & 0.35 & 178 \\\\\n8 & 52136.5031 & 0.0002 & 0.0126 & 0.77 & 170 \\\\\n9 & 52136.5416 & 0.0006 & $-$0.0057 & 0.45 & 100 \\\\\n9 & 52136.5591 & 0.0004 & 0.0118 & 0.76 & 120 \\\\\n10 & 52136.5923 & 0.0011 & $-$0.0119 & 0.34 & 245 \\\\\n10 & 52136.6145 & 0.0004 & 0.0103 & 0.74 & 153 \\\\\n11 & 52136.6507 & 0.0006 & $-$0.0102 & 0.38 & 122 \\\\\n11 & 52136.6718 & 0.0004 & 0.0108 & 0.75 & 137 \\\\\n12 & 52136.7083 & 0.0007 & $-$0.0095 & 0.39 & 126 \\\\\n12 & 52136.7288 & 0.0004 & 0.0110 & 0.75 & 174 \\\\\n13 & 52136.7647 & 0.0005 & $-$0.0100 & 0.39 & 165 \\\\\n13 & 52136.7869 & 0.0004 & 0.0123 & 0.78 & 154 \\\\\n14 & 52136.8221 & 0.0002 & $-$0.0094 & 0.40 & 195 \\\\\n14 & 52136.8427 & 0.0003 & 0.0112 & 0.76 & 158 \\\\\n15 & 52136.8804 & 0.0006 & $-$0.0079 & 0.43 & 72 \\\\\n15 & 52136.9005 & 0.0004 & 0.0122 & 0.78 & 76 \\\\\n16 & 52136.9403 & 0.0016 & $-$0.0049 & 0.48 & 90 \\\\\n16 & 52136.9554 & 0.0004 & 0.0102 & 0.75 & 277 \\\\\n17 & 52136.9943 & 0.0006 & $-$0.0077 & 0.44 & 201 \\\\\n17 & 52137.0109 & 0.0008 & 0.0089 & 0.73 & 147 \\\\\n19 & 52137.1079 & 0.0007 & $-$0.0078 & 0.44 & 167 \\\\\n19 & 52137.1261 & 0.0002 & 0.0104 & 0.76 & 199 \\\\\n20 & 52137.1669 & 0.0005 & $-$0.0056 & 0.48 & 197 \\\\\n20 & 52137.1869 & 0.0013 & 0.0144 & 0.83 & 198 \\\\\n21 & 52137.2269 & 0.0008 & $-$0.0025 & 0.54 & 202 \\\\\n21 & 52137.2384 & 0.0004 & 0.0090 & 0.74 & 204 \\\\\n22 & 52137.2930 & 0.0015 & 0.0068 & 0.71 & 89 \\\\\n23 & 52137.3367 & 0.0005 & $-$0.0064 & 0.48 & 35 \\\\\n23 & 52137.3546 & 0.0002 & 0.0116 & 0.79 & 41 \\\\\n24 & 52137.4096 & 0.0004 & 0.0097 & 0.76 & 46 \\\\\n25 & 52137.4677 & 0.0001 & 0.0110 & 0.79 & 170 \\\\\n26 & 52137.5235 & 0.0001 & 0.0099 & 0.77 & 235 \\\\\n28 & 52137.6380 & 0.0003 & 0.0108 & 0.79 & 98 \\\\\n29 & 52137.6952 & 0.0002 & 0.0111 & 0.80 & 133 \\\\\n30 & 52137.7523 & 0.0003 & 0.0114 & 0.81 & 70 \\\\\n31 & 52137.8089 & 0.0004 & 0.0111 & 0.81 & 74 \\\\\n32 & 52137.8659 & 0.0004 & 0.0113 & 0.81 & 80 \\\\\n33 & 52137.9216 & 0.0003 & 0.0102 & 0.80 & 83 \\\\\n35 & 52138.0362 & 0.0002 & 0.0111 & 0.82 & 335 \\\\\n36 & 52138.0561 & 0.0003 & $-$0.0258 & 0.17 & 388 \\\\\n36 & 52138.0934 & 0.0002 & 0.0114 & 0.82 & 309 \\\\\n37 & 52138.1125 & 0.0010 & $-$0.0263 & 0.16 & 311 \\\\\n37 & 52138.1505 & 0.0001 & 0.0117 & 0.83 & 390 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2452136.0357 + 0.056839 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Hump Maxima of WZ Sge during the end stage of the superoutburst plateau (2001).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n38 & 52138.1666 & 0.0020 & $-$0.0290 & 0.12 & 349 \\\\\n38 & 52138.2079 & 0.0003 & 0.0123 & 0.85 & 257 \\\\\n47 & 52138.6953 & 0.0004 & $-$0.0118 & 0.44 & 34 \\\\\n47 & 52138.7204 & 0.0021 & 0.0132 & 0.89 & 35 \\\\\n48 & 52138.7483 & 0.0005 & $-$0.0157 & 0.38 & 35 \\\\\n48 & 52138.7764 & 0.0011 & 0.0124 & 0.87 & 35 \\\\\n49 & 52138.8029 & 0.0011 & $-$0.0180 & 0.34 & 35 \\\\\n49 & 52138.8353 & 0.0007 & 0.0145 & 0.91 & 35 \\\\\n50 & 52138.8585 & 0.0014 & $-$0.0192 & 0.32 & 35 \\\\\n50 & 52138.8886 & 0.0008 & 0.0110 & 0.85 & 36 \\\\\n51 & 52138.9189 & 0.0021 & $-$0.0156 & 0.39 & 35 \\\\\n52 & 52139.0021 & 0.0029 & 0.0108 & 0.86 & 211 \\\\\n53 & 52139.0353 & 0.0005 & $-$0.0129 & 0.44 & 202 \\\\\n53 & 52139.0637 & 0.0078 & 0.0155 & 0.94 & 193 \\\\\n59 & 52139.3739 & 0.0015 & $-$0.0153 & 0.41 & 29 \\\\\n60 & 52139.4296 & 0.0003 & $-$0.0164 & 0.40 & 83 \\\\\n61 & 52139.4872 & 0.0008 & $-$0.0157 & 0.41 & 57 \\\\\n61 & 52139.5014 & 0.0004 & $-$0.0015 & 0.66 & 48 \\\\\n69 & 52139.9411 & 0.0008 & $-$0.0165 & 0.42 & 130 \\\\\n69 & 52139.9680 & 0.0028 & 0.0104 & 0.89 & 137 \\\\\n70 & 52140.0171 & 0.0007 & 0.0027 & 0.76 & 129 \\\\\n71 & 52140.0605 & 0.0037 & $-$0.0108 & 0.53 & 105 \\\\\n71 & 52140.0750 & 0.0012 & 0.0037 & 0.78 & 96 \\\\\n74 & 52140.2474 & 0.0005 & 0.0056 & 0.82 & 94 \\\\\n76 & 52140.3591 & 0.0003 & 0.0036 & 0.79 & 27 \\\\\n77 & 52140.4164 & 0.0007 & 0.0041 & 0.80 & 20 \\\\\n78 & 52140.4735 & 0.0004 & 0.0044 & 0.81 & 58 \\\\\n79 & 52140.5291 & 0.0003 & 0.0031 & 0.79 & 60 \\\\\n80 & 52140.5861 & 0.0004 & 0.0033 & 0.80 & 36 \\\\\n87 & 52140.9850 & 0.0005 & 0.0043 & 0.83 & 181 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the rebrightening phase (2001).}\\label{tab:wzsgeoc2001reb}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 52141.3245 & 0.0006 & $-$0.0065 & 0.82 & 34 \\\\\n1 & 52141.3826 & 0.0002 & $-$0.0059 & 0.85 & 120 \\\\\n2 & 52141.4386 & 0.0003 & $-$0.0073 & 0.84 & 167 \\\\\n3 & 52141.5002 & 0.0006 & $-$0.0030 & 0.92 & 150 \\\\\n7 & 52141.7229 & 0.0005 & $-$0.0099 & 0.85 & 44 \\\\\n8 & 52141.7779 & 0.0009 & $-$0.0123 & 0.82 & 45 \\\\\n9 & 52141.8361 & 0.0006 & $-$0.0115 & 0.85 & 44 \\\\\n14 & 52142.1305 & 0.0011 & $-$0.0042 & 0.04 & 65 \\\\\n16 & 52142.2373 & 0.0015 & $-$0.0122 & 0.92 & 25 \\\\\n18 & 52142.3543 & 0.0008 & $-$0.0100 & 0.99 & 164 \\\\\n19 & 52142.4057 & 0.0011 & $-$0.0159 & 0.90 & 229 \\\\\n20 & 52142.4646 & 0.0008 & $-$0.0144 & 0.94 & 154 \\\\\n21 & 52142.5218 & 0.0008 & $-$0.0146 & 0.94 & 152 \\\\\n22 & 52142.5840 & 0.0019 & $-$0.0099 & 0.04 & 145 \\\\\n23 & 52142.6436 & 0.0011 & $-$0.0076 & 0.09 & 59 \\\\\n24 & 52142.7050 & 0.0016 & $-$0.0037 & 0.18 & 40 \\\\\n25 & 52142.7564 & 0.0009 & $-$0.0097 & 0.08 & 59 \\\\\n26 & 52142.8164 & 0.0023 & $-$0.0070 & 0.14 & 42 \\\\\n29 & 52142.9974 & 0.0014 & 0.0018 & 0.33 & 176 \\\\\n35 & 52143.3303 & 0.0009 & $-$0.0097 & 0.21 & 42 \\\\\n36 & 52143.3878 & 0.0007 & $-$0.0096 & 0.22 & 204 \\\\\n37 & 52143.4457 & 0.0009 & $-$0.0091 & 0.24 & 454 \\\\\n38 & 52143.5010 & 0.0006 & $-$0.0112 & 0.22 & 430 \\\\\n39 & 52143.5585 & 0.0008 & $-$0.0111 & 0.23 & 518 \\\\\n42 & 52143.7413 & 0.0009 & $-$0.0005 & 0.46 & 72 \\\\\n43 & 52143.7936 & 0.0007 & $-$0.0056 & 0.38 & 105 \\\\\n44 & 52143.8448 & 0.0011 & $-$0.0118 & 0.28 & 104 \\\\\n46 & 52143.9639 & 0.0004 & $-$0.0075 & 0.38 & 868 \\\\\n47 & 52144.0237 & 0.0011 & $-$0.0051 & 0.44 & 855 \\\\\n48 & 52144.0782 & 0.0014 & $-$0.0080 & 0.40 & 158 \\\\\n49 & 52144.1373 & 0.0002 & $-$0.0063 & 0.44 & 1393 \\\\\n50 & 52144.1943 & 0.0003 & $-$0.0067 & 0.45 & 1065 \\\\\n51 & 52144.2461 & 0.0041 & $-$0.0123 & 0.36 & 235 \\\\\n53 & 52144.3673 & 0.0039 & $-$0.0059 & 0.50 & 51 \\\\\n54 & 52144.4210 & 0.0016 & $-$0.0096 & 0.45 & 117 \\\\\n55 & 52144.4747 & 0.0012 & $-$0.0133 & 0.39 & 134 \\\\\n56 & 52144.5372 & 0.0022 & $-$0.0082 & 0.50 & 86 \\\\\n57 & 52144.5963 & 0.0035 & $-$0.0065 & 0.54 & 88 \\\\\n63 & 52144.9453 & 0.0007 & $-$0.0019 & 0.70 & 851 \\\\\n64 & 52145.0067 & 0.0002 & 0.0021 & 0.78 & 1155 \\\\\n65 & 52145.0648 & 0.0002 & 0.0028 & 0.80 & 1191 \\\\\n66 & 52145.1213 & 0.0002 & 0.0019 & 0.80 & 1177 \\\\\n67 & 52145.1799 & 0.0002 & 0.0031 & 0.83 & 1225 \\\\\n68 & 52145.2368 & 0.0006 & 0.0026 & 0.84 & 256 \\\\\n69 & 52145.2979 & 0.0063 & 0.0064 & 0.92 & 87 \\\\\n70 & 52145.3497 & 0.0005 & 0.0007 & 0.83 & 150 \\\\\n71 & 52145.4017 & 0.0015 & $-$0.0047 & 0.75 & 43 \\\\\n72 & 52145.4700 & 0.0013 & 0.0062 & 0.95 & 104 \\\\\n73 & 52145.5226 & 0.0005 & 0.0014 & 0.88 & 89 \\\\\n74 & 52145.5739 & 0.0009 & $-$0.0046 & 0.79 & 64 \\\\\n75 & 52145.6314 & 0.0013 & $-$0.0046 & 0.80 & 35 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2452141.3310 + 0.057399 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the rebrightening phase (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n76 & 52145.6890 & 0.0016 & $-$0.0043 & 0.82 & 56 \\\\\n82 & 52146.0280 & 0.0011 & $-$0.0098 & 0.80 & 736 \\\\\n84 & 52146.1568 & 0.0026 & 0.0043 & 0.07 & 319 \\\\\n88 & 52146.3762 & 0.0017 & $-$0.0059 & 0.94 & 182 \\\\\n90 & 52146.4906 & 0.0005 & $-$0.0064 & 0.96 & 179 \\\\\n92 & 52146.6244 & 0.0057 & 0.0126 & 0.32 & 210 \\\\\n93 & 52146.6804 & 0.0030 & 0.0113 & 0.30 & 145 \\\\\n95 & 52146.7839 & 0.0036 & $-$0.0000 & 0.13 & 103 \\\\\n99 & 52147.0093 & 0.0019 & $-$0.0042 & 0.11 & 133 \\\\\n104 & 52147.3142 & 0.0005 & 0.0136 & 0.48 & 288 \\\\\n105 & 52147.3697 & 0.0003 & 0.0118 & 0.46 & 331 \\\\\n106 & 52147.4259 & 0.0003 & 0.0106 & 0.46 & 427 \\\\\n107 & 52147.4841 & 0.0003 & 0.0113 & 0.48 & 450 \\\\\n108 & 52147.5416 & 0.0004 & 0.0115 & 0.50 & 325 \\\\\n111 & 52147.7134 & 0.0006 & 0.0110 & 0.53 & 64 \\\\\n112 & 52147.7707 & 0.0008 & 0.0109 & 0.54 & 64 \\\\\n113 & 52147.8091 & 0.0017 & $-$0.0081 & 0.21 & 59 \\\\\n114 & 52147.8645 & 0.0017 & $-$0.0100 & 0.19 & 39 \\\\\n122 & 52148.3443 & 0.0005 & 0.0105 & 0.66 & 58 \\\\\n123 & 52148.3963 & 0.0006 & 0.0051 & 0.57 & 58 \\\\\n130 & 52148.8007 & 0.0017 & 0.0078 & 0.71 & 45 \\\\\n135 & 52149.0913 & 0.0003 & 0.0113 & 0.83 & 1456 \\\\\n136 & 52149.1510 & 0.0008 & 0.0137 & 0.89 & 1339 \\\\\n137 & 52149.2139 & 0.0007 & 0.0191 & 1.00 & 489 \\\\\n138 & 52149.2679 & 0.0013 & 0.0158 & 0.95 & 261 \\\\\n140 & 52149.3792 & 0.0007 & 0.0123 & 0.91 & 146 \\\\\n141 & 52149.4309 & 0.0004 & 0.0065 & 0.82 & 138 \\\\\n142 & 52149.4837 & 0.0005 & 0.0019 & 0.76 & 141 \\\\\n143 & 52149.5444 & 0.0004 & 0.0053 & 0.83 & 163 \\\\\n144 & 52149.5963 & 0.0003 & $-$0.0002 & 0.74 & 187 \\\\\n145 & 52149.6529 & 0.0004 & $-$0.0011 & 0.74 & 91 \\\\\n146 & 52149.7123 & 0.0003 & 0.0009 & 0.79 & 97 \\\\\n147 & 52149.7684 & 0.0004 & $-$0.0003 & 0.78 & 96 \\\\\n148 & 52149.8290 & 0.0040 & 0.0029 & 0.85 & 54 \\\\\n151 & 52149.9995 & 0.0023 & 0.0012 & 0.86 & 178 \\\\\n155 & 52150.2421 & 0.0018 & 0.0141 & 0.13 & 236 \\\\\n161 & 52150.5730 & 0.0011 & 0.0007 & 0.97 & 461 \\\\\n162 & 52150.6340 & 0.0055 & 0.0043 & 0.05 & 180 \\\\\n164 & 52150.7512 & 0.0013 & 0.0067 & 0.11 & 79 \\\\\n165 & 52150.8174 & 0.0009 & 0.0155 & 0.28 & 45 \\\\\n166 & 52150.8765 & 0.0028 & 0.0172 & 0.32 & 45 \\\\\n167 & 52150.9226 & 0.0014 & 0.0059 & 0.14 & 46 \\\\\n168 & 52150.9846 & 0.0016 & 0.0104 & 0.23 & 357 \\\\\n169 & 52151.0457 & 0.0012 & 0.0142 & 0.31 & 375 \\\\\n171 & 52151.1603 & 0.0019 & 0.0140 & 0.33 & 178 \\\\\n172 & 52151.2225 & 0.0020 & 0.0188 & 0.43 & 121 \\\\\n175 & 52151.3901 & 0.0016 & 0.0142 & 0.39 & 91 \\\\\n176 & 52151.4395 & 0.0010 & 0.0062 & 0.26 & 78 \\\\\n177 & 52151.5040 & 0.0012 & 0.0133 & 0.39 & 88 \\\\\n178 & 52151.5513 & 0.0005 & 0.0032 & 0.23 & 190 \\\\\n179 & 52151.6012 & 0.0010 & $-$0.0043 & 0.11 & 208 \\\\\n180 & 52151.6599 & 0.0008 & $-$0.0030 & 0.14 & 172 \\\\\n181 & 52151.7204 & 0.0018 & 0.0001 & 0.21 & 164 \\\\\n182 & 52151.7735 & 0.0008 & $-$0.0042 & 0.15 & 143 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the rebrightening phase (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n183 & 52151.8308 & 0.0007 & $-$0.0044 & 0.16 & 62 \\\\\n184 & 52151.8859 & 0.0019 & $-$0.0067 & 0.13 & 46 \\\\\n199 & 52152.7568 & 0.0012 & 0.0033 & 0.49 & 54 \\\\\n202 & 52152.9320 & 0.0009 & 0.0062 & 0.58 & 324 \\\\\n205 & 52153.1043 & 0.0006 & 0.0064 & 0.62 & 436 \\\\\n206 & 52153.1650 & 0.0007 & 0.0097 & 0.69 & 294 \\\\\n207 & 52153.2187 & 0.0007 & 0.0060 & 0.64 & 270 \\\\\n209 & 52153.3334 & 0.0004 & 0.0059 & 0.67 & 79 \\\\\n210 & 52153.3812 & 0.0004 & $-$0.0037 & 0.51 & 83 \\\\\n214 & 52153.6159 & 0.0064 & 0.0014 & 0.65 & 47 \\\\\n215 & 52153.6629 & 0.0057 & $-$0.0090 & 0.48 & 94 \\\\\n216 & 52153.7241 & 0.0027 & $-$0.0052 & 0.56 & 93 \\\\\n220 & 52153.9736 & 0.0023 & 0.0147 & 0.96 & 315 \\\\\n222 & 52154.1001 & 0.0012 & 0.0264 & 0.19 & 231 \\\\\n227 & 52154.3722 & 0.0014 & 0.0115 & 0.99 & 97 \\\\\n229 & 52154.4853 & 0.0015 & 0.0098 & 0.99 & 145 \\\\\n230 & 52154.5418 & 0.0008 & 0.0089 & 0.98 & 189 \\\\\n231 & 52154.6058 & 0.0026 & 0.0155 & 0.11 & 130 \\\\\n232 & 52154.6550 & 0.0011 & 0.0073 & 0.98 & 97 \\\\\n233 & 52154.7101 & 0.0012 & 0.0051 & 0.95 & 93 \\\\\n234 & 52154.7683 & 0.0008 & 0.0058 & 0.98 & 96 \\\\\n248 & 52155.5728 & 0.0006 & 0.0068 & 0.17 & 207 \\\\\n249 & 52155.6335 & 0.0010 & 0.0101 & 0.24 & 199 \\\\\n250 & 52155.6919 & 0.0006 & 0.0111 & 0.27 & 213 \\\\\n251 & 52155.7569 & 0.0006 & 0.0186 & 0.42 & 208 \\\\\n252 & 52155.8156 & 0.0023 & 0.0199 & 0.45 & 145 \\\\\n265 & 52156.5536 & 0.0007 & 0.0118 & 0.47 & 101 \\\\\n266 & 52156.6031 & 0.0005 & 0.0039 & 0.35 & 114 \\\\\n267 & 52156.6581 & 0.0009 & 0.0015 & 0.32 & 88 \\\\\n268 & 52156.7176 & 0.0008 & 0.0035 & 0.36 & 134 \\\\\n269 & 52156.7744 & 0.0004 & 0.0030 & 0.37 & 144 \\\\\n270 & 52156.8261 & 0.0009 & $-$0.0028 & 0.28 & 134 \\\\\n272 & 52156.9287 & 0.0003 & $-$0.0150 & 0.09 & 572 \\\\\n274 & 52157.0620 & 0.0002 & 0.0035 & 0.44 & 961 \\\\\n275 & 52157.1213 & 0.0002 & 0.0054 & 0.49 & 1003 \\\\\n276 & 52157.1748 & 0.0005 & 0.0015 & 0.43 & 815 \\\\\n277 & 52157.2308 & 0.0013 & 0.0001 & 0.42 & 275 \\\\\n283 & 52157.5737 & 0.0017 & $-$0.0013 & 0.47 & 42 \\\\\n299 & 52158.4869 & 0.0012 & $-$0.0066 & 0.58 & 51 \\\\\n300 & 52158.5508 & 0.0005 & $-$0.0000 & 0.70 & 55 \\\\\n301 & 52158.6048 & 0.0017 & $-$0.0034 & 0.66 & 51 \\\\\n302 & 52158.6653 & 0.0016 & $-$0.0004 & 0.72 & 94 \\\\\n303 & 52158.7314 & 0.0018 & 0.0084 & 0.89 & 41 \\\\\n304 & 52158.7753 & 0.0008 & $-$0.0052 & 0.66 & 44 \\\\\n306 & 52158.8940 & 0.0038 & $-$0.0012 & 0.76 & 30 \\\\\n314 & 52159.3590 & 0.0017 & 0.0046 & 0.96 & 182 \\\\\n315 & 52159.4173 & 0.0007 & 0.0055 & 0.99 & 92 \\\\\n337 & 52160.6761 & 0.0019 & 0.0015 & 0.19 & 42 \\\\\n338 & 52160.7328 & 0.0005 & 0.0008 & 0.20 & 45 \\\\\n339 & 52160.7884 & 0.0003 & $-$0.0010 & 0.18 & 42 \\\\\n340 & 52160.8461 & 0.0010 & $-$0.0008 & 0.19 & 45 \\\\\n341 & 52160.9130 & 0.0040 & 0.0088 & 0.37 & 54 \\\\\n342 & 52160.9626 & 0.0009 & 0.0010 & 0.25 & 280 \\\\\n343 & 52161.0174 & 0.0010 & $-$0.0016 & 0.22 & 237 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the rebrightening phase (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n344 & 52161.0790 & 0.0007 & 0.0026 & 0.30 & 300 \\\\\n345 & 52161.1318 & 0.0008 & $-$0.0020 & 0.23 & 271 \\\\\n346 & 52161.1867 & 0.0017 & $-$0.0045 & 0.20 & 175 \\\\\n347 & 52161.2443 & 0.0018 & $-$0.0043 & 0.22 & 170 \\\\\n354 & 52161.6440 & 0.0009 & $-$0.0064 & 0.27 & 48 \\\\\n355 & 52161.7043 & 0.0006 & $-$0.0035 & 0.33 & 75 \\\\\n356 & 52161.7592 & 0.0010 & $-$0.0060 & 0.30 & 101 \\\\\n357 & 52161.8180 & 0.0006 & $-$0.0046 & 0.34 & 70 \\\\\n372 & 52162.6760 & 0.0006 & $-$0.0076 & 0.47 & 75 \\\\\n373 & 52162.7283 & 0.0005 & $-$0.0126 & 0.40 & 59 \\\\\n374 & 52162.7905 & 0.0008 & $-$0.0079 & 0.49 & 55 \\\\\n375 & 52162.8368 & 0.0077 & $-$0.0190 & 0.31 & 46 \\\\\n389 & 52163.6628 & 0.0007 & 0.0034 & 0.88 & 38 \\\\\n394 & 52163.9414 & 0.0010 & $-$0.0050 & 0.80 & 254 \\\\\n395 & 52163.9993 & 0.0012 & $-$0.0045 & 0.82 & 143 \\\\\n396 & 52164.0530 & 0.0006 & $-$0.0081 & 0.77 & 108 \\\\\n397 & 52164.1059 & 0.0003 & $-$0.0127 & 0.70 & 279 \\\\\n398 & 52164.1695 & 0.0006 & $-$0.0064 & 0.82 & 124 \\\\\n399 & 52164.2240 & 0.0007 & $-$0.0094 & 0.78 & 182 \\\\\n411 & 52164.9142 & 0.0011 & $-$0.0080 & 0.96 & 237 \\\\\n412 & 52164.9758 & 0.0013 & $-$0.0038 & 0.04 & 297 \\\\\n413 & 52165.0297 & 0.0014 & $-$0.0072 & 0.99 & 243 \\\\\n442 & 52166.6843 & 0.0005 & $-$0.0172 & 0.18 & 46 \\\\\n443 & 52166.7384 & 0.0009 & $-$0.0205 & 0.14 & 45 \\\\\n444 & 52166.7939 & 0.0008 & $-$0.0224 & 0.12 & 45 \\\\\n445 & 52166.8547 & 0.0008 & $-$0.0191 & 0.19 & 45 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the post-superoutburst stage (2001).}\\label{tab:wzsgeoc2001late}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & phase$^c$ & $N^d$ \\\\\n\\hline\n0 & 52167.7152 & 0.0004 & 0.0046 & 0.37 & 38 \\\\\n1 & 52167.7785 & 0.0009 & 0.0106 & 0.48 & 44 \\\\\n2 & 52167.8265 & 0.0006 & 0.0012 & 0.33 & 45 \\\\\n3 & 52167.8875 & 0.0014 & 0.0048 & 0.41 & 34 \\\\\n10 & 52168.2867 & 0.0004 & 0.0026 & 0.45 & 169 \\\\\n11 & 52168.3431 & 0.0003 & 0.0017 & 0.44 & 173 \\\\\n12 & 52168.3933 & 0.0009 & $-$0.0054 & 0.33 & 113 \\\\\n15 & 52168.5702 & 0.0037 & $-$0.0006 & 0.45 & 41 \\\\\n16 & 52168.6284 & 0.0034 & 0.0003 & 0.48 & 53 \\\\\n17 & 52168.6826 & 0.0007 & $-$0.0029 & 0.43 & 45 \\\\\n18 & 52168.7457 & 0.0006 & 0.0029 & 0.55 & 44 \\\\\n19 & 52168.8052 & 0.0004 & 0.0051 & 0.60 & 45 \\\\\n20 & 52168.8616 & 0.0009 & 0.0041 & 0.59 & 45 \\\\\n39 & 52169.9512 & 0.0006 & 0.0042 & 0.81 & 240 \\\\\n40 & 52170.0119 & 0.0003 & 0.0075 & 0.88 & 255 \\\\\n41 & 52170.0639 & 0.0004 & 0.0022 & 0.80 & 216 \\\\\n42 & 52170.1220 & 0.0007 & 0.0030 & 0.83 & 186 \\\\\n45 & 52170.2923 & 0.0005 & 0.0012 & 0.83 & 220 \\\\\n46 & 52170.3525 & 0.0003 & 0.0041 & 0.89 & 159 \\\\\n47 & 52170.4062 & 0.0003 & 0.0005 & 0.84 & 225 \\\\\n48 & 52170.4605 & 0.0007 & $-$0.0026 & 0.80 & 135 \\\\\n49 & 52170.5203 & 0.0014 & $-$0.0001 & 0.85 & 44 \\\\\n56 & 52170.9274 & 0.0007 & 0.0056 & 0.03 & 278 \\\\\n57 & 52170.9862 & 0.0005 & 0.0070 & 0.07 & 275 \\\\\n58 & 52171.0335 & 0.0005 & $-$0.0030 & 0.90 & 279 \\\\\n59 & 52171.0912 & 0.0009 & $-$0.0027 & 0.92 & 280 \\\\\n60 & 52171.1541 & 0.0005 & 0.0029 & 0.03 & 276 \\\\\n61 & 52171.2148 & 0.0019 & 0.0063 & 0.10 & 243 \\\\\n74 & 52171.9623 & 0.0022 & 0.0084 & 0.29 & 180 \\\\\n75 & 52172.0089 & 0.0004 & $-$0.0024 & 0.11 & 340 \\\\\n76 & 52172.0676 & 0.0003 & $-$0.0011 & 0.15 & 340 \\\\\n77 & 52172.1338 & 0.0020 & 0.0078 & 0.31 & 280 \\\\\n78 & 52172.1844 & 0.0011 & 0.0011 & 0.21 & 274 \\\\\n80 & 52172.3068 & 0.0005 & 0.0088 & 0.36 & 133 \\\\\n81 & 52172.3481 & 0.0009 & $-$0.0073 & 0.09 & 133 \\\\\n83 & 52172.4726 & 0.0006 & 0.0026 & 0.29 & 108 \\\\\n84 & 52172.5304 & 0.0019 & 0.0030 & 0.31 & 59 \\\\\n86 & 52172.6444 & 0.0018 & 0.0023 & 0.32 & 37 \\\\\n87 & 52172.6959 & 0.0006 & $-$0.0035 & 0.23 & 44 \\\\\n88 & 52172.7624 & 0.0012 & 0.0057 & 0.40 & 45 \\\\\n89 & 52172.8147 & 0.0007 & 0.0006 & 0.33 & 45 \\\\\n90 & 52172.8683 & 0.0012 & $-$0.0032 & 0.27 & 26 \\\\\n91 & 52172.9311 & 0.0054 & 0.0023 & 0.38 & 321 \\\\\n92 & 52172.9850 & 0.0007 & $-$0.0011 & 0.33 & 340 \\\\\n93 & 52173.0414 & 0.0007 & $-$0.0021 & 0.32 & 340 \\\\\n102 & 52173.5496 & 0.0013 & $-$0.0099 & 0.29 & 75 \\\\\n103 & 52173.6098 & 0.0006 & $-$0.0071 & 0.35 & 26 \\\\\n104 & 52173.6692 & 0.0005 & $-$0.0050 & 0.40 & 45 \\\\\n105 & 52173.7286 & 0.0007 & $-$0.0030 & 0.45 & 45 \\\\\n106 & 52173.7854 & 0.0011 & $-$0.0035 & 0.45 & 42 \\\\\n107 & 52173.8388 & 0.0034 & $-$0.0075 & 0.39 & 37 \\\\\n\\hline\n \\multicolumn{6}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{6}{l}{$^{b}$ Against $max = 2452167.7106 + 0.057342 E$.} \\\\\n \\multicolumn{6}{l}{$^{c}$ Orbital phase.} \\\\\n \\multicolumn{6}{l}{$^{d}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the post-superoutburst stage (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n112 & 52174.1434 & 0.0015 & 0.0104 & 0.76 & 266 \\\\\n115 & 52174.3175 & 0.0009 & 0.0125 & 0.84 & 94 \\\\\n116 & 52174.3688 & 0.0015 & 0.0065 & 0.74 & 50 \\\\\n117 & 52174.4182 & 0.0008 & $-$0.0014 & 0.61 & 107 \\\\\n118 & 52174.4818 & 0.0018 & 0.0048 & 0.73 & 44 \\\\\n121 & 52174.6492 & 0.0015 & 0.0001 & 0.69 & 80 \\\\\n122 & 52174.7055 & 0.0011 & $-$0.0008 & 0.68 & 75 \\\\\n123 & 52174.7706 & 0.0027 & 0.0069 & 0.83 & 45 \\\\\n124 & 52174.8175 & 0.0004 & $-$0.0036 & 0.66 & 45 \\\\\n126 & 52174.9424 & 0.0007 & 0.0066 & 0.86 & 338 \\\\\n128 & 52175.0539 & 0.0004 & 0.0034 & 0.83 & 338 \\\\\n130 & 52175.1666 & 0.0005 & 0.0014 & 0.81 & 281 \\\\\n131 & 52175.2158 & 0.0031 & $-$0.0067 & 0.68 & 206 \\\\\n132 & 52175.2816 & 0.0006 & 0.0018 & 0.84 & 34 \\\\\n133 & 52175.3385 & 0.0006 & 0.0014 & 0.85 & 40 \\\\\n134 & 52175.3874 & 0.0031 & $-$0.0071 & 0.71 & 39 \\\\\n135 & 52175.4565 & 0.0014 & 0.0046 & 0.93 & 43 \\\\\n143 & 52175.8992 & 0.0035 & $-$0.0113 & 0.74 & 164 \\\\\n144 & 52175.9668 & 0.0004 & $-$0.0011 & 0.93 & 341 \\\\\n145 & 52176.0207 & 0.0008 & $-$0.0045 & 0.88 & 341 \\\\\n146 & 52176.0776 & 0.0011 & $-$0.0050 & 0.88 & 344 \\\\\n147 & 52176.1383 & 0.0005 & $-$0.0016 & 0.96 & 297 \\\\\n148 & 52176.1949 & 0.0012 & $-$0.0024 & 0.95 & 251 \\\\\n150 & 52176.3088 & 0.0008 & $-$0.0032 & 0.96 & 45 \\\\\n157 & 52176.7135 & 0.0009 & 0.0002 & 0.10 & 43 \\\\\n158 & 52176.7704 & 0.0013 & $-$0.0003 & 0.11 & 46 \\\\\n159 & 52176.8280 & 0.0011 & $-$0.0001 & 0.12 & 45 \\\\\n161 & 52176.9449 & 0.0003 & 0.0021 & 0.18 & 1274 \\\\\n162 & 52177.0015 & 0.0002 & 0.0014 & 0.18 & 1273 \\\\\n163 & 52177.0460 & 0.0007 & $-$0.0114 & 0.97 & 1202 \\\\\n164 & 52177.1102 & 0.0006 & $-$0.0046 & 0.10 & 873 \\\\\n168 & 52177.3449 & 0.0003 & 0.0008 & 0.24 & 81 \\\\\n169 & 52177.4020 & 0.0007 & 0.0006 & 0.25 & 88 \\\\\n170 & 52177.4615 & 0.0012 & 0.0027 & 0.30 & 55 \\\\\n178 & 52177.9167 & 0.0005 & $-$0.0008 & 0.33 & 889 \\\\\n186 & 52178.3723 & 0.0008 & $-$0.0040 & 0.36 & 60 \\\\\n187 & 52178.4347 & 0.0010 & 0.0011 & 0.46 & 100 \\\\\n188 & 52178.4824 & 0.0020 & $-$0.0085 & 0.31 & 90 \\\\\n191 & 52178.6561 & 0.0004 & $-$0.0069 & 0.37 & 44 \\\\\n192 & 52178.7115 & 0.0006 & $-$0.0088 & 0.35 & 44 \\\\\n196 & 52178.9391 & 0.0034 & $-$0.0106 & 0.36 & 572 \\\\\n197 & 52178.9996 & 0.0007 & $-$0.0074 & 0.43 & 1028 \\\\\n198 & 52179.0539 & 0.0005 & $-$0.0105 & 0.39 & 1229 \\\\\n200 & 52179.1703 & 0.0031 & $-$0.0088 & 0.44 & 108 \\\\\n209 & 52179.6818 & 0.0013 & $-$0.0133 & 0.46 & 43 \\\\\n210 & 52179.7385 & 0.0009 & $-$0.0140 & 0.46 & 20 \\\\\n219 & 52180.2690 & 0.0019 & 0.0005 & 0.82 & 28 \\\\\n220 & 52180.3236 & 0.0010 & $-$0.0023 & 0.79 & 41 \\\\\n221 & 52180.3794 & 0.0023 & $-$0.0039 & 0.77 & 29 \\\\\n222 & 52180.4385 & 0.0014 & $-$0.0021 & 0.81 & 44 \\\\\n223 & 52180.4922 & 0.0009 & $-$0.0058 & 0.76 & 34 \\\\\n230 & 52180.8963 & 0.0012 & $-$0.0030 & 0.89 & 700 \\\\\n231 & 52180.9542 & 0.0002 & $-$0.0024 & 0.91 & 1053 \\\\\n232 & 52181.0074 & 0.0003 & $-$0.0067 & 0.85 & 1084 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the post-superoutburst stage (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n233 & 52181.0690 & 0.0004 & $-$0.0023 & 0.94 & 1296 \\\\\n234 & 52181.1325 & 0.0011 & 0.0039 & 0.06 & 341 \\\\\n235 & 52181.1795 & 0.0024 & $-$0.0065 & 0.88 & 252 \\\\\n238 & 52181.3776 & 0.0028 & 0.0195 & 0.38 & 136 \\\\\n239 & 52181.4147 & 0.0014 & $-$0.0007 & 0.03 & 159 \\\\\n240 & 52181.4671 & 0.0019 & $-$0.0056 & 0.96 & 106 \\\\\n250 & 52182.0429 & 0.0005 & $-$0.0032 & 0.12 & 747 \\\\\n273 & 52183.3655 & 0.0004 & 0.0004 & 0.45 & 82 \\\\\n274 & 52183.4148 & 0.0006 & $-$0.0076 & 0.32 & 87 \\\\\n275 & 52183.4586 & 0.0006 & $-$0.0211 & 0.09 & 55 \\\\\n284 & 52183.9913 & 0.0007 & $-$0.0045 & 0.49 & 279 \\\\\n285 & 52184.0472 & 0.0013 & $-$0.0060 & 0.47 & 276 \\\\\n286 & 52184.1011 & 0.0016 & $-$0.0094 & 0.42 & 253 \\\\\n295 & 52184.6117 & 0.0042 & $-$0.0149 & 0.43 & 49 \\\\\n296 & 52184.6709 & 0.0005 & $-$0.0130 & 0.47 & 37 \\\\\n297 & 52184.7343 & 0.0008 & $-$0.0070 & 0.59 & 38 \\\\\n298 & 52184.7897 & 0.0010 & $-$0.0089 & 0.57 & 34 \\\\\n300 & 52184.9113 & 0.0007 & $-$0.0020 & 0.71 & 190 \\\\\n301 & 52184.9682 & 0.0004 & $-$0.0024 & 0.72 & 330 \\\\\n302 & 52185.0293 & 0.0010 & 0.0013 & 0.80 & 280 \\\\\n303 & 52185.0869 & 0.0014 & 0.0016 & 0.81 & 222 \\\\\n307 & 52185.3096 & 0.0019 & $-$0.0051 & 0.74 & 36 \\\\\n308 & 52185.3701 & 0.0008 & $-$0.0019 & 0.81 & 44 \\\\\n309 & 52185.4299 & 0.0020 & 0.0005 & 0.86 & 29 \\\\\n313 & 52185.6746 & 0.0029 & 0.0159 & 0.18 & 38 \\\\\n314 & 52185.7230 & 0.0007 & 0.0069 & 0.03 & 38 \\\\\n318 & 52185.9421 & 0.0020 & $-$0.0033 & 0.90 & 318 \\\\\n319 & 52185.9983 & 0.0015 & $-$0.0045 & 0.89 & 276 \\\\\n320 & 52186.0610 & 0.0015 & 0.0009 & 1.00 & 279 \\\\\n321 & 52186.1120 & 0.0008 & $-$0.0055 & 0.90 & 276 \\\\\n322 & 52186.1802 & 0.0078 & 0.0054 & 0.10 & 170 \\\\\n329 & 52186.5745 & 0.0015 & $-$0.0017 & 0.05 & 54 \\\\\n342 & 52187.3206 & 0.0010 & $-$0.0010 & 0.22 & 67 \\\\\n343 & 52187.3853 & 0.0014 & 0.0063 & 0.36 & 82 \\\\\n344 & 52187.4377 & 0.0016 & 0.0014 & 0.28 & 52 \\\\\n347 & 52187.6112 & 0.0009 & 0.0028 & 0.34 & 38 \\\\\n348 & 52187.6624 & 0.0016 & $-$0.0033 & 0.24 & 38 \\\\\n349 & 52187.7255 & 0.0011 & 0.0024 & 0.36 & 37 \\\\\n350 & 52187.7797 & 0.0033 & $-$0.0006 & 0.32 & 31 \\\\\n359 & 52188.2963 & 0.0014 & $-$0.0002 & 0.43 & 37 \\\\\n360 & 52188.3519 & 0.0018 & $-$0.0019 & 0.41 & 22 \\\\\n365 & 52188.6296 & 0.0016 & $-$0.0110 & 0.31 & 40 \\\\\n366 & 52188.6862 & 0.0029 & $-$0.0116 & 0.31 & 41 \\\\\n383 & 52189.6783 & 0.0007 & 0.0056 & 0.81 & 30 \\\\\n384 & 52189.7299 & 0.0015 & $-$0.0001 & 0.72 & 29 \\\\\n412 & 52191.3370 & 0.0012 & 0.0014 & 0.07 & 43 \\\\\n413 & 52191.4051 & 0.0049 & 0.0121 & 0.27 & 45 \\\\\n429 & 52192.3124 & 0.0014 & 0.0020 & 0.27 & 54 \\\\\n431 & 52192.4257 & 0.0012 & 0.0006 & 0.27 & 20 \\\\\n432 & 52192.4824 & 0.0009 & 0.0000 & 0.27 & 30 \\\\\n435 & 52192.6544 & 0.0015 & $-$0.0001 & 0.31 & 36 \\\\\n436 & 52192.7149 & 0.0022 & 0.0031 & 0.37 & 34 \\\\\n446 & 52193.2790 & 0.0018 & $-$0.0062 & 0.33 & 25 \\\\\n447 & 52193.3361 & 0.0016 & $-$0.0064 & 0.33 & 72 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge during the post-superoutburst stage (2001) (continued).}\n\\begin{center}\n\\begin{tabular}{cccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & phase & $N$ \\\\\n\\hline\n448 & 52193.3991 & 0.0036 & $-$0.0008 & 0.44 & 84 \\\\\n449 & 52193.4550 & 0.0063 & $-$0.0023 & 0.43 & 51 \\\\\n457 & 52193.9174 & 0.0008 & 0.0014 & 0.59 & 944 \\\\\n458 & 52193.9687 & 0.0009 & $-$0.0046 & 0.49 & 833 \\\\\n459 & 52194.0223 & 0.0009 & $-$0.0084 & 0.44 & 641 \\\\\n463 & 52194.2662 & 0.0012 & 0.0061 & 0.74 & 40 \\\\\n464 & 52194.3174 & 0.0024 & $-$0.0000 & 0.64 & 79 \\\\\n465 & 52194.3804 & 0.0006 & 0.0056 & 0.75 & 77 \\\\\n466 & 52194.4394 & 0.0035 & 0.0073 & 0.79 & 81 \\\\\n470 & 52194.6676 & 0.0009 & 0.0062 & 0.82 & 40 \\\\\n471 & 52194.7182 & 0.0010 & $-$0.0006 & 0.71 & 33 \\\\\n474 & 52194.8941 & 0.0006 & 0.0033 & 0.82 & 263 \\\\\n475 & 52194.9520 & 0.0006 & 0.0038 & 0.84 & 333 \\\\\n476 & 52195.0111 & 0.0013 & 0.0056 & 0.88 & 315 \\\\\n477 & 52195.0646 & 0.0014 & 0.0018 & 0.82 & 336 \\\\\n478 & 52195.1229 & 0.0014 & 0.0027 & 0.85 & 290 \\\\\n482 & 52195.3570 & 0.0071 & 0.0075 & 0.98 & 85 \\\\\n487 & 52195.6398 & 0.0015 & 0.0035 & 0.97 & 34 \\\\\n488 & 52195.7128 & 0.0078 & 0.0192 & 0.26 & 35 \\\\\n492 & 52195.9284 & 0.0004 & 0.0054 & 0.06 & 633 \\\\\n493 & 52195.9927 & 0.0013 & 0.0124 & 0.20 & 514 \\\\\n498 & 52196.2764 & 0.0018 & 0.0094 & 0.20 & 43 \\\\\n499 & 52196.3317 & 0.0012 & 0.0073 & 0.18 & 68 \\\\\n500 & 52196.3921 & 0.0012 & 0.0104 & 0.24 & 61 \\\\\n501 & 52196.4416 & 0.0021 & 0.0025 & 0.11 & 31 \\\\\n509 & 52196.9004 & 0.0005 & 0.0027 & 0.21 & 713 \\\\\n510 & 52196.9722 & 0.0012 & 0.0171 & 0.48 & 504 \\\\\n511 & 52197.0160 & 0.0005 & 0.0035 & 0.25 & 390 \\\\\n516 & 52197.3066 & 0.0003 & 0.0074 & 0.37 & 69 \\\\\n517 & 52197.3630 & 0.0007 & 0.0065 & 0.37 & 93 \\\\\n518 & 52197.4108 & 0.0020 & $-$0.0031 & 0.21 & 35 \\\\\n533 & 52198.2742 & 0.0031 & 0.0002 & 0.44 & 41 \\\\\n534 & 52198.3298 & 0.0032 & $-$0.0016 & 0.42 & 23 \\\\\n551 & 52199.3195 & 0.0012 & 0.0133 & 0.88 & 37 \\\\\n552 & 52199.3703 & 0.0019 & 0.0068 & 0.78 & 43 \\\\\n553 & 52199.4198 & 0.0010 & $-$0.0010 & 0.65 & 42 \\\\\n580 & 52200.9884 & 0.0018 & 0.0193 & 0.32 & 281 \\\\\n581 & 52201.0403 & 0.0011 & 0.0138 & 0.24 & 273 \\\\\n586 & 52201.3275 & 0.0011 & 0.0143 & 0.30 & 69 \\\\\n597 & 52201.9606 & 0.0017 & 0.0167 & 0.47 & 355 \\\\\n598 & 52202.0090 & 0.0016 & 0.0078 & 0.33 & 331 \\\\\n848 & 52216.3123 & 0.0011 & $-$0.0244 & 0.64 & 30 \\\\\n849 & 52216.3733 & 0.0015 & $-$0.0208 & 0.72 & 36 \\\\\n865 & 52217.3061 & 0.0012 & $-$0.0055 & 0.17 & 31 \\\\\n866 & 52217.3680 & 0.0025 & $-$0.0009 & 0.27 & 33 \\\\\n901 & 52219.3688 & 0.0009 & $-$0.0071 & 0.56 & 35 \\\\\n969 & 52223.2643 & 0.0012 & $-$0.0109 & 0.28 & 16 \\\\\n970 & 52223.3227 & 0.0012 & $-$0.0098 & 0.31 & 25 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of WZ Sge (1978).}\\label{tab:wzsgeoc1978}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & $O-C^b$ & Ref.$^c$ \\\\\n\\hline\n0 & 43857.4731 & $-$0.0053 & 3 \\\\\n0 & 43857.4767 & $-$0.0017 & 4 \\\\\n1 & 43857.5365 & 0.0008 & 2 \\\\\n1 & 43857.5394 & 0.0037 & 3 \\\\\n2 & 43857.5934 & 0.0005 & 1 \\\\\n17 & 43858.4496 & $-$0.0018 & 4 \\\\\n71 & 43861.5563 & 0.0144 & 1 \\\\\n83 & 43862.2360 & 0.0073 & 2 \\\\\n87 & 43862.4575 & $-$0.0001 & 4 \\\\\n117 & 43864.1710 & $-$0.0036 & 2 \\\\\n118 & 43864.2280 & $-$0.0039 & 2 \\\\\n119 & 43864.2850 & $-$0.0041 & 2 \\\\\n124 & 43864.5694 & $-$0.0058 & 1 \\\\\n135 & 43865.2010 & $-$0.0038 & 2 \\\\\n140 & 43865.4899 & $-$0.0011 & 3 \\\\\n141 & 43865.5488 & 0.0006 & 3 \\\\\n159 & 43866.5709 & $-$0.0075 & 1 \\\\\n176 & 43867.5505 & $-$0.0008 & 1 \\\\\n193 & 43868.5263 & 0.0020 & 3 \\\\\n193 & 43868.5299 & 0.0056 & 1 \\\\\n194 & 43868.5859 & 0.0044 & 1 \\\\\n210 & 43869.4950 & $-$0.0022 & 1 \\\\\n228 & 43870.5299 & 0.0025 & 1 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ HJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2443857.4782 + 0.057232 E$.} \\\\\n \\multicolumn{4}{l}{$^{c}$ 1: \\citet{pat81wzsge}, 2: \\citet{boh79wzsge},} \\\\\n \\multicolumn{4}{l}{\\phantom{$^{c}$} 3: \\citet{hei79wzsge}, 4: \\citet{tar79wzsge}} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{AW Sagittae}\\label{obj:awsge}\n\n This dwarf nova has long been known since its early discovery\n\\citep{wol06awsge}. The SU UMa-type nature was established during\nthe 2000 superoutburst (vsnet-alert 5111, 5112, 5114).\n\\citet{llo07awsge} summarized the history of outbursts of this object\nand \\citet{llo08awsge} presented observations during the 2007 normal outburst.\nWe analyzed the available AAVSO observation of the 2006 superoutburst,\na part of the data reported in \\citet{she08awsge}.\nThe observation apparently covered the middle-to-late stage\nof the superoutburst.\nThe times of superhump maxima are listed in table \\ref{tab:awsgeoc2006}.\nThe mean $P_{\\rm SH}$ with the PDM method was 0.07449(2) d\n(figure \\ref{fig:awsgeshpdm}) and\n$P_{\\rm dot}$ = $-7.9(6.4) \\times 10^{-5}$, which may be a result\nof combination of stage B and C superhumps.\nWe also give times of superhump maxima during the 2000 superoutburst\n(table \\ref{tab:awsgeoc2000}). The mean mean $P_{\\rm SH}$ with\nthe PDM method was 0.07473(8) d.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig135.eps}\n \\end{center}\n \\caption{Superhumps in AW Sge (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:awsgeshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of AW Sge (2000).}\\label{tab:awsgeoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51741.5174 & 0.0010 & $-$0.0001 & 61 \\\\\n12 & 51742.4131 & 0.0025 & 0.0014 & 40 \\\\\n13 & 51742.4849 & 0.0012 & $-$0.0013 & 52 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451741.5175 + 0.074519 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of AW Sge (2006).}\\label{tab:awsgeoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54056.3222 & 0.0007 & $-$0.0004 & 53 \\\\\n30 & 54058.5593 & 0.0004 & 0.0009 & 139 \\\\\n31 & 54058.6336 & 0.0003 & 0.0006 & 139 \\\\\n43 & 54059.5258 & 0.0009 & $-$0.0015 & 47 \\\\\n44 & 54059.6022 & 0.0004 & 0.0004 & 115 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454056.3226 + 0.074528 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V551 Sagittarii}\\label{obj:v551sgr}\n\n V551 Sgr has long been suspected to be a candidate WZ Sge-type\ndwarf nova (cf. \\cite{dow90wxcet}).\nDuring the 2003 superoutburst, we managed to obtain excellent time-series\nphotometry. A PDM analysis has yielded a mean period of 0.06757(1) d\n(figure \\ref{fig:v551sgrshpdm}). The times of superhump maxima are\nlisted in table \\ref{tab:v551sgroc2003}.\nThe $O-C$ diagram clearly shows a positive period derivative except\nfor the earliest part (figure \\ref{fig:v551sgr2003oc}).\nExcluding $E = 0$ (stage A), we obtained\n$P_{\\rm dot}$ = $+6.0(1.5) \\times 10^{-5}$.\nThere were no indication of early superhumps. Together with the\nrelatively long superhump period, and a likely supercycle of $\\sim$ 1 yr,\nthe object is likely an SU UMa-type dwarf nova similar to UV Per\n(subsection \\ref{sec:uvper}) and QY Per (subsection \\ref{sec:qyper}),\nrather than a genuine WZ Sge-type object.\n\n The 2004 superoutburst was less sufficiently observed\n(table \\ref{tab:v551sgroc2004}).\nThe $P_{\\rm dot}$ was likely positive and apparently recorded during\nthe stage B (figure \\ref{fig:v551sgrcomp}), but we did not attempt\nto measure the $P_{\\rm dot}$ because of the short baseline.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig136.eps}\n \\end{center}\n \\caption{Superhumps in V551 Sgr (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v551sgrshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig137.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps V551 Sgr (2003).\n (Upper): $O-C$ diagram. The curve represents a quadratic fit to\n $E \\ge 22$.\n (Lower): Light curve.\n Large dots represent CCD observations. Small dots and a ``V'' mark\n represent visual observations and a upper limit, respectively.\n }\n \\label{fig:v551sgr2003oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig138.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V551 Sgr between different\n superoutbursts. A period of 0.06757 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:v551sgrcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V551 Sgr (2003).}\\label{tab:v551sgroc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52904.3030 & 0.0029 & $-$0.0187 & 68 \\\\\n22 & 52905.8189 & 0.0003 & 0.0084 & 165 \\\\\n29 & 52906.2914 & 0.0006 & 0.0072 & 68 \\\\\n30 & 52906.3589 & 0.0008 & 0.0070 & 49 \\\\\n44 & 52907.3025 & 0.0006 & 0.0032 & 74 \\\\\n45 & 52907.3669 & 0.0012 & $-$0.0000 & 62 \\\\\n51 & 52907.7764 & 0.0006 & 0.0034 & 123 \\\\\n52 & 52907.8408 & 0.0006 & 0.0001 & 167 \\\\\n54 & 52907.9760 & 0.0006 & $-$0.0000 & 32 \\\\\n55 & 52908.0433 & 0.0004 & $-$0.0003 & 46 \\\\\n58 & 52908.2460 & 0.0009 & $-$0.0007 & 61 \\\\\n59 & 52908.3128 & 0.0009 & $-$0.0016 & 61 \\\\\n70 & 52909.0569 & 0.0006 & $-$0.0019 & 45 \\\\\n84 & 52910.0047 & 0.0009 & $-$0.0014 & 153 \\\\\n85 & 52910.0734 & 0.0011 & $-$0.0004 & 177 \\\\\n89 & 52910.3426 & 0.0044 & $-$0.0019 & 37 \\\\\n118 & 52912.3094 & 0.0013 & 0.0024 & 63 \\\\\n125 & 52912.7813 & 0.0007 & 0.0006 & 145 \\\\\n126 & 52912.8430 & 0.0048 & $-$0.0054 & 154 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452904.3217 + 0.067672 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V551 Sgr (2004).}\\label{tab:v551sgroc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53153.5658 & 0.0008 & 0.0010 & 150 \\\\\n1 & 53153.6341 & 0.0007 & 0.0015 & 153 \\\\\n12 & 53154.3802 & 0.0008 & 0.0018 & 151 \\\\\n13 & 53154.4424 & 0.0011 & $-$0.0038 & 153 \\\\\n14 & 53154.5129 & 0.0012 & $-$0.0011 & 153 \\\\\n15 & 53154.5797 & 0.0008 & $-$0.0021 & 153 \\\\\n26 & 53155.3275 & 0.0008 & $-$0.0002 & 131 \\\\\n27 & 53155.3984 & 0.0043 & 0.0029 & 16 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453153.5648 + 0.067803 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V4140 Sagittarii}\\label{obj:v4140sgr}\n\n V4140 Sgr has long been known as an eclipsing CV below the period gap\n\\citep{jab87v4140sgr}. The dwarf nova-type nature was confirmed only\nvery recently \\citep{bor05v4140sgr}, who interpreted short outbursts\nof this object as being normal outbursts of an SU UMa-type dwarf nova.\nIn 2004, B. Monard detected a long outburst and reported the existence\nof superhumps (vsnet-alert 8313). We analyzed the data obtained during\nthis superoutburst. We used out-of-eclipse observations as was done for\nV2051 Oph, using the ephemeris by \\citet{bap03v4140sgr}.\nThe times of superhump maxima are listed in table \\ref{tab:v4140sgroc2004}\n(the identification of maxima was slightly uncertain for $E \\ge 149$\ndue to the faintness of the object and shortness of the observing runs).\nDisregarding the first night, when superhumps were likely still evolving,\nthe $O-C$ diagram seems to be composed of the stage B with a positive\n$P_{\\rm dot}$ ($16 \\le E \\le 70$), followed by a transition to the stage C\nwith a shorter period. The $P_{\\rm dot}$ for the stage B was\n$+25.3(12.3) \\times 10^{-5}$. The mean superhump period from the\nfirst five nights (with better statistics) was 0.06324(3) d,\nyielding a fractional superhump excess of 2.9(1) \\%.\n\n\\begin{table}\n\\caption{Superhump maxima of V4140 Sgr (2004).}\\label{tab:v4140sgroc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53269.2561 & 0.0025 & 0.0047 & 176 \\\\\n1 & 53269.3193 & 0.0013 & 0.0045 & 238 \\\\\n2 & 53269.3858 & 0.0013 & 0.0079 & 240 \\\\\n16 & 53270.2604 & 0.0021 & $-$0.0035 & 118 \\\\\n17 & 53270.3227 & 0.0021 & $-$0.0045 & 116 \\\\\n18 & 53270.3850 & 0.0019 & $-$0.0054 & 107 \\\\\n19 & 53270.4474 & 0.0032 & $-$0.0063 & 113 \\\\\n53 & 53272.6051 & 0.0043 & $-$0.0002 & 97 \\\\\n69 & 53273.6226 & 0.0021 & 0.0049 & 113 \\\\\n70 & 53273.6919 & 0.0026 & 0.0109 & 111 \\\\\n133 & 53277.6735 & 0.0023 & 0.0059 & 93 \\\\\n140 & 53278.1180 & 0.0030 & 0.0075 & 26 \\\\\n155 & 53279.0477 & 0.0023 & $-$0.0120 & 26 \\\\\n156 & 53279.1107 & 0.0050 & $-$0.0123 & 27 \\\\\n165 & 53279.6901 & 0.0098 & $-$0.0024 & 106 \\\\\n181 & 53280.6891 & 0.0131 & $-$0.0159 & 87 \\\\\n275 & 53286.6694 & 0.0025 & 0.0162 & 121 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453269.2514 + 0.063279 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V701 Tauri}\\label{obj:v701tau}\n\n V701 Tau was discovered by \\citet{era73v701tau} as an eruptive object.\nThe SU UMa-type nature was first reported by us during the 1995--1996\noutburst (vsnet-alert 303). \\citet{she07v701tau} further reported\nthe 2005 superoutburst and obtained a superhump period of 0.0690(2) d,\nor its one-day alias, 0.0663(2) d.\nBased on our 1995--1996 observations, we obtained a mean period\nof 0.06898(3) d. The times of superhump maxima are listed in table\n\\ref{tab:v701tauoc1995}.\nDuring the interval $0 \\le E \\le 3$, the superhumps were still in\nthe growing stage (stage A) and the mean period (0.073(1) d) significantly\ndiffered from the later observations. The $P_{\\rm dot}$ estimated from\nthe segment of $31 \\le E \\le 159$ was $-2.6(0.8) \\times 10^{-5}$.\n\n We also analyzed the 2005 superoutburst (table \\ref{tab:v701tauoc2005}).\nThe mean superhump period with the PDM method was 0.069037(12) d\n(figure \\ref{fig:v701taushpdm}).\nThe $P_{\\rm SH}$ showed a clear increase (stage B) at\n$P_{\\rm dot}$ = $+11.0(3.5) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig139.eps}\n \\end{center}\n \\caption{Superhumps in V701 Tau (2005). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v701taushpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V701 Tau (1995--1996).}\\label{tab:v701tauoc1995}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50078.9780 & 0.0016 & $-$0.0077 & 61 \\\\\n1 & 50079.0485 & 0.0020 & $-$0.0061 & 65 \\\\\n2 & 50079.1260 & 0.0035 & 0.0024 & 64 \\\\\n3 & 50079.1946 & 0.0013 & 0.0021 & 55 \\\\\n31 & 50081.1266 & 0.0005 & 0.0029 & 65 \\\\\n58 & 50082.9901 & 0.0016 & 0.0042 & 46 \\\\\n59 & 50083.0577 & 0.0116 & 0.0028 & 46 \\\\\n60 & 50083.1280 & 0.0021 & 0.0042 & 44 \\\\\n159 & 50089.9471 & 0.0059 & $-$0.0047 & 37 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450078.9857 + 0.068970 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V701 Tau (2005).}\\label{tab:v701tauoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53711.4936 & 0.0007 & 0.0033 & 67 \\\\\n1 & 53711.5650 & 0.0013 & 0.0056 & 34 \\\\\n14 & 53712.4576 & 0.0005 & 0.0008 & 57 \\\\\n23 & 53713.0767 & 0.0007 & $-$0.0015 & 137 \\\\\n24 & 53713.1447 & 0.0007 & $-$0.0025 & 146 \\\\\n25 & 53713.2144 & 0.0009 & $-$0.0019 & 127 \\\\\n27 & 53713.3536 & 0.0007 & $-$0.0007 & 68 \\\\\n28 & 53713.4233 & 0.0020 & $-$0.0000 & 42 \\\\\n36 & 53713.9687 & 0.0095 & $-$0.0070 & 86 \\\\\n37 & 53714.0437 & 0.0009 & $-$0.0010 & 145 \\\\\n38 & 53714.1135 & 0.0009 & $-$0.0002 & 145 \\\\\n39 & 53714.1764 & 0.0047 & $-$0.0063 & 83 \\\\\n40 & 53714.2561 & 0.0012 & 0.0043 & 71 \\\\\n41 & 53714.3195 & 0.0008 & $-$0.0013 & 60 \\\\\n54 & 53715.2204 & 0.0046 & 0.0021 & 121 \\\\\n69 & 53716.2549 & 0.0021 & 0.0010 & 34 \\\\\n70 & 53716.3218 & 0.0016 & $-$0.0011 & 36 \\\\\n71 & 53716.3959 & 0.0007 & 0.0040 & 33 \\\\\n73 & 53716.5323 & 0.0009 & 0.0023 & 88 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453711.4903 + 0.069036 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{V1208 Tauri}\\label{obj:v1208tau}\n\n V1208 Tau was originally identified as a CV\nduring the course of identification of ROSAT sources \\citep{mot96CVROSAT}.\nP. Schmeer detected the first-ever recorded outburst in 2000\n(vsnet-alert 4118). Time-resolved photometry during this superoutburst\nestablished the SU UMa-type dwarf novae (vsnet-alert 4122).\n\n We observed two superoutbursts in 2000 and 2002--2003.\nThe superhump profile for the 2002--2003 superoutburst is shown\nin figure \\ref{fig:v1208taushpdm}.\nThe times of superhump maxima are listed in tables \\ref{tab:v1208tauoc2000}\nand \\ref{tab:v1208tauoc2002}, respectively.\nThe values of $P_{\\rm dot}$ were $-2.8(4.0) \\times 10^{-5}$ and\n$-6.3(3.8) \\times 10^{-5}$, respectively. These negative values appear\nto have resulted from stage B--C transitions (figure \\ref{fig:v1208taucomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig140.eps}\n \\end{center}\n \\caption{Superhumps in V1208 Tau (2002--2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:v1208taushpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig141.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of V1208 Tau between different\n superoutbursts. A period of 0.07060 d was used to draw this figure.\n Since the start of the outburst was unknown, the start of time-resolved\n photometry was chosen as $E=0$.\n }\n \\label{fig:v1208taucomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of V1208 Tau (2000).}\\label{tab:v1208tauoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51580.3069 & 0.0008 & 0.0013 & 67 \\\\\n1 & 51580.3761 & 0.0012 & $-$0.0001 & 65 \\\\\n9 & 51580.9383 & 0.0007 & $-$0.0019 & 55 \\\\\n10 & 51581.0109 & 0.0006 & 0.0002 & 77 \\\\\n12 & 51581.1505 & 0.0150 & $-$0.0012 & 88 \\\\\n23 & 51581.9230 & 0.0023 & $-$0.0042 & 178 \\\\\n24 & 51581.9997 & 0.0016 & 0.0020 & 140 \\\\\n38 & 51582.9904 & 0.0012 & 0.0057 & 82 \\\\\n39 & 51583.0557 & 0.0015 & 0.0005 & 65 \\\\\n66 & 51584.9573 & 0.0045 & $-$0.0015 & 139 \\\\\n80 & 51585.9450 & 0.0072 & $-$0.0008 & 139 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451580.3057 + 0.070501 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of V1208 Tau (2002--2003).}\\label{tab:v1208tauoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52635.1220 & 0.0008 & $-$0.0013 & 85 \\\\\n1 & 52635.1918 & 0.0016 & $-$0.0020 & 57 \\\\\n12 & 52635.9711 & 0.0009 & 0.0015 & 162 \\\\\n13 & 52636.0419 & 0.0006 & 0.0017 & 186 \\\\\n14 & 52636.1083 & 0.0007 & $-$0.0024 & 215 \\\\\n15 & 52636.1804 & 0.0025 & $-$0.0009 & 38 \\\\\n26 & 52636.9570 & 0.0011 & $-$0.0002 & 102 \\\\\n29 & 52637.1695 & 0.0008 & 0.0007 & 134 \\\\\n30 & 52637.2430 & 0.0012 & 0.0036 & 72 \\\\\n40 & 52637.9436 & 0.0020 & $-$0.0011 & 81 \\\\\n42 & 52638.0891 & 0.0008 & 0.0033 & 136 \\\\\n43 & 52638.1550 & 0.0008 & $-$0.0013 & 136 \\\\\n44 & 52638.2266 & 0.0009 & $-$0.0003 & 137 \\\\\n54 & 52638.9354 & 0.0015 & 0.0032 & 129 \\\\\n55 & 52638.9984 & 0.0024 & $-$0.0043 & 107 \\\\\n56 & 52639.0768 & 0.0008 & 0.0035 & 136 \\\\\n57 & 52639.1436 & 0.0008 & $-$0.0002 & 136 \\\\\n58 & 52639.2144 & 0.0018 & $-$0.0000 & 96 \\\\\n69 & 52639.9925 & 0.0020 & 0.0023 & 50 \\\\\n72 & 52640.1962 & 0.0018 & $-$0.0057 & 37 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452635.1232 + 0.070537 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{KK Telescopii}\\label{obj:kktel}\n\n \\citet{kat03v877arakktelpucma} reported the detection of superhumps\nand derived an exceptionally large rate of period decrease.\nWe also observed the 2003 superoutburst, and identified an unambiguous\nsuperhump period of 0.08753(5) d, which is in good agreement with\n\\citet{pat03suumas}, who observed the 2000 superoutburst.\nBased on this identification of the period, we give refined\n$O-C$'s for the 2002 superoutburst (table \\ref{tab:kkteloc2002}).\nIt is now evident the times of superhumps for $22 \\le E \\le 47$ are\nwell expressed by this improved superhump period.\nThe maximum at $E = 0$ has a strongly negative $O-C$, indicating that\nthis maximum was observed during the stage A evolution.\nThe period derivative shown in \\citet{kat03v877arakktelpucma} was\nthus a result of a stage A--B transition, and should not be used as\na global $P_{\\rm dot}$.\nThe times of superhump maxima during the 2003 superoutburst are\nlisted in table \\ref{tab:kkteloc2003}.\nThe mean period of 0.08734(6) d determined from the late stage of the\n2004 superoutburst (table \\ref{tab:kkteloc2004}) suggests that\na shortening of the period (stage C) near the termination of\nthe superoutburst also occurred in this system\n(see also the combined $O-C$ diagram in figure \\ref{fig:kktelcomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig142.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of KK Tel between different\n superoutbursts. A period of 0.08761 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:kktelcomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of KK Tel (2002).}\\label{tab:kkteloc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52444.0061 & 0.0104 & $-$0.0139 & 185 \\\\\n22 & 52445.9501 & 0.0029 & 0.0028 & 20 \\\\\n23 & 52446.0360 & 0.0022 & 0.0010 & 30 \\\\\n24 & 52446.1269 & 0.0016 & 0.0043 & 48 \\\\\n25 & 52446.2123 & 0.0013 & 0.0021 & 37 \\\\\n47 & 52448.1421 & 0.0006 & 0.0045 & 90 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452444.2000 + 0.08761 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KK Tel (2003).}\\label{tab:kkteloc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52816.0225 & 0.0004 & 0.0018 & 91 \\\\\n1 & 52816.1105 & 0.0003 & 0.0020 & 90 \\\\\n2 & 52816.1936 & 0.0005 & $-$0.0026 & 83 \\\\\n3 & 52816.2833 & 0.0004 & $-$0.0007 & 91 \\\\\n4 & 52816.3705 & 0.0011 & $-$0.0012 & 52 \\\\\n12 & 52817.0732 & 0.0008 & $-$0.0006 & 64 \\\\\n13 & 52817.1629 & 0.0009 & 0.0014 & 25 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452816.0207 + 0.087756 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KK Tel (2004).}\\label{tab:kkteloc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53151.4369 & 0.0003 & $-$0.0001 & 157 \\\\\n1 & 53151.5242 & 0.0003 & $-$0.0001 & 199 \\\\\n2 & 53151.6116 & 0.0003 & $-$0.0000 & 198 \\\\\n12 & 53152.4861 & 0.0003 & 0.0011 & 198 \\\\\n13 & 53152.5730 & 0.0003 & 0.0006 & 199 \\\\\n14 & 53152.6581 & 0.0006 & $-$0.0015 & 120 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453151.4370 + 0.087335 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{EK Trianguli Australis}\\label{obj:ektra}\n\n Although EK TrA had long been known as an SU UMa-type dwarf nova\n\\citep{vog80ektra}, the precise superhump period was not reported.\nWe observed the 2007 superoutburst and obtained a mean superhump\nperiod of 0.064309(6) with the PDM method (figure \\ref{fig:ektrashpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:ektraoc2007}.\nThe $O-C$'s were almost zero, and the $P_{\\rm dot}$ for the entire observation\nwas $-0.5(0.5) \\times 10^{-5}$. There was no noticeable structure in\nthe $O-C$ diagram. Individual superhumps, however, showed strongly\nvariable profiles: double-humped around\n$0 \\le E \\le 1$ (maxima matching the ephemeris were given in the table),\nand around $E = 63$, a complex, double wave-like profile emerged with\nreduced superhump amplitudes (maxima not determined).\nThe latter feature somewhat resembled the behavior observed in\nOT J055718$+$683226 \\citep{uem09j0557}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig143.eps}\n \\end{center}\n \\caption{Superhumps in EK TrA (2007). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:ektrashpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of EK TrA (2007).}\\label{tab:ektraoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54294.2815 & 0.0015 & $-$0.0060 & 148 \\\\\n1 & 54294.3559 & 0.0016 & 0.0041 & 91 \\\\\n16 & 54295.3112 & 0.0008 & $-$0.0056 & 148 \\\\\n31 & 54296.2840 & 0.0008 & 0.0021 & 148 \\\\\n32 & 54296.3473 & 0.0011 & 0.0011 & 148 \\\\\n33 & 54296.4101 & 0.0007 & $-$0.0004 & 149 \\\\\n46 & 54297.2488 & 0.0005 & 0.0020 & 148 \\\\\n47 & 54297.3105 & 0.0015 & $-$0.0007 & 148 \\\\\n48 & 54297.3760 & 0.0004 & 0.0005 & 148 \\\\\n49 & 54297.4317 & 0.0016 & $-$0.0081 & 148 \\\\\n77 & 54299.2400 & 0.0008 & $-$0.0012 & 149 \\\\\n78 & 54299.3099 & 0.0011 & 0.0043 & 148 \\\\\n79 & 54299.3763 & 0.0009 & 0.0064 & 148 \\\\\n80 & 54299.4360 & 0.0008 & 0.0017 & 148 \\\\\n93 & 54300.2697 & 0.0010 & $-$0.0009 & 149 \\\\\n94 & 54300.3375 & 0.0012 & 0.0026 & 148 \\\\\n95 & 54300.4075 & 0.0013 & 0.0082 & 149 \\\\\n108 & 54301.2350 & 0.0014 & $-$0.0005 & 148 \\\\\n109 & 54301.2989 & 0.0010 & $-$0.0011 & 148 \\\\\n110 & 54301.3618 & 0.0007 & $-$0.0024 & 149 \\\\\n124 & 54302.2590 & 0.0007 & $-$0.0059 & 148 \\\\\n125 & 54302.3328 & 0.0007 & 0.0035 & 148 \\\\\n126 & 54302.3889 & 0.0007 & $-$0.0047 & 148 \\\\\n127 & 54302.4575 & 0.0007 & $-$0.0005 & 141 \\\\\n155 & 54304.2554 & 0.0009 & $-$0.0039 & 149 \\\\\n156 & 54304.3223 & 0.0012 & $-$0.0013 & 148 \\\\\n157 & 54304.3915 & 0.0010 & 0.0035 & 149 \\\\\n158 & 54304.4523 & 0.0010 & $-$0.0001 & 140 \\\\\n172 & 54305.3570 & 0.0010 & 0.0040 & 149 \\\\\n173 & 54305.4195 & 0.0014 & 0.0021 & 141 \\\\\n186 & 54306.2550 & 0.0018 & 0.0013 & 121 \\\\\n187 & 54306.3107 & 0.0018 & $-$0.0073 & 149 \\\\\n188 & 54306.3916 & 0.0029 & 0.0093 & 150 \\\\\n249 & 54310.2996 & 0.0007 & $-$0.0072 & 142 \\\\\n250 & 54310.3722 & 0.0014 & 0.0011 & 122 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454294.2875 + 0.064335 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{UW Trianguli}\\label{obj:uwtri}\n\n This object was originally reported as a nova\n(\\cite{kur84newCV}; \\cite{arg83uwtriiauc}). The detection of a second\noutburst in 1995 by T. Vanmunster led to an identification as\na large-amplitude dwarf nova \\citep{kat01uwtri}.\n\\citet{kat01uwtri} reported a candidate superhump period 0.0569 d,\nwhose selection was based on the period distribution of known CVs.\nOther one-day aliases were not excluded due to the shortness of\nobservations.\n\n The object underwent a new outburst in 2008 (vsnet-alert 10635).\nThe data taken during this superoutburst now strongly favor\na shorter period of 0.05334(2) d for early superhumps and\n0.05427(2) for ordinary superhumps\n(figures \\ref{fig:uwtrieshpdm}, \\ref{fig:uwtrishpdm}).\nWe adopted these values as the basic periods for the following analysis.\nWe also reanalyzed the data in \\citet{kat01uwtri} and yielded\na period of 0.05330(2) d based on the present alias selection.\nThe light curve of the 1995 observation averaged with this period now\nexhibits double-wave modulations characteristic to early superhumps\n(figure \\ref{fig:uwtrieshpdm1995}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig144.eps}\n \\end{center}\n \\caption{Early superhumps in UW Tri (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:uwtrieshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig145.eps}\n \\end{center}\n \\caption{Ordinary superhumps in UW Tri (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:uwtrishpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig146.eps}\n \\end{center}\n \\caption{Early superhumps in UW Tri (1995). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:uwtrieshpdm1995}\n\\end{figure}\n\n The maxima of ordinary superhump in 2008 are listed in table\n\\ref{tab:uwtrioc2008}. The resultant $P_{\\rm dot}$ was\n$+3.7(0.6) \\times 10^{-5}$, although there remained some uncertainty\nin the constancy of the $P_{\\rm dot}$ due to long gaps between observations.\nIf the $P_{\\rm dot}$ is confirmed, the parameters of superhumps\nand outbursts resemble those of another short $P_{\\rm SH}$ WZ Sge-type\ndwarf nova OT J0238 (subsection \\ref{sec:j0238}).\n\n The details will be presented in Ohshima et al., in preparation.\n\n\\begin{table}\n\\caption{Superhump maxima of UW Tri (2008).}\\label{tab:uwtrioc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54777.4487 & 0.0007 & 0.0144 & 40 \\\\\n1 & 54777.5041 & 0.0007 & 0.0156 & 40 \\\\\n101 & 54782.9032 & 0.0023 & $-$0.0047 & 86 \\\\\n102 & 54782.9616 & 0.0024 & $-$0.0005 & 110 \\\\\n104 & 54783.0654 & 0.0017 & $-$0.0051 & 109 \\\\\n105 & 54783.1148 & 0.0009 & $-$0.0100 & 113 \\\\\n106 & 54783.1829 & 0.0017 & 0.0040 & 111 \\\\\n107 & 54783.2300 & 0.0014 & $-$0.0031 & 107 \\\\\n108 & 54783.2810 & 0.0024 & $-$0.0063 & 87 \\\\\n123 & 54784.0994 & 0.0015 & $-$0.0008 & 104 \\\\\n124 & 54784.1527 & 0.0052 & $-$0.0017 & 85 \\\\\n125 & 54784.1944 & 0.0017 & $-$0.0142 & 95 \\\\\n126 & 54784.2621 & 0.0054 & $-$0.0007 & 110 \\\\\n217 & 54789.1923 & 0.0023 & $-$0.0022 & 100 \\\\\n233 & 54790.0511 & 0.0146 & $-$0.0105 & 65 \\\\\n234 & 54790.1127 & 0.0012 & $-$0.0031 & 117 \\\\\n235 & 54790.1698 & 0.0012 & $-$0.0002 & 115 \\\\\n236 & 54790.2187 & 0.0039 & $-$0.0055 & 96 \\\\\n271 & 54792.1292 & 0.0059 & 0.0082 & 30 \\\\\n272 & 54792.1780 & 0.0070 & 0.0028 & 44 \\\\\n288 & 54793.0662 & 0.0133 & 0.0239 & 44 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454777.4343 + 0.054194 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{WY Trianguli}\\label{obj:wytri}\n\n WY Tri is a dwarf nova discovered by \\citet{mei86uztri}.\nThe SU UMa-type nature was established during its 2000 superoutburst\n\\citep{van01wytri}.\nSince the original data in \\citet{van01wytri} were not available,\nwe extracted the data from a scanned figure. The quality of the\nextracted data were sufficient for the following analysis.\nThe times of maxima determined from the combined data set with\n\\citet{van01wytri} are listed in table \\ref{tab:wytrioc2000}.\nAlthough the global $P_{\\rm dot}$ was $-18.3(5.9) \\times 10^{-5}$,\nthis variation can be attributed to a stage B--C transition.\nThe parameters are given in table \\ref{tab:perlist}.\nA PDM analysis of the stage B superhumps yielded a period of\n0.07838(5) d.\n\n\\begin{table}\n\\caption{Superhump maxima of WY Tri(2000).}\\label{tab:wytrioc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51899.3738 & 0.0015 & $-$0.0038 & -- \\\\\n1 & 51899.4552 & 0.0027 & $-$0.0007 & -- \\\\\n2 & 51899.5306 & 0.0027 & $-$0.0036 & -- \\\\\n12 & 51900.3197 & 0.0015 & 0.0026 & -- \\\\\n13 & 51900.3951 & 0.0024 & $-$0.0002 & -- \\\\\n14 & 51900.4758 & 0.0033 & 0.0022 & -- \\\\\n15 & 51900.5547 & 0.0030 & 0.0028 & -- \\\\\n20 & 51900.9382 & 0.0047 & $-$0.0052 & 82 \\\\\n21 & 51901.0216 & 0.0019 & $-$0.0000 & 113 \\\\\n22 & 51901.0999 & 0.0038 & $-$0.0001 & 62 \\\\\n24 & 51901.2571 & 0.0024 & 0.0006 & -- \\\\\n25 & 51901.3355 & 0.0021 & 0.0007 & -- \\\\\n26 & 51901.4140 & 0.0015 & 0.0009 & -- \\\\\n27 & 51901.4923 & 0.0021 & 0.0009 & -- \\\\\n37 & 51902.2808 & 0.0030 & 0.0066 & -- \\\\\n38 & 51902.3551 & 0.0015 & 0.0025 & -- \\\\\n39 & 51902.4357 & 0.0024 & 0.0049 & -- \\\\\n40 & 51902.5101 & 0.0033 & 0.0009 & -- \\\\\n46 & 51902.9736 & 0.0046 & $-$0.0053 & 82 \\\\\n47 & 51903.0572 & 0.0035 & 0.0001 & 83 \\\\\n58 & 51903.9114 & 0.0129 & $-$0.0069 & 113 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451899.3776 + 0.078287 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SU Ursae Majoris}\\label{obj:suuma}\n\n We observed the 1999 January superoutburst. This outburst had\na precursor outburst, and the observation covered the precursor phase.\nThe times of superhump maxima are listed in table \\ref{tab:suumaoc1999}.\nThe segment of $0 \\le E \\le 2$ corresponds to the precursor phase,\nwhen the superhump period rapidly evolved. Since there were multiple\nhump maxima within one cycle after $E > 170$ (post-superoutburst stage),\nwe restricted our analysis to $E \\le 165$.\nAlthough the global $P_{\\rm dot}$ was $-10.2(1.9) \\times 10^{-5}$\n($13 \\le E \\le $165), the $O-C$ diagram can be better interpreted as\na combination of A--C stages. The $P_{\\rm dot}$ for the stage B was\n$-0.2(3.9) \\times 10^{-5}$ ($34 \\le E \\le 92$,\ndisregarding $E = 78$ and $E = 79$). Other parameters are presented\nin table \\ref{tab:perlist}.\nA comparison between the 1989 and 1999 superoutbursts is shown in\nfigure \\ref{fig:suumacomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig147.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of SU UMa between different\n superoutbursts. A period of 0.07908 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:suumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SU UMa (1999).}\\label{tab:suumaoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51185.9020 & 0.0050 & $-$0.0152 & 80 \\\\\n1 & 51185.9863 & 0.0039 & $-$0.0100 & 98 \\\\\n2 & 51186.0566 & 0.0013 & $-$0.0188 & 87 \\\\\n13 & 51186.9220 & 0.0031 & $-$0.0233 & 120 \\\\\n14 & 51187.0053 & 0.0015 & $-$0.0190 & 124 \\\\\n15 & 51187.0949 & 0.0008 & $-$0.0085 & 122 \\\\\n26 & 51187.9757 & 0.0004 & 0.0025 & 134 \\\\\n27 & 51188.0569 & 0.0003 & 0.0046 & 146 \\\\\n28 & 51188.1345 & 0.0002 & 0.0031 & 152 \\\\\n34 & 51188.6157 & 0.0002 & 0.0099 & 51 \\\\\n51 & 51189.9591 & 0.0012 & 0.0089 & 77 \\\\\n52 & 51190.0468 & 0.0011 & 0.0175 & 44 \\\\\n53 & 51190.1210 & 0.0005 & 0.0127 & 50 \\\\\n64 & 51190.9881 & 0.0009 & 0.0099 & 96 \\\\\n65 & 51191.0672 & 0.0010 & 0.0100 & 34 \\\\\n66 & 51191.1441 & 0.0010 & 0.0078 & 68 \\\\\n76 & 51191.9386 & 0.0004 & 0.0116 & 115 \\\\\n77 & 51192.0190 & 0.0025 & 0.0129 & 40 \\\\\n78 & 51192.0867 & 0.0012 & 0.0015 & 67 \\\\\n79 & 51192.1574 & 0.0016 & $-$0.0069 & 21 \\\\\n90 & 51193.0477 & 0.0006 & 0.0135 & 152 \\\\\n91 & 51193.1263 & 0.0007 & 0.0131 & 68 \\\\\n92 & 51193.2019 & 0.0007 & 0.0096 & 91 \\\\\n114 & 51194.9355 & 0.0030 & 0.0035 & 41 \\\\\n127 & 51195.9598 & 0.0009 & $-$0.0001 & 117 \\\\\n128 & 51196.0383 & 0.0004 & $-$0.0008 & 118 \\\\\n139 & 51196.9031 & 0.0011 & $-$0.0058 & 138 \\\\\n140 & 51196.9962 & 0.0009 & 0.0082 & 156 \\\\\n141 & 51197.0573 & 0.0012 & $-$0.0098 & 98 \\\\\n165 & 51198.9548 & 0.0016 & $-$0.0101 & 107 \\\\\n177 & 51199.8867 & 0.0018 & $-$0.0271 & 62 \\\\\n178 & 51200.0048 & 0.0007 & 0.0119 & 143 \\\\\n190 & 51200.9208 & 0.0016 & $-$0.0210 & 109 \\\\\n191 & 51201.0514 & 0.0005 & 0.0306 & 126 \\\\\n193 & 51201.1521 & 0.0016 & $-$0.0269 & 91 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451185.9172 + 0.079077 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SW Ursae Majoris}\\label{sec:swuma}\\label{obj:swuma}\n\n We present observations of the 1991, 1997, 2000, 2002,\nand 2006 superoutbursts\n(tables \\ref{tab:swumaoc1991}, \\ref{tab:swumaoc1997}, \\ref{tab:swumaoc2000},\n\\ref{tab:swumaoc2002}, \\ref{tab:swumaoc2006}), a part of which are\na reanalysis of the data in \\citet{soe09swuma}.\n\n The 1991 superoutburst was a faint superoutburst reaching a visual\nmagnitude of $\\sim$ 11.0.\nThe superoutburst was associated with a precursor outburst\n(figure \\ref{fig:swuma1991prec}).\nThe identification of $E$ in table \\ref{tab:swumaoc1991}\\footnote{\n Since original data have become unavailable,\n we extracted observations from printed light curves. The errors of\n maxima times may be larger than the listed values.\n}\nis based on the present knowledge, assuming that the object experienced\nstage A during the precursor phase and the presence of the stage C\nduring the post-superoutburst stage. The segment $52 \\le E \\le 88$ seems\nto be the early phase of the stage B. The shortness of the mean\n$P_{\\rm SH}$ = 0.05825(2) d probably reflects a short $P_{\\rm SH}$\nat the beginning of the stage B.\n\n The 1997 superoutburst showed $P_{\\rm dot}$ = $+8.6(0.5) \\times 10^{-5}$.\n\n The $O-C$ diagram of the 2000 superoutburst was clearly composed of\nthe three distinct stages A--C. We obtained\n$P_{\\rm dot}$ = $+5.1(0.5) \\times 10^{-5}$ (stage B, $27 \\le E \\le 217$).\n\n During the 2002 superoutburst, we obtained $P_{\\rm dot}$ =\n$+9.9(0.9) \\times 10^{-5}$ for the interval $E \\le 142$ (stage B).\nAfter $E = 142$, the $O-C$ diagram showed a clear transition to a shorter\nsuperhump period (stage C).\n\n During the 2006 superoutburst, we obtained $P_{\\rm dot}$ =\n$+9.5(0.6) \\times 10^{-5}$ during the stage B ($33 \\le E \\le 189$).\nAlthough this superoutburst was one of the brightest\n(reaching a visual magnitude of 10.2) in the last decade, the behavior\nin the $O-C$ diagram during the stage B was similar to the ones in other\nsuperoutbursts.\nThe start of the stage B was $\\sim$8.5 d after the initial detection\nof the outburst. The corresponding delay time for the 2000 superoutburst\nwas $\\sim$ 7 d, and the delay time for the 1991 superoutburst was\nless than 3 d. The duration before the start of the stage B (or\nthe appearance of superhumps) depends on the extent of the superoutburst,\nas pointed out by \\citet{kat08wzsgelateSH}. A comparison of the\n$O-C$ diagrams further indicates that the stage B evolution was also\ndifferent in this superoutburst (figure \\ref{fig:swumacomp}).\n\n During the rapid fading stage of this superoutburst, large-amplitude\nquasi-periodic oscillations (QPOs) were recorded (figure \\ref{fig:swumaqpo}).\nThe appearance of large-amplitude QPOs during the rapid fading stage\nwas recorded during the 2000 and 2002 superoutbursts \\citep{soe09swuma}.\nThe present period of the QPOs is close to theirs (i.e. about the double\nof ``super-QPOs'' observed during the 1992 superoutburst,\n\\cite{kat92swumasuperQPO}). There must be a common mechanism to excite\nthese QPOs during the terminal stage of superoutbursts.\n\n In summary, although the behavior of period variation is generally\nsimilar between different superoutbursts of SW UMa, there was a subtle\ndependence on the extent of superoutbursts.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(70mm,60mm){fig148.eps}\n \\end{center}\n \\caption{Precursor outburst of SW UMa on 1991 February 26.}\n \\label{fig:swuma1991prec}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig149.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps SW UMa (1991).\n (Upper): $O-C$ diagram.\n (Lower): Light curve. Large dots are our CCD observations and small\n dots are visual observation from the VSOLJ and AAVSO databases.}\n \\label{fig:swuma1991oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig150.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of SW UMa between different\n superoutbursts. A period of 0.05822 d was used to draw this figure.\n Since the delay in the appearance of superhumps is known to vary\n in SW UMa, we shifted individual $O-C$ diagrams to get a best\n match (approximately corresponds to a definition of the appearance of\n superhumps to be $E=0$). The evolution of the bright 2008 superoutburst\n was apparently different from the other superoutbursts.\n }\n \\label{fig:swumacomp}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig151.eps}\n \\end{center}\n \\caption{Quasi-periodic oscillations (QPOs) on 2006 October 4.\n (Upper): Light curve.\n (Lower): Power spectrum after subtracting superhumps. The signal\n around a frequency 134 cycle\/d (11 m) corresponds to the QPOs.}\n \\label{fig:swumaqpo}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (1991).}\\label{tab:swumaoc1991}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ \\\\\n\\hline\n0 & 48314.0851 & 0.0028 & $-$0.0274 \\\\\n1 & 48314.1524 & 0.0010 & $-$0.0186 \\\\\n52 & 48317.1611 & 0.0004 & 0.0091 \\\\\n53 & 48317.2185 & 0.0004 & 0.0080 \\\\\n54 & 48317.2771 & 0.0004 & 0.0082 \\\\\n67 & 48318.0346 & 0.0014 & 0.0059 \\\\\n68 & 48318.0937 & 0.0004 & 0.0065 \\\\\n69 & 48318.1497 & 0.0004 & 0.0040 \\\\\n70 & 48318.2070 & 0.0004 & 0.0029 \\\\\n71 & 48318.2656 & 0.0008 & 0.0030 \\\\\n84 & 48319.0261 & 0.0012 & 0.0036 \\\\\n85 & 48319.0823 & 0.0004 & 0.0014 \\\\\n86 & 48319.1413 & 0.0004 & 0.0019 \\\\\n87 & 48319.1998 & 0.0004 & 0.0019 \\\\\n88 & 48319.2565 & 0.0008 & 0.0002 \\\\\n343 & 48334.1581 & 0.0014 & $-$0.0034 \\\\\n344 & 48334.2127 & 0.0016 & $-$0.0072 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2448314.1125 + 0.058452 E$.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (1997).}\\label{tab:swumaoc1997}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50744.5437 & 0.0005 & 0.0113 & 27 \\\\\n69 & 50748.5497 & 0.0023 & $-$0.0043 & 17 \\\\\n70 & 50748.6075 & 0.0006 & $-$0.0048 & 33 \\\\\n71 & 50748.6648 & 0.0006 & $-$0.0058 & 28 \\\\\n85 & 50749.4834 & 0.0006 & $-$0.0032 & 25 \\\\\n86 & 50749.5422 & 0.0009 & $-$0.0026 & 33 \\\\\n87 & 50749.5986 & 0.0010 & $-$0.0045 & 28 \\\\\n138 & 50752.5794 & 0.0009 & 0.0038 & 31 \\\\\n139 & 50752.6382 & 0.0009 & 0.0043 & 33 \\\\\n140 & 50752.6980 & 0.0016 & 0.0058 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450744.5324 + 0.058284 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (2000).}\\label{tab:swumaoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51590.5432 & 0.0008 & $-$0.0071 & 17 \\\\\n1 & 51590.6002 & 0.0009 & $-$0.0083 & 16 \\\\\n2 & 51590.6565 & 0.0016 & $-$0.0101 & 16 \\\\\n3 & 51590.7242 & 0.0016 & $-$0.0007 & 18 \\\\\n7 & 51590.9567 & 0.0008 & $-$0.0009 & 241 \\\\\n10 & 51591.1346 & 0.0064 & 0.0023 & 137 \\\\\n11 & 51591.1908 & 0.0012 & 0.0003 & 176 \\\\\n12 & 51591.2507 & 0.0019 & 0.0020 & 131 \\\\\n13 & 51591.3085 & 0.0004 & 0.0016 & 285 \\\\\n14 & 51591.3665 & 0.0006 & 0.0014 & 257 \\\\\n19 & 51591.6628 & 0.0002 & 0.0067 & 36 \\\\\n20 & 51591.7190 & 0.0003 & 0.0047 & 36 \\\\\n21 & 51591.7791 & 0.0002 & 0.0066 & 37 \\\\\n22 & 51591.8369 & 0.0002 & 0.0062 & 36 \\\\\n23 & 51591.8946 & 0.0004 & 0.0057 & 127 \\\\\n24 & 51591.9528 & 0.0004 & 0.0057 & 233 \\\\\n25 & 51592.0123 & 0.0002 & 0.0070 & 301 \\\\\n26 & 51592.0710 & 0.0002 & 0.0075 & 284 \\\\\n27 & 51592.1301 & 0.0003 & 0.0085 & 207 \\\\\n28 & 51592.1864 & 0.0005 & 0.0065 & 176 \\\\\n30 & 51592.2984 & 0.0010 & 0.0021 & 37 \\\\\n37 & 51592.7077 & 0.0003 & 0.0040 & 37 \\\\\n38 & 51592.7663 & 0.0003 & 0.0044 & 35 \\\\\n39 & 51592.8227 & 0.0002 & 0.0026 & 37 \\\\\n40 & 51592.8797 & 0.0008 & 0.0014 & 51 \\\\\n41 & 51592.9404 & 0.0004 & 0.0040 & 273 \\\\\n42 & 51592.9969 & 0.0002 & 0.0022 & 279 \\\\\n43 & 51593.0573 & 0.0013 & 0.0044 & 174 \\\\\n54 & 51593.7085 & 0.0002 & 0.0154 & 114 \\\\\n55 & 51593.7522 & 0.0002 & 0.0009 & 140 \\\\\n56 & 51593.8099 & 0.0003 & 0.0004 & 132 \\\\\n57 & 51593.8634 & 0.0006 & $-$0.0043 & 110 \\\\\n66 & 51594.3875 & 0.0004 & $-$0.0040 & 87 \\\\\n67 & 51594.4462 & 0.0004 & $-$0.0035 & 91 \\\\\n75 & 51594.9080 & 0.0019 & $-$0.0073 & 99 \\\\\n76 & 51594.9686 & 0.0009 & $-$0.0049 & 190 \\\\\n77 & 51595.0268 & 0.0005 & $-$0.0049 & 242 \\\\\n78 & 51595.0878 & 0.0018 & $-$0.0021 & 160 \\\\\n80 & 51595.2022 & 0.0011 & $-$0.0041 & 228 \\\\\n81 & 51595.2587 & 0.0006 & $-$0.0058 & 244 \\\\\n82 & 51595.3207 & 0.0017 & $-$0.0020 & 108 \\\\\n83 & 51595.3785 & 0.0031 & $-$0.0024 & 81 \\\\\n84 & 51595.4329 & 0.0004 & $-$0.0062 & 32 \\\\\n85 & 51595.4901 & 0.0006 & $-$0.0072 & 33 \\\\\n86 & 51595.5490 & 0.0006 & $-$0.0065 & 33 \\\\\n87 & 51595.6060 & 0.0005 & $-$0.0077 & 33 \\\\\n88 & 51595.6651 & 0.0005 & $-$0.0068 & 33 \\\\\n89 & 51595.7235 & 0.0011 & $-$0.0066 & 18 \\\\\n92 & 51595.8951 & 0.0015 & $-$0.0096 & 145 \\\\\n93 & 51595.9572 & 0.0007 & $-$0.0057 & 221 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451590.5503 + 0.058200 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (2000) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n94 & 51596.0145 & 0.0006 & $-$0.0067 & 262 \\\\\n95 & 51596.0739 & 0.0010 & $-$0.0054 & 238 \\\\\n96 & 51596.1334 & 0.0005 & $-$0.0041 & 233 \\\\\n97 & 51596.1916 & 0.0017 & $-$0.0042 & 151 \\\\\n99 & 51596.3039 & 0.0005 & $-$0.0082 & 258 \\\\\n111 & 51597.0047 & 0.0006 & $-$0.0058 & 273 \\\\\n112 & 51597.0656 & 0.0012 & $-$0.0031 & 136 \\\\\n113 & 51597.1237 & 0.0007 & $-$0.0032 & 176 \\\\\n114 & 51597.1800 & 0.0005 & $-$0.0051 & 284 \\\\\n115 & 51597.2382 & 0.0005 & $-$0.0051 & 258 \\\\\n116 & 51597.2946 & 0.0017 & $-$0.0069 & 155 \\\\\n117 & 51597.3544 & 0.0008 & $-$0.0053 & 281 \\\\\n127 & 51597.9382 & 0.0010 & $-$0.0035 & 220 \\\\\n128 & 51597.9992 & 0.0017 & $-$0.0007 & 227 \\\\\n129 & 51598.0581 & 0.0011 & $-$0.0000 & 251 \\\\\n130 & 51598.1168 & 0.0017 & 0.0005 & 215 \\\\\n144 & 51598.9327 & 0.0042 & 0.0015 & 111 \\\\\n145 & 51598.9897 & 0.0015 & 0.0003 & 266 \\\\\n147 & 51599.1070 & 0.0034 & 0.0013 & 123 \\\\\n150 & 51599.2834 & 0.0013 & 0.0030 & 29 \\\\\n151 & 51599.3418 & 0.0012 & 0.0032 & 45 \\\\\n161 & 51599.9262 & 0.0021 & 0.0057 & 294 \\\\\n162 & 51599.9854 & 0.0039 & 0.0067 & 198 \\\\\n163 & 51600.0434 & 0.0023 & 0.0065 & 155 \\\\\n198 & 51602.0826 & 0.0004 & 0.0087 & 284 \\\\\n199 & 51602.1420 & 0.0003 & 0.0098 & 294 \\\\\n200 & 51602.1993 & 0.0005 & 0.0090 & 277 \\\\\n201 & 51602.2573 & 0.0004 & 0.0088 & 365 \\\\\n202 & 51602.3145 & 0.0005 & 0.0078 & 349 \\\\\n204 & 51602.4315 & 0.0004 & 0.0083 & 82 \\\\\n205 & 51602.4898 & 0.0006 & 0.0085 & 89 \\\\\n213 & 51602.9608 & 0.0015 & 0.0139 & 157 \\\\\n214 & 51603.0182 & 0.0013 & 0.0131 & 192 \\\\\n215 & 51603.0760 & 0.0019 & 0.0126 & 109 \\\\\n216 & 51603.1274 & 0.0015 & 0.0058 & 203 \\\\\n217 & 51603.1921 & 0.0084 & 0.0124 & 60 \\\\\n247 & 51604.9273 & 0.0006 & 0.0015 & 294 \\\\\n248 & 51604.9843 & 0.0006 & 0.0004 & 286 \\\\\n249 & 51605.0433 & 0.0004 & 0.0011 & 284 \\\\\n250 & 51605.1009 & 0.0005 & 0.0006 & 280 \\\\\n251 & 51605.1575 & 0.0006 & $-$0.0010 & 276 \\\\\n252 & 51605.2103 & 0.0007 & $-$0.0065 & 293 \\\\\n253 & 51605.2672 & 0.0012 & $-$0.0077 & 227 \\\\\n254 & 51605.3258 & 0.0013 & $-$0.0073 & 30 \\\\\n255 & 51605.3832 & 0.0015 & $-$0.0082 & 25 \\\\\n256 & 51605.4440 & 0.0014 & $-$0.0056 & 33 \\\\\n257 & 51605.5025 & 0.0013 & $-$0.0053 & 34 \\\\\n258 & 51605.5640 & 0.0010 & $-$0.0020 & 31 \\\\\n259 & 51605.6188 & 0.0017 & $-$0.0054 & 22 \\\\\n266 & 51606.0209 & 0.0007 & $-$0.0107 & 120 \\\\\n267 & 51606.0805 & 0.0008 & $-$0.0093 & 116 \\\\\n269 & 51606.1935 & 0.0015 & $-$0.0126 & 120 \\\\\n271 & 51606.3342 & 0.0028 & 0.0117 & 125 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (2002).}\\label{tab:swumaoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52575.0555 & 0.0010 & 0.0090 & 66 \\\\\n4 & 52575.2830 & 0.0005 & 0.0035 & 88 \\\\\n17 & 52576.0405 & 0.0005 & 0.0035 & 90 \\\\\n18 & 52576.0953 & 0.0004 & $-$0.0000 & 90 \\\\\n19 & 52576.1532 & 0.0004 & $-$0.0004 & 126 \\\\\n20 & 52576.2109 & 0.0002 & $-$0.0009 & 467 \\\\\n21 & 52576.2686 & 0.0002 & $-$0.0015 & 479 \\\\\n22 & 52576.3280 & 0.0002 & $-$0.0004 & 404 \\\\\n35 & 52577.0803 & 0.0008 & $-$0.0055 & 53 \\\\\n36 & 52577.1405 & 0.0002 & $-$0.0036 & 90 \\\\\n37 & 52577.1984 & 0.0005 & $-$0.0039 & 261 \\\\\n38 & 52577.2506 & 0.0012 & $-$0.0100 & 335 \\\\\n39 & 52577.3140 & 0.0004 & $-$0.0049 & 377 \\\\\n53 & 52578.1293 & 0.0004 & $-$0.0053 & 90 \\\\\n54 & 52578.1874 & 0.0005 & $-$0.0054 & 87 \\\\\n55 & 52578.2432 & 0.0004 & $-$0.0080 & 90 \\\\\n56 & 52578.3021 & 0.0005 & $-$0.0073 & 85 \\\\\n89 & 52580.2331 & 0.0011 & 0.0009 & 90 \\\\\n90 & 52580.2875 & 0.0007 & $-$0.0030 & 90 \\\\\n91 & 52580.3446 & 0.0009 & $-$0.0041 & 49 \\\\\n106 & 52581.2179 & 0.0011 & $-$0.0049 & 131 \\\\\n122 & 52582.1591 & 0.0009 & 0.0040 & 88 \\\\\n123 & 52582.2170 & 0.0010 & 0.0037 & 88 \\\\\n124 & 52582.2748 & 0.0015 & 0.0033 & 88 \\\\\n139 & 52583.1558 & 0.0022 & 0.0103 & 102 \\\\\n140 & 52583.2123 & 0.0008 & 0.0084 & 103 \\\\\n141 & 52583.2716 & 0.0009 & 0.0095 & 274 \\\\\n142 & 52583.3287 & 0.0005 & 0.0083 & 287 \\\\\n155 & 52584.0859 & 0.0006 & 0.0080 & 89 \\\\\n156 & 52584.1450 & 0.0005 & 0.0089 & 102 \\\\\n157 & 52584.2018 & 0.0005 & 0.0074 & 102 \\\\\n158 & 52584.2592 & 0.0004 & 0.0066 & 102 \\\\\n159 & 52584.3179 & 0.0004 & 0.0070 & 310 \\\\\n173 & 52585.1398 & 0.0015 & 0.0132 & 85 \\\\\n174 & 52585.1912 & 0.0007 & 0.0063 & 101 \\\\\n175 & 52585.2476 & 0.0008 & 0.0044 & 86 \\\\\n207 & 52587.1061 & 0.0017 & $-$0.0016 & 101 \\\\\n208 & 52587.1767 & 0.0029 & 0.0107 & 102 \\\\\n209 & 52587.2253 & 0.0016 & 0.0011 & 101 \\\\\n210 & 52587.2765 & 0.0017 & $-$0.0060 & 46 \\\\\n224 & 52588.0826 & 0.0015 & $-$0.0156 & 204 \\\\\n226 & 52588.1977 & 0.0008 & $-$0.0170 & 345 \\\\\n227 & 52588.2582 & 0.0006 & $-$0.0148 & 455 \\\\\n228 & 52588.3172 & 0.0011 & $-$0.0141 & 325 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452575.0465 + 0.058267 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SW UMa (2006).}\\label{tab:swumaoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53997.6540 & 0.0012 & $-$0.0201 & 113 \\\\\n1 & 53997.7107 & 0.0026 & $-$0.0216 & 59 \\\\\n16 & 53998.6010 & 0.0006 & $-$0.0030 & 87 \\\\\n28 & 53999.3044 & 0.0004 & 0.0031 & 65 \\\\\n30 & 53999.4218 & 0.0002 & 0.0043 & 56 \\\\\n31 & 53999.4797 & 0.0002 & 0.0041 & 56 \\\\\n32 & 53999.5394 & 0.0002 & 0.0057 & 57 \\\\\n33 & 53999.5993 & 0.0004 & 0.0075 & 31 \\\\\n45 & 54000.2950 & 0.0005 & 0.0058 & 206 \\\\\n62 & 54001.2783 & 0.0006 & 0.0012 & 157 \\\\\n65 & 54001.4498 & 0.0004 & $-$0.0016 & 119 \\\\\n66 & 54001.5096 & 0.0002 & 0.0001 & 237 \\\\\n67 & 54001.5677 & 0.0002 & 0.0001 & 272 \\\\\n68 & 54001.6247 & 0.0003 & $-$0.0010 & 80 \\\\\n79 & 54002.2629 & 0.0002 & $-$0.0020 & 257 \\\\\n96 & 54003.2486 & 0.0020 & $-$0.0042 & 37 \\\\\n97 & 54003.3048 & 0.0018 & $-$0.0061 & 48 \\\\\n101 & 54003.5393 & 0.0004 & $-$0.0040 & 96 \\\\\n102 & 54003.5986 & 0.0003 & $-$0.0029 & 99 \\\\\n116 & 54004.4121 & 0.0003 & $-$0.0029 & 74 \\\\\n118 & 54004.5282 & 0.0004 & $-$0.0030 & 92 \\\\\n119 & 54004.5863 & 0.0002 & $-$0.0030 & 87 \\\\\n147 & 54006.2248 & 0.0021 & 0.0084 & 78 \\\\\n148 & 54006.2785 & 0.0004 & 0.0040 & 174 \\\\\n187 & 54008.5582 & 0.0006 & 0.0173 & 152 \\\\\n188 & 54008.6185 & 0.0003 & 0.0195 & 236 \\\\\n189 & 54008.6760 & 0.0003 & 0.0189 & 206 \\\\\n199 & 54009.2552 & 0.0006 & 0.0171 & 126 \\\\\n255 & 54012.4915 & 0.0006 & $-$0.0009 & 241 \\\\\n256 & 54012.5562 & 0.0008 & 0.0057 & 241 \\\\\n257 & 54012.6118 & 0.0008 & 0.0032 & 135 \\\\\n303 & 54015.2693 & 0.0021 & $-$0.0124 & 25 \\\\\n304 & 54015.3300 & 0.0019 & $-$0.0098 & 36 \\\\\n320 & 54016.2620 & 0.0010 & $-$0.0076 & 149 \\\\\n321 & 54016.3181 & 0.0007 & $-$0.0095 & 159 \\\\\n338 & 54017.3050 & 0.0011 & $-$0.0105 & 118 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453997.6742 + 0.058110 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BC Ursae Majoris}\\label{sec:bcuma}\\label{obj:bcuma}\n\n BC UMa was one of the classically known objects displaying\na diversity in the extent of (super)outbursts \\citep{rom64bcuma}.\nAlthough the SU UMa-type nature had long been suspected, the definite\ndetection of superhumps awaited the 1994 detection by M. Iida and\nconfirmation by C. Kunjaya (unpublished; vsnet-alert 154).\\footnote{\n$<$http:\/\/www.kusastro.kyoto-u.ac.jp\/vsnet\/DNe\/bcuma.html$>$.\n}\n\n \\citet{mae07bcuma} observed the 2003 superoutburst and obtained\n$P_{\\rm dot}$ = $+3.2(0.8) \\times 10^{-5}$. \\citet{mae07bcuma} also\ndetected double-wave ``early superhumps'' before ordinary superhumps\nappeared.\n\n We observed the 2000 and 2003 superoutbursts, the latter\nalso including the data used in \\citet{mae07bcuma}.\nThe times of superhump maxima are listed in tables\n\\ref{tab:bcumaoc2000} and \\ref{tab:bcumaoc2003}.\nThese epochs do not include maxima of early superhumps.\nThe times of maxima for the 2003 superoutburst systematically differ\nfrom those in \\citet{mae07bcuma}, probably reflecting the difference\nin the template superhump light curve. This difference was almost\nconstant during the outburst and did not affect the determination\nof the $P_{\\rm dot}$.\nThe both sets of $O-C$'s showed all stages A--C.\nWe measured $P_{\\rm dot}$ for the stage B:\n$+4.0(1.4) \\times 10^{-5}$ (2000, $16 \\le E \\le 99$) and\n$+4.2(0.8) \\times 10^{-5}$ (2003, $15 \\le E \\le 114$).\nThe 2003 data also include the times of superhump maxima during the rapidly\nfading stage. The maxima times for $123 \\le E \\le 189$ were very\nwell expressed by a constant period of 0.06418(2) d, 0.5 \\% shorter\nthan the mean superhump period. No apparent phase shift, corresponding\nto traditional late superhumps, was detected during\nthe rapid fading.\n\n A comparison of $O-C$ diagrams between different superoutbursts\nis shown in figure \\ref{fig:bcumacomp}. The duration of the stage B\nwas shorter in the 2003 superoutburst, corresponding to the maximum\nbrightness of the outbursts (11.1 mag for 2000 and 12.2 mag for 2003).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig152.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of BC UMa between different\n superoutbursts. A period of 0.06455 d was used to draw this figure.\n Approximate cycle counts ($E$) after the appearance of the\n superhumps were used.\n }\n \\label{fig:bcumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of BC UMa (2000).}\\label{tab:bcumaoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51639.5559 & 0.0017 & $-$0.0066 & 21 \\\\\n16 & 51640.5985 & 0.0003 & 0.0031 & 54 \\\\\n28 & 51641.3715 & 0.0004 & 0.0016 & 140 \\\\\n29 & 51641.4356 & 0.0004 & 0.0011 & 157 \\\\\n30 & 51641.4992 & 0.0002 & 0.0001 & 71 \\\\\n37 & 51641.9517 & 0.0009 & 0.0007 & 125 \\\\\n75 & 51644.4051 & 0.0005 & 0.0012 & 89 \\\\\n76 & 51644.4698 & 0.0007 & 0.0013 & 54 \\\\\n99 & 51645.9555 & 0.0006 & 0.0023 & 121 \\\\\n116 & 51647.0456 & 0.0010 & $-$0.0050 & 124 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451639.5625 + 0.064553 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of BC UMa (2003).}\\label{tab:bcumaoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52673.1330 & 0.0022 & $-$0.0100 & 46 \\\\\n1 & 52673.1935 & 0.0017 & $-$0.0139 & 49 \\\\\n2 & 52673.2615 & 0.0020 & $-$0.0104 & 50 \\\\\n3 & 52673.3256 & 0.0013 & $-$0.0107 & 48 \\\\\n15 & 52674.1088 & 0.0006 & $-$0.0010 & 55 \\\\\n16 & 52674.1742 & 0.0003 & $-$0.0001 & 71 \\\\\n17 & 52674.2381 & 0.0003 & $-$0.0007 & 118 \\\\\n18 & 52674.3021 & 0.0003 & $-$0.0011 & 73 \\\\\n19 & 52674.3678 & 0.0003 & 0.0002 & 155 \\\\\n21 & 52674.4977 & 0.0002 & 0.0011 & 66 \\\\\n46 & 52676.1075 & 0.0007 & $-$0.0006 & 56 \\\\\n47 & 52676.1718 & 0.0006 & $-$0.0007 & 68 \\\\\n48 & 52676.2371 & 0.0006 & 0.0001 & 151 \\\\\n49 & 52676.2992 & 0.0008 & $-$0.0022 & 51 \\\\\n50 & 52676.3645 & 0.0004 & $-$0.0014 & 116 \\\\\n51 & 52676.4290 & 0.0004 & $-$0.0014 & 67 \\\\\n52 & 52676.4943 & 0.0004 & $-$0.0006 & 61 \\\\\n62 & 52677.1400 & 0.0005 & 0.0006 & 171 \\\\\n63 & 52677.2053 & 0.0005 & 0.0014 & 180 \\\\\n64 & 52677.2688 & 0.0005 & 0.0005 & 197 \\\\\n65 & 52677.3346 & 0.0005 & 0.0018 & 135 \\\\\n67 & 52677.4656 & 0.0010 & 0.0039 & 42 \\\\\n78 & 52678.1753 & 0.0009 & 0.0045 & 107 \\\\\n79 & 52678.2432 & 0.0013 & 0.0079 & 56 \\\\\n80 & 52678.3011 & 0.0016 & 0.0014 & 91 \\\\\n81 & 52678.3691 & 0.0031 & 0.0050 & 88 \\\\\n108 & 52680.1131 & 0.0006 & 0.0085 & 178 \\\\\n109 & 52680.1789 & 0.0012 & 0.0099 & 73 \\\\\n110 & 52680.2412 & 0.0010 & 0.0077 & 145 \\\\\n111 & 52680.3075 & 0.0013 & 0.0096 & 66 \\\\\n112 & 52680.3713 & 0.0008 & 0.0089 & 80 \\\\\n113 & 52680.4372 & 0.0006 & 0.0103 & 132 \\\\\n114 & 52680.5004 & 0.0010 & 0.0090 & 81 \\\\\n123 & 52681.0754 & 0.0018 & 0.0040 & 81 \\\\\n124 & 52681.1420 & 0.0013 & 0.0061 & 75 \\\\\n125 & 52681.2068 & 0.0002 & 0.0064 & 300 \\\\\n126 & 52681.2710 & 0.0012 & 0.0061 & 167 \\\\\n128 & 52681.3981 & 0.0006 & 0.0044 & 67 \\\\\n129 & 52681.4609 & 0.0013 & 0.0027 & 51 \\\\\n130 & 52681.5277 & 0.0010 & 0.0051 & 48 \\\\\n139 & 52682.1077 & 0.0020 & 0.0049 & 102 \\\\\n142 & 52682.2967 & 0.0020 & 0.0005 & 63 \\\\\n143 & 52682.3592 & 0.0015 & $-$0.0015 & 84 \\\\\n154 & 52683.0702 & 0.0014 & 0.0005 & 113 \\\\\n155 & 52683.1338 & 0.0017 & $-$0.0004 & 173 \\\\\n156 & 52683.1954 & 0.0011 & $-$0.0032 & 326 \\\\\n157 & 52683.2625 & 0.0006 & $-$0.0006 & 265 \\\\\n158 & 52683.3239 & 0.0010 & $-$0.0036 & 150 \\\\\n159 & 52683.3930 & 0.0016 & 0.0010 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452673.1429 + 0.064459 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of BC UMa (2003). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n160 & 52683.4547 & 0.0010 & $-$0.0017 & 55 \\\\\n169 & 52684.0316 & 0.0020 & $-$0.0049 & 102 \\\\\n170 & 52684.0933 & 0.0020 & $-$0.0078 & 74 \\\\\n175 & 52684.4138 & 0.0015 & $-$0.0095 & 45 \\\\\n176 & 52684.4805 & 0.0034 & $-$0.0073 & 44 \\\\\n187 & 52685.1823 & 0.0012 & $-$0.0145 & 123 \\\\\n188 & 52685.2474 & 0.0052 & $-$0.0139 & 129 \\\\\n189 & 52685.3155 & 0.0020 & $-$0.0103 & 130 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{BZ Ursae Majoris}\\label{sec:bzuma}\\label{obj:bzuma}\n\n Although BZ UMa had long been suspected to be an SU UMa-type dwarf\nnova, no definite superoutbursts were recorded before 2007\n(\\cite{jur94bzuma}; \\cite{rin90bzuma}).\nThe first-ever recorded superoutburst occurred in 2007.\nThe times of superhump maxima during this superoutburst are listed\nin table \\ref{tab:bzumaoc2007}. We included hump maxima during the\npost-superoutburst stage, which will be discussed later.\nDuring the first night of the observation ($E \\le 4$), we observed\nthe growing stage of superhumps. The superhump period was almost\nconstant for $19 \\le E \\le 64$ with\n$P_{\\rm dot}$ = $+3.6(3.3) \\times 10^{-5}$. We regard this as\nthe stage B. An discontinuous transition to a shorter period\n(stage C, $72 \\le E \\le 138$) occurred. The mean periods for the stages\nB and C were 0.07018(1) d and 0.06979(1) d, 3.3 \\% and 2.6 \\% longer than\nthe orbital period, respectively. The superhump period further experienced\na discontinuous shortening after $E=138$ to 0.06968(5) d, 2.4 \\% longer than\nthe orbital period.\nBZ UMa is a rare SU UMa-type object around $P_{\\rm SH} = $0.07 d without\na distinct segment having a positive $P_{\\rm dot}$. This feature may be\nrelated to the extreme rarity of its superoutbursts. Furthermore,\nthe present superoutburst was accompanied by a slow rise before superhumps\ngrew, suggesting that the outburst was an ``inside-out'' type\n(vsnet-alert 9300), rarely met in SU UMa-type dwarf novae.\nThere was also a suggestion of the presence of a precursor-type\noutburst (figure \\ref{fig:bzumaoc}).\nThese features possibly suggest that the 3:1 resonance is difficult to\nachieve in this system, and the superhumps were critically excited during\nthis superoutburst, likely leaving little mass beyond the 3:1 resonance.\n\n After $E = 167$ (around the start of the post-superoutburst stage),\nsecondary hump maxima were sometimes present, which later became stronger\nthan the original hump maxima. The times of these secondary humps are\nlisted in table \\ref{tab:bzumaoc2007b}, giving $O-C$'s using the same\nephemeris as in the earlier maxima. These data indicated that\npost-superoutburst superhumps persisted at least for $\\sim$150 cycles,\nor $\\sim$10 d.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig153.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps BZ UMa (2007).\n (Upper): $O-C$ diagram. The values of $O-C$'s are different from\n those listed in table \\ref{tab:j0824oc2007} and were calculated from\n a linear fit for the times of superhumps for $19 \\le E \\le 64$.\n The curve represents a quadratic fit with $P_{\\rm dot}$\n = $+3.2 \\times 10^{-5}$.\n (Lower): Light curve. The rise of the superoutburst was very slow,\n apparently accompanied by a stagnation phase (BJD 2454201.5--2454201.8).\n There was a relatively rapid fading probably corresponding to a\n precursor outburst (BJD 2454203.3--2454203.7)}\n \\label{fig:bzumaoc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of BZ UMa (2007).}\\label{tab:bzumaoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54204.3391 & 0.0010 & $-$0.0185 & 41 \\\\\n1 & 54204.4092 & 0.0009 & $-$0.0182 & 111 \\\\\n2 & 54204.4748 & 0.0013 & $-$0.0224 & 82 \\\\\n3 & 54204.5525 & 0.0006 & $-$0.0145 & 43 \\\\\n4 & 54204.6245 & 0.0006 & $-$0.0124 & 60 \\\\\n5 & 54204.6943 & 0.0003 & $-$0.0124 & 26 \\\\\n6 & 54204.7647 & 0.0002 & $-$0.0118 & 27 \\\\\n7 & 54204.8343 & 0.0002 & $-$0.0121 & 26 \\\\\n15 & 54205.3965 & 0.0002 & $-$0.0085 & 491 \\\\\n16 & 54205.4671 & 0.0002 & $-$0.0077 & 512 \\\\\n17 & 54205.5368 & 0.0002 & $-$0.0078 & 452 \\\\\n18 & 54205.6073 & 0.0001 & $-$0.0072 & 340 \\\\\n19 & 54205.6786 & 0.0002 & $-$0.0058 & 163 \\\\\n20 & 54205.7483 & 0.0002 & $-$0.0058 & 156 \\\\\n21 & 54205.8185 & 0.0005 & $-$0.0055 & 37 \\\\\n23 & 54205.9590 & 0.0002 & $-$0.0046 & 101 \\\\\n24 & 54206.0295 & 0.0002 & $-$0.0040 & 102 \\\\\n29 & 54206.3789 & 0.0003 & $-$0.0037 & 502 \\\\\n30 & 54206.4492 & 0.0003 & $-$0.0032 & 422 \\\\\n31 & 54206.5231 & 0.0005 & 0.0008 & 220 \\\\\n32 & 54206.5906 & 0.0005 & $-$0.0016 & 396 \\\\\n33 & 54206.6610 & 0.0003 & $-$0.0010 & 483 \\\\\n34 & 54206.7317 & 0.0004 & $-$0.0001 & 278 \\\\\n35 & 54206.8012 & 0.0003 & $-$0.0005 & 139 \\\\\n43 & 54207.3620 & 0.0003 & 0.0017 & 250 \\\\\n44 & 54207.4336 & 0.0004 & 0.0035 & 275 \\\\\n45 & 54207.5022 & 0.0006 & 0.0023 & 150 \\\\\n46 & 54207.5729 & 0.0006 & 0.0031 & 249 \\\\\n47 & 54207.6417 & 0.0007 & 0.0021 & 272 \\\\\n48 & 54207.7126 & 0.0007 & 0.0032 & 197 \\\\\n49 & 54207.7822 & 0.0010 & 0.0029 & 49 \\\\\n52 & 54207.9923 & 0.0005 & 0.0035 & 57 \\\\\n57 & 54208.3454 & 0.0003 & 0.0074 & 207 \\\\\n58 & 54208.4159 & 0.0004 & 0.0082 & 438 \\\\\n59 & 54208.4864 & 0.0003 & 0.0088 & 428 \\\\\n60 & 54208.5581 & 0.0015 & 0.0107 & 92 \\\\\n61 & 54208.6262 & 0.0005 & 0.0090 & 72 \\\\\n62 & 54208.6954 & 0.0005 & 0.0083 & 89 \\\\\n63 & 54208.7655 & 0.0006 & 0.0086 & 55 \\\\\n64 & 54208.8365 & 0.0006 & 0.0097 & 53 \\\\\n72 & 54209.3952 & 0.0003 & 0.0098 & 611 \\\\\n73 & 54209.4659 & 0.0003 & 0.0106 & 416 \\\\\n81 & 54210.0235 & 0.0002 & 0.0096 & 252 \\\\\n86 & 54210.3711 & 0.0002 & 0.0081 & 266 \\\\\n87 & 54210.4425 & 0.0004 & 0.0096 & 210 \\\\\n88 & 54210.5127 & 0.0003 & 0.0100 & 142 \\\\\n89 & 54210.5803 & 0.0004 & 0.0078 & 43 \\\\\n90 & 54210.6500 & 0.0003 & 0.0077 & 50 \\\\\n91 & 54210.7220 & 0.0003 & 0.0098 & 131 \\\\\n100 & 54211.3510 & 0.0006 & 0.0103 & 134 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454204.3575 + 0.069831 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of BZ UMa (2007). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n101 & 54211.4202 & 0.0005 & 0.0096 & 276 \\\\\n102 & 54211.4893 & 0.0005 & 0.0089 & 323 \\\\\n103 & 54211.5581 & 0.0006 & 0.0079 & 229 \\\\\n104 & 54211.6288 & 0.0004 & 0.0088 & 136 \\\\\n105 & 54211.6970 & 0.0005 & 0.0072 & 12 \\\\\n106 & 54211.7692 & 0.0010 & 0.0095 & 7 \\\\\n115 & 54212.3952 & 0.0005 & 0.0070 & 496 \\\\\n116 & 54212.4636 & 0.0005 & 0.0056 & 403 \\\\\n117 & 54212.5356 & 0.0009 & 0.0078 & 113 \\\\\n118 & 54212.6065 & 0.0004 & 0.0088 & 154 \\\\\n119 & 54212.6754 & 0.0004 & 0.0079 & 77 \\\\\n129 & 54213.3729 & 0.0005 & 0.0071 & 389 \\\\\n130 & 54213.4424 & 0.0011 & 0.0068 & 285 \\\\\n131 & 54213.5158 & 0.0012 & 0.0103 & 109 \\\\\n132 & 54213.5816 & 0.0004 & 0.0064 & 103 \\\\\n138 & 54214.0024 & 0.0006 & 0.0081 & 196 \\\\\n159 & 54215.4565 & 0.0017 & $-$0.0042 & 109 \\\\\n160 & 54215.5306 & 0.0017 & 0.0000 & 33 \\\\\n172 & 54216.3636 & 0.0006 & $-$0.0049 & 38 \\\\\n173 & 54216.4340 & 0.0008 & $-$0.0043 & 127 \\\\\n188 & 54217.4801 & 0.0019 & $-$0.0057 & 83 \\\\\n201 & 54218.3918 & 0.0008 & $-$0.0019 & 76 \\\\\n202 & 54218.4608 & 0.0005 & $-$0.0027 & 84 \\\\\n203 & 54218.5288 & 0.0005 & $-$0.0045 & 88 \\\\\n204 & 54218.5896 & 0.0010 & $-$0.0136 & 70 \\\\\n209 & 54218.9454 & 0.0009 & $-$0.0069 & 53 \\\\\n210 & 54219.0132 & 0.0007 & $-$0.0089 & 73 \\\\\n215 & 54219.3614 & 0.0046 & $-$0.0099 & 58 \\\\\n216 & 54219.4333 & 0.0005 & $-$0.0078 & 205 \\\\\n217 & 54219.5048 & 0.0006 & $-$0.0062 & 40 \\\\\n224 & 54219.9837 & 0.0006 & $-$0.0161 & 162 \\\\\n225 & 54220.0630 & 0.0009 & $-$0.0066 & 128 \\\\\n231 & 54220.4672 & 0.0019 & $-$0.0214 & 52 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Secondary Maxima of BZ UMa (2007).}\\label{tab:bzumaoc2007b}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n167 & 54216.0487 & 0.0004 & 0.0291 & 193 \\\\\n181 & 54217.0363 & 0.0024 & 0.0391 & 64 \\\\\n187 & 54217.4455 & 0.0009 & 0.0294 & 84 \\\\\n188 & 54217.5202 & 0.0015 & 0.0342 & 54 \\\\\n189 & 54217.5908 & 0.0018 & 0.0350 & 46 \\\\\n201 & 54218.4225 & 0.0014 & 0.0287 & 88 \\\\\n202 & 54218.4932 & 0.0018 & 0.0295 & 87 \\\\\n224 & 54220.0259 & 0.0007 & 0.0259 & 131 \\\\\n229 & 54220.3687 & 0.0032 & 0.0196 & 56 \\\\\n230 & 54220.4371 & 0.0059 & 0.0181 & 50 \\\\\n244 & 54221.4154 & 0.0006 & 0.0188 & 287 \\\\\n245 & 54221.4962 & 0.0011 & 0.0297 & 244 \\\\\n246 & 54221.5601 & 0.0013 & 0.0238 & 88 \\\\\n259 & 54222.4642 & 0.0050 & 0.0201 & 88 \\\\\n260 & 54222.5345 & 0.0053 & 0.0205 & 46 \\\\\n272 & 54223.3672 & 0.0016 & 0.0153 & 108 \\\\\n287 & 54224.4043 & 0.0049 & 0.0049 & 21 \\\\\n315 & 54226.3639 & 0.0020 & 0.0092 & 80 \\\\\n316 & 54226.4287 & 0.0014 & 0.0042 & 144 \\\\\n317 & 54226.4951 & 0.0021 & 0.0007 & 88 \\\\\n318 & 54226.5706 & 0.0053 & 0.0064 & 47 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454204.3576 + 0.069832 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CI Ursae Majoris}\\label{obj:ciuma}\n\n CI UMa was discovered as a dwarf nova by \\citet{gor72ciuma}.\n\\citet{nog97ciuma} observed the 1995 superoutburst and reported\nthe superhump period. This observation was not long enough to determine\nthe period derivative. Although \\citet{nog97ciuma} suggested a supercycle\nof $\\sim$ 140 d based on the shortest interval between apparent superoutbursts\n\\citep{kol79cpdraciuma}, recent observations suggest that superoutbursts\noccur less regularly.\n\n We further observed the 2001, 2003 and 2006 superoutburst\n(tables \\ref{tab:ciumaoc2001}, \\ref{tab:ciumaoc2003},\n\\ref{tab:ciumaoc2006}).\nThe 2001 observation probably covered only the later part of the\nsuperoutburst and likely recorded a stage B--C transition.\nThe 2003 $O-C$ diagram showed a clear stage B--C transition\n(cf. figure \\ref{fig:octrans}).\nWe determined $P_{\\rm dot}$ = $+6.4(1.2) \\times 10^{-5}$ for $E \\le 93$.\nThe 2006 observation recorded the terminal stage of the superoutburst\n(stage C superhumps).\nA combined $O-C$ diagram is presented in figure \\ref{fig:ciumacomp}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig154.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of CI UMa between different\n superoutbursts. A period of 0.06264 d was used to draw this figure.\n Since the start of the outbursts were not clearly defined, the $O-C$\n diagrams were shifted to best match the 2003 one.\n }\n \\label{fig:ciumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CI UMa (2001).}\\label{tab:ciumaoc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52214.2376 & 0.0010 & 0.0026 & 115 \\\\\n1 & 52214.3000 & 0.0008 & 0.0023 & 118 \\\\\n31 & 52216.1772 & 0.0077 & $-$0.0011 & 31 \\\\\n32 & 52216.2460 & 0.0044 & 0.0050 & 32 \\\\\n64 & 52218.2364 & 0.0024 & $-$0.0105 & 71 \\\\\n65 & 52218.3018 & 0.0037 & $-$0.0077 & 113 \\\\\n112 & 52221.2651 & 0.0096 & 0.0093 & 31 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452214.2350 + 0.062686 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CI UMa (2003).}\\label{tab:ciumaoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52739.3819 & 0.0006 & $-$0.0012 & 64 \\\\\n1 & 52739.4469 & 0.0006 & 0.0012 & 64 \\\\\n2 & 52739.5067 & 0.0006 & $-$0.0017 & 57 \\\\\n10 & 52740.0071 & 0.0008 & $-$0.0022 & 84 \\\\\n14 & 52740.2572 & 0.0030 & $-$0.0027 & 70 \\\\\n33 & 52741.4455 & 0.0005 & $-$0.0042 & 58 \\\\\n59 & 52743.0778 & 0.0005 & $-$0.0000 & 144 \\\\\n60 & 52743.1390 & 0.0005 & $-$0.0015 & 145 \\\\\n61 & 52743.2024 & 0.0009 & $-$0.0007 & 99 \\\\\n80 & 52744.3972 & 0.0010 & 0.0043 & 43 \\\\\n81 & 52744.4589 & 0.0011 & 0.0034 & 45 \\\\\n89 & 52744.9599 & 0.0005 & 0.0034 & 133 \\\\\n90 & 52745.0222 & 0.0004 & 0.0030 & 105 \\\\\n91 & 52745.0871 & 0.0006 & 0.0054 & 204 \\\\\n92 & 52745.1490 & 0.0008 & 0.0046 & 264 \\\\\n93 & 52745.2116 & 0.0011 & 0.0046 & 205 \\\\\n96 & 52745.3967 & 0.0013 & 0.0018 & 44 \\\\\n97 & 52745.4582 & 0.0011 & 0.0007 & 41 \\\\\n107 & 52746.0820 & 0.0009 & $-$0.0017 & 156 \\\\\n108 & 52746.1420 & 0.0018 & $-$0.0043 & 228 \\\\\n109 & 52746.2122 & 0.0022 & 0.0032 & 216 \\\\\n112 & 52746.4000 & 0.0023 & 0.0032 & 43 \\\\\n113 & 52746.4560 & 0.0020 & $-$0.0035 & 45 \\\\\n128 & 52747.3937 & 0.0030 & $-$0.0051 & 45 \\\\\n144 & 52748.3985 & 0.0019 & $-$0.0023 & 42 \\\\\n145 & 52748.4556 & 0.0012 & $-$0.0078 & 66 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452739.3831 + 0.062622 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CI UMa (2006).}\\label{tab:ciumaoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53936.4310 & 0.0003 & 0.0006 & 90 \\\\\n1 & 53936.4922 & 0.0003 & $-$0.0007 & 89 \\\\\n15 & 53937.3686 & 0.0008 & 0.0009 & 54 \\\\\n16 & 53937.4293 & 0.0006 & $-$0.0008 & 65 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453936.4304 + 0.062479 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CY Ursae Majoris}\\label{obj:cyuma}\n\n \\citet{har95cyuma} observed the 1995 superoutburst and reported\na global $P_{\\rm dot}$ of $-5.8 \\times 10^{-5}$. Their $O-C$ diagram,\nhowever, also can be interpreted as a transition from a longer to\na shorter period (stage B--C transition) during the late stage of\nthe superoutburst.\nUsing the earlier part ($E \\le 73$) of their table of superhump maxima,\nwe obtained $P_{\\rm dot}$ = $+2.7(1.0) \\times 10^{-5}$.\n\n We analyzed the 1998 AAVSO data and found a clear stage B--C\ntransition (table \\ref{tab:cyumaoc1998}). The parameters are given\nin table \\ref{tab:perlist}.\nOur 1999 observation \\citep{kat99cyuma} did not show a clear tendency of\na period decrease, probably because of the insufficient data coverage\n(table \\ref{tab:cyumaoc1999}).\nThe 2009 superoutburst was well-observed during the middle-to-late\nstage (table \\ref{tab:cyumaoc2009}). A clear stage B--C transition\nwas recorded.\nA comparison of $O-C$ diagrams between different superoutbursts\nis shown in figure \\ref{fig:cyumacomp}. There was a possible slight\ndifference in behavior during the stage B between different superoutbursts.\nObservations at early epochs of superoutbursts are wanted.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig155.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of CY UMa between different\n superoutbursts. A period of 0.07212 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:cyumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CY UMa (1998).}\\label{tab:cyumaoc1998}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50882.5614 & 0.0140 & $-$0.0176 & 42 \\\\\n1 & 50882.6379 & 0.0040 & $-$0.0131 & 41 \\\\\n40 & 50885.4614 & 0.0009 & 0.0003 & 28 \\\\\n41 & 50885.5363 & 0.0008 & 0.0032 & 28 \\\\\n42 & 50885.6176 & 0.0069 & 0.0125 & 15 \\\\\n52 & 50886.3333 & 0.0009 & 0.0077 & 28 \\\\\n53 & 50886.4012 & 0.0009 & 0.0035 & 28 \\\\\n54 & 50886.4730 & 0.0012 & 0.0032 & 28 \\\\\n55 & 50886.5477 & 0.0009 & 0.0059 & 28 \\\\\n56 & 50886.6237 & 0.0010 & 0.0099 & 28 \\\\\n122 & 50891.3689 & 0.0023 & $-$0.0003 & 28 \\\\\n123 & 50891.4404 & 0.0009 & $-$0.0009 & 28 \\\\\n124 & 50891.5116 & 0.0022 & $-$0.0017 & 28 \\\\\n153 & 50893.5936 & 0.0012 & $-$0.0093 & 20 \\\\\n154 & 50893.6716 & 0.0053 & $-$0.0033 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450882.5789 + 0.072052 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CY UMa (1999).}\\label{tab:cyumaoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51222.9702 & 0.0003 & 0.0002 & 140 \\\\\n1 & 51223.0417 & 0.0004 & $-$0.0005 & 102 \\\\\n14 & 51223.9806 & 0.0005 & $-$0.0004 & 124 \\\\\n29 & 51225.0659 & 0.0008 & 0.0017 & 90 \\\\\n42 & 51226.0010 & 0.0011 & $-$0.0019 & 105 \\\\\n43 & 51226.0761 & 0.0007 & 0.0009 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451222.9699 + 0.072216 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of CY UMa (2009).}\\label{tab:cyumaoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54917.9589 & 0.0012 & $-$0.0063 & 95 \\\\\n1 & 54918.0313 & 0.0006 & $-$0.0058 & 137 \\\\\n2 & 54918.1025 & 0.0004 & $-$0.0065 & 102 \\\\\n3 & 54918.1735 & 0.0006 & $-$0.0075 & 121 \\\\\n15 & 54919.0415 & 0.0005 & $-$0.0026 & 131 \\\\\n16 & 54919.1154 & 0.0009 & $-$0.0006 & 139 \\\\\n17 & 54919.1855 & 0.0003 & $-$0.0024 & 141 \\\\\n18 & 54919.2573 & 0.0004 & $-$0.0026 & 150 \\\\\n31 & 54920.1967 & 0.0006 & 0.0018 & 136 \\\\\n32 & 54920.2688 & 0.0009 & 0.0019 & 104 \\\\\n34 & 54920.4138 & 0.0004 & 0.0031 & 527 \\\\\n35 & 54920.4858 & 0.0004 & 0.0031 & 528 \\\\\n37 & 54920.6311 & 0.0005 & 0.0046 & 67 \\\\\n44 & 54921.1328 & 0.0005 & 0.0028 & 123 \\\\\n47 & 54921.3518 & 0.0005 & 0.0060 & 67 \\\\\n48 & 54921.4227 & 0.0004 & 0.0051 & 456 \\\\\n49 & 54921.4948 & 0.0004 & 0.0052 & 522 \\\\\n51 & 54921.6373 & 0.0004 & 0.0038 & 47 \\\\\n61 & 54922.3542 & 0.0004 & 0.0014 & 378 \\\\\n62 & 54922.4268 & 0.0005 & 0.0021 & 423 \\\\\n63 & 54922.4966 & 0.0009 & 0.0000 & 474 \\\\\n64 & 54922.5703 & 0.0006 & 0.0018 & 183 \\\\\n65 & 54922.6445 & 0.0008 & 0.0041 & 47 \\\\\n74 & 54923.2896 & 0.0004 & 0.0018 & 120 \\\\\n75 & 54923.3667 & 0.0005 & 0.0069 & 244 \\\\\n76 & 54923.4351 & 0.0007 & 0.0034 & 208 \\\\\n77 & 54923.5052 & 0.0010 & 0.0017 & 196 \\\\\n78 & 54923.5795 & 0.0006 & 0.0040 & 191 \\\\\n79 & 54923.6506 & 0.0015 & 0.0032 & 65 \\\\\n85 & 54924.0760 & 0.0007 & $-$0.0030 & 131 \\\\\n86 & 54924.1506 & 0.0013 & $-$0.0004 & 174 \\\\\n87 & 54924.2254 & 0.0020 & 0.0025 & 113 \\\\\n88 & 54924.2920 & 0.0019 & $-$0.0028 & 72 \\\\\n90 & 54924.4383 & 0.0010 & $-$0.0004 & 133 \\\\\n91 & 54924.5132 & 0.0008 & 0.0026 & 128 \\\\\n92 & 54924.5828 & 0.0009 & 0.0003 & 85 \\\\\n102 & 54925.3024 & 0.0017 & 0.0006 & 88 \\\\\n104 & 54925.4399 & 0.0010 & $-$0.0058 & 136 \\\\\n105 & 54925.5109 & 0.0016 & $-$0.0066 & 137 \\\\\n106 & 54925.5814 & 0.0016 & $-$0.0081 & 134 \\\\\n116 & 54926.2962 & 0.0014 & $-$0.0126 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454917.9652 + 0.071927 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DV Ursae Majoris}\\label{obj:dvuma}\n\n This eclipsing SU UMa-type dwarf nova has been well documented\n(\\cite{pat00dvuma}, \\cite{nog01dvuma}). Relatively large negative\nperiod derivatives have been reported. We summarize our observations\nof five superoutbursts (1997, 1999, 2002, 2005 and 2007).\nThe maxima were determined from observations\noutside the eclipses, as described in V2051 Oph.\n\n The times of superhump maxima for the 1997 superoutburst\n(table \\ref{tab:dvumaoc1997}) were determined by using a combination of\nthe AAVSO and data in \\citet{nog01dvuma}.\nWe also incorporated times of superhump maxima reported in\n\\citet{pat00dvuma}. Although the AAVSO data we analyzed were included\nin \\citet{pat00dvuma}, we presented our new determinations because\n\\citet{pat00dvuma} gave epochs only to 0.001 d. Since the mean difference\nbetween our measurements and those by \\citet{pat00dvuma} was negligible\n(0.0010(9) d), we did not make a systematic correction between them.\nThe combined result showed negative $O-C$'s for the earliest stage\n(stage A, $E \\le 5$), followed\nby a segment of relatively constant period (stage B, $7 \\le E \\le 79$),\nthen by a transition to a shorter period (stage C, $104 \\le E \\le 184$).\nThe mean superhump periods of the stages B and C\nwere 0.08878(4) d and 0.08840(3) d, respectively. The $P_{\\rm dot}$\nfor the stage B was $-0.9(4.0) \\times 10^{-5}$.\n\n During The 1999 superoutburst (table \\ref{tab:dvumaoc1999}),\nthere was a discontinuous shortening (stage B to C)\nof the period after $E = 80$ as in the 1997 superoutburst.\nThe mean periods before and after this transitions were\n0.08893(3) d and 0.08836(8) d, respectively. The $P_{\\rm dot}$\nbefore the transition was $-4.7(3.4) \\times 10^{-5}$.\nThe 2002 superoutburst showed a similar pattern of $O-C$ variation\n(table \\ref{tab:dvumaoc2002}), although the observations were rather\nsparse.\n\n The 2005 and 2007 observations well\ncovered the growing stage of superhumps (tables \\ref{tab:dvumaoc2005}\nand \\ref{tab:dvumaoc2007}).\nAs in other systems and as in 1997 superoutburst, the $O-C$'s of this\nevolutionary stage were negative.\nRegarding the 2007 superoutburst, we can determine\n$P_{\\rm dot}$ = $-1.7(1.8) \\times 10^{-5}$ after this evolutionary stage,\ncorresponding to the stage B of the 1997 superoutburst.\nIn summary, we did not find strong difference in the behavior of period\nvariation between different superoutbursts (figure \\ref{fig:dvumacomp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig156.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of DV UMa between different\n superoutbursts. The $O-C$'s were calculated against a period of\n 0.0888 d. Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:dvumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (1997).}\\label{tab:dvumaoc1997}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50548.4270 & -- & $-$0.0395 & 0 \\\\\n1 & 50548.5140 & -- & $-$0.0411 & 0 \\\\\n2 & 50548.6050 & -- & $-$0.0386 & 0 \\\\\n3 & 50548.6890 & -- & $-$0.0432 & 0 \\\\\n4 & 50548.7800 & -- & $-$0.0408 & 0 \\\\\n5 & 50548.8580 & -- & $-$0.0513 & 0 \\\\\n7 & 50549.0757 & 0.0043 & $-$0.0107 & 80 \\\\\n8 & 50549.1712 & 0.0015 & $-$0.0038 & 92 \\\\\n11 & 50549.4470 & -- & 0.0063 & 0 \\\\\n12 & 50549.5330 & -- & 0.0037 & 0 \\\\\n22 & 50550.4146 & 0.0007 & $-$0.0003 & 47 \\\\\n22 & 50550.4100 & -- & $-$0.0049 & 0 \\\\\n23 & 50550.5031 & 0.0007 & $-$0.0004 & 41 \\\\\n23 & 50550.5000 & -- & $-$0.0035 & 0 \\\\\n33 & 50551.3900 & -- & 0.0009 & 0 \\\\\n33 & 50551.3929 & 0.0020 & 0.0038 & 41 \\\\\n34 & 50551.4810 & -- & 0.0034 & 0 \\\\\n34 & 50551.4854 & 0.0017 & 0.0078 & 41 \\\\\n37 & 50551.7490 & -- & 0.0057 & 0 \\\\\n38 & 50551.8440 & -- & 0.0121 & 0 \\\\\n40 & 50552.0186 & 0.0005 & 0.0096 & 74 \\\\\n41 & 50552.1068 & 0.0005 & 0.0092 & 74 \\\\\n44 & 50552.3680 & -- & 0.0047 & 0 \\\\\n46 & 50552.5400 & -- & $-$0.0004 & 0 \\\\\n47 & 50552.6330 & -- & 0.0040 & 0 \\\\\n55 & 50553.3418 & 0.0007 & 0.0043 & 40 \\\\\n55 & 50553.3440 & -- & 0.0065 & 0 \\\\\n56 & 50553.4313 & 0.0008 & 0.0053 & 43 \\\\\n56 & 50553.4340 & -- & 0.0080 & 0 \\\\\n58 & 50553.6120 & -- & 0.0089 & 0 \\\\\n66 & 50554.3230 & -- & 0.0114 & 0 \\\\\n66 & 50554.3287 & 0.0034 & 0.0171 & 32 \\\\\n67 & 50554.4130 & -- & 0.0128 & 0 \\\\\n67 & 50554.4160 & 0.0032 & 0.0158 & 41 \\\\\n68 & 50554.5070 & -- & 0.0182 & 0 \\\\\n68 & 50554.5050 & 0.0013 & 0.0162 & 41 \\\\\n69 & 50554.5880 & -- & 0.0107 & 0 \\\\\n70 & 50554.6780 & -- & 0.0121 & 0 \\\\\n71 & 50554.7680 & -- & 0.0135 & 0 \\\\\n72 & 50554.8560 & -- & 0.0130 & 0 \\\\\n78 & 50555.3872 & 0.0012 & 0.0128 & 47 \\\\\n78 & 50555.3830 & -- & 0.0086 & 0 \\\\\n79 & 50555.4749 & 0.0018 & 0.0119 & 47 \\\\\n79 & 50555.4730 & -- & 0.0100 & 0 \\\\\n100 & 50557.3390 & 0.0014 & 0.0162 & 37 \\\\\n101 & 50557.4279 & 0.0020 & 0.0166 & 43 \\\\\n102 & 50557.5135 & 0.0015 & 0.0136 & 20 \\\\\n104 & 50557.6910 & -- & 0.0140 & 0 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450548.4665 + 0.088563 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{$^{c}$ $N=0$ refers to \\citet{pat00dvuma}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (1997). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n105 & 50557.7800 & -- & 0.0144 & 0 \\\\\n106 & 50557.8670 & -- & 0.0128 & 0 \\\\\n112 & 50558.3994 & 0.0014 & 0.0139 & 43 \\\\\n112 & 50558.3990 & -- & 0.0135 & 0 \\\\\n123 & 50559.3555 & 0.0053 & $-$0.0042 & 34 \\\\\n134 & 50560.3410 & 0.0116 & 0.0071 & 29 \\\\\n138 & 50560.6870 & -- & $-$0.0012 & 0 \\\\\n139 & 50560.7840 & -- & 0.0073 & 0 \\\\\n149 & 50561.6720 & -- & 0.0097 & 0 \\\\\n150 & 50561.7590 & -- & 0.0081 & 0 \\\\\n160 & 50562.6430 & -- & 0.0065 & 0 \\\\\n161 & 50562.7300 & -- & 0.0049 & 0 \\\\\n164 & 50562.9995 & 0.0053 & 0.0087 & 38 \\\\\n171 & 50563.6120 & -- & 0.0013 & 0 \\\\\n172 & 50563.7010 & -- & 0.0017 & 0 \\\\\n173 & 50563.7890 & -- & 0.0011 & 0 \\\\\n176 & 50564.0658 & 0.0040 & 0.0123 & 76 \\\\\n183 & 50564.6700 & -- & $-$0.0035 & 0 \\\\\n184 & 50564.7620 & -- & $-$0.0000 & 0 \\\\\n194 & 50565.6190 & -- & $-$0.0287 & 0 \\\\\n206 & 50566.6600 & -- & $-$0.0504 & 0 \\\\\n207 & 50566.7490 & -- & $-$0.0500 & 0 \\\\\n208 & 50566.8320 & -- & $-$0.0555 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (1999).}\\label{tab:dvumaoc1999}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51521.2279 & 0.0037 & $-$0.0063 & 80 \\\\\n1 & 51521.3090 & 0.0010 & $-$0.0138 & 121 \\\\\n9 & 51522.0272 & 0.0028 & $-$0.0050 & 85 \\\\\n10 & 51522.1122 & 0.0011 & $-$0.0086 & 140 \\\\\n11 & 51522.2010 & 0.0009 & $-$0.0085 & 132 \\\\\n12 & 51522.2921 & 0.0010 & $-$0.0061 & 142 \\\\\n22 & 51523.1879 & 0.0007 & 0.0031 & 149 \\\\\n23 & 51523.2751 & 0.0005 & 0.0017 & 138 \\\\\n24 & 51523.3635 & 0.0007 & 0.0014 & 130 \\\\\n25 & 51523.4509 & 0.0006 & 0.0001 & 47 \\\\\n26 & 51523.5383 & 0.0007 & $-$0.0011 & 40 \\\\\n27 & 51523.6263 & 0.0009 & $-$0.0017 & 26 \\\\\n32 & 51524.0720 & 0.0037 & 0.0006 & 42 \\\\\n33 & 51524.1557 & 0.0043 & $-$0.0044 & 48 \\\\\n44 & 51525.1453 & 0.0014 & 0.0099 & 146 \\\\\n45 & 51525.2324 & 0.0015 & 0.0084 & 146 \\\\\n57 & 51526.2885 & 0.0017 & 0.0006 & 69 \\\\\n58 & 51526.3868 & 0.0015 & 0.0103 & 85 \\\\\n59 & 51526.4690 & 0.0010 & 0.0038 & 44 \\\\\n67 & 51527.1843 & 0.0010 & 0.0097 & 121 \\\\\n68 & 51527.2684 & 0.0021 & 0.0053 & 140 \\\\\n69 & 51527.3703 & 0.0029 & 0.0185 & 61 \\\\\n78 & 51528.1614 & 0.0011 & 0.0116 & 138 \\\\\n79 & 51528.2509 & 0.0007 & 0.0124 & 146 \\\\\n80 & 51528.3368 & 0.0007 & 0.0097 & 146 \\\\\n89 & 51529.1194 & 0.0018 & $-$0.0057 & 137 \\\\\n90 & 51529.2196 & 0.0015 & 0.0059 & 143 \\\\\n91 & 51529.2942 & 0.0063 & $-$0.0081 & 51 \\\\\n116 & 51531.5186 & 0.0014 & $-$0.0003 & 38 \\\\\n117 & 51531.6032 & 0.0019 & $-$0.0043 & 41 \\\\\n122 & 51532.0553 & 0.0053 & 0.0044 & 74 \\\\\n123 & 51532.1356 & 0.0017 & $-$0.0040 & 161 \\\\\n126 & 51532.3993 & 0.0028 & $-$0.0062 & 72 \\\\\n127 & 51532.4802 & 0.0027 & $-$0.0140 & 28 \\\\\n128 & 51532.5755 & 0.0024 & $-$0.0073 & 43 \\\\\n129 & 51532.6594 & 0.0019 & $-$0.0121 & 41 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451521.2342 + 0.088661 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (2002).}\\label{tab:dvumaoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52377.0138 & 0.0005 & $-$0.0103 & 99 \\\\\n1 & 52377.1026 & 0.0004 & $-$0.0101 & 145 \\\\\n2 & 52377.1928 & 0.0005 & $-$0.0084 & 139 \\\\\n13 & 52378.1912 & 0.0021 & 0.0157 & 57 \\\\\n23 & 52379.0605 & 0.0020 & $-$0.0006 & 73 \\\\\n24 & 52379.1648 & 0.0011 & 0.0151 & 43 \\\\\n57 & 52382.0744 & 0.0027 & 0.0021 & 100 \\\\\n61 & 52382.4312 & 0.0006 & 0.0046 & 34 \\\\\n95 & 52385.4362 & 0.0026 & $-$0.0015 & 43 \\\\\n118 & 52387.4681 & 0.0008 & $-$0.0066 & 49 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452377.0241 + 0.088564 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (2005).}\\label{tab:dvumaoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53413.2479 & 0.0006 & $-$0.0102 & 165 \\\\\n11 & 53414.2300 & 0.0020 & $-$0.0031 & 55 \\\\\n20 & 53415.0339 & 0.0002 & 0.0030 & 156 \\\\\n21 & 53415.1206 & 0.0003 & 0.0011 & 247 \\\\\n22 & 53415.2095 & 0.0003 & 0.0014 & 266 \\\\\n100 & 53422.1268 & 0.0012 & 0.0049 & 76 \\\\\n101 & 53422.2090 & 0.0040 & $-$0.0016 & 68 \\\\\n102 & 53422.3133 & 0.0021 & 0.0140 & 68 \\\\\n111 & 53423.1032 & 0.0016 & 0.0062 & 181 \\\\\n112 & 53423.1906 & 0.0016 & 0.0050 & 159 \\\\\n113 & 53423.2692 & 0.0028 & $-$0.0051 & 95 \\\\\n123 & 53424.1582 & 0.0008 & $-$0.0025 & 144 \\\\\n168 & 53428.1363 & 0.0023 & $-$0.0131 & 157 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453413.2581 + 0.088638 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of DV UMa (2007).}\\label{tab:dvumaoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54177.7552 & 0.0015 & $-$0.0096 & 54 \\\\\n3 & 54178.0184 & 0.0004 & $-$0.0124 & 237 \\\\\n4 & 54178.1104 & 0.0007 & $-$0.0091 & 126 \\\\\n5 & 54178.1985 & 0.0005 & $-$0.0097 & 197 \\\\\n11 & 54178.7343 & 0.0007 & $-$0.0058 & 55 \\\\\n12 & 54178.8256 & 0.0008 & $-$0.0032 & 38 \\\\\n21 & 54179.6333 & 0.0009 & 0.0065 & 10 \\\\\n22 & 54179.7248 & 0.0008 & 0.0094 & 13 \\\\\n23 & 54179.8096 & 0.0009 & 0.0056 & 13 \\\\\n26 & 54180.0746 & 0.0004 & 0.0045 & 118 \\\\\n27 & 54180.1700 & 0.0013 & 0.0113 & 60 \\\\\n30 & 54180.4252 & 0.0005 & 0.0005 & 211 \\\\\n31 & 54180.5147 & 0.0001 & 0.0013 & 744 \\\\\n32 & 54180.6016 & 0.0002 & $-$0.0005 & 636 \\\\\n33 & 54180.6906 & 0.0003 & $-$0.0001 & 316 \\\\\n48 & 54182.0254 & 0.0013 & 0.0048 & 98 \\\\\n49 & 54182.1176 & 0.0010 & 0.0082 & 108 \\\\\n50 & 54182.2056 & 0.0055 & 0.0076 & 47 \\\\\n61 & 54183.1792 & 0.0014 & 0.0058 & 72 \\\\\n116 & 54188.0485 & 0.0015 & $-$0.0014 & 78 \\\\\n138 & 54189.9866 & 0.0020 & $-$0.0139 & 101 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454177.7648 + 0.088664 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ER Ursae Majoris}\\label{obj:eruma}\n\n The times of superhump maxima used to draw figure \\ref{fig:erumahumpall}\nare listed in tables \\ref{tab:erumaoc1995-1} and \\ref{tab:erumaoc1995-2}.\n\n\\begin{table}\n\\caption{Superhump maxima (1) of ER UMa (1995).}\\label{tab:erumaoc1995-1}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 49744.2521 & 0.0006 & 0.0027 & 16 \\\\\n1 & 49744.3196 & 0.0003 & 0.0045 & 31 \\\\\n14 & 49745.1720 & 0.0003 & 0.0022 & 21 \\\\\n15 & 49745.2371 & 0.0003 & 0.0015 & 23 \\\\\n16 & 49745.3010 & 0.0005 & $-$0.0004 & 20 \\\\\n17 & 49745.3675 & 0.0002 & 0.0004 & 31 \\\\\n28 & 49746.0889 & 0.0004 & $-$0.0014 & 30 \\\\\n29 & 49746.1560 & 0.0007 & 0.0000 & 22 \\\\\n31 & 49746.2860 & 0.0005 & $-$0.0015 & 24 \\\\\n32 & 49746.3507 & 0.0003 & $-$0.0025 & 30 \\\\\n43 & 49747.0719 & 0.0004 & $-$0.0046 & 38 \\\\\n59 & 49748.1244 & 0.0017 & $-$0.0040 & 18 \\\\\n60 & 49748.1906 & 0.0064 & $-$0.0036 & 17 \\\\\n62 & 49748.3257 & 0.0016 & 0.0000 & 22 \\\\\n90 & 49750.1636 & 0.0012 & $-$0.0030 & 21 \\\\\n91 & 49750.2351 & 0.0015 & 0.0028 & 31 \\\\\n107 & 49751.2878 & 0.0021 & 0.0035 & 21 \\\\\n121 & 49752.2090 & 0.0041 & 0.0042 & 24 \\\\\n122 & 49752.2798 & 0.0051 & 0.0094 & 25 \\\\\n123 & 49752.3260 & 0.0053 & $-$0.0102 & 14 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449744.2494 + 0.065747 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima (2) of ER UMa (1995).}\\label{tab:erumaoc1995-2}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n58 & 49748.0946 & 0.0004 & 0.0319 & 15 \\\\\n59 & 49748.1542 & 0.0035 & 0.0257 & 15 \\\\\n60 & 49748.2242 & 0.0033 & 0.0300 & 15 \\\\\n61 & 49748.2885 & 0.0010 & 0.0285 & 14 \\\\\n62 & 49748.3510 & 0.0008 & 0.0253 & 22 \\\\\n76 & 49749.2744 & 0.0011 & 0.0282 & 16 \\\\\n90 & 49750.1782 & 0.0018 & 0.0115 & 18 \\\\\n91 & 49750.2561 & 0.0009 & 0.0237 & 16 \\\\\n120 & 49752.1620 & 0.0006 & 0.0230 & 42 \\\\\n121 & 49752.2282 & 0.0008 & 0.0234 & 24 \\\\\n167 & 49755.2366 & 0.0006 & 0.0074 & 31 \\\\\n168 & 49755.3038 & 0.0008 & 0.0089 & 30 \\\\\n183 & 49756.2848 & 0.0004 & 0.0037 & 31 \\\\\n184 & 49756.3525 & 0.0006 & 0.0057 & 31 \\\\\n197 & 49757.1990 & 0.0017 & $-$0.0026 & 12 \\\\\n229 & 49759.2950 & 0.0005 & $-$0.0105 & 22 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2449744.2494 + 0.065747 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{IY Ursae Majoris}\\label{obj:iyuma}\n\n This eclipsing SU UMa-type dwarf nova has been well documented\n(\\cite{uem00iyuma}; \\cite{pat00iyuma}). The superhump maxima\nwere determined from observations outside the eclipses, as described\nin V2051 Oph.\n\n \\citet{pat00iyuma} reported a ``normal'' negative period derivative.\nWe combined the reported times of superhump maxima with ours,\nby adding a systematic difference of 0.0028 d (presumably due to\nthe difference in the procedure of determination of maxima) to\nthe times of \\citet{pat00iyuma}. The resultant times are listed in\ntable \\ref{tab:iyumaoc2000}. We restricted the analysis to the interval\nbefore the rapid fading started, i.e. excluding times of late superhumps.\nThe $O-C$ diagram was complex and was different from the one in\n\\citet{pat00iyuma}, in that the present diagram clearly showed\na transition from a longer period to a stable period around $E = 23$\n(stage A--B transition).\nThe main difference in appearance between \\citet{pat00iyuma} and ours\nwas thus caused by the lack of early-stage superhumps in \\citet{pat00iyuma}.\n\n The $P_{\\rm dot}$ during the later interval was much closer\nto zero than the global $P_{\\rm dot}$ reported in \\citet{pat00iyuma}.\nThe behavior after $E = 106$ was slightly different between ours\nand \\citet{pat00iyuma}. Our data suggested a shortening of the\nperiod while \\citet{pat00iyuma} showed a steady increase.\nThis may have been caused by the increasing signal of late superhumps,\nwhich predominated in later epochs, during the observation of\n\\citet{pat00iyuma}. Excluding $E < 23$ and $E \\ge 106$,\nwe obtained $P_{\\rm dot}$ = $-1.8(2.2) \\times 10^{-5}$.\n\n We also analyzed the 2002, 2004 and 2006 superoutbursts\n(table \\ref{tab:iyumaoc2002}, \\ref{tab:iyumaoc2004} and\n\\ref{tab:iyumaoc2006}).\nThe 2002 observation covered the middle-to-late part of the outburst.\nThere was an apparent discontinuous transition to a shorter\nperiod around $E = 137$. Due to the gap in the observation, we could\nnot significantly determine the $P_{\\rm dot}$ before this transition.\nThis 2004 observation covered the middle part to the latter half of\nthe outburst.\nAlthough the initial stage of the 2006 superoutburst\nwas observed, the superhump maxima incidentally fell amid the eclipses.\nWe excluded most of the first two nights for calculating times of\nsuperhump maxima.\nThe superhump profile at this stage was probably double-peaked.\nSuch a feature may have reflected the growing stage of the superhumps\nand needs to be investigated in future superoutbursts.\nThe $O-C$'s after $E > 221$ apparently showed a phase shift attributable\nto traditional late superhumps, as in the 2000 superoutburst.\nThe periods given in table \\ref{tab:perlist} were determined\nby excluding the maximum $E=176$.\n\n The 2007 superoutburst was caught by chance at $V=14$. Judging from\nthe superhump maxima (table \\ref{tab:iyumaoc2007}), there was a clear\ndecrease in the superhump period. In conjunction with the faintness,\nwe probably observed the late stage of a superoutburst associated\nwith a stage B--C transition. The nominal value\n$P_{\\rm dot}$ = $-16.0(6.5) \\times 10^{-5}$ would not be a good\nrepresentative period derivative.\n\n The 2009 superoutburst was well-observed during the middle-to-late\nstages (table \\ref{tab:iyumaoc2009}). The $O-C$ diagram clearly depicts\nthe presence of stages B and C. The first ($E=0$ epoch probably corresponds\nto the stage A. Although orbital humps emerged after the rapid decline\nfrom the superoutburst plateau, no prominent traditional late superhumps\nwere recorded (cf. the 2000 superoutburst, \\cite{pat00iyuma}).\n\n A combined $O-C$ diagram drawn from all the superoutburst is\npresented in figure \\ref{fig:iyumacomp}.\nThe combined diagram appears to show stage B\nlasting for $\\sim$ 120 cycles with a positive $P_{\\rm dot}$.\nThe duration of the stage B is compatible that during the 2009\nsuperoutburst, although the behavior of the 2009 $O-C$ looks slightly\ndifferent from others during its early stage.\nThe likely presence of a positive $P_{\\rm dot}$, then\nwould suggest the similarity to NSV 4838 \\citep{ima09nsv4838}.\nThe lack of a positive $P_{\\rm dot}$ in individual superoutbursts\nmay have been a result from the deficiency of observations around\nthe end of the stage B. Some of superoutbursts seem to show\nstage C superhumps while others tend to show humps resembling\ntraditional late superhumps. Future observations of this object\nat these epochs will be particularly important.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig157.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of IY UMa between different\n superoutbursts. A period of 0.07610 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:iyumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2000).}\\label{tab:iyumaoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51561.2170 & 0.0006 & $-$0.0116 & 77 \\\\\n1 & 51561.2956 & 0.0003 & $-$0.0089 & 120 \\\\\n2 & 51561.3719 & 0.0012 & $-$0.0084 & 51 \\\\\n13 & 51562.2164 & 0.0007 & 0.0014 & 145 \\\\\n14 & 51562.2935 & 0.0011 & 0.0027 & 156 \\\\\n14 & 51562.2878 & -- & $-$0.0030 & 0 \\\\\n15 & 51562.3661 & 0.0010 & $-$0.0006 & 157 \\\\\n15 & 51562.3646 & -- & $-$0.0021 & 0 \\\\\n16 & 51562.4414 & 0.0011 & $-$0.0012 & 35 \\\\\n16 & 51562.4428 & -- & 0.0003 & 0 \\\\\n17 & 51562.5173 & 0.0013 & $-$0.0011 & 34 \\\\\n17 & 51562.5177 & -- & $-$0.0007 & 0 \\\\\n18 & 51562.5940 & 0.0018 & $-$0.0003 & 34 \\\\\n18 & 51562.5955 & -- & 0.0012 & 0 \\\\\n19 & 51562.6716 & 0.0010 & 0.0015 & 26 \\\\\n19 & 51562.6730 & -- & 0.0028 & 0 \\\\\n22 & 51562.9033 & 0.0016 & 0.0056 & 13 \\\\\n23 & 51562.9797 & 0.0017 & 0.0061 & 19 \\\\\n23 & 51562.9758 & -- & 0.0022 & 0 \\\\\n24 & 51563.0507 & -- & 0.0012 & 0 \\\\\n27 & 51563.2799 & 0.0009 & 0.0027 & 149 \\\\\n28 & 51563.3557 & 0.0005 & 0.0027 & 135 \\\\\n33 & 51563.7371 & -- & 0.0048 & 0 \\\\\n34 & 51563.8133 & -- & 0.0051 & 0 \\\\\n35 & 51563.8874 & -- & 0.0033 & 0 \\\\\n36 & 51563.9641 & -- & 0.0041 & 0 \\\\\n37 & 51564.0385 & -- & 0.0027 & 0 \\\\\n41 & 51564.3425 & -- & 0.0032 & 0 \\\\\n42 & 51564.4130 & -- & $-$0.0022 & 0 \\\\\n42 & 51564.4133 & 0.0015 & $-$0.0019 & 81 \\\\\n43 & 51564.4913 & -- & 0.0003 & 0 \\\\\n43 & 51564.4929 & 0.0099 & 0.0018 & 36 \\\\\n44 & 51564.5680 & 0.0019 & 0.0011 & 31 \\\\\n44 & 51564.5738 & -- & 0.0069 & 0 \\\\\n48 & 51564.8713 & 0.0015 & 0.0009 & 12 \\\\\n49 & 51564.9483 & -- & 0.0020 & 0 \\\\\n59 & 51565.7068 & -- & 0.0018 & 0 \\\\\n60 & 51565.7814 & -- & 0.0006 & 0 \\\\\n69 & 51566.4643 & 0.0066 & 0.0006 & 23 \\\\\n72 & 51566.6989 & -- & 0.0076 & 0 \\\\\n74 & 51566.8463 & -- & 0.0033 & 0 \\\\\n75 & 51566.9216 & -- & 0.0027 & 0 \\\\\n76 & 51566.9968 & -- & 0.0020 & 0 \\\\\n77 & 51567.0729 & -- & 0.0023 & 0 \\\\\n79 & 51567.2199 & -- & $-$0.0025 & 0 \\\\\n79 & 51567.2168 & 0.0044 & $-$0.0056 & 19 \\\\\n80 & 51567.2977 & -- & $-$0.0005 & 0 \\\\\n80 & 51567.2957 & 0.0018 & $-$0.0025 & 35 \\\\\n81 & 51567.3727 & -- & $-$0.0014 & 0 \\\\\n81 & 51567.3701 & 0.0015 & $-$0.0041 & 49 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451561.22862 + 0.075870 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N=0$ refers to \\citet{pat00iyuma}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2000) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n82 & 51567.4456 & -- & $-$0.0044 & 0 \\\\\n82 & 51567.4429 & 0.0012 & $-$0.0070 & 88 \\\\\n83 & 51567.5234 & -- & $-$0.0025 & 0 \\\\\n83 & 51567.5235 & 0.0009 & $-$0.0024 & 136 \\\\\n84 & 51567.5978 & -- & $-$0.0039 & 0 \\\\\n85 & 51567.6748 & -- & $-$0.0028 & 0 \\\\\n86 & 51567.7528 & -- & $-$0.0007 & 0 \\\\\n87 & 51567.8328 & -- & 0.0035 & 0 \\\\\n93 & 51568.2798 & -- & $-$0.0048 & 0 \\\\\n93 & 51568.2793 & 0.0012 & $-$0.0053 & 119 \\\\\n94 & 51568.3558 & -- & $-$0.0046 & 0 \\\\\n94 & 51568.3570 & 0.0012 & $-$0.0035 & 158 \\\\\n95 & 51568.4308 & -- & $-$0.0055 & 0 \\\\\n95 & 51568.4331 & 0.0014 & $-$0.0032 & 118 \\\\\n96 & 51568.5078 & -- & $-$0.0044 & 0 \\\\\n96 & 51568.5113 & 0.0010 & $-$0.0009 & 70 \\\\\n97 & 51568.5858 & -- & $-$0.0022 & 0 \\\\\n97 & 51568.5834 & 0.0011 & $-$0.0047 & 71 \\\\\n98 & 51568.6568 & -- & $-$0.0071 & 0 \\\\\n98 & 51568.6650 & 0.0018 & 0.0011 & 76 \\\\\n99 & 51568.7374 & -- & $-$0.0024 & 0 \\\\\n99 & 51568.7422 & 0.0024 & 0.0024 & 43 \\\\\n101 & 51568.8878 & -- & $-$0.0037 & 0 \\\\\n106 & 51569.2798 & -- & 0.0089 & 0 \\\\\n107 & 51569.3488 & -- & 0.0021 & 0 \\\\\n107 & 51569.3478 & 0.0008 & 0.0011 & 85 \\\\\n108 & 51569.4238 & -- & 0.0012 & 0 \\\\\n108 & 51569.4229 & 0.0008 & 0.0003 & 86 \\\\\n109 & 51569.4975 & 0.0009 & $-$0.0010 & 62 \\\\\n112 & 51569.7396 & -- & 0.0135 & 0 \\\\\n113 & 51569.8156 & -- & 0.0136 & 0 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2002).}\\label{tab:iyumaoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52405.7582 & 0.0005 & $-$0.0105 & 50 \\\\\n4 & 52406.0660 & 0.0009 & $-$0.0059 & 119 \\\\\n5 & 52406.1500 & 0.0020 & 0.0023 & 95 \\\\\n17 & 52407.0486 & 0.0004 & $-$0.0083 & 423 \\\\\n18 & 52407.1241 & 0.0005 & $-$0.0086 & 452 \\\\\n19 & 52407.1981 & 0.0009 & $-$0.0103 & 189 \\\\\n29 & 52407.9622 & 0.0017 & $-$0.0039 & 163 \\\\\n30 & 52408.0434 & 0.0005 & 0.0015 & 263 \\\\\n31 & 52408.1188 & 0.0005 & 0.0011 & 233 \\\\\n111 & 52414.2016 & 0.0005 & 0.0222 & 328 \\\\\n123 & 52415.1079 & 0.0009 & 0.0194 & 160 \\\\\n124 & 52415.1785 & 0.0011 & 0.0142 & 254 \\\\\n135 & 52416.0254 & 0.0026 & 0.0276 & 235 \\\\\n137 & 52416.1737 & 0.0024 & 0.0244 & 174 \\\\\n175 & 52419.0231 & 0.0036 & $-$0.0056 & 193 \\\\\n176 & 52419.0941 & 0.0029 & $-$0.0103 & 117 \\\\\n189 & 52420.0723 & 0.0018 & $-$0.0171 & 75 \\\\\n190 & 52420.1619 & 0.0048 & $-$0.0033 & 103 \\\\\n215 & 52422.0515 & 0.0024 & $-$0.0079 & 117 \\\\\n228 & 52423.0235 & 0.0042 & $-$0.0210 & 80 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452405.7688 + 0.075771 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2004).}\\label{tab:iyumaoc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53332.4726 & 0.0015 & $-$0.0043 & 31 \\\\\n1 & 53332.5550 & 0.0016 & 0.0020 & 33 \\\\\n2 & 53332.6321 & 0.0017 & 0.0032 & 22 \\\\\n3 & 53332.7052 & 0.0010 & 0.0002 & 35 \\\\\n13 & 53333.4605 & 0.0012 & $-$0.0046 & 91 \\\\\n14 & 53333.5398 & 0.0002 & $-$0.0013 & 137 \\\\\n39 & 53335.4423 & 0.0008 & 0.0009 & 62 \\\\\n40 & 53335.5195 & 0.0014 & 0.0021 & 35 \\\\\n62 & 53337.1886 & 0.0003 & $-$0.0011 & 146 \\\\\n63 & 53337.2638 & 0.0006 & $-$0.0019 & 192 \\\\\n64 & 53337.3424 & 0.0012 & 0.0006 & 136 \\\\\n67 & 53337.5679 & 0.0011 & $-$0.0018 & 60 \\\\\n68 & 53337.6471 & 0.0007 & 0.0014 & 59 \\\\\n115 & 53341.2228 & 0.0004 & 0.0044 & 206 \\\\\n116 & 53341.2998 & 0.0003 & 0.0054 & 216 \\\\\n126 & 53342.0566 & 0.0025 & 0.0021 & 129 \\\\\n127 & 53342.1309 & 0.0037 & 0.0004 & 76 \\\\\n128 & 53342.2067 & 0.0003 & 0.0002 & 192 \\\\\n129 & 53342.2840 & 0.0004 & 0.0014 & 194 \\\\\n130 & 53342.3573 & 0.0007 & $-$0.0013 & 122 \\\\\n168 & 53345.2429 & 0.0005 & $-$0.0041 & 135 \\\\\n169 & 53345.3190 & 0.0006 & $-$0.0040 & 134 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453332.4769 + 0.076012 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2006).}\\label{tab:iyumaoc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53834.3769 & 0.0022 & $-$0.0127 & 90 \\\\\n42 & 53837.5859 & 0.0003 & 0.0039 & 90 \\\\\n53 & 53838.4185 & 0.0001 & 0.0003 & 29 \\\\\n56 & 53838.6462 & 0.0002 & $-$0.0001 & 72 \\\\\n57 & 53838.7215 & 0.0003 & $-$0.0008 & 70 \\\\\n58 & 53838.7968 & 0.0003 & $-$0.0014 & 72 \\\\\n59 & 53838.8740 & 0.0006 & $-$0.0002 & 64 \\\\\n61 & 53839.0273 & 0.0006 & 0.0010 & 52 \\\\\n62 & 53839.1021 & 0.0004 & $-$0.0002 & 91 \\\\\n79 & 53840.3958 & 0.0008 & 0.0013 & 48 \\\\\n101 & 53842.0657 & 0.0007 & $-$0.0011 & 92 \\\\\n102 & 53842.1393 & 0.0012 & $-$0.0035 & 87 \\\\\n113 & 53842.9852 & 0.0014 & 0.0064 & 85 \\\\\n114 & 53843.0602 & 0.0010 & 0.0053 & 92 \\\\\n153 & 53846.0274 & 0.0011 & 0.0081 & 80 \\\\\n154 & 53846.1044 & 0.0006 & 0.0091 & 111 \\\\\n166 & 53847.0108 & 0.0010 & 0.0033 & 38 \\\\\n167 & 53847.0860 & 0.0009 & 0.0026 & 76 \\\\\n168 & 53847.1621 & 0.0005 & 0.0026 & 214 \\\\\n205 & 53849.9676 & 0.0010 & $-$0.0043 & 93 \\\\\n206 & 53850.0461 & 0.0013 & $-$0.0018 & 90 \\\\\n207 & 53850.1190 & 0.0015 & $-$0.0050 & 92 \\\\\n218 & 53850.9628 & 0.0026 & 0.0027 & 92 \\\\\n219 & 53851.0288 & 0.0023 & $-$0.0072 & 147 \\\\\n220 & 53851.1034 & 0.0035 & $-$0.0087 & 123 \\\\\n221 & 53851.1835 & 0.0012 & $-$0.0046 & 84 \\\\\n259 & 53854.0846 & 0.0032 & 0.0081 & 98 \\\\\n312 & 53858.1018 & 0.0008 & $-$0.0033 & 30 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453834.3896 + 0.076011 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2007).}\\label{tab:iyumaoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54134.2161 & 0.0002 & $-$0.0017 & 179 \\\\\n1 & 54134.2913 & 0.0003 & $-$0.0021 & 190 \\\\\n13 & 54135.2023 & 0.0006 & 0.0019 & 188 \\\\\n14 & 54135.2763 & 0.0006 & 0.0003 & 189 \\\\\n15 & 54135.3545 & 0.0007 & 0.0030 & 159 \\\\\n53 & 54138.2209 & 0.0029 & $-$0.0025 & 102 \\\\\n54 & 54138.3001 & 0.0038 & 0.0011 & 134 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454134.2178 + 0.075577 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of IY UMa (2009).}\\label{tab:iyumaoc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54934.6870 & 0.0102 & $-$0.0346 & 51 \\\\\n30 & 54937.0007 & 0.0003 & $-$0.0034 & 144 \\\\\n31 & 54937.0746 & 0.0003 & $-$0.0055 & 201 \\\\\n43 & 54937.9897 & 0.0007 & $-$0.0034 & 119 \\\\\n56 & 54938.9851 & 0.0003 & 0.0029 & 123 \\\\\n57 & 54939.0607 & 0.0002 & 0.0024 & 126 \\\\\n58 & 54939.1363 & 0.0003 & 0.0019 & 82 \\\\\n64 & 54939.5900 & 0.0007 & $-$0.0009 & 84 \\\\\n65 & 54939.6674 & 0.0002 & 0.0004 & 122 \\\\\n69 & 54939.9721 & 0.0003 & 0.0008 & 83 \\\\\n70 & 54940.0470 & 0.0004 & $-$0.0004 & 123 \\\\\n71 & 54940.1226 & 0.0007 & $-$0.0008 & 108 \\\\\n83 & 54941.0402 & 0.0017 & 0.0038 & 104 \\\\\n84 & 54941.1188 & 0.0009 & 0.0063 & 97 \\\\\n87 & 54941.3447 & 0.0004 & 0.0039 & 55 \\\\\n88 & 54941.4244 & 0.0004 & 0.0075 & 70 \\\\\n89 & 54941.4979 & 0.0003 & 0.0049 & 69 \\\\\n90 & 54941.5743 & 0.0003 & 0.0053 & 73 \\\\\n100 & 54942.3364 & 0.0003 & 0.0065 & 58 \\\\\n101 & 54942.4109 & 0.0002 & 0.0050 & 144 \\\\\n102 & 54942.4877 & 0.0003 & 0.0057 & 142 \\\\\n103 & 54942.5639 & 0.0005 & 0.0058 & 68 \\\\\n108 & 54942.9499 & 0.0008 & 0.0113 & 53 \\\\\n109 & 54943.0255 & 0.0006 & 0.0109 & 88 \\\\\n110 & 54943.1011 & 0.0004 & 0.0104 & 62 \\\\\n122 & 54944.0107 & 0.0005 & 0.0070 & 86 \\\\\n123 & 54944.0868 & 0.0005 & 0.0070 & 88 \\\\\n135 & 54944.9910 & 0.0004 & $-$0.0018 & 177 \\\\\n136 & 54945.0690 & 0.0003 & 0.0001 & 213 \\\\\n137 & 54945.1446 & 0.0006 & $-$0.0004 & 79 \\\\\n138 & 54945.2195 & 0.0008 & $-$0.0015 & 80 \\\\\n161 & 54946.9621 & 0.0016 & $-$0.0088 & 44 \\\\\n162 & 54947.0416 & 0.0015 & $-$0.0054 & 61 \\\\\n167 & 54947.4203 & 0.0011 & $-$0.0071 & 72 \\\\\n168 & 54947.4950 & 0.0008 & $-$0.0085 & 70 \\\\\n169 & 54947.5724 & 0.0008 & $-$0.0072 & 64 \\\\\n175 & 54948.0261 & 0.0008 & $-$0.0100 & 139 \\\\\n189 & 54949.0909 & 0.0013 & $-$0.0103 & 191 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454934.7216 + 0.076083 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{KS Ursae Majoris}\\label{obj:ksuma}\n\n KS UMa (=SBS1017$+$533) was originally discovered as an emission-line\nobject \\citep{bal97SBS2spec}. In 1998, the object was found to be\nin outburst during a spectroscopic survey (P. Garnavich, vsnet-alert 1441).\nT. Vanmunster reported the detection of superhumps with a period of\n0.069(1) d during this outburst (CVC 161, also in vsnet-alert 1448).\n\\citet{haz99ksuma} surveyed historical outbursts. \\citet{jia00RASSCV}\nalso selected this CV from the ROSAT all-sky survey.\n\n \\citet{ole03ksuma} reported on the period variation of superhumps\nin KS UMa. We had more extensive data on the same superoutburst,\nnotably covering the earlier stage than in \\citet{ole03ksuma}.\nTable \\ref{tab:ksumaoc2003} presents the combined list of times of\nsuperhump maxima, after adding a systematic difference of 0.003 d to\n\\citet{ole03ksuma}.\nThe entire data now clearly show a sharp transition from a longer period\nin the early stage (before $E = 15$), stabilized segment with a slightly\npositive $P_{\\rm dot}$, and followed by a sharp transition to\na shorter period after $E = 95$. The pattern of period change can\nbe reasonably interpreted as stages A--C.\nThe negative $P_{\\rm dot}$ in \\citet{ole03ksuma} was a result of\nthe fit to the stages B and C together.\nOur data yielded $P_{\\rm dot}$ = $+2.2(1.1) \\times 10^{-5}$ for the stage B.\n\n We also observed the 2007 superoutburst (table \\ref{tab:ksumaoc2007}).\nThe observation covered the middle-to-late plateau stage. Excluding\nthe last point (taken during the rapid fading stage), we obtained\n$P_{\\rm dot}$ = $+1.5(1.9) \\times 10^{-5}$, probably corresponding to\nthe stage B of the 2003 superoutburst.\n\n The $O-C$ behavior was slightly different between the 2003 and 2007\nsuperoutbursts (figure \\ref{fig:ksumacomp}). This may have been a result\nof a longer duration of the 2003 superoutburst than the 2007 one.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig158.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of KS UMa between different\n superoutbursts. A period of 0.07019 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used.\n }\n \\label{fig:ksumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of KS UMa (2003).}\\label{tab:ksumaoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52690.0021 & 0.0042 & $-$0.0128 & 129 \\\\\n8 & 52690.5677 & 0.0005 & $-$0.0081 & 69 \\\\\n9 & 52690.6414 & 0.0003 & $-$0.0045 & 114 \\\\\n10 & 52690.7120 & 0.0002 & $-$0.0041 & 114 \\\\\n15 & 52691.0665 & 0.0002 & $-$0.0001 & 153 \\\\\n16 & 52691.1366 & 0.0002 & $-$0.0001 & 179 \\\\\n17 & 52691.2058 & 0.0002 & $-$0.0011 & 217 \\\\\n19 & 52691.3455 & 0.0003 & $-$0.0017 & 180 \\\\\n22 & 52691.5562 & 0.0002 & $-$0.0013 & 78 \\\\\n23 & 52691.6273 & 0.0002 & $-$0.0004 & 113 \\\\\n24 & 52691.6975 & 0.0002 & $-$0.0002 & 115 \\\\\n27 & 52691.9107 & 0.0008 & 0.0026 & 75 \\\\\n29 & 52692.0486 & 0.0003 & 0.0003 & 126 \\\\\n33 & 52692.3280 & 0.0009 & $-$0.0008 & 64 \\\\\n33 & 52692.331 & -- & 0.0022 & 0 \\\\\n34 & 52692.4007 & 0.0004 & 0.0018 & 93 \\\\\n35 & 52692.4690 & 0.0003 & $-$0.0001 & 167 \\\\\n36 & 52692.541 & -- & 0.0018 & 0 \\\\\n37 & 52692.6085 & 0.0004 & $-$0.0008 & 114 \\\\\n38 & 52692.6787 & 0.0003 & $-$0.0007 & 115 \\\\\n38 & 52692.679 & -- & $-$0.0004 & 0 \\\\\n46 & 52693.241 & -- & 0.0006 & 0 \\\\\n47 & 52693.310 & -- & $-$0.0005 & 0 \\\\\n48 & 52693.3796 & 0.0008 & $-$0.0010 & 82 \\\\\n48 & 52693.380 & -- & $-$0.0006 & 0 \\\\\n49 & 52693.4485 & 0.0008 & $-$0.0022 & 97 \\\\\n49 & 52693.449 & -- & $-$0.0017 & 0 \\\\\n50 & 52693.520 & -- & $-$0.0009 & 0 \\\\\n51 & 52693.5902 & 0.0006 & $-$0.0008 & 139 \\\\\n51 & 52693.592 & -- & 0.0010 & 0 \\\\\n52 & 52693.6600 & 0.0004 & $-$0.0011 & 142 \\\\\n52 & 52693.661 & -- & $-$0.0001 & 0 \\\\\n53 & 52693.7320 & 0.0004 & 0.0008 & 117 \\\\\n54 & 52693.8000 & 0.0007 & $-$0.0014 & 28 \\\\\n55 & 52693.8708 & 0.0008 & $-$0.0006 & 32 \\\\\n56 & 52693.9446 & 0.0009 & 0.0030 & 30 \\\\\n58 & 52694.0839 & 0.0016 & 0.0020 & 96 \\\\\n61 & 52694.293 & -- & 0.0008 & 0 \\\\\n62 & 52694.3598 & 0.0009 & $-$0.0025 & 73 \\\\\n62 & 52694.363 & -- & 0.0007 & 0 \\\\\n64 & 52694.5075 & 0.0009 & 0.0050 & 40 \\\\\n64 & 52694.502 & -- & $-$0.0005 & 0 \\\\\n67 & 52694.7143 & 0.0008 & 0.0014 & 32 \\\\\n68 & 52694.7854 & 0.0007 & 0.0024 & 32 \\\\\n69 & 52694.8541 & 0.0007 & 0.0009 & 33 \\\\\n70 & 52694.9258 & 0.0008 & 0.0025 & 32 \\\\\n71 & 52694.9932 & 0.0012 & $-$0.0001 & 108 \\\\\n72 & 52695.0674 & 0.0005 & 0.0039 & 139 \\\\\n73 & 52695.1348 & 0.0008 & 0.0011 & 190 \\\\\n75 & 52695.2739 & 0.0007 & 0.0001 & 132 \\\\\n75 & 52695.276 & -- & 0.0021 & 0 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452690.0148 + 0.070120 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N=0$ refers to \\citet{ole03ksuma}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of KS UMa (2003) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n76 & 52695.3459 & 0.0005 & 0.0019 & 168 \\\\\n76 & 52695.345 & -- & 0.0010 & 0 \\\\\n77 & 52695.4147 & 0.0008 & 0.0006 & 97 \\\\\n77 & 52695.417 & -- & 0.0029 & 0 \\\\\n78 & 52695.4891 & 0.0004 & 0.0049 & 148 \\\\\n78 & 52695.489 & -- & 0.0048 & 0 \\\\\n79 & 52695.5568 & 0.0006 & 0.0024 & 118 \\\\\n80 & 52695.6292 & 0.0005 & 0.0047 & 107 \\\\\n81 & 52695.6988 & 0.0006 & 0.0042 & 102 \\\\\n85 & 52695.9779 & 0.0008 & 0.0028 & 264 \\\\\n86 & 52696.0480 & 0.0014 & 0.0028 & 129 \\\\\n87 & 52696.1211 & 0.0021 & 0.0058 & 71 \\\\\n89 & 52696.2585 & 0.0008 & 0.0030 & 139 \\\\\n89 & 52696.261 & -- & 0.0054 & 0 \\\\\n90 & 52696.3281 & 0.0005 & 0.0025 & 248 \\\\\n90 & 52696.329 & -- & 0.0033 & 0 \\\\\n91 & 52696.3997 & 0.0020 & 0.0039 & 74 \\\\\n91 & 52696.395 & -- & $-$0.0008 & 0 \\\\\n92 & 52696.4687 & 0.0007 & 0.0027 & 73 \\\\\n92 & 52696.467 & -- & 0.0011 & 0 \\\\\n93 & 52696.5407 & 0.0007 & 0.0046 & 71 \\\\\n93 & 52696.539 & -- & 0.0030 & 0 \\\\\n94 & 52696.6096 & 0.0006 & 0.0034 & 93 \\\\\n95 & 52696.6789 & 0.0007 & 0.0026 & 92 \\\\\n106 & 52697.4467 & 0.0015 & $-$0.0009 & 104 \\\\\n106 & 52697.451 & -- & 0.0034 & 0 \\\\\n107 & 52697.517 & -- & $-$0.0007 & 0 \\\\\n108 & 52697.5873 & 0.0015 & $-$0.0006 & 51 \\\\\n109 & 52697.6545 & 0.0008 & $-$0.0035 & 102 \\\\\n110 & 52697.7248 & 0.0007 & $-$0.0033 & 43 \\\\\n114 & 52698.0058 & 0.0024 & $-$0.0028 & 34 \\\\\n115 & 52698.0747 & 0.0021 & $-$0.0040 & 55 \\\\\n117 & 52698.2151 & 0.0021 & $-$0.0038 & 220 \\\\\n118 & 52698.283 & -- & $-$0.0060 & 0 \\\\\n118 & 52698.2836 & 0.0007 & $-$0.0054 & 306 \\\\\n119 & 52698.353 & -- & $-$0.0062 & 0 \\\\\n120 & 52698.423 & -- & $-$0.0063 & 0 \\\\\n124 & 52698.7030 & 0.0008 & $-$0.0068 & 49 \\\\\n147 & 52700.3103 & 0.0044 & $-$0.0123 & 27 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of KS UMa (2007).}\\label{tab:ksumaoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54148.1875 & 0.0005 & $-$0.0003 & 65 \\\\\n1 & 54148.2550 & 0.0003 & $-$0.0030 & 97 \\\\\n28 & 54150.1530 & 0.0003 & $-$0.0007 & 94 \\\\\n29 & 54150.2240 & 0.0003 & 0.0001 & 102 \\\\\n30 & 54150.2930 & 0.0007 & $-$0.0011 & 59 \\\\\n42 & 54151.1353 & 0.0005 & $-$0.0013 & 97 \\\\\n43 & 54151.2068 & 0.0005 & $-$0.0000 & 101 \\\\\n44 & 54151.2776 & 0.0007 & 0.0005 & 33 \\\\\n56 & 54152.1206 & 0.0019 & 0.0010 & 42 \\\\\n57 & 54152.1909 & 0.0011 & 0.0012 & 103 \\\\\n58 & 54152.2621 & 0.0010 & 0.0021 & 83 \\\\\n71 & 54153.1727 & 0.0005 & $-$0.0000 & 102 \\\\\n72 & 54153.2440 & 0.0006 & 0.0010 & 103 \\\\\n73 & 54153.3181 & 0.0009 & 0.0049 & 53 \\\\\n140 & 54158.0130 & 0.0083 & $-$0.0042 & 103 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454148.1878 + 0.070210 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{KV Ursae Majoris}\\label{sec:kvuma}\\label{obj:kvuma}\n\n This object is a BHXT. The times of superhump maxima, a reanalysis\nof \\citet{uem02j1118}, used for drawing figure \\ref{fig:kvumaoc}\n(subsection \\ref{sec:BHXT}) are listed in table \\ref{tab:kvumaoc2000}.\n\n The $O-C$ diagram was composed of three stages as in SU UMa-type\ndwarf novae: stage A ($E \\le 124$) with a mean $P_{\\rm SH}$ = 0.17082(7) d,\nstage B for $124 \\le E \\le 348$ (mean $P_{\\rm SH}$ ($P_1$) = 0.17056(3) d\nand $P_{\\rm dot}$ = $+0.9(0.6) \\times 10^{-5}$)\nand stage C for $E \\ge 238$ (mean $P_{\\rm SH}$ ($P_2$) = 0.17038(3) d).\nThe global $P_{\\rm dot}$ was $-0.43(0.05) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of KV UMa (2000).}\\label{tab:kvumaoc2000}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 51634.6924 & 0.0049 & $-$0.0016 & 262 \\\\\n6 & 51635.6902 & 0.0076 & $-$0.0269 & 269 \\\\\n7 & 51635.8547 & 0.0029 & $-$0.0329 & 332 \\\\\n9 & 51636.2067 & 0.0026 & $-$0.0219 & 339 \\\\\n11 & 51636.5675 & 0.0061 & $-$0.0022 & 139 \\\\\n12 & 51636.7238 & 0.0016 & $-$0.0163 & 322 \\\\\n13 & 51636.8721 & 0.0034 & $-$0.0386 & 256 \\\\\n44 & 51642.1861 & 0.0060 & $-$0.0106 & 216 \\\\\n47 & 51642.7033 & 0.0030 & $-$0.0050 & 302 \\\\\n50 & 51643.2040 & 0.0035 & $-$0.0159 & 319 \\\\\n67 & 51646.1234 & 0.0032 & 0.0047 & 301 \\\\\n68 & 51646.2830 & 0.0090 & $-$0.0062 & 183 \\\\\n73 & 51647.1499 & 0.0029 & 0.0081 & 291 \\\\\n74 & 51647.3038 & 0.0084 & $-$0.0085 & 204 \\\\\n79 & 51648.1637 & 0.0067 & $-$0.0012 & 116 \\\\\n97 & 51651.2340 & 0.0034 & $-$0.0002 & 303 \\\\\n124 & 51655.8592 & 0.0030 & 0.0209 & 91 \\\\\n143 & 51659.0872 & 0.0021 & 0.0091 & 207 \\\\\n157 & 51661.4826 & 0.0014 & 0.0172 & 423 \\\\\n168 & 51663.3514 & 0.0015 & 0.0103 & 329 \\\\\n169 & 51663.5266 & 0.0024 & 0.0150 & 258 \\\\\n170 & 51663.6969 & 0.0021 & 0.0148 & 325 \\\\\n174 & 51664.3556 & 0.0013 & $-$0.0086 & 253 \\\\\n176 & 51664.7106 & 0.0021 & 0.0054 & 414 \\\\\n192 & 51667.4434 & 0.0016 & 0.0099 & 255 \\\\\n196 & 51668.1256 & 0.0022 & 0.0100 & 339 \\\\\n197 & 51668.2866 & 0.0059 & 0.0005 & 169 \\\\\n198 & 51668.4571 & 0.0048 & 0.0005 & 136 \\\\\n208 & 51670.1646 & 0.0110 & 0.0027 & 200 \\\\\n225 & 51673.0836 & 0.0022 & 0.0230 & 336 \\\\\n231 & 51674.0974 & 0.0025 & 0.0137 & 330 \\\\\n288 & 51683.8159 & 0.0039 & 0.0126 & 213 \\\\\n301 & 51686.0379 & 0.0036 & 0.0178 & 317 \\\\\n302 & 51686.2179 & 0.0144 & 0.0273 & 159 \\\\\n313 & 51688.0759 & 0.0041 & 0.0096 & 330 \\\\\n319 & 51689.1095 & 0.0027 & 0.0201 & 341 \\\\\n325 & 51690.1186 & 0.0049 & 0.0061 & 325 \\\\\n348 & 51694.0587 & 0.0025 & 0.0242 & 268 \\\\\n366 & 51697.1087 & 0.0167 & 0.0049 & 73 \\\\\n383 & 51700.0164 & 0.0016 & 0.0138 & 342 \\\\\n384 & 51700.1707 & 0.0033 & $-$0.0024 & 191 \\\\\n389 & 51701.0352 & 0.0018 & 0.0095 & 249 \\\\\n395 & 51702.0577 & 0.0018 & 0.0089 & 340 \\\\\n401 & 51703.0799 & 0.0019 & 0.0080 & 327 \\\\\n448 & 51711.0806 & 0.0053 & $-$0.0058 & 273 \\\\\n471 & 51715.0013 & 0.0033 & $-$0.0070 & 283 \\\\\n524 & 51724.0308 & 0.0039 & $-$0.0150 & 249 \\\\\n565 & 51731.0189 & 0.0108 & $-$0.0181 & 249 \\\\\n571 & 51732.0578 & 0.0068 & $-$0.0024 & 178 \\\\\n606 & 51737.9900 & 0.0041 & $-$0.0383 & 160 \\\\\n641 & 51743.9930 & 0.0062 & $-$0.0034 & 256 \\\\\n647 & 51744.9802 & 0.0184 & $-$0.0394 & 232 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2451634.6939 + 0.170519 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{MR Ursae Majoris}\\label{obj:mruma}\n\n MR UMa = 1RXP J113123$+$4322.5 is an ROSAT-selected CV\n\\citep{wei97mruma}, which underwent the first secure recorded\noutburst in 2002 (vsnet-alert 7221).\nWe observed the middle-to-late stage of the 2002 superoutburst\n(table \\ref{tab:mrumaoc2002}, figure \\ref{fig:octrans}).\nThe data clearly indicated a stage B--C transition around $E = 80$.\nThe $P_{\\rm dot}$ of the stage B was $+9.3(1.2) \\times 10^{-5}$.\nThe behavior was very similar during the 2003 and 2007 superoutbursts\n(tables \\ref{tab:mrumaoc2003}, \\ref{tab:mrumaoc2007};\nfigure \\ref{fig:mrumacomp}),\nwith $P_{\\rm dot}$ = $+6.0(2.3) \\times 10^{-5}$ (2003, $E \\le 84$) and\n$P_{\\rm dot}$ = $+3.8(1.6) \\times 10^{-5}$ (2007, $E \\le 79$).\nFor more information of the 2003, 2004 and 2005 superoutbursts,\nsee \\citet{tan07mruma}, although they did not distinguish different\nstages of period evolution.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig159.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of MR UMa between different\n superoutbursts. A period of 0.06512 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n 2007 superoutburst were used. Since the starts of the 2002 and 2003\n superoutburst were not well constrained, we shifted the $O-C$ diagrams\n to best fit the 2007 one.\n }\n \\label{fig:mrumacomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of MR UMa (2002).}\\label{tab:mrumaoc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52340.2579 & 0.0002 & 0.0003 & 123 \\\\\n28 & 52342.0774 & 0.0003 & $-$0.0013 & 150 \\\\\n29 & 52342.1416 & 0.0003 & $-$0.0021 & 166 \\\\\n30 & 52342.2069 & 0.0002 & $-$0.0019 & 277 \\\\\n31 & 52342.2717 & 0.0002 & $-$0.0021 & 333 \\\\\n32 & 52342.3371 & 0.0004 & $-$0.0018 & 122 \\\\\n46 & 52343.2493 & 0.0003 & $-$0.0002 & 329 \\\\\n47 & 52343.3135 & 0.0003 & $-$0.0010 & 203 \\\\\n74 & 52345.0771 & 0.0007 & 0.0065 & 120 \\\\\n76 & 52345.2052 & 0.0006 & 0.0045 & 76 \\\\\n77 & 52345.2708 & 0.0007 & 0.0050 & 125 \\\\\n78 & 52345.3374 & 0.0006 & 0.0066 & 121 \\\\\n89 & 52346.0458 & 0.0006 & $-$0.0004 & 74 \\\\\n92 & 52346.2435 & 0.0007 & 0.0022 & 120 \\\\\n93 & 52346.3070 & 0.0007 & 0.0006 & 117 \\\\\n105 & 52347.0863 & 0.0006 & $-$0.0006 & 109 \\\\\n107 & 52347.2153 & 0.0007 & $-$0.0016 & 118 \\\\\n108 & 52347.2765 & 0.0006 & $-$0.0055 & 115 \\\\\n109 & 52347.3398 & 0.0005 & $-$0.0072 & 89 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452340.2576 + 0.065041 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of MR UMa (2003).}\\label{tab:mrumaoc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52711.9773 & 0.0042 & $-$0.0067 & 75 \\\\\n1 & 52712.0441 & 0.0003 & $-$0.0049 & 250 \\\\\n2 & 52712.1100 & 0.0002 & $-$0.0039 & 424 \\\\\n3 & 52712.1743 & 0.0002 & $-$0.0046 & 456 \\\\\n4 & 52712.2381 & 0.0004 & $-$0.0058 & 209 \\\\\n5 & 52712.3044 & 0.0007 & $-$0.0044 & 166 \\\\\n6 & 52712.3681 & 0.0006 & $-$0.0056 & 96 \\\\\n7 & 52712.4333 & 0.0003 & $-$0.0054 & 66 \\\\\n8 & 52712.4983 & 0.0005 & $-$0.0053 & 51 \\\\\n16 & 52713.0191 & 0.0006 & $-$0.0041 & 108 \\\\\n22 & 52713.4080 & 0.0005 & $-$0.0049 & 80 \\\\\n23 & 52713.4704 & 0.0004 & $-$0.0075 & 59 \\\\\n24 & 52713.5377 & 0.0004 & $-$0.0051 & 63 \\\\\n25 & 52713.6043 & 0.0007 & $-$0.0035 & 64 \\\\\n37 & 52714.3810 & 0.0007 & $-$0.0061 & 68 \\\\\n38 & 52714.4491 & 0.0007 & $-$0.0030 & 68 \\\\\n39 & 52714.5191 & 0.0011 & 0.0020 & 61 \\\\\n40 & 52714.5753 & 0.0006 & $-$0.0067 & 57 \\\\\n52 & 52715.3607 & 0.0012 & $-$0.0007 & 68 \\\\\n53 & 52715.4291 & 0.0019 & 0.0027 & 68 \\\\\n54 & 52715.4930 & 0.0017 & 0.0017 & 39 \\\\\n62 & 52716.0228 & 0.0014 & 0.0119 & 79 \\\\\n63 & 52716.0846 & 0.0036 & 0.0088 & 82 \\\\\n67 & 52716.3375 & 0.0013 & 0.0018 & 43 \\\\\n68 & 52716.4062 & 0.0008 & 0.0057 & 94 \\\\\n69 & 52716.4719 & 0.0003 & 0.0064 & 79 \\\\\n77 & 52716.9882 & 0.0045 & 0.0031 & 105 \\\\\n78 & 52717.0615 & 0.0011 & 0.0114 & 104 \\\\\n79 & 52717.1233 & 0.0014 & 0.0083 & 134 \\\\\n80 & 52717.1907 & 0.0006 & 0.0108 & 187 \\\\\n81 & 52717.2516 & 0.0037 & 0.0067 & 122 \\\\\n82 & 52717.3200 & 0.0011 & 0.0101 & 134 \\\\\n83 & 52717.3817 & 0.0047 & 0.0069 & 69 \\\\\n84 & 52717.4504 & 0.0006 & 0.0106 & 68 \\\\\n85 & 52717.5134 & 0.0012 & 0.0087 & 67 \\\\\n93 & 52718.0305 & 0.0010 & 0.0062 & 230 \\\\\n94 & 52718.0971 & 0.0011 & 0.0078 & 150 \\\\\n95 & 52718.1596 & 0.0017 & 0.0054 & 154 \\\\\n96 & 52718.2253 & 0.0015 & 0.0061 & 185 \\\\\n97 & 52718.2884 & 0.0011 & 0.0043 & 235 \\\\\n98 & 52718.3552 & 0.0016 & 0.0061 & 94 \\\\\n99 & 52718.4225 & 0.0011 & 0.0085 & 67 \\\\\n100 & 52718.4825 & 0.0011 & 0.0036 & 68 \\\\\n108 & 52719.0098 & 0.0026 & 0.0112 & 157 \\\\\n109 & 52719.0643 & 0.0009 & 0.0008 & 114 \\\\\n110 & 52719.1407 & 0.0014 & 0.0122 & 120 \\\\\n111 & 52719.1939 & 0.0011 & 0.0005 & 100 \\\\\n113 & 52719.3239 & 0.0011 & 0.0006 & 191 \\\\\n114 & 52719.3919 & 0.0007 & 0.0037 & 130 \\\\\n115 & 52719.4549 & 0.0005 & 0.0017 & 130 \\\\\n139 & 52720.9997 & 0.0017 & $-$0.0123 & 68 \\\\\n140 & 52721.0633 & 0.0018 & $-$0.0136 & 100 \\\\\n141 & 52721.1181 & 0.0012 & $-$0.0237 & 68 \\\\\n143 & 52721.2431 & 0.0016 & $-$0.0287 & 110 \\\\\n144 & 52721.3065 & 0.0089 & $-$0.0303 & 107 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452711.9840 + 0.064949 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of MR UMa (2007).}\\label{tab:mrumaoc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54207.5744 & 0.0004 & $-$0.0008 & 26 \\\\\n1 & 54207.6398 & 0.0005 & $-$0.0005 & 34 \\\\\n2 & 54207.7043 & 0.0003 & $-$0.0010 & 34 \\\\\n3 & 54207.7705 & 0.0006 & 0.0001 & 23 \\\\\n16 & 54208.6139 & 0.0006 & $-$0.0021 & 34 \\\\\n17 & 54208.6801 & 0.0008 & $-$0.0010 & 34 \\\\\n18 & 54208.7456 & 0.0011 & $-$0.0006 & 21 \\\\\n46 & 54210.5662 & 0.0012 & $-$0.0014 & 30 \\\\\n47 & 54210.6355 & 0.0007 & 0.0028 & 39 \\\\\n48 & 54210.6987 & 0.0009 & 0.0010 & 29 \\\\\n78 & 54212.6537 & 0.0007 & 0.0045 & 38 \\\\\n79 & 54212.7186 & 0.0007 & 0.0043 & 40 \\\\\n92 & 54213.5610 & 0.0011 & 0.0010 & 34 \\\\\n93 & 54213.6250 & 0.0008 & $-$0.0001 & 39 \\\\\n94 & 54213.6916 & 0.0011 & 0.0015 & 35 \\\\\n108 & 54214.6025 & 0.0015 & 0.0017 & 44 \\\\\n109 & 54214.6644 & 0.0013 & $-$0.0014 & 44 \\\\\n110 & 54214.7313 & 0.0017 & 0.0004 & 39 \\\\\n124 & 54215.6412 & 0.0030 & $-$0.0005 & 43 \\\\\n125 & 54215.6989 & 0.0013 & $-$0.0079 & 44 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454207.5752 + 0.065052 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CU Velorum}\\label{obj:cuvel}\n\n Although CU Vel had long been known as an SU UMa-type dwarf nova\n\\citep{vog80suumastars}, the details of the reported superhump period\n(0.0799 d, \\cite{RitterCV3}) was not reported in a solid publication.\n\\citet{men96cuvel} reported an orbital period of 0.0785 d.\n\n We observed the 2002 superoutburst.\nThe times of superhumps maxima are listed in table \\ref{tab:cuveloc2002}.\nThe object clearly showed the stage A development with a longer period.\nExcluding this epoch ($E = 0$), we obtained $P_{\\rm dot}$ =\n$-8.4(1.4) \\times 10^{-5}$ for the stage B.\nA PDM analysis yielded a mean superhump period of 0.080789(5) d\n(figure \\ref{fig:cuvelshpdm}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig160.eps}\n \\end{center}\n \\caption{Superhumps in CU Vel (2002). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:cuvelshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of CU Vel (2002).}\\label{tab:cuveloc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52620.2188 & 0.0003 & $-$0.0205 & 239 \\\\\n22 & 52622.0161 & 0.0007 & $-$0.0012 & 20 \\\\\n35 & 52623.0687 & 0.0002 & 0.0007 & 192 \\\\\n36 & 52623.1495 & 0.0002 & 0.0006 & 408 \\\\\n37 & 52623.2310 & 0.0003 & 0.0013 & 295 \\\\\n49 & 52624.2007 & 0.0002 & 0.0011 & 146 \\\\\n50 & 52624.2806 & 0.0004 & 0.0002 & 155 \\\\\n51 & 52624.3687 & 0.0003 & 0.0075 & 124 \\\\\n59 & 52625.0117 & 0.0003 & 0.0040 & 173 \\\\\n60 & 52625.0935 & 0.0004 & 0.0049 & 220 \\\\\n61 & 52625.1785 & 0.0003 & 0.0091 & 158 \\\\\n72 & 52626.0623 & 0.0002 & 0.0038 & 304 \\\\\n73 & 52626.1437 & 0.0002 & 0.0044 & 456 \\\\\n74 & 52626.2257 & 0.0002 & 0.0056 & 506 \\\\\n75 & 52626.3052 & 0.0003 & 0.0043 & 197 \\\\\n97 & 52628.0777 & 0.0002 & $-$0.0013 & 111 \\\\\n98 & 52628.1591 & 0.0002 & $-$0.0007 & 184 \\\\\n109 & 52629.0445 & 0.0003 & $-$0.0044 & 281 \\\\\n110 & 52629.1249 & 0.0002 & $-$0.0048 & 427 \\\\\n111 & 52629.2062 & 0.0002 & $-$0.0043 & 301 \\\\\n122 & 52630.0946 & 0.0006 & $-$0.0049 & 116 \\\\\n123 & 52630.1752 & 0.0005 & $-$0.0051 & 113 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452620.2393 + 0.080822 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{HS Virginis}\\label{sec:hsvir}\\label{obj:hsvir}\n\n We reanalyzed the data in \\citet{kat98hsvir}. Double-wave modulations\nwere observed on 1996 March 18 (BJD 2450161) during the fading stage from\nthe superoutburst plateau (the same feature was also recorded by\n\\cite{pat03suumas}). These modulations were probably associated\nwith the manifestation of traditional late superhumps. We listed\ntimes of maxima of ordinary superhumps in table \\ref{tab:hsviroc1996} and\nsecondary maxima in table \\ref{tab:hsviroc1996-2}. The agreement of\nperiods independently determined from these two sets strengthens the\nidentification of the latter as being traditional late superhumps.\nSince \\citet{kat98hsvir} did not take into account the present knowledge\nin period variation and late superhumps, their period was contaminated\nby these phenomena. The mean $P_{\\rm SH}$ for $23 \\le E \\le 99$ was\n0.08006(3) d, giving a fractional period excess of 4.1 \\%, slightly smaller\nthan the previous estimate. The global $P_{\\rm dot}$ was\n$-18.3(3.8) \\times 10^{-5}$, which is apparently affected by the stage A\nevolution ($E \\le 23$).\n\n The analysis of the 2008 superoutburst (table \\ref{tab:hsviroc2008})\nduring its middle-to-late stage yielded a period of 0.08003(3) d,\nin good agreement with the above analysis of the 1996 superoutburst.\n\n\\begin{table}\n\\caption{Superhump maxima of HS Vir (1996).}\\label{tab:hsviroc1996}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50153.3417 & 0.0006 & $-$0.0158 & 89 \\\\\n12 & 50154.3201 & 0.0007 & 0.0002 & 88 \\\\\n23 & 50155.2087 & 0.0018 & 0.0067 & 52 \\\\\n35 & 50156.1718 & 0.0006 & 0.0073 & 124 \\\\\n36 & 50156.2465 & 0.0008 & 0.0018 & 49 \\\\\n37 & 50156.3324 & 0.0006 & 0.0074 & 73 \\\\\n98 & 50161.2147 & 0.0020 & $-$0.0024 & 142 \\\\\n99 & 50161.2922 & 0.0021 & $-$0.0052 & 125 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450153.3575 + 0.080201 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Secondary Maxima of HS Vir (1996).}\\label{tab:hsviroc1996-2}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 50161.1697 & 0.0016 & $-$0.0003 & 86 \\\\\n1 & 50161.2506 & 0.0014 & 0.0003 & 147 \\\\\n26 & 50163.2594 & 0.0006 & $-$0.0000 & 95 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2450161.1700 + 0.080361 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of HS Vir (2008).}\\label{tab:hsviroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54619.0407 & 0.0006 & 0.0016 & 130 \\\\\n11 & 54619.9184 & 0.0006 & $-$0.0010 & 106 \\\\\n12 & 54619.9983 & 0.0005 & $-$0.0010 & 87 \\\\\n62 & 54624.0011 & 0.0072 & 0.0004 & 66 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454619.0390 + 0.080028 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{HV Virginis}\\label{obj:hvvir}\n\n Analyses of superhumps of this WZ Sge-type dwarf nova have been\nwell documented (\\cite{kat01hvvir}; \\cite{ish03hvvir}).\nWe present our new observation of the 2008 superoutburst.\nOnly ordinary superhumps are treated here (table \\ref{tab:hvviroc2008}).\nThe $O-C$ diagram resembles those of many systems with short superhump\nperiods, consisting of stages A--C (note, however, these stages\nwere preceded by a stage of early superhumps in this object).\nThe $P_{\\rm dot}$ of the stage B was $+7.1(1.9) \\times 10^{-5}$\n($18 \\le E \\le 157$). The value is in good agreement with those\nobtained during previous superoutbursts:\n$+7(1) \\times 10^{-5}$ \\citep{ish03hvvir} and\n$+5.7(0.6) \\times 10^{-5}$ \\citep{kat01hvvir}.\n\n The $O-C$ diagrams after the appearance of ordinary superhumps were\nsimilar between superoutburst (figure \\ref{fig:hvvircomp}), although\nthe delay before the appearance of ordinary superhumps was shorter\nin a fainter superoutburst in 2002 (subsection \\ref{sec:wzsgedelay}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig161.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of HV Vir between different\n superoutbursts. A period of 0.05828 d was used to draw this figure.\n Approximate cycle counts ($E$) after the appearance of the ordinary\n superhumps were used.\n }\n \\label{fig:hvvircomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of HV Vir (2008).}\\label{tab:hvviroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54517.1492 & 0.0005 & 0.0001 & 103 \\\\\n1 & 54517.2071 & 0.0007 & $-$0.0003 & 146 \\\\\n2 & 54517.2634 & 0.0009 & $-$0.0023 & 60 \\\\\n3 & 54517.3248 & 0.0020 & 0.0009 & 61 \\\\\n18 & 54518.2019 & 0.0003 & 0.0040 & 239 \\\\\n19 & 54518.2590 & 0.0003 & 0.0029 & 219 \\\\\n51 & 54520.1195 & 0.0008 & $-$0.0010 & 99 \\\\\n52 & 54520.1751 & 0.0005 & $-$0.0037 & 103 \\\\\n69 & 54521.1593 & 0.0007 & $-$0.0100 & 102 \\\\\n70 & 54521.2194 & 0.0010 & $-$0.0081 & 92 \\\\\n71 & 54521.2803 & 0.0009 & $-$0.0055 & 60 \\\\\n120 & 54524.1479 & 0.0017 & 0.0072 & 103 \\\\\n124 & 54524.3735 & 0.0015 & $-$0.0002 & 58 \\\\\n125 & 54524.4331 & 0.0014 & 0.0011 & 65 \\\\\n126 & 54524.4885 & 0.0010 & $-$0.0018 & 50 \\\\\n138 & 54525.1888 & 0.0022 & $-$0.0006 & 389 \\\\\n140 & 54525.3173 & 0.0029 & 0.0114 & 302 \\\\\n154 & 54526.1273 & 0.0011 & 0.0057 & 96 \\\\\n155 & 54526.1862 & 0.0008 & 0.0063 & 130 \\\\\n156 & 54526.2456 & 0.0028 & 0.0075 & 55 \\\\\n157 & 54526.3021 & 0.0030 & 0.0057 & 55 \\\\\n171 & 54527.1136 & 0.0016 & 0.0015 & 36 \\\\\n172 & 54527.1744 & 0.0005 & 0.0041 & 178 \\\\\n173 & 54527.2329 & 0.0012 & 0.0043 & 135 \\\\\n174 & 54527.2893 & 0.0010 & 0.0024 & 70 \\\\\n188 & 54528.0919 & 0.0058 & $-$0.0106 & 32 \\\\\n189 & 54528.1605 & 0.0009 & $-$0.0003 & 59 \\\\\n190 & 54528.2164 & 0.0016 & $-$0.0026 & 60 \\\\\n191 & 54528.2763 & 0.0020 & $-$0.0010 & 44 \\\\\n205 & 54529.1004 & 0.0036 & 0.0074 & 37 \\\\\n207 & 54529.2104 & 0.0023 & 0.0009 & 58 \\\\\n208 & 54529.2605 & 0.0014 & $-$0.0073 & 60 \\\\\n209 & 54529.3214 & 0.0070 & $-$0.0047 & 58 \\\\\n225 & 54530.2533 & 0.0021 & $-$0.0050 & 38 \\\\\n226 & 54530.3084 & 0.0039 & $-$0.0082 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454517.1491 + 0.058263 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OU Virginis}\\label{obj:ouvir}\n\n OU Vir was a CV discovered through a survey for quasars \\citep{ber92LBQS}.\n\\citet{van00ouvir} established that the object is an eclipsing SU UMa-type\ndwarf nova, but their superhump period was rather poorly determined.\n\\citet{pat05SH} presented an analysis of the 2003 superoutburst\nand reported a superhump period of 0.0751(1) d. They did not give times\nof superhump maxima.\n\n We present the analysis of the 2003 superoutburst, the data partly\noverlapping those in \\citet{pat05SH}. Observations outside the eclipses,\nas described in V2051 Oph, were used in analysis.\nThe mean superhump period with the PDM method was 0.074950(7) d\n(figure \\ref{fig:ouvirshpdm}). The times of superhump maxima are\nlisted in table \\ref{tab:ouviroc2003}.\nThe $O-C$'s showed a slight signature\nof a discontinuous change around $E = 50$, but its nature remained\nuncertain because of the relatively large scatter in the data.\nAlthough we determined a global $P_{\\rm dot}$ of $-1.8(0.6) \\times 10^{-5}$,\nthis value apparently needs to be verified by a detailed future study\nsince eclipsing SU UMa-type dwarf novae are often associated\nwith more or less complexity in analysis. The early stage of the\n2008 superoutburst was also observed (table \\ref{tab:ouviroc2008}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig162.eps}\n \\end{center}\n \\caption{Superhumps in OU Vir (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:ouvirshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OU Vir (2003).}\\label{tab:ouviroc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52764.9749 & 0.0019 & $-$0.0033 & 197 \\\\\n1 & 52765.0514 & 0.0007 & $-$0.0017 & 230 \\\\\n2 & 52765.1208 & 0.0004 & $-$0.0072 & 309 \\\\\n4 & 52765.2722 & 0.0015 & $-$0.0056 & 157 \\\\\n33 & 52767.4449 & 0.0020 & $-$0.0054 & 84 \\\\\n34 & 52767.5222 & 0.0016 & $-$0.0030 & 50 \\\\\n43 & 52768.2004 & 0.0012 & 0.0010 & 84 \\\\\n44 & 52768.2699 & 0.0026 & $-$0.0045 & 100 \\\\\n46 & 52768.4237 & 0.0068 & $-$0.0004 & 29 \\\\\n47 & 52768.5053 & 0.0014 & 0.0062 & 70 \\\\\n48 & 52768.5829 & 0.0014 & 0.0090 & 48 \\\\\n59 & 52769.4050 & 0.0013 & 0.0070 & 71 \\\\\n60 & 52769.4777 & 0.0012 & 0.0048 & 69 \\\\\n61 & 52769.5518 & 0.0016 & 0.0040 & 70 \\\\\n72 & 52770.3765 & 0.0024 & 0.0046 & 89 \\\\\n73 & 52770.4489 & 0.0013 & 0.0022 & 155 \\\\\n99 & 52772.3966 & 0.0015 & 0.0021 & 65 \\\\\n100 & 52772.4674 & 0.0026 & $-$0.0020 & 58 \\\\\n209 & 52780.6333 & 0.0026 & $-$0.0015 & 32 \\\\\n216 & 52781.1498 & 0.0058 & $-$0.0094 & 264 \\\\\n217 & 52781.2372 & 0.0043 & 0.0031 & 185 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452764.9782 + 0.074912 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of OU Vir (2008).}\\label{tab:ouviroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54556.4839 & 0.0006 & 0.0000 & 102 \\\\\n1 & 54556.5565 & 0.0010 & $-$0.0023 & 107 \\\\\n2 & 54556.6333 & 0.0030 & $-$0.0005 & 54 \\\\\n11 & 54557.3122 & 0.0030 & 0.0038 & 47 \\\\\n21 & 54558.0646 & 0.0063 & 0.0065 & 105 \\\\\n22 & 54558.1318 & 0.0009 & $-$0.0012 & 99 \\\\\n23 & 54558.2049 & 0.0014 & $-$0.0031 & 141 \\\\\n24 & 54558.2797 & 0.0019 & $-$0.0032 & 64 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454556.4839 + 0.074962 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{QZ Virginis}\\label{obj:qzvir}\n\n We reanalyzed the data in \\citet{kat97tleo}. The refined times of\nsuperhump maxima, together with those in \\citet{lem93tleo}, are listed\nin table \\ref{tab:qzviroc1993}. The earliest part ($E \\le 1$) showed\nlarge deviations from the nominal superhump period, as discussed in\n\\citet{kat97tleo}. A strongly negative $O-C$ at $E = 9$ may be\ninterpreted as early development with a longer period (stage A).\nThanks to the improvement in determination of times of maxima,\nit has now become evident that the segment $15 \\le E \\le 101$ showed\na positive $P_{\\rm dot}$ (stage B).\nDisregarding the discrepant points $E = 34$ and $E = 50$,\nwe obtained $P_{\\rm dot}$ = $+7.0(1.4) \\times 10^{-5}$.\n\n This period derivative and the overall behavior is similar to\nthose during the 2007 and 2008 superoutbursts (tables\n\\ref{tab:qzviroc2007}, \\ref{tab:qzviroc2008};\nfigure \\ref{fig:qzvircomp}).\nThe $P_{\\rm dot}$'s for the corresponding segment\nwere $+4.5(7.6) \\times 10^{-5}$ ($E \\le 53$, 2007)\nand $+4.7(1.9) \\times 10^{-5}$ ($E \\le 85$, 2008).\nA fragmentary observation of the 2005 superoutburst is also given\n(table \\ref{tab:qzviroc2005}).\nThe negative $P_{\\rm dot}$ in \\citet{lem93tleo}\nprobably resulted from a stage A--B transition and sparse sampling.\n\n The 2009 superoutburst was particularly well observed\n(table \\ref{tab:qzviroc2009}). This superoutburst was preceded by\na distinct precursor and followed by a rebrightening.\nDespite the presence of a precursor, the $P_{\\rm dot}$ during the\nstage B ($E \\le 91$) was positive with $+11.4(1.8) \\times 10^{-5}$.\nThe stage C superhumps had a period of 0.06000(1) before $E=152$,\nthen the period slightly shortened to 0.05992(7) d.\nThese late-stage superhumps apparently endured during the period\nof the rebrightening.\n\n Further detailed analysis will be presented in \\citet{ohs09qzvir}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig163.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of QZ Vir between different\n superoutbursts. A period of 0.06038 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n superoutburst were used. The start of the 2008 superoutburst was\n missed. The $O-C$ analysis suggests that the superoutburst started\n two days before the initial detection. The $O-C$ diagram was shifted\n by this value.\n }\n \\label{fig:qzvircomp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of QZ Vir (1993).}\\label{tab:qzviroc1993}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 48990.3101 & 0.0008 & 0.0053 & 138 \\\\\n1 & 48990.3617 & 0.0006 & $-$0.0034 & 134 \\\\\n9 & 48990.8417 & -- & $-$0.0054 & 0 \\\\\n15 & 48991.2056 & 0.0022 & $-$0.0030 & 55 \\\\\n16 & 48991.2678 & 0.0006 & $-$0.0010 & 99 \\\\\n17 & 48991.3273 & 0.0010 & $-$0.0019 & 89 \\\\\n18 & 48991.3873 & 0.0021 & $-$0.0021 & 22 \\\\\n25 & 48991.8096 & -- & $-$0.0015 & 0 \\\\\n26 & 48991.8689 & -- & $-$0.0025 & 0 \\\\\n34 & 48992.3636 & 0.0050 & 0.0102 & 49 \\\\\n41 & 48992.7735 & -- & $-$0.0017 & 0 \\\\\n42 & 48992.8348 & -- & $-$0.0006 & 0 \\\\\n49 & 48993.2570 & 0.0003 & $-$0.0002 & 121 \\\\\n50 & 48993.3249 & 0.0016 & 0.0074 & 97 \\\\\n51 & 48993.3751 & 0.0012 & $-$0.0026 & 74 \\\\\nc58 & 48993.7958 & -- & $-$0.0037 & 0 \\\\\n59 & 48993.8561 & -- & $-$0.0036 & 0 \\\\\n98 & 48996.2138 & 0.0013 & 0.0042 & 124 \\\\\n99 & 48996.2755 & 0.0007 & 0.0056 & 136 \\\\\n100 & 48996.3367 & 0.0011 & 0.0066 & 131 \\\\\n101 & 48996.3968 & 0.0014 & 0.0064 & 71 \\\\\n150 & 48999.3414 & 0.0023 & $-$0.0014 & 71 \\\\\n164 & 49000.1857 & 0.0025 & $-$0.0006 & 79 \\\\\n165 & 49000.2361 & 0.0015 & $-$0.0105 & 138 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2448990.3048 + 0.060253 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N = 0$ refers to \\citet{lem93tleo}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of QZ Vir (2005).}\\label{tab:qzviroc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53678.2944 & 0.0005 & 0.0014 & 178 \\\\\n1 & 53678.3520 & 0.0005 & $-$0.0014 & 143 \\\\\n50 & 53681.3174 & 0.0035 & 0.0000 & 45 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453678.2930 + 0.060488 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of QZ Vir (2007).}\\label{tab:qzviroc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54111.1604 & 0.0005 & $-$0.0031 & 137 \\\\\n1 & 54111.2177 & 0.0002 & $-$0.0061 & 428 \\\\\n2 & 54111.2782 & 0.0004 & $-$0.0058 & 338 \\\\\n3 & 54111.3396 & 0.0003 & $-$0.0047 & 299 \\\\\n18 & 54112.2430 & 0.0012 & $-$0.0052 & 89 \\\\\n19 & 54112.3038 & 0.0010 & $-$0.0046 & 45 \\\\\n35 & 54113.2777 & 0.0009 & 0.0052 & 88 \\\\\n36 & 54113.3362 & 0.0004 & 0.0035 & 269 \\\\\n50 & 54114.1820 & 0.0004 & 0.0057 & 137 \\\\\n51 & 54114.2428 & 0.0003 & 0.0063 & 149 \\\\\n52 & 54114.3023 & 0.0002 & 0.0055 & 321 \\\\\n53 & 54114.3619 & 0.0002 & 0.0049 & 289 \\\\\n66 & 54115.1480 & 0.0007 & 0.0077 & 168 \\\\\n67 & 54115.2030 & 0.0003 & 0.0024 & 426 \\\\\n68 & 54115.2626 & 0.0003 & 0.0018 & 326 \\\\\n69 & 54115.3241 & 0.0003 & 0.0030 & 322 \\\\\n83 & 54116.1652 & 0.0008 & 0.0006 & 67 \\\\\n84 & 54116.2248 & 0.0007 & $-$0.0001 & 131 \\\\\n135 & 54119.2808 & 0.0006 & $-$0.0170 & 133 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454111.1636 + 0.060254 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of QZ Vir (2008).}\\label{tab:qzviroc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54470.2452 & 0.0002 & $-$0.0075 & 346 \\\\\n1 & 54470.3062 & 0.0004 & $-$0.0067 & 322 \\\\\n2 & 54470.3653 & 0.0006 & $-$0.0078 & 214 \\\\\n16 & 54471.2088 & 0.0004 & $-$0.0065 & 114 \\\\\n17 & 54471.2705 & 0.0002 & $-$0.0050 & 307 \\\\\n18 & 54471.3302 & 0.0002 & $-$0.0055 & 598 \\\\\n19 & 54471.3905 & 0.0002 & $-$0.0054 & 206 \\\\\n31 & 54472.1143 & 0.0006 & $-$0.0035 & 107 \\\\\n32 & 54472.1773 & 0.0004 & $-$0.0006 & 105 \\\\\n33 & 54472.2352 & 0.0003 & $-$0.0029 & 107 \\\\\n51 & 54473.3237 & 0.0010 & 0.0027 & 213 \\\\\n52 & 54473.3834 & 0.0007 & 0.0023 & 237 \\\\\n68 & 54474.3561 & 0.0004 & 0.0123 & 281 \\\\\n81 & 54475.1356 & 0.0004 & 0.0097 & 253 \\\\\n82 & 54475.2009 & 0.0005 & 0.0148 & 273 \\\\\n83 & 54475.2589 & 0.0002 & 0.0127 & 334 \\\\\n84 & 54475.3197 & 0.0004 & 0.0133 & 287 \\\\\n85 & 54475.3794 & 0.0003 & 0.0129 & 254 \\\\\n99 & 54476.2200 & 0.0004 & 0.0112 & 106 \\\\\n132 & 54478.1997 & 0.0006 & 0.0055 & 114 \\\\\n133 & 54478.2569 & 0.0008 & 0.0026 & 115 \\\\\n134 & 54478.3211 & 0.0005 & 0.0067 & 115 \\\\\n150 & 54479.2678 & 0.0008 & $-$0.0093 & 108 \\\\\n151 & 54479.3350 & 0.0006 & $-$0.0022 & 115 \\\\\n154 & 54479.5139 & 0.0005 & $-$0.0039 & 65 \\\\\n155 & 54479.5672 & 0.0007 & $-$0.0106 & 105 \\\\\n156 & 54479.6343 & 0.0005 & $-$0.0038 & 103 \\\\\n157 & 54479.6948 & 0.0006 & $-$0.0034 & 111 \\\\\n165 & 54480.1799 & 0.0011 & 0.0004 & 118 \\\\\n166 & 54480.2327 & 0.0007 & $-$0.0069 & 127 \\\\\n167 & 54480.2912 & 0.0004 & $-$0.0086 & 232 \\\\\n168 & 54480.3530 & 0.0004 & $-$0.0070 & 229 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454470.2527 + 0.060162 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of QZ Vir (2009).}\\label{tab:qzviroc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54856.1944 & 0.0006 & $-$0.0097 & 118 \\\\\n1 & 54856.2497 & 0.0003 & $-$0.0144 & 118 \\\\\n15 & 54857.0893 & 0.0004 & $-$0.0159 & 38 \\\\\n16 & 54857.1517 & 0.0002 & $-$0.0136 & 213 \\\\\n17 & 54857.2130 & 0.0003 & $-$0.0124 & 158 \\\\\n18 & 54857.2726 & 0.0002 & $-$0.0129 & 223 \\\\\n19 & 54857.3322 & 0.0003 & $-$0.0134 & 168 \\\\\n40 & 54858.5987 & 0.0002 & $-$0.0086 & 120 \\\\\n51 & 54859.2629 & 0.0002 & $-$0.0053 & 340 \\\\\n52 & 54859.3232 & 0.0001 & $-$0.0050 & 562 \\\\\n67 & 54860.2321 & 0.0003 & 0.0026 & 268 \\\\\n68 & 54860.2912 & 0.0007 & 0.0016 & 285 \\\\\n69 & 54860.3498 & 0.0008 & 0.0001 & 247 \\\\\n73 & 54860.5924 & 0.0004 & 0.0024 & 112 \\\\\n74 & 54860.6544 & 0.0004 & 0.0043 & 116 \\\\\n88 & 54861.5045 & 0.0004 & 0.0133 & 143 \\\\\n89 & 54861.5626 & 0.0003 & 0.0113 & 143 \\\\\n90 & 54861.6220 & 0.0003 & 0.0107 & 143 \\\\\n91 & 54861.6830 & 0.0004 & 0.0115 & 142 \\\\\n105 & 54862.5245 & 0.0002 & 0.0119 & 261 \\\\\n106 & 54862.5843 & 0.0003 & 0.0116 & 259 \\\\\n107 & 54862.6439 & 0.0004 & 0.0111 & 149 \\\\\n108 & 54862.7028 & 0.0004 & 0.0099 & 142 \\\\\n122 & 54863.5435 & 0.0004 & 0.0095 & 143 \\\\\n123 & 54863.6040 & 0.0004 & 0.0099 & 143 \\\\\n124 & 54863.6638 & 0.0005 & 0.0097 & 143 \\\\\n125 & 54863.7223 & 0.0003 & 0.0081 & 135 \\\\\n132 & 54864.1464 & 0.0008 & 0.0116 & 348 \\\\\n133 & 54864.2049 & 0.0002 & 0.0100 & 391 \\\\\n134 & 54864.2638 & 0.0003 & 0.0088 & 384 \\\\\n135 & 54864.3207 & 0.0005 & 0.0057 & 384 \\\\\n149 & 54865.1638 & 0.0009 & 0.0076 & 97 \\\\\n150 & 54865.2219 & 0.0004 & 0.0057 & 189 \\\\\n151 & 54865.2848 & 0.0004 & 0.0084 & 193 \\\\\n152 & 54865.3427 & 0.0013 & 0.0063 & 116 \\\\\n200 & 54868.2184 & 0.0009 & $-$0.0019 & 94 \\\\\n201 & 54868.2717 & 0.0021 & $-$0.0088 & 111 \\\\\n216 & 54869.1734 & 0.0012 & $-$0.0083 & 64 \\\\\n217 & 54869.2311 & 0.0006 & $-$0.0107 & 153 \\\\\n218 & 54869.2965 & 0.0005 & $-$0.0053 & 132 \\\\\n232 & 54870.1265 & 0.0017 & $-$0.0165 & 56 \\\\\n233 & 54870.1963 & 0.0005 & $-$0.0068 & 62 \\\\\n234 & 54870.2555 & 0.0007 & $-$0.0076 & 62 \\\\\n249 & 54871.1532 & 0.0017 & $-$0.0111 & 224 \\\\\n251 & 54871.2689 & 0.0072 & $-$0.0156 & 157 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454856.2040 + 0.060082 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{RX Volantis}\\label{obj:rxvol}\n\n Although RX Vol was listed as a possible SU UMa-type dwarf nova\nwith a maximum of magnitude 16 \\citep{GCVS}, little had been known\nuntil 2003.\nThe first-ever outburst since the discovery, at an exceptional\nbrightness of 14.7, was reported on 2003 May 4\n(R. Stubbings, vsnet-outburst 5482). This outburst turned out\nto be a superoutburst (vsnet-outburst 5502).\nThe mean superhump period with the PDM method was 0.061348(7) d\n(figure \\ref{fig:rxvolshpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:rxvoloc2003}.\nThe object clearly showed positive superhump derivative except for\nthe earliest part. $P_{\\rm dot}$ was $+5.8(0.8) \\times 10^{-5}$ for\n($E \\ge 12$). \\citet{sch05rxvol} summarized the history of this\nobject and presented a spectrum in quiescence.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig164.eps}\n \\end{center}\n \\caption{Superhumps in RX Vol (2003). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:rxvolshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of RX Vol (2003).}\\label{tab:rxvoloc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52764.0491 & 0.0009 & 0.0029 & 110 \\\\\n1 & 52764.1074 & 0.0008 & $-$0.0001 & 100 \\\\\n12 & 52764.7858 & 0.0005 & 0.0032 & 159 \\\\\n13 & 52764.8466 & 0.0004 & 0.0026 & 270 \\\\\n14 & 52764.9077 & 0.0004 & 0.0023 & 204 \\\\\n15 & 52764.9688 & 0.0004 & 0.0021 & 204 \\\\\n16 & 52765.0301 & 0.0004 & 0.0020 & 205 \\\\\n19 & 52765.2143 & 0.0006 & 0.0022 & 62 \\\\\n20 & 52765.2770 & 0.0007 & 0.0035 & 66 \\\\\n21 & 52765.3368 & 0.0008 & 0.0019 & 70 \\\\\n22 & 52765.3954 & 0.0009 & $-$0.0008 & 70 \\\\\n31 & 52765.9479 & 0.0009 & $-$0.0006 & 161 \\\\\n36 & 52766.2529 & 0.0006 & $-$0.0024 & 57 \\\\\n37 & 52766.3164 & 0.0006 & $-$0.0003 & 61 \\\\\n38 & 52766.3728 & 0.0012 & $-$0.0053 & 68 \\\\\n52 & 52767.2333 & 0.0010 & $-$0.0039 & 72 \\\\\n53 & 52767.2934 & 0.0012 & $-$0.0051 & 71 \\\\\n54 & 52767.3553 & 0.0011 & $-$0.0046 & 58 \\\\\n68 & 52768.2145 & 0.0010 & $-$0.0045 & 72 \\\\\n69 & 52768.2757 & 0.0017 & $-$0.0046 & 71 \\\\\n70 & 52768.3399 & 0.0012 & $-$0.0018 & 71 \\\\\n85 & 52769.2619 & 0.0019 & $-$0.0003 & 71 \\\\\n86 & 52769.3237 & 0.0016 & 0.0002 & 69 \\\\\n101 & 52770.2446 & 0.0027 & 0.0006 & 70 \\\\\n133 & 52772.2127 & 0.0013 & 0.0050 & 71 \\\\\n134 & 52772.2747 & 0.0027 & 0.0057 & 71 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452764.0462 + 0.061364 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TY Vulpeculae}\\label{obj:tyvul}\n\n \\citet{kat99tyvul} suggested the SU UMa-type nature of this object\nbased on the observation of the 1999 September short outburst.\nThe SU UMa-type nature of TY Vul was established by Vanmunster et al.\n(aavso-photometry message on 2003 December 7)\\footnote{\n $<$http:\/\/www.aavso.org\/pipermail\/aavso-photometry\/2003-December\/000153.html$>$.\n}, who reported a period of 0.0809(2) d. We observed the same superoutburst\nand obtained the times of superhump maxima after incorporating the\nAAVSO data (table \\ref{tab:tyvuloc2003}).\nThe period of 0.08048(7) d can satisfactorily expressed the maxima,\nand the period was in agreement with the one by Vanmunster et al.\nThe resultant $O-C$ diagram showed a large negative period derivative\n$P_{\\rm dot}$ = $-14.8(3.0) \\times 10^{-5}$ for the entire span of\nobservations. This large variation can be attributed to a stage B--C\ntransition. The parameters based on this interpretation are given\nin table \\ref{tab:perlist}.\nThe object may be similar to AX Cap and SDSS J1627 in the evolution\nof the superhump period (see subsection \\ref{sec:longp}).\n\n\\begin{table}\n\\caption{Superhump maxima of TY Vul (2003).}\\label{tab:tyvuloc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52976.8787 & 0.0017 & $-$0.0213 & 115 \\\\\n1 & 52976.9653 & 0.0036 & $-$0.0153 & 139 \\\\\n7 & 52977.4546 & 0.0012 & $-$0.0088 & 45 \\\\\n8 & 52977.5447 & 0.0008 & 0.0008 & 67 \\\\\n9 & 52977.6266 & 0.0019 & 0.0022 & 37 \\\\\n12 & 52977.8734 & 0.0009 & 0.0075 & 110 \\\\\n13 & 52977.9471 & 0.0015 & 0.0007 & 148 \\\\\n14 & 52978.0234 & 0.0037 & $-$0.0035 & 45 \\\\\n42 & 52980.2944 & 0.0023 & 0.0140 & 112 \\\\\n50 & 52980.9377 & 0.0024 & 0.0134 & 119 \\\\\n51 & 52981.0194 & 0.0032 & 0.0147 & 72 \\\\\n54 & 52981.2534 & 0.0011 & 0.0072 & 104 \\\\\n55 & 52981.3292 & 0.0018 & 0.0025 & 97 \\\\\n63 & 52981.9853 & 0.0044 & 0.0147 & 115 \\\\\n67 & 52982.2998 & 0.0010 & 0.0073 & 89 \\\\\n68 & 52982.3786 & 0.0019 & 0.0057 & 49 \\\\\n70 & 52982.5368 & 0.0061 & 0.0029 & 61 \\\\\n79 & 52983.2488 & 0.0006 & $-$0.0095 & 43 \\\\\n80 & 52983.3292 & 0.0022 & $-$0.0096 & 43 \\\\\n116 & 52986.2255 & 0.0014 & $-$0.0107 & 37 \\\\\n120 & 52986.5434 & 0.0051 & $-$0.0148 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452976.9001 + 0.080484 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{DO Vulpeculae}\\label{obj:dovul}\n\n Although DO Vul had long been known as a dwarf nova \\citep{baa28VS},\nthe identification was only recently known (\\cite{ski97dovul};\n\\cite{hen01dovul}).\n\n Vanmunster reported the detection of superhumps with a period of\n0.065 d during the 2005 outburst.\n\n Observations of the 2008 superoutburst yielded a mean period\nof 0.058286(14) d (PDM analysis, figure \\ref{fig:dovulshpdm})\nand a $P_{\\rm dot}$ of $+9.9(2.1) \\times 10^{-5}$\n(table \\ref{tab:dovuloc2008}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig165.eps}\n \\end{center}\n \\caption{Superhumps in DO Vul (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:dovulshpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of DO Vul (2008).}\\label{tab:dovuloc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54671.1058 & 0.0070 & 0.0170 & 83 \\\\\n19 & 54672.1978 & 0.0060 & 0.0032 & 58 \\\\\n33 & 54673.0010 & 0.0030 & $-$0.0085 & 76 \\\\\n34 & 54673.0668 & 0.0008 & $-$0.0009 & 107 \\\\\n50 & 54673.9948 & 0.0015 & $-$0.0041 & 67 \\\\\n51 & 54674.0489 & 0.0003 & $-$0.0082 & 125 \\\\\n52 & 54674.1111 & 0.0004 & $-$0.0043 & 96 \\\\\n71 & 54675.2216 & 0.0027 & 0.0004 & 82 \\\\\n120 & 54678.0700 & 0.0025 & $-$0.0032 & 29 \\\\\n121 & 54678.1308 & 0.0045 & $-$0.0006 & 22 \\\\\n137 & 54679.0580 & 0.0030 & $-$0.0046 & 120 \\\\\n138 & 54679.1190 & 0.0015 & $-$0.0019 & 124 \\\\\n155 & 54680.1195 & 0.0075 & 0.0092 & 84 \\\\\n156 & 54680.1748 & 0.0018 & 0.0063 & 119 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454671.0887 + 0.058204 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{NSV 4838}\\label{obj:nsv4838}\n\n The times of superhump maxima during the 2005 and 2007 superoutbursts\nare listed in tables \\ref{tab:nsv4838oc2005} and \\ref{tab:nsv4838oc2007}\nThe observations used here partly include the data in \\citet{ima09nsv4838}.\nThe $P_{\\rm dot}$ for the 2007 superoutburst ($0 \\le E \\le 101$, stage B)\nwas $+7.4(1.9) \\times 10^{-5}$. The 2005 superoutburst was apparently\nobserved during the stage C. The period of 0.06960(3) d obtained by\nthe PDM analysis confirmed the $O-C$ analysis. The object underwent\nanother superoutburst in 2009 February.\n\n\\begin{table}\n\\caption{Superhump maxima of NSV 4838 (2005).}\\label{tab:nsv4838oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53528.4392 & 0.0046 & $-$0.0040 & 39 \\\\\n14 & 53529.4228 & 0.0016 & 0.0042 & 92 \\\\\n15 & 53529.4787 & 0.0020 & $-$0.0095 & 42 \\\\\n28 & 53530.3987 & 0.0015 & 0.0048 & 86 \\\\\n29 & 53530.4660 & 0.0006 & 0.0024 & 162 \\\\\n43 & 53531.4406 & 0.0014 & 0.0016 & 75 \\\\\n44 & 53531.5142 & 0.0052 & 0.0056 & 27 \\\\\n86 & 53534.4297 & 0.0018 & $-$0.0050 & 55 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453528.4432 + 0.069668 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of NSV 4838 (2007).}\\label{tab:nsv4838oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54139.1208 & 0.0011 & $-$0.0018 & 176 \\\\\n1 & 54139.1858 & 0.0004 & $-$0.0066 & 233 \\\\\n2 & 54139.2561 & 0.0004 & $-$0.0061 & 208 \\\\\n3 & 54139.3275 & 0.0004 & $-$0.0045 & 185 \\\\\n58 & 54143.1687 & 0.0007 & $-$0.0021 & 155 \\\\\n59 & 54143.2408 & 0.0006 & 0.0001 & 249 \\\\\n73 & 54144.2176 & 0.0009 & $-$0.0002 & 250 \\\\\n74 & 54144.2898 & 0.0010 & 0.0022 & 208 \\\\\n101 & 54146.1839 & 0.0015 & 0.0117 & 60 \\\\\n115 & 54147.1579 & 0.0008 & 0.0086 & 117 \\\\\n116 & 54147.2293 & 0.0007 & 0.0101 & 146 \\\\\n117 & 54147.2975 & 0.0014 & 0.0085 & 91 \\\\\n129 & 54148.1327 & 0.0005 & 0.0062 & 123 \\\\\n130 & 54148.2021 & 0.0007 & 0.0057 & 257 \\\\\n131 & 54148.2710 & 0.0009 & 0.0049 & 217 \\\\\n157 & 54150.0767 & 0.0017 & $-$0.0041 & 148 \\\\\n158 & 54150.1483 & 0.0012 & $-$0.0024 & 149 \\\\\n159 & 54150.2179 & 0.0012 & $-$0.0025 & 133 \\\\\n171 & 54151.0560 & 0.0007 & $-$0.0020 & 140 \\\\\n172 & 54151.1248 & 0.0010 & $-$0.0031 & 128 \\\\\n185 & 54152.0349 & 0.0037 & $-$0.0003 & 141 \\\\\n186 & 54152.0939 & 0.0017 & $-$0.0111 & 116 \\\\\n187 & 54152.1749 & 0.0041 & 0.0001 & 117 \\\\\n188 & 54152.2372 & 0.0085 & $-$0.0074 & 124 \\\\\n189 & 54152.3104 & 0.0025 & $-$0.0040 & 127 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454139.1226 + 0.069798 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{NSV 5285}\\label{obj:nsv5285}\n\n NSV 5285 was originally discovered as a blue eruptive object\nthat underwent an outburst at $B = 14.5$ \\citep{kow75nsv5285}.\nThe object remained bright at least for five days and faded to\n$B \\sim 20$ thereafter. \\citet{kow75nsv5285} suggested that this\nobject is probably a quasar which underwent a 5.5-mag outburst.\n\\citet{dus08nsv5285cbet1574} detected an outbursting variable star,\nwhich turned out to be identical with NSV 5285. Subsequent photometric\nobservations established that this is an superoutburst of an SU UMa-type\ndwarf nova (vsnet-alert 10726). The times of superhump maxima are\ngiven in table \\ref{tab:nsv5285oc2008}. The mean $P_{\\rm SH}$\nusing the PDM method was 0.08082(3) d.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig166.eps}\n \\end{center}\n \\caption{Superhumps in NSV 5285 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:nsv5285shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of NSV 5285 (2008).}\\label{tab:nsv5285oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54791.3043 & 0.0013 & 0.0019 & 52 \\\\\n11 & 54792.2686 & 0.0008 & $-$0.0015 & 94 \\\\\n12 & 54792.3566 & 0.0009 & $-$0.0014 & 97 \\\\\n34 & 54794.2945 & 0.0008 & 0.0010 & 179 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454791.3024 + 0.087973 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{NSV 14652}\\label{obj:nsv14652}\n\n NSV 14652 was discovered by \\citet{rei30VS} as a variable star\n(AN 254.1930). The object was positively recorded twice in 1901 and 1904.\nThe object was identified with a ROSAT source (vsnet-chat 3314).\nT. Kinnunen detected the object in outburst on a Palomar Observatory\nSky Survey scan (cf. vsnet-alert 5203, 5205).\n\n We present times of superhump maxima during a superoutburst in 2004\nSeptember (table \\ref{tab:nsv14652oc2004}). The mean $P_{\\rm SH}$\nwith the PDM method was 0.08148(1) d (figure \\ref{fig:nsv14652shpdm}).\nThe $O-C$ diagram showed a stage B--C transition around $E=50$.\nThe $P_{\\rm dot}$ during the stage B was close to zero,\n$-3.0(3.6) \\times 10^{-5}$. The other parameters are listed in\ntable \\ref{tab:perlist}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig167.eps}\n \\end{center}\n \\caption{Superhumps in NSV 14652 (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:nsv14652shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of NSV 14652 (2004).}\\label{tab:nsv14652oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53251.4459 & 0.0006 & $-$0.0016 & 79 \\\\\n1 & 53251.5282 & 0.0007 & $-$0.0008 & 82 \\\\\n2 & 53251.6107 & 0.0010 & 0.0003 & 64 \\\\\n12 & 53252.4245 & 0.0008 & $-$0.0005 & 69 \\\\\n13 & 53252.5057 & 0.0016 & $-$0.0007 & 59 \\\\\n36 & 53254.3814 & 0.0007 & 0.0015 & 68 \\\\\n37 & 53254.4646 & 0.0008 & 0.0032 & 56 \\\\\n38 & 53254.5438 & 0.0008 & 0.0010 & 52 \\\\\n48 & 53255.3602 & 0.0011 & 0.0028 & 69 \\\\\n49 & 53255.4397 & 0.0007 & 0.0008 & 67 \\\\\n50 & 53255.5212 & 0.0008 & 0.0009 & 63 \\\\\n60 & 53256.3308 & 0.0007 & $-$0.0041 & 53 \\\\\n61 & 53256.4137 & 0.0015 & $-$0.0027 & 35 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453251.4475 + 0.081457 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{1RXS J023238.8-371812}\\label{sec:j0232}\\label{obj:j0232}\n\n In 2007 October, K. Malek (``Pi of the Sky''\\footnote{\n $<$http:\/\/grb.fuw.edu.pl\/pi\/index.html$>$.\n}) reported a possible nova outburst (vsnet-alert 9622) close to\nthe location of 1RXS J023238.8$-$371812 (hereafter 1RXS J0232).\nT. Kato suggested that the object\ncan be identified with a 6dF Galactic object and that it is most likely\na large-amplitude dwarf nova (vsnet-alert 9620). This suggestion\nwas later confirmed by the detection of superhumps\n(vsnet-alert 9634). The superoutburst was unusual in that it had both\na ``dip'', characteristic to type-A superoutbursts\n(subsection \\ref{sec:wzsgeouttype}), during the superoutburst plateau and\nfour distinct post-superoutburst rebrightenings, characteristic to type-B\nsuperoutbursts (figure \\ref{fig:j0232lc}).\n\n The times of superhump maxima during the main superoutburst are\nlisted in table \\ref{tab:j0232oc2007}.\nThe resultant $P_{\\rm dot}$ was $-1.7(0.7) \\times 10^{-5}$.\nSince the only later portion of the superoutburst was observed,\nthis value may have been affected by a possible stage B--C transition.\nThe only small variation of the $P_{\\rm SH}$, however,\nmay be associated with the extreme WZ Sge-type nature of this object.\n\n The period analyses and superhump profiles are presented in figures\n\\ref{fig:j0232mainpdm} and \\ref{fig:j0232rebpdm}. The analysis\nduring the rebrightening phase follows the same way as in SDSS J0804\n\\citep{kat09j0804}. The mean $P_{\\rm SH}$ during the main superoutburst\nwas 0.066191(4) d. During the rebrightening phase, two candidate\nperiods were present: 0.066963(4) d and 0.065851(4) d.\nSince the former period is 1.2 \\% longer than the $P_{\\rm SH}$ during\nthe main superoutburst, it appears to be slightly too long for a superhump\nperiod at this stage (see subsection \\ref{sec:latestage}).\nThe latter period, 0.5 \\% shorter than the $P_{\\rm SH}$, which\nmight represent the orbital period.\nThe phase-averaged profile also resembles that\nof orbital humps rather than superhumps (cf. \\cite{kat09j0804}).\nIf this identification of the period is confirmed, the small $\\epsilon$\nwould place 1RXS J0232 similar to EG Cnc. Since the periodicity can be\nvery complex during rebrightenings \\citep{kat09j0804} and since the\ncoverage of the rebrightening phase was not sufficient, further\nobservations are needed to correctly identify the periods.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig168.eps}\n \\end{center}\n \\caption{Superoutburst of 1RXS J0232 in 2007. The data are a combination\n of our observations, VSNET, ASAS-3 and ``Pi of the Sky'' observations.\n The ``V''-marks indicate upper limits. There was a ``dip'' during the\n superoutburst plateau (around BJD 2454374).\n Four post-superoutburst rebrightenings were recorded.}\n \\label{fig:j0232lc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig169.eps}\n \\end{center}\n \\caption{Superhumps in 1RXS J0232 during the main superoutburst.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0232mainpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig170.eps}\n \\end{center}\n \\caption{Hump features in 1RXS J0232 during the rebrightening phase.\n (Upper): PDM analysis. A period of 0.065850(4) is selected\n by a comparison with the superhump period (see text).\n Another potential period is 0.066963(4) d.\n (Lower): Phase-averaged profile at the period of 0.065850 d.}\n \\label{fig:j0232rebpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of 1RXS J0232 (2007).}\\label{tab:j0232oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54376.0443 & 0.0003 & $-$0.0020 & 191 \\\\\n1 & 54376.1127 & 0.0002 & 0.0002 & 285 \\\\\n46 & 54379.0904 & 0.0003 & 0.0005 & 66 \\\\\n47 & 54379.1566 & 0.0003 & 0.0005 & 68 \\\\\n48 & 54379.2231 & 0.0003 & 0.0009 & 65 \\\\\n49 & 54379.2886 & 0.0004 & 0.0001 & 68 \\\\\n50 & 54379.3550 & 0.0003 & 0.0004 & 69 \\\\\n60 & 54380.0178 & 0.0004 & 0.0015 & 287 \\\\\n61 & 54380.0835 & 0.0005 & 0.0010 & 337 \\\\\n62 & 54380.1487 & 0.0004 & 0.0001 & 339 \\\\\n63 & 54380.2149 & 0.0003 & 0.0001 & 68 \\\\\n64 & 54380.2811 & 0.0003 & 0.0002 & 69 \\\\\n65 & 54380.3467 & 0.0003 & $-$0.0004 & 69 \\\\\n75 & 54381.0065 & 0.0005 & $-$0.0023 & 160 \\\\\n106 & 54383.0589 & 0.0005 & $-$0.0010 & 152 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454376.0463 + 0.066166 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{1RXS J042332$+$745300}\\label{sec:j0423}\\label{obj:j0423}\n\n 1RXS J042332$+$745300 (=HS 0417$+$7445, hereafter 1RXS J0423) is\na CV \\citep{wu01j0209j0423} selected from the ROSAT catalog and also\nselected spectroscopically \\citep{aun06HSCV}. Although \\citet{aun06HSCV}\ndetected superhumps during the 2001 superoutburst, the period was not\nprecisely determined.\n\n We observed the 2008 superoutburst and identified the correct\n$P_{\\rm SH}$. Combined with the AAVSO observations, we obtained\na mean $P_{\\rm SH}$ of 0.078320(6) d.\nAmong candidate $P_{\\rm orb}$ given in \\citet{aun06HSCV}, the period\nof 0.07632 d best fits our $P_{\\rm SH}$, and gives a fractional superhump\nexcess of 2.6 \\%.\nThe times of superhump maxima are listed in table \\ref{tab:j0423oc2008}.\n\n This outburst was associated with a precursor\n($E \\le 2$, figure \\ref{fig:j0423oc}).\nA longer period was observed for $E \\le 30$ during the developmental\nstage of superhumps.\nThis duration of stage A was thus rather unusually long. Although there was\na slight indication of a stage B--C transition around $E=68$, the change\nin the period was smaller than in other systems with similar\nsuperhump periods. The periods listed in table \\ref{tab:perlist} are\nbased on this interpretation.\nThe presence of a precursor and the relatively short ($\\sim$ 10 d) duration\nof this superoutburst might signify a ``borderline'' superoutburst\nas observed in BZ UMa in 2007 (subsection \\ref{sec:bzuma}), which may be\nresponsible for the unusual development of superhumps.\nFurther investigation of this object is still needed.\n\n The light curve became double-humped during the post-superoutburst stage.\nThe three maxima of secondary humps ($E=153$, the first one of $E=166$,\nand $E=167$) were excluded in the period analysis presented\nin table \\ref{tab:perlist}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig171.eps}\n \\end{center}\n \\caption{Ordinary superhumps in 1RXS J0423 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0423shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig172.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps 1RXS J0423 (2008).\n (Upper): $O-C$ diagram. The $O-C$ values were against the global\n mean period of 0.078320 d. Open squares represent likely secondary\n hump maxima.\n (Lower): Light curve. The last pre-outburst observation was\n on BJD 2454525.5 at magnitude 17.4.}\n \\label{fig:j0423oc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of 1RXS J0423 (2008).}\\label{tab:j0423oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54530.3689 & 0.0019 & $-$0.0412 & 247 \\\\\n1 & 54530.4581 & 0.0008 & $-$0.0302 & 294 \\\\\n2 & 54530.5199 & 0.0016 & $-$0.0466 & 195 \\\\\n15 & 54531.5647 & 0.0021 & $-$0.0186 & 86 \\\\\n16 & 54531.6461 & 0.0003 & $-$0.0155 & 167 \\\\\n17 & 54531.7271 & 0.0002 & $-$0.0127 & 163 \\\\\n18 & 54531.8075 & 0.0002 & $-$0.0105 & 158 \\\\\n24 & 54532.2842 & 0.0002 & $-$0.0031 & 155 \\\\\n25 & 54532.3641 & 0.0002 & $-$0.0014 & 158 \\\\\n26 & 54532.4432 & 0.0002 & $-$0.0005 & 163 \\\\\n27 & 54532.5204 & 0.0002 & $-$0.0016 & 168 \\\\\n28 & 54532.6013 & 0.0004 & 0.0011 & 328 \\\\\n29 & 54532.6814 & 0.0004 & 0.0030 & 164 \\\\\n30 & 54532.7615 & 0.0002 & 0.0049 & 205 \\\\\n31 & 54532.8376 & 0.0005 & 0.0027 & 85 \\\\\n35 & 54533.1552 & 0.0003 & 0.0075 & 239 \\\\\n36 & 54533.2294 & 0.0010 & 0.0035 & 147 \\\\\n37 & 54533.3123 & 0.0003 & 0.0082 & 495 \\\\\n38 & 54533.3916 & 0.0002 & 0.0093 & 378 \\\\\n39 & 54533.4680 & 0.0002 & 0.0075 & 591 \\\\\n40 & 54533.5478 & 0.0003 & 0.0090 & 278 \\\\\n41 & 54533.6247 & 0.0004 & 0.0076 & 129 \\\\\n45 & 54533.9369 & 0.0005 & 0.0071 & 165 \\\\\n46 & 54534.0140 & 0.0003 & 0.0059 & 173 \\\\\n50 & 54534.3272 & 0.0004 & 0.0062 & 213 \\\\\n51 & 54534.4050 & 0.0002 & 0.0058 & 343 \\\\\n52 & 54534.4882 & 0.0002 & 0.0108 & 262 \\\\\n53 & 54534.5648 & 0.0002 & 0.0092 & 121 \\\\\n59 & 54535.0365 & 0.0005 & 0.0115 & 150 \\\\\n63 & 54535.3475 & 0.0003 & 0.0097 & 338 \\\\\n64 & 54535.4280 & 0.0003 & 0.0120 & 212 \\\\\n65 & 54535.5042 & 0.0004 & 0.0100 & 193 \\\\\n66 & 54535.5828 & 0.0004 & 0.0104 & 293 \\\\\n67 & 54535.6624 & 0.0004 & 0.0118 & 104 \\\\\n68 & 54535.7439 & 0.0006 & 0.0150 & 51 \\\\\n72 & 54536.0504 & 0.0008 & 0.0087 & 160 \\\\\n73 & 54536.1253 & 0.0006 & 0.0053 & 161 \\\\\n77 & 54536.4406 & 0.0004 & 0.0077 & 99 \\\\\n78 & 54536.5177 & 0.0005 & 0.0066 & 101 \\\\\n79 & 54536.5986 & 0.0003 & 0.0093 & 167 \\\\\n80 & 54536.6770 & 0.0003 & 0.0094 & 165 \\\\\n81 & 54536.7533 & 0.0003 & 0.0075 & 149 \\\\\n82 & 54536.8352 & 0.0007 & 0.0112 & 98 \\\\\n103 & 54538.4714 & 0.0006 & 0.0048 & 108 \\\\\n104 & 54538.5501 & 0.0003 & 0.0053 & 137 \\\\\n105 & 54538.6310 & 0.0003 & 0.0080 & 102 \\\\\n106 & 54538.7092 & 0.0008 & 0.0080 & 82 \\\\\n107 & 54538.7881 & 0.0004 & 0.0087 & 69 \\\\\n153 & 54542.3301 & 0.0009 & $-$0.0473 & 102 \\\\\n166 & 54543.3462 & 0.0038 & $-$0.0481 & 61 \\\\\n166 & 54543.4001 & 0.0022 & 0.0058 & 54 \\\\\n167 & 54543.4535 & 0.0008 & $-$0.0189 & 65 \\\\\n168 & 54543.5606 & 0.0018 & 0.0099 & 18 \\\\\n169 & 54543.6203 & 0.0037 & $-$0.0086 & 18 \\\\\n170 & 54543.7092 & 0.0036 & 0.0020 & 18 \\\\\n171 & 54543.7824 & 0.0014 & $-$0.0029 & 18 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454530.4101 + 0.078218 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{1RXS J053234.9$+$624755}\\label{obj:j0532}\n\n This object (hereafter 1RXS J0532) was discovered as a dwarf nova\nby \\citet{ber05j0532}. \\citet{kap06j0532} provided a radial-velocity\nstudy and yielded an orbital period of 0.05620(4) d. (See also\n\\cite{kap06j0532} for the history of superhump observation).\n\\citet{par06j0532} observed the 2006 July superoutburst and reported\na period of 0.05707(12) d. We report on the 2005 and 2008 superoutbursts.\nThe 2005 superoutburst (data from \\cite{ima09j0532},\na combination of our data and the AAVSO observations)\nshowed a prominent precursor outburst\nassociated with superhumps. This behavior was very similar to QZ Vir\n(=T Leo) in 1993 \\citep{kat97tleo}.\nThe mean superhump period with the PDM method was 0.057120(6) d\n(figure \\ref{fig:j0532shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0532oc2005}.\nThe $O-C$ diagram showed a stage B--C transition\n(figure \\ref{fig:j05322005oc}).\nThe behavior in the period during the transition from the\nprecursor outburst was quite different from the one in QZ Vir in 1993\n\\citep{kat97tleo}. The $P_{\\rm dot}$ in the former interval\n($E \\le 162$) was $+5.7(0.8) \\times 10^{-5}$.\nThe 2008 superoutburst was observed except for the late stage\n(table \\ref{tab:j0532oc2008}). The $O-C$ behavior was similar to\nthat of the 2005 one, giving $P_{\\rm dot}$ = $+10.2(0.8) \\times 10^{-5}$\n($E \\le 138$). Since there was no clear precursor at the onset of the\n2008 superoutburst, the $P_{\\rm dot}$ does not seem to show\nvery strong dependence on the presence of a precursor, on the contrary to\n\\citet{uem05tvcrv}. The development of the superhumps during the 2005\nsuperoutburst, however, may have been earlier by $\\sim$ 26 superhump\ncycles compared to the 2008 one (figure \\ref{fig:j0532comp}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig173.eps}\n \\end{center}\n \\caption{Superhumps in 1RXS J0532 (2005). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0532shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig174.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps 1RXS J0532 (2005).\n (Upper): $O-C$ diagram. The curve represents a quadratic fit to\n $E \\le 162$.\n (Lower): Light curve. The superoutburst was preceded by a precursor.\n }\n \\label{fig:j05322005oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig175.eps}\n \\end{center}\n \\caption{Comparison of $O-C$ diagrams of 1RXS J0532 between different\n superoutbursts. A period of 0.05716 d was used to draw this figure.\n Approximate cycle counts ($E$) after the start of the\n 2008 superoutburst were used. The $O-C$ diagram of the 2005 superoutburst\n bet fits the 2008 one by assuming an earlier development of the\n superhumps by $\\sim$ 26 superhump cycles.\n }\n \\label{fig:j0532comp}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of 1RXS J0532 (2005).}\\label{tab:j0532oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53447.3252 & 0.0021 & 0.0014 & 34 \\\\\n1 & 53447.3834 & 0.0016 & 0.0025 & 44 \\\\\n2 & 53447.4384 & 0.0006 & 0.0004 & 34 \\\\\n3 & 53447.4980 & 0.0009 & 0.0028 & 29 \\\\\n4 & 53447.5494 & 0.0011 & $-$0.0028 & 33 \\\\\n5 & 53447.6069 & 0.0008 & $-$0.0024 & 33 \\\\\n17 & 53448.2963 & 0.0005 & 0.0018 & 36 \\\\\n18 & 53448.3502 & 0.0006 & $-$0.0014 & 133 \\\\\n19 & 53448.4069 & 0.0004 & $-$0.0018 & 161 \\\\\n20 & 53448.4648 & 0.0004 & $-$0.0010 & 174 \\\\\n21 & 53448.5265 & 0.0014 & 0.0036 & 66 \\\\\n22 & 53448.5817 & 0.0006 & 0.0017 & 33 \\\\\n23 & 53448.6351 & 0.0007 & $-$0.0020 & 23 \\\\\n31 & 53449.0926 & 0.0004 & $-$0.0013 & 93 \\\\\n35 & 53449.3202 & 0.0004 & $-$0.0020 & 111 \\\\\n36 & 53449.3776 & 0.0002 & $-$0.0018 & 143 \\\\\n37 & 53449.4354 & 0.0002 & $-$0.0011 & 143 \\\\\n38 & 53449.4920 & 0.0004 & $-$0.0016 & 32 \\\\\n39 & 53449.5481 & 0.0004 & $-$0.0026 & 28 \\\\\n40 & 53449.6063 & 0.0011 & $-$0.0015 & 19 \\\\\n48 & 53450.0615 & 0.0003 & $-$0.0031 & 104 \\\\\n53 & 53450.3475 & 0.0004 & $-$0.0026 & 33 \\\\\n54 & 53450.4041 & 0.0004 & $-$0.0031 & 33 \\\\\n55 & 53450.4628 & 0.0005 & $-$0.0015 & 34 \\\\\n56 & 53450.5191 & 0.0006 & $-$0.0023 & 33 \\\\\n57 & 53450.5762 & 0.0004 & $-$0.0022 & 33 \\\\\n58 & 53450.6337 & 0.0007 & $-$0.0019 & 30 \\\\\n90 & 53452.4606 & 0.0006 & $-$0.0021 & 68 \\\\\n91 & 53452.5182 & 0.0004 & $-$0.0016 & 99 \\\\\n92 & 53452.5727 & 0.0003 & $-$0.0043 & 80 \\\\\n105 & 53453.3128 & 0.0014 & $-$0.0064 & 52 \\\\\n106 & 53453.3732 & 0.0008 & $-$0.0032 & 178 \\\\\n107 & 53453.4296 & 0.0008 & $-$0.0038 & 171 \\\\\n108 & 53453.4888 & 0.0014 & $-$0.0018 & 159 \\\\\n109 & 53453.5449 & 0.0004 & $-$0.0027 & 81 \\\\\n110 & 53453.5994 & 0.0008 & $-$0.0053 & 58 \\\\\n136 & 53455.0887 & 0.0010 & $-$0.0006 & 179 \\\\\n137 & 53455.1520 & 0.0014 & 0.0056 & 107 \\\\\n140 & 53455.3248 & 0.0049 & 0.0072 & 81 \\\\\n141 & 53455.3818 & 0.0013 & 0.0070 & 103 \\\\\n153 & 53456.0686 & 0.0005 & 0.0087 & 176 \\\\\n157 & 53456.3115 & 0.0014 & 0.0231 & 34 \\\\\n158 & 53456.3547 & 0.0012 & 0.0093 & 37 \\\\\n159 & 53456.4114 & 0.0007 & 0.0088 & 37 \\\\\n160 & 53456.4697 & 0.0008 & 0.0100 & 38 \\\\\n161 & 53456.5189 & 0.0014 & 0.0021 & 37 \\\\\n162 & 53456.5927 & 0.0014 & 0.0188 & 37 \\\\\n194 & 53458.4126 & 0.0008 & 0.0115 & 26 \\\\\n195 & 53458.4636 & 0.0010 & 0.0054 & 38 \\\\\n196 & 53458.5165 & 0.0020 & 0.0012 & 37 \\\\\n197 & 53458.5804 & 0.0012 & 0.0081 & 38 \\\\\n211 & 53459.3739 & 0.0012 & 0.0022 & 40 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453447.3238 + 0.057099 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of 1RXS J0532 (2005) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n212 & 53459.4268 & 0.0009 & $-$0.0021 & 39 \\\\\n213 & 53459.4844 & 0.0021 & $-$0.0015 & 39 \\\\\n214 & 53459.5389 & 0.0019 & $-$0.0041 & 39 \\\\\n215 & 53459.6001 & 0.0026 & $-$0.0000 & 39 \\\\\n225 & 53460.1637 & 0.0027 & $-$0.0074 & 160 \\\\\n228 & 53460.3343 & 0.0018 & $-$0.0081 & 73 \\\\\n229 & 53460.3866 & 0.0011 & $-$0.0129 & 70 \\\\\n230 & 53460.4394 & 0.0009 & $-$0.0172 & 61 \\\\\n246 & 53461.3520 & 0.0020 & $-$0.0181 & 39 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of 1RXS J0532 (2008).}\\label{tab:j0532oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54474.1642 & 0.0013 & 0.0093 & 102 \\\\\n1 & 54474.2167 & 0.0010 & 0.0046 & 37 \\\\\n14 & 54474.9549 & 0.0003 & 0.0002 & 80 \\\\\n15 & 54475.0125 & 0.0002 & 0.0006 & 108 \\\\\n33 & 54476.0371 & 0.0002 & $-$0.0030 & 121 \\\\\n66 & 54477.9196 & 0.0004 & $-$0.0057 & 98 \\\\\n68 & 54478.0352 & 0.0005 & $-$0.0044 & 92 \\\\\n93 & 54479.4644 & 0.0004 & $-$0.0034 & 108 \\\\\n94 & 54479.5208 & 0.0005 & $-$0.0041 & 110 \\\\\n95 & 54479.5756 & 0.0004 & $-$0.0064 & 114 \\\\\n96 & 54479.6343 & 0.0004 & $-$0.0048 & 117 \\\\\n102 & 54479.9764 & 0.0008 & $-$0.0055 & 90 \\\\\n103 & 54480.0383 & 0.0005 & $-$0.0007 & 107 \\\\\n107 & 54480.2642 & 0.0005 & $-$0.0033 & 110 \\\\\n108 & 54480.3243 & 0.0011 & $-$0.0004 & 117 \\\\\n109 & 54480.3804 & 0.0003 & $-$0.0014 & 117 \\\\\n110 & 54480.4375 & 0.0005 & $-$0.0014 & 117 \\\\\n111 & 54480.4970 & 0.0013 & 0.0009 & 79 \\\\\n118 & 54480.8995 & 0.0011 & 0.0036 & 107 \\\\\n119 & 54480.9550 & 0.0007 & 0.0019 & 96 \\\\\n120 & 54481.0125 & 0.0009 & 0.0024 & 108 \\\\\n136 & 54481.9287 & 0.0008 & 0.0045 & 87 \\\\\n137 & 54481.9888 & 0.0009 & 0.0074 & 108 \\\\\n138 & 54482.0498 & 0.0008 & 0.0113 & 92 \\\\\n171 & 54483.9207 & 0.0006 & $-$0.0030 & 261 \\\\\n172 & 54483.9802 & 0.0005 & $-$0.0005 & 385 \\\\\n173 & 54484.0392 & 0.0013 & 0.0013 & 185 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454474.1550 + 0.057127 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{2QZ J021927.9$-$304545}\\label{obj:j0219}\n\n \\citet{ima06j0219} reported the 2005 superoutburst of this object\n(hereafter 2QZ J0219). We also observed the 2009 superoutburst\nduring its middle-to-late stage. The mean superhump period with\nthe PDM method was 0.08100(1) d, in good agreement with that of\nstage C superhumps during the 2005 superoutburst.\nThe times of superhump maxima are listed in table \\ref{tab:j0219oc2009}.\n\n\\begin{table}\n\\caption{Superhump maxima of 2QZ J0219 (2009)}\\label{tab:j0219oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54841.9576 & 0.0010 & 0.0015 & 94 \\\\\n12 & 54842.9286 & 0.0004 & 0.0002 & 395 \\\\\n24 & 54843.8982 & 0.0006 & $-$0.0023 & 253 \\\\\n25 & 54843.9810 & 0.0006 & $-$0.0005 & 271 \\\\\n49 & 54845.9290 & 0.0011 & 0.0032 & 260 \\\\\n50 & 54846.0001 & 0.0011 & $-$0.0068 & 127 \\\\\n61 & 54846.9029 & 0.0014 & 0.0049 & 224 \\\\\n62 & 54846.9821 & 0.0012 & 0.0030 & 267 \\\\\n74 & 54847.9480 & 0.0017 & $-$0.0032 & 189 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454841.9562 + 0.081014 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J002511$+$1217.2}\\label{sec:asas0025}\\label{obj:asas0025}\n\n ASAS J002511+1217.2 (hereafter ASAS J0025) is a dwarf nova discovered\nby the ASAS-3 \\citep{ASAS3} survey\n(cf. \\cite{pri04asas0025iauc8410}; for more information\nsee. e.g. \\cite{gol05asas0025} and \\cite{tem06asas0025}).\n\n \\citet{gol05asas0025} presented a preliminary period analysis and\nan $O-C$ diagram showing the presence of a variation in the superhump period.\n\\citet{tem06asas0025} claimed that the object belongs to WZ Sge-type\nsubclass based on their findings in the period variation and the presence\nof a rebrightening. The claim by \\citet{tem06asas0025}, however,\nled to a rather misguided conclusion because they compared the portions\nof different stages (ordinary superhumps in ASAS J0025 and early superhumps\nin WZ Sge), thereby resulting an inadequate period selection in drawing\nthe $O-C$ diagram. We used combined data set used in\n\\citet{tem06asas0025} and ours, and determined superhump maxima\nduring the superoutburst plateau and subsequent rapid fading\n(table \\ref{tab:asas0025oc2004}).\nThe object showed a clear positive period\nderivative before the terminal brightening (this agrees with\nthe general tendency in \\cite{gol05asas0025}). \nThe $P_{\\rm dot}$ in this interval ($E \\le 151$) was\n$+8.7(0.4) \\times 10^{-5}$.\nThe mean periods for the initial part ($E \\le 30$) and the last part\n($165 \\le E \\le 219$) were 0.05682(5) d and 0.05686(3) d, respectively,\nwhile the mean period during the entire plateau was 0.057109(7) d.\n\n The superhumps in this object showed complex behavior\n(see figure \\ref{fig:asas0025humpall}).\nAfter the termination of the main superoutburst, the superhumps became\ndoubly humped.\nOne the maxima (peak 1, dots in figure \\ref{fig:asas0025humpall})\nof these double waves, which are listed in table\n\\ref{tab:asas0025ochump2}, are on a smooth extension of the times of\nmaxima listed in table \\ref{tab:asas0025oc2004} (filled circles\nin figure \\ref{fig:asas0025humpall}), but had a shorter period.\nThe other (peak 2, open squares in figure \\ref{fig:asas0025humpall})\nare on a smooth extension of the times of the maxima\nduring the post-rebrightening stage (table \\ref{tab:asas0025ochump3}).\nThe mean periods of two components of the humps between the termination\nof the main superoutburst and rebrightening were 0.056833(12) d (peak 1)\nand 0.056829(21) d (peak 2), respectively. These periods almost exactly\nmatch the mean period during initial and last parts of the superoutburst\nplateau.\n\nThe mean period of the\nsuperhumps during the post-rebrightening stage (corresponding to\n$347 \\le E \\le 661$) was 0.057000(6) d. This period, longer than some\nof observed (super)hump periods at earlier times, is unlikely the\norbital period. Furthermore, the humps during the post-rebrightening\nstage ($347 \\le E \\le 661$) appear to be on a smooth extension of the\nsuperhumps at late stage of the superoutburst plateau ($165 \\le E \\le 219$).\nThe combined set of them yielded a mean period of 0.056995(3) d.\nThe stability of the period and phase for such a long interval\n($166 \\le E \\le 661$, 28 d) is surprising. These humps bear strong\nresemblance to post-superoutburst superhumps in some of well-observed\nWZ Sge-type dwarf novae\n(\\cite{kat08wzsgelateSH}; subsection \\ref{sec:latestage}).\nFollowing the same procedure as in \\citet{kat08wzsgelateSH},\nthe mean period of these post-superoutburst superhumps\nwas found to be 0.3 \\% longer than the superhump period near the onset\nof the superoutburst (see discussion in \\cite{kat08wzsgelateSH} for this\nselection), which is close to the universal $\\sim$ 0.5 \\% excess described\nin \\citet{kat08wzsgelateSH}.\n\n We also performed a period analysis of the post-superoutburst stage\n(BJD after 2453282) after subtracting fitted superhump signals\n(figure \\ref{fig:asas0025orb}).\nThe candidate $P_{\\rm dot}$ was found with a period of 0.056540(3) d.\nAlthough further spectroscopic confirmation is required, this period\ngives $\\epsilon$ of 1.0 \\%.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig176.eps}\n \\end{center}\n \\caption{Candidate orbital period after subtracting the superhump signal.\n (Upper): PDM analysis. The tick denotes the candidate orbital period.\n The strong signal around $P=0.0570$ d is the residual superhump signal.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas0025orb}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (2004).}\\label{tab:asas0025oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53264.3302 & 0.0007 & 0.0120 & 46 \\\\\n1 & 53264.3810 & 0.0005 & 0.0057 & 41 \\\\\n2 & 53264.4408 & 0.0002 & 0.0084 & 160 \\\\\n3 & 53264.4971 & 0.0001 & 0.0076 & 238 \\\\\n4 & 53264.5544 & 0.0002 & 0.0078 & 160 \\\\\n9 & 53264.8371 & 0.0001 & 0.0050 & 159 \\\\\n10 & 53264.8950 & 0.0001 & 0.0058 & 170 \\\\\n11 & 53264.9512 & 0.0001 & 0.0049 & 170 \\\\\n12 & 53265.0123 & 0.0004 & 0.0089 & 180 \\\\\n13 & 53265.0656 & 0.0002 & 0.0051 & 465 \\\\\n14 & 53265.1215 & 0.0002 & 0.0039 & 389 \\\\\n15 & 53265.1825 & 0.0004 & 0.0078 & 207 \\\\\n16 & 53265.2352 & 0.0005 & 0.0034 & 262 \\\\\n17 & 53265.2921 & 0.0005 & 0.0032 & 296 \\\\\n18 & 53265.3500 & 0.0002 & 0.0040 & 181 \\\\\n19 & 53265.4064 & 0.0003 & 0.0033 & 116 \\\\\n20 & 53265.4635 & 0.0003 & 0.0033 & 143 \\\\\n21 & 53265.5198 & 0.0002 & 0.0025 & 91 \\\\\n30 & 53266.0316 & 0.0003 & 0.0004 & 90 \\\\\n31 & 53266.0893 & 0.0002 & 0.0010 & 114 \\\\\n32 & 53266.1455 & 0.0002 & 0.0001 & 285 \\\\\n33 & 53266.2010 & 0.0003 & $-$0.0015 & 351 \\\\\n34 & 53266.2594 & 0.0003 & $-$0.0002 & 227 \\\\\n35 & 53266.3164 & 0.0006 & $-$0.0003 & 72 \\\\\n37 & 53266.4306 & 0.0006 & $-$0.0003 & 64 \\\\\n40 & 53266.6011 & 0.0003 & $-$0.0011 & 30 \\\\\n41 & 53266.6573 & 0.0002 & $-$0.0020 & 37 \\\\\n42 & 53266.7141 & 0.0003 & $-$0.0023 & 37 \\\\\n44 & 53266.8279 & 0.0002 & $-$0.0026 & 162 \\\\\n47 & 53266.9947 & 0.0023 & $-$0.0072 & 109 \\\\\n48 & 53267.0575 & 0.0004 & $-$0.0015 & 90 \\\\\n49 & 53267.1131 & 0.0004 & $-$0.0030 & 68 \\\\\n50 & 53267.1682 & 0.0005 & $-$0.0050 & 85 \\\\\n51 & 53267.2240 & 0.0003 & $-$0.0063 & 89 \\\\\n53 & 53267.3428 & 0.0004 & $-$0.0016 & 110 \\\\\n54 & 53267.3979 & 0.0002 & $-$0.0037 & 216 \\\\\n55 & 53267.4559 & 0.0002 & $-$0.0028 & 278 \\\\\n56 & 53267.5123 & 0.0002 & $-$0.0035 & 247 \\\\\n57 & 53267.5692 & 0.0003 & $-$0.0037 & 129 \\\\\n58 & 53267.6253 & 0.0002 & $-$0.0047 & 170 \\\\\n59 & 53267.6830 & 0.0002 & $-$0.0041 & 256 \\\\\n60 & 53267.7406 & 0.0002 & $-$0.0036 & 247 \\\\\n61 & 53267.8010 & 0.0006 & $-$0.0002 & 392 \\\\\n62 & 53267.8549 & 0.0009 & $-$0.0035 & 314 \\\\\n64 & 53267.9652 & 0.0013 & $-$0.0073 & 101 \\\\\n65 & 53268.0262 & 0.0004 & $-$0.0035 & 329 \\\\\n66 & 53268.0833 & 0.0003 & $-$0.0035 & 177 \\\\\n67 & 53268.1378 & 0.0004 & $-$0.0061 & 172 \\\\\n68 & 53268.1921 & 0.0017 & $-$0.0089 & 85 \\\\\n69 & 53268.2518 & 0.0006 & $-$0.0063 & 232 \\\\\n70 & 53268.3121 & 0.0004 & $-$0.0031 & 98 \\\\\n71 & 53268.3691 & 0.0005 & $-$0.0031 & 63 \\\\\n72 & 53268.4264 & 0.0008 & $-$0.0030 & 103 \\\\\n73 & 53268.4792 & 0.0015 & $-$0.0073 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453264.3182 + 0.057099 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (2004) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n75 & 53268.5953 & 0.0003 & $-$0.0054 & 158 \\\\\n76 & 53268.6533 & 0.0003 & $-$0.0045 & 461 \\\\\n77 & 53268.7070 & 0.0004 & $-$0.0078 & 292 \\\\\n78 & 53268.7731 & 0.0005 & 0.0012 & 309 \\\\\n79 & 53268.8248 & 0.0003 & $-$0.0043 & 405 \\\\\n80 & 53268.8804 & 0.0003 & $-$0.0058 & 162 \\\\\n81 & 53268.9356 & 0.0005 & $-$0.0077 & 187 \\\\\n82 & 53268.9989 & 0.0009 & $-$0.0014 & 296 \\\\\n83 & 53269.0551 & 0.0003 & $-$0.0024 & 515 \\\\\n84 & 53269.1111 & 0.0011 & $-$0.0035 & 181 \\\\\n85 & 53269.1649 & 0.0005 & $-$0.0068 & 287 \\\\\n86 & 53269.2266 & 0.0005 & $-$0.0021 & 215 \\\\\n88 & 53269.3348 & 0.0004 & $-$0.0082 & 61 \\\\\n91 & 53269.5104 & 0.0009 & $-$0.0039 & 68 \\\\\n92 & 53269.5645 & 0.0006 & $-$0.0069 & 53 \\\\\n96 & 53269.7960 & 0.0011 & $-$0.0038 & 314 \\\\\n97 & 53269.8540 & 0.0015 & $-$0.0028 & 393 \\\\\n98 & 53269.9110 & 0.0002 & $-$0.0030 & 280 \\\\\n99 & 53269.9732 & 0.0009 & 0.0022 & 106 \\\\\n100 & 53270.0234 & 0.0006 & $-$0.0048 & 212 \\\\\n101 & 53270.0828 & 0.0005 & $-$0.0024 & 244 \\\\\n102 & 53270.1390 & 0.0005 & $-$0.0034 & 218 \\\\\n103 & 53270.1979 & 0.0006 & $-$0.0015 & 245 \\\\\n104 & 53270.2542 & 0.0004 & $-$0.0024 & 235 \\\\\n108 & 53270.4826 & 0.0012 & $-$0.0023 & 26 \\\\\n109 & 53270.5399 & 0.0014 & $-$0.0021 & 41 \\\\\n110 & 53270.5973 & 0.0025 & $-$0.0019 & 25 \\\\\n111 & 53270.6553 & 0.0006 & $-$0.0010 & 39 \\\\\n112 & 53270.7129 & 0.0007 & $-$0.0005 & 38 \\\\\n113 & 53270.7708 & 0.0011 & 0.0004 & 311 \\\\\n114 & 53270.8243 & 0.0007 & $-$0.0032 & 366 \\\\\n115 & 53270.8836 & 0.0003 & $-$0.0010 & 162 \\\\\n116 & 53270.9407 & 0.0003 & $-$0.0011 & 162 \\\\\n128 & 53271.6280 & 0.0016 & 0.0010 & 266 \\\\\n130 & 53271.7378 & 0.0010 & $-$0.0033 & 231 \\\\\n131 & 53271.8054 & 0.0014 & 0.0072 & 478 \\\\\n132 & 53271.8597 & 0.0009 & 0.0044 & 151 \\\\\n135 & 53272.0370 & 0.0013 & 0.0103 & 203 \\\\\n136 & 53272.0847 & 0.0013 & 0.0010 & 117 \\\\\n141 & 53272.3738 & 0.0021 & 0.0045 & 59 \\\\\n142 & 53272.4346 & 0.0009 & 0.0083 & 147 \\\\\n143 & 53272.4867 & 0.0007 & 0.0033 & 162 \\\\\n144 & 53272.5497 & 0.0017 & 0.0092 & 59 \\\\\n148 & 53272.7788 & 0.0007 & 0.0099 & 445 \\\\\n149 & 53272.8355 & 0.0006 & 0.0095 & 217 \\\\\n150 & 53272.8921 & 0.0005 & 0.0089 & 152 \\\\\n151 & 53272.9467 & 0.0005 & 0.0065 & 100 \\\\\n165 & 53273.7524 & 0.0008 & 0.0128 & 248 \\\\\n166 & 53273.8051 & 0.0004 & 0.0084 & 300 \\\\\n167 & 53273.8622 & 0.0004 & 0.0084 & 155 \\\\\n168 & 53273.9187 & 0.0002 & 0.0078 & 156 \\\\\n169 & 53273.9776 & 0.0003 & 0.0096 & 86 \\\\\n176 & 53274.3737 & 0.0007 & 0.0060 & 73 \\\\\n177 & 53274.4309 & 0.0007 & 0.0061 & 47 \\\\\n184 & 53274.8282 & 0.0003 & 0.0037 & 156 \\\\\n185 & 53274.8866 & 0.0003 & 0.0050 & 152 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (2004) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n186 & 53274.9414 & 0.0003 & 0.0027 & 155 \\\\\n197 & 53275.5699 & 0.0008 & 0.0031 & 179 \\\\\n198 & 53275.6251 & 0.0007 & 0.0013 & 194 \\\\\n199 & 53275.6807 & 0.0008 & $-$0.0003 & 198 \\\\\n200 & 53275.7391 & 0.0005 & 0.0010 & 219 \\\\\n201 & 53275.7959 & 0.0004 & 0.0007 & 264 \\\\\n202 & 53275.8520 & 0.0003 & $-$0.0003 & 262 \\\\\n203 & 53275.9072 & 0.0005 & $-$0.0022 & 251 \\\\\n204 & 53275.9699 & 0.0011 & 0.0035 & 206 \\\\\n205 & 53276.0252 & 0.0035 & 0.0016 & 67 \\\\\n206 & 53276.0874 & 0.0016 & 0.0067 & 169 \\\\\n210 & 53276.3114 & 0.0011 & 0.0023 & 71 \\\\\n216 & 53276.6502 & 0.0016 & $-$0.0015 & 77 \\\\\n217 & 53276.7020 & 0.0012 & $-$0.0068 & 78 \\\\\n218 & 53276.7573 & 0.0018 & $-$0.0086 & 387 \\\\\n219 & 53276.8210 & 0.0018 & $-$0.0019 & 208 \\\\\n233 & 53277.6047 & 0.0023 & $-$0.0177 & 53 \\\\\n236 & 53277.7781 & 0.0023 & $-$0.0156 & 38 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (secondary).}\\label{tab:asas0025ochump2}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n233 & 53277.6047 & 0.0023 & $-$0.0196 & 53 \\\\\n236 & 53277.7781 & 0.0023 & $-$0.0175 & 38 \\\\\n250 & 53278.5726 & 0.0015 & $-$0.0224 & 24 \\\\\n251 & 53278.6297 & 0.0018 & $-$0.0224 & 19 \\\\\n252 & 53278.6842 & 0.0015 & $-$0.0250 & 20 \\\\\n253 & 53278.7424 & 0.0003 & $-$0.0239 & 171 \\\\\n254 & 53278.7987 & 0.0005 & $-$0.0247 & 158 \\\\\n258 & 53279.0230 & 0.0010 & $-$0.0288 & 123 \\\\\n259 & 53279.0847 & 0.0011 & $-$0.0242 & 129 \\\\\n260 & 53279.1406 & 0.0013 & $-$0.0254 & 56 \\\\\n261 & 53279.1955 & 0.0005 & $-$0.0276 & 60 \\\\\n262 & 53279.2567 & 0.0013 & $-$0.0235 & 60 \\\\\n263 & 53279.3078 & 0.0014 & $-$0.0295 & 62 \\\\\n264 & 53279.3643 & 0.0008 & $-$0.0301 & 73 \\\\\n265 & 53279.4231 & 0.0011 & $-$0.0284 & 104 \\\\\n266 & 53279.4825 & 0.0010 & $-$0.0261 & 89 \\\\\n267 & 53279.5426 & 0.0011 & $-$0.0231 & 19 \\\\\n268 & 53279.5945 & 0.0008 & $-$0.0283 & 31 \\\\\n269 & 53279.6508 & 0.0015 & $-$0.0291 & 39 \\\\\n270 & 53279.7072 & 0.0006 & $-$0.0298 & 40 \\\\\n271 & 53279.7660 & 0.0006 & $-$0.0281 & 98 \\\\\n272 & 53279.8204 & 0.0004 & $-$0.0307 & 39 \\\\\n273 & 53279.8787 & 0.0003 & $-$0.0296 & 38 \\\\\n274 & 53279.9317 & 0.0019 & $-$0.0337 & 39 \\\\\n275 & 53279.9928 & 0.0008 & $-$0.0297 & 81 \\\\\n276 & 53280.0481 & 0.0005 & $-$0.0315 & 146 \\\\\n277 & 53280.1072 & 0.0007 & $-$0.0295 & 57 \\\\\n288 & 53280.7305 & 0.0004 & $-$0.0343 & 163 \\\\\n289 & 53280.7868 & 0.0003 & $-$0.0351 & 173 \\\\\n290 & 53280.8454 & 0.0003 & $-$0.0336 & 13 \\\\\n291 & 53280.9008 & 0.0008 & $-$0.0353 & 13 \\\\\n292 & 53280.9558 & 0.0013 & $-$0.0374 & 14 \\\\\n294 & 53281.0744 & 0.0025 & $-$0.0330 & 67 \\\\\n295 & 53281.1286 & 0.0006 & $-$0.0359 & 78 \\\\\n296 & 53281.1862 & 0.0009 & $-$0.0354 & 30 \\\\\n297 & 53281.2434 & 0.0004 & $-$0.0353 & 29 \\\\\n300 & 53281.4104 & 0.0021 & $-$0.0396 & 60 \\\\\n301 & 53281.4667 & 0.0011 & $-$0.0404 & 65 \\\\\n302 & 53281.5246 & 0.0012 & $-$0.0396 & 64 \\\\\n306 & 53281.7553 & 0.0005 & $-$0.0373 & 13 \\\\\n307 & 53281.8106 & 0.0004 & $-$0.0391 & 13 \\\\\n309 & 53281.9226 & 0.0057 & $-$0.0413 & 13 \\\\\n313 & 53282.1501 & 0.0003 & $-$0.0422 & 80 \\\\\n314 & 53282.2111 & 0.0015 & $-$0.0383 & 20 \\\\\n315 & 53282.2727 & 0.0033 & $-$0.0338 & 21 \\\\\n320 & 53282.5523 & 0.0018 & $-$0.0397 & 90 \\\\\n336 & 53283.4611 & 0.0015 & $-$0.0445 & 64 \\\\\n338 & 53283.5737 & 0.0018 & $-$0.0461 & 18 \\\\\n339 & 53283.6312 & 0.0008 & $-$0.0457 & 20 \\\\\n340 & 53283.6758 & 0.0039 & $-$0.0582 & 19 \\\\\n342 & 53283.7987 & 0.0029 & $-$0.0495 & 13 \\\\\n343 & 53283.8649 & 0.0045 & $-$0.0404 & 13 \\\\\n344 & 53283.9182 & 0.0023 & $-$0.0442 & 13 \\\\\n345 & 53283.9693 & 0.0018 & $-$0.0502 & 11 \\\\\n346 & 53284.0245 & 0.0004 & $-$0.0521 & 18 \\\\\n347 & 53284.0832 & 0.0014 & $-$0.0505 & 25 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453264.3200 + 0.057100 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (late stage).}\\label{tab:asas0025ochump3}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n250 & 53278.5472 & 0.0009 & $-$0.0478 & 70 \\\\\n251 & 53278.5962 & 0.0032 & $-$0.0559 & 20 \\\\\n252 & 53278.6610 & 0.0010 & $-$0.0482 & 19 \\\\\n253 & 53278.7125 & 0.0011 & $-$0.0538 & 19 \\\\\n254 & 53278.7774 & 0.0027 & $-$0.0460 & 158 \\\\\n258 & 53278.9998 & 0.0019 & $-$0.0520 & 85 \\\\\n259 & 53279.0531 & 0.0007 & $-$0.0558 & 136 \\\\\n260 & 53279.1227 & 0.0065 & $-$0.0433 & 95 \\\\\n261 & 53279.1790 & 0.0042 & $-$0.0441 & 60 \\\\\n262 & 53279.2317 & 0.0017 & $-$0.0485 & 60 \\\\\n263 & 53279.2859 & 0.0018 & $-$0.0514 & 61 \\\\\n264 & 53279.3427 & 0.0025 & $-$0.0517 & 59 \\\\\n265 & 53279.3939 & 0.0042 & $-$0.0576 & 90 \\\\\n266 & 53279.4544 & 0.0011 & $-$0.0542 & 90 \\\\\n267 & 53279.5112 & 0.0061 & $-$0.0545 & 87 \\\\\n268 & 53279.5736 & 0.0019 & $-$0.0492 & 20 \\\\\n269 & 53279.6345 & 0.0019 & $-$0.0454 & 44 \\\\\n270 & 53279.6803 & 0.0005 & $-$0.0567 & 43 \\\\\n271 & 53279.7349 & 0.0013 & $-$0.0592 & 186 \\\\\n272 & 53279.7884 & 0.0011 & $-$0.0628 & 29 \\\\\n273 & 53279.8433 & 0.0056 & $-$0.0650 & 34 \\\\\n274 & 53279.9020 & 0.0013 & $-$0.0634 & 38 \\\\\n275 & 53279.9595 & 0.0020 & $-$0.0630 & 72 \\\\\n276 & 53280.0178 & 0.0038 & $-$0.0618 & 112 \\\\\n277 & 53280.0731 & 0.0011 & $-$0.0636 & 115 \\\\\n278 & 53280.1385 & 0.0012 & $-$0.0553 & 28 \\\\\n289 & 53280.7640 & 0.0007 & $-$0.0579 & 174 \\\\\n290 & 53280.8171 & 0.0014 & $-$0.0619 & 20 \\\\\n291 & 53280.8733 & 0.0058 & $-$0.0628 & 13 \\\\\n292 & 53280.9369 & 0.0025 & $-$0.0563 & 13 \\\\\n294 & 53281.0452 & 0.0016 & $-$0.0622 & 33 \\\\\n295 & 53281.1093 & 0.0031 & $-$0.0552 & 65 \\\\\n296 & 53281.1566 & 0.0016 & $-$0.0650 & 48 \\\\\n297 & 53281.2198 & 0.0010 & $-$0.0589 & 37 \\\\\n298 & 53281.2851 & 0.0062 & $-$0.0507 & 29 \\\\\n300 & 53281.3864 & 0.0005 & $-$0.0636 & 64 \\\\\n301 & 53281.4422 & 0.0015 & $-$0.0649 & 64 \\\\\n302 & 53281.5187 & 0.0014 & $-$0.0455 & 64 \\\\\n303 & 53281.5615 & 0.0112 & $-$0.0598 & 52 \\\\\n306 & 53281.7292 & 0.0017 & $-$0.0634 & 12 \\\\\n307 & 53281.7853 & 0.0008 & $-$0.0644 & 13 \\\\\n308 & 53281.8391 & 0.0012 & $-$0.0677 & 13 \\\\\n309 & 53281.8952 & 0.0014 & $-$0.0687 & 13 \\\\\n310 & 53281.9526 & 0.0003 & $-$0.0684 & 91 \\\\\n312 & 53282.0689 & 0.0004 & $-$0.0663 & 33 \\\\\n313 & 53282.1250 & 0.0003 & $-$0.0673 & 94 \\\\\n314 & 53282.1787 & 0.0011 & $-$0.0707 & 27 \\\\\n315 & 53282.2343 & 0.0013 & $-$0.0722 & 20 \\\\\n316 & 53282.2921 & 0.0015 & $-$0.0715 & 13 \\\\\n319 & 53282.5229 & 0.0022 & $-$0.0120 & 73 \\\\\n320 & 53282.5825 & 0.0037 & $-$0.0095 & 40 \\\\\n321 & 53282.6361 & 0.0030 & $-$0.0131 & 35 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453264.3200 + 0.057100 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (late stage, continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n322 & 53282.6940 & 0.0043 & $-$0.0122 & 20 \\\\\n329 & 53283.0874 & 0.0011 & $-$0.0185 & 111 \\\\\n330 & 53283.1498 & 0.0046 & $-$0.0132 & 29 \\\\\n333 & 53283.3209 & 0.0007 & $-$0.0134 & 91 \\\\\n334 & 53283.3801 & 0.0023 & $-$0.0113 & 83 \\\\\n335 & 53283.4307 & 0.0016 & $-$0.0178 & 50 \\\\\n336 & 53283.4890 & 0.0010 & $-$0.0166 & 63 \\\\\n337 & 53283.5459 & 0.0026 & $-$0.0168 & 47 \\\\\n338 & 53283.6062 & 0.0018 & $-$0.0136 & 19 \\\\\n339 & 53283.6640 & 0.0023 & $-$0.0129 & 19 \\\\\n340 & 53283.7158 & 0.0014 & $-$0.0182 & 24 \\\\\n341 & 53283.7745 & 0.0013 & $-$0.0166 & 23 \\\\\n342 & 53283.8296 & 0.0012 & $-$0.0186 & 13 \\\\\n343 & 53283.8839 & 0.0035 & $-$0.0214 & 11 \\\\\n354 & 53284.5242 & 0.0056 & $-$0.0092 & 8 \\\\\n355 & 53284.5778 & 0.0024 & $-$0.0127 & 15 \\\\\n356 & 53284.6310 & 0.0008 & $-$0.0166 & 15 \\\\\n357 & 53284.6888 & 0.0039 & $-$0.0159 & 15 \\\\\n360 & 53284.8582 & 0.0011 & $-$0.0178 & 14 \\\\\n361 & 53284.9206 & 0.0029 & $-$0.0125 & 14 \\\\\n362 & 53284.9771 & 0.0231 & $-$0.0131 & 38 \\\\\n363 & 53285.0282 & 0.0027 & $-$0.0191 & 84 \\\\\n364 & 53285.0842 & 0.0005 & $-$0.0202 & 53 \\\\\n366 & 53285.2073 & 0.0014 & $-$0.0113 & 49 \\\\\n367 & 53285.2684 & 0.0063 & $-$0.0073 & 46 \\\\\n370 & 53285.4228 & 0.0014 & $-$0.0242 & 20 \\\\\n371 & 53285.4786 & 0.0012 & $-$0.0255 & 19 \\\\\n372 & 53285.5398 & 0.0009 & $-$0.0214 & 20 \\\\\n373 & 53285.5988 & 0.0035 & $-$0.0195 & 20 \\\\\n385 & 53286.2793 & 0.0010 & $-$0.0242 & 24 \\\\\n386 & 53286.3371 & 0.0012 & $-$0.0235 & 32 \\\\\n387 & 53286.4023 & 0.0034 & $-$0.0154 & 32 \\\\\n388 & 53286.4559 & 0.0019 & $-$0.0189 & 31 \\\\\n393 & 53286.7365 & 0.0018 & $-$0.0238 & 160 \\\\\n394 & 53286.7980 & 0.0092 & $-$0.0194 & 123 \\\\\n402 & 53287.2410 & 0.0017 & $-$0.0332 & 32 \\\\\n403 & 53287.3080 & 0.0021 & $-$0.0233 & 33 \\\\\n404 & 53287.3638 & 0.0049 & $-$0.0246 & 32 \\\\\n405 & 53287.4223 & 0.0009 & $-$0.0232 & 32 \\\\\n406 & 53287.4793 & 0.0021 & $-$0.0233 & 31 \\\\\n407 & 53287.5323 & 0.0016 & $-$0.0274 & 25 \\\\\n426 & 53288.6193 & 0.0014 & $-$0.0253 & 15 \\\\\n427 & 53288.6787 & 0.0029 & $-$0.0230 & 15 \\\\\n428 & 53288.7304 & 0.0013 & $-$0.0284 & 9 \\\\\n430 & 53288.8398 & 0.0095 & $-$0.0332 & 9 \\\\\n431 & 53288.9068 & 0.0031 & $-$0.0233 & 14 \\\\\n432 & 53288.9730 & 0.0059 & $-$0.0142 & 7 \\\\\n437 & 53289.2404 & 0.0013 & $-$0.0323 & 15 \\\\\n440 & 53289.4162 & 0.0011 & $-$0.0278 & 15 \\\\\n441 & 53289.4720 & 0.0012 & $-$0.0291 & 15 \\\\\n442 & 53289.5446 & 0.0012 & $-$0.0136 & 15 \\\\\n443 & 53289.5998 & 0.0033 & $-$0.0155 & 15 \\\\\n444 & 53289.6469 & 0.0043 & $-$0.0255 & 15 \\\\\n447 & 53289.8176 & 0.0022 & $-$0.0261 & 7 \\\\\n448 & 53289.8722 & 0.0019 & $-$0.0286 & 9 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0025 (late stage, continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n449 & 53289.9291 & 0.0017 & $-$0.0288 & 72 \\\\\n450 & 53289.9885 & 0.0018 & $-$0.0265 & 59 \\\\\n452 & 53290.1029 & 0.0011 & $-$0.0263 & 60 \\\\\n453 & 53290.1585 & 0.0003 & $-$0.0278 & 55 \\\\\n455 & 53290.2744 & 0.0008 & $-$0.0261 & 30 \\\\\n456 & 53290.3270 & 0.0011 & $-$0.0306 & 30 \\\\\n458 & 53290.4338 & 0.0005 & $-$0.0380 & 30 \\\\\n465 & 53290.8337 & 0.0200 & $-$0.0378 & 15 \\\\\n466 & 53290.8986 & 0.0023 & $-$0.0300 & 11 \\\\\n467 & 53290.9596 & 0.0008 & $-$0.0261 & 13 \\\\\n469 & 53291.0679 & 0.0007 & $-$0.0320 & 16 \\\\\n473 & 53291.3023 & 0.0023 & $-$0.0260 & 12 \\\\\n474 & 53291.3581 & 0.0021 & $-$0.0273 & 19 \\\\\n475 & 53291.4106 & 0.0010 & $-$0.0319 & 19 \\\\\n482 & 53291.8093 & 0.0015 & $-$0.0329 & 13 \\\\\n483 & 53291.8712 & 0.0013 & $-$0.0281 & 14 \\\\\n484 & 53291.9256 & 0.0009 & $-$0.0308 & 71 \\\\\n485 & 53291.9818 & 0.0006 & $-$0.0317 & 59 \\\\\n486 & 53292.0430 & 0.0010 & $-$0.0276 & 72 \\\\\n487 & 53292.0926 & 0.0010 & $-$0.0351 & 47 \\\\\n491 & 53292.3158 & 0.0006 & $-$0.0403 & 40 \\\\\n492 & 53292.3818 & 0.0009 & $-$0.0314 & 38 \\\\\n493 & 53292.4401 & 0.0010 & $-$0.0302 & 38 \\\\\n508 & 53293.2965 & 0.0045 & $-$0.0303 & 15 \\\\\n509 & 53293.3562 & 0.0120 & $-$0.0277 & 14 \\\\\n510 & 53293.4054 & 0.0013 & $-$0.0356 & 19 \\\\\n511 & 53293.4661 & 0.0034 & $-$0.0320 & 20 \\\\\n512 & 53293.5218 & 0.0018 & $-$0.0334 & 20 \\\\\n519 & 53293.9220 & 0.0034 & $-$0.0329 & 58 \\\\\n520 & 53293.9750 & 0.0010 & $-$0.0370 & 68 \\\\\n521 & 53294.0282 & 0.0009 & $-$0.0409 & 110 \\\\\n525 & 53294.2583 & 0.0010 & $-$0.0392 & 43 \\\\\n544 & 53295.3481 & 0.0011 & $-$0.0343 & 32 \\\\\n545 & 53295.4075 & 0.0011 & $-$0.0320 & 32 \\\\\n546 & 53295.4561 & 0.0019 & $-$0.0405 & 32 \\\\\n560 & 53296.2596 & 0.0005 & $-$0.0364 & 28 \\\\\n561 & 53296.3127 & 0.0012 & $-$0.0404 & 29 \\\\\n568 & 53296.7112 & 0.0013 & $-$0.0416 & 146 \\\\\n601 & 53298.5985 & 0.0009 & $-$0.0386 & 158 \\\\\n622 & 53299.7986 & 0.0013 & $-$0.0376 & 16 \\\\\n623 & 53299.8454 & 0.0059 & $-$0.0479 & 16 \\\\\n624 & 53299.9045 & 0.0010 & $-$0.0459 & 16 \\\\\n626 & 53300.0194 & 0.0021 & $-$0.0452 & 47 \\\\\n627 & 53300.0728 & 0.0024 & $-$0.0489 & 58 \\\\\n638 & 53300.7013 & 0.0016 & $-$0.0485 & 14 \\\\\n639 & 53300.7655 & 0.0022 & $-$0.0414 & 14 \\\\\n640 & 53300.8217 & 0.0103 & $-$0.0423 & 17 \\\\\n641 & 53300.8770 & 0.0051 & $-$0.0441 & 15 \\\\\n642 & 53300.9418 & 0.0095 & $-$0.0364 & 13 \\\\\n661 & 53302.0138 & 0.0039 & $-$0.0493 & 34 \\\\\n747 & 53306.9570 & 0.0024 & $-$0.0167 & 35 \\\\\n748 & 53306.9952 & 0.0016 & $-$0.0356 & 50 \\\\\n904 & 53315.9164 & 0.0016 & $-$0.0220 & 29 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J023322$-$1047.0}\\label{obj:asas0233}\n\n ASAS J023322$-$1047.0 (hereafter ASAS J0233) is a dwarf nova detected\nby ASAS-3 on 2006 January 20 ($V = 12.1$, vsnet-alert 8801).\nEarly superhumps were immediately detected (vsnet-alert 8815), and\nordinary superhumps developed eight days after the outburst detection\n(vsnet-alert 8825). \\citet{van06asas0233asas1025} summarized this\noutburst and reported period analyses.\nThe data was a combination of ours and the AAVSO data, as utilized in\n\\citet{van06asas0233asas1025}.\nThe mean periods of early and ordinary superhumps determined with\nthe PDM method were 0.054895(23) d (figure \\ref{fig:asas0233eshpdm})\nand 0.055970(9) d (figure \\ref{fig:asas0233shpdm}), respectively.\nThe times of ordinary superhump maxima are listed in table\n\\ref{tab:asas0233oc2006}. The $O-C$ diagram\n(cf. figure \\ref{fig:ocsamp}) clearly\ndemonstrates the presence of the early development stage (stage A, $E \\le 2$),\nstage B with a positive period derivative, and the final transition\nto a shorter period (stage C). The $P_{\\rm dot}$ for the stage B\n($7 \\le E \\le 216$) was $+4.9(0.5) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig177.eps}\n \\end{center}\n \\caption{Early superhumps in ASAS J0233 (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas0233eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig178.eps}\n \\end{center}\n \\caption{Ordinary superhumps in ASAS J0233 (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas0233shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0233 (2006).}\\label{tab:asas0233oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53763.8972 & 0.0009 & $-$0.0004 & 135 \\\\\n1 & 53763.9533 & 0.0004 & $-$0.0003 & 252 \\\\\n2 & 53764.0095 & 0.0006 & $-$0.0001 & 251 \\\\\n7 & 53764.2952 & 0.0004 & 0.0056 & 51 \\\\\n8 & 53764.3509 & 0.0005 & 0.0053 & 53 \\\\\n12 & 53764.5774 & 0.0002 & 0.0078 & 83 \\\\\n13 & 53764.6310 & 0.0003 & 0.0054 & 74 \\\\\n14 & 53764.6880 & 0.0002 & 0.0064 & 105 \\\\\n18 & 53764.9097 & 0.0004 & 0.0040 & 216 \\\\\n19 & 53764.9660 & 0.0004 & 0.0044 & 310 \\\\\n20 & 53765.0212 & 0.0020 & 0.0036 & 105 \\\\\n25 & 53765.2996 & 0.0003 & 0.0019 & 56 \\\\\n26 & 53765.3557 & 0.0004 & 0.0021 & 55 \\\\\n30 & 53765.5790 & 0.0002 & 0.0013 & 93 \\\\\n31 & 53765.6340 & 0.0002 & 0.0003 & 93 \\\\\n32 & 53765.6897 & 0.0003 & 0.0001 & 93 \\\\\n48 & 53766.5841 & 0.0003 & $-$0.0016 & 58 \\\\\n49 & 53766.6425 & 0.0011 & 0.0008 & 59 \\\\\n61 & 53767.3092 & 0.0006 & $-$0.0045 & 45 \\\\\n66 & 53767.5893 & 0.0022 & $-$0.0045 & 45 \\\\\n73 & 53767.9802 & 0.0007 & $-$0.0056 & 79 \\\\\n79 & 53768.3155 & 0.0005 & $-$0.0062 & 54 \\\\\n84 & 53768.5961 & 0.0003 & $-$0.0057 & 53 \\\\\n85 & 53768.6508 & 0.0004 & $-$0.0070 & 58 \\\\\n86 & 53768.7066 & 0.0012 & $-$0.0072 & 33 \\\\\n91 & 53768.9892 & 0.0028 & $-$0.0046 & 42 \\\\\n120 & 53770.6146 & 0.0005 & $-$0.0033 & 58 \\\\\n121 & 53770.6683 & 0.0006 & $-$0.0056 & 58 \\\\\n126 & 53770.9530 & 0.0026 & $-$0.0009 & 288 \\\\\n127 & 53770.9957 & 0.0023 & $-$0.0142 & 129 \\\\\n137 & 53771.5623 & 0.0015 & $-$0.0076 & 108 \\\\\n138 & 53771.6199 & 0.0007 & $-$0.0060 & 102 \\\\\n139 & 53771.6825 & 0.0018 & 0.0006 & 54 \\\\\n143 & 53771.9139 & 0.0040 & 0.0080 & 166 \\\\\n144 & 53771.9557 & 0.0015 & $-$0.0062 & 156 \\\\\n161 & 53772.9160 & 0.0019 & 0.0021 & 18 \\\\\n214 & 53775.8936 & 0.0058 & 0.0115 & 46 \\\\\n216 & 53776.0035 & 0.0035 & 0.0094 & 51 \\\\\n244 & 53777.5705 & 0.0018 & 0.0083 & 45 \\\\\n245 & 53777.6248 & 0.0019 & 0.0066 & 58 \\\\\n246 & 53777.6714 & 0.0053 & $-$0.0028 & 57 \\\\\n263 & 53778.6282 & 0.0012 & 0.0020 & 58 \\\\\n264 & 53778.6805 & 0.0017 & $-$0.0018 & 58 \\\\\n280 & 53779.5786 & 0.0011 & 0.0003 & 49 \\\\\n281 & 53779.6327 & 0.0023 & $-$0.0016 & 58 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453763.8976 + 0.056003 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J091858$-$2942.6 = Dwarf nova in Pyxis 2005}\\label{obj:asas0918}\n\n This object (hereafter ASAS J0918) was independently discovered\nby G. Pojmanski and K. Haseda \\citep{poj05dnpyx}.\nFollow-up spectroscopy revealed that the object\nwas not a nova, but a dwarf nova in outburst \\citep{kaw05dnpyx}.\nWe undertook time-series photometry soon after the discovery announcement.\n\n A PDM analysis yielded a mean superhump period of 0.06267(2) d\n(figure \\ref{fig:asas0918shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:dnpyxoc2005}.\nAlthough we can derive a global $P_{\\rm dot}$ = $-15.6(4.3) \\times 10^{-5}$,\nthis value should not be regarded as the representative period derivative\nof this system since the object showed a remarkable terminal rebrightening\nbefore $E = 78$ and the observed $O-C$'s most likely reflected a shortening\nof the superhump period between stage B and C.\nThe period derivative for the stage B was not significantly determined\nfrom a short segment $E \\le 32$.\nFuture observations starting from the early epoch of a superoutburst\nare necessary to determine the period derivative, although continuous\nmonitoring by ASAS-3 has not detected any further outburst.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig179.eps}\n \\end{center}\n \\caption{Superhumps in ASAS J0918 (2005). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas0918shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J0918 (2005).}\\label{tab:dnpyxoc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53448.0457 & 0.0011 & $-$0.0049 & 275 \\\\\n1 & 53448.1088 & 0.0020 & $-$0.0044 & 171 \\\\\n14 & 53448.9300 & 0.0021 & 0.0025 & 58 \\\\\n15 & 53448.9939 & 0.0016 & 0.0037 & 91 \\\\\n16 & 53449.0527 & 0.0041 & $-$0.0002 & 107 \\\\\n17 & 53449.1128 & 0.0037 & $-$0.0027 & 93 \\\\\n30 & 53449.9332 & 0.0014 & 0.0033 & 62 \\\\\n31 & 53449.9968 & 0.0007 & 0.0043 & 84 \\\\\n32 & 53450.0583 & 0.0007 & 0.0031 & 236 \\\\\n78 & 53452.9311 & 0.0020 & $-$0.0055 & 63 \\\\\n79 & 53453.0001 & 0.0013 & 0.0008 & 63 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453448.0506 + 0.062642 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J102522$-$1542.4}\\label{obj:asas1025}\n\n ASAS J102522$-$1542.4 (hereafter ASAS J1025) is a dwarf nova detected\nby ASAS-3 on 2006 January 26 ($V = 12.2$, vsnet-alert 8821).\nThe detection of early superhumps (vsnet-alert 8824;\nfigure \\ref{fig:j1025eshpdm}, period 0.06136(6) d) and ordinary\nsuperhumps (vsnet-alert 8843; figure \\ref{fig:j1025shpdm},\nmean period 0.063314(5) d) led to a likely classification\nas a WZ Sge-type dwarf nova. \\citet{van06asas0233asas1025} provided\na provisional analysis.\n\n The times of superhump maxima (excluding early superhumps)\nare listed in table \\ref{tab:asas1025oc2006}.\nThe $O-C$ diagram (cf. figure \\ref{fig:ocsamp})\nconsisted of three stages A--C. We obtained\n$P_{\\rm dot}$ = $+10.9(0.6) \\times 10^{-5}$ (stage B, $27 \\le E \\le 142$).\nThe stage C superhumps persisted until the start of the rebrightening.\n\n The fractional superhump excess determined from the period of\nearly and ordinary superhumps was 3.2(1) \\%, which is unusually large\nfor a WZ Sge-type dwarf nova. Combined with the large $P_{\\rm dot}$\nand the short delay before ordinary superhumps emerged,\nthe object appears to be a ``borderline'' long-$P_{\\rm SH}$ WZ Sge-like\ndwarf nova similar to BC UMa \\citep{pat03suumas} and\nASAS J1600 \\citep{soe09asas1600}.\nThe exact identification of the $P_{\\rm orb}$, however, should await\nfurther observation because the period of early superhumps was determined\nfrom a short baseline.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig180.eps}\n \\end{center}\n \\caption{Early superhumps in ASAS J1025 (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1025eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig181.eps}\n \\end{center}\n \\caption{Ordinary superhumps in ASAS J1025 (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1025shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J1025 (2006).}\\label{tab:asas1025oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53764.0703 & 0.0014 & $-$0.0134 & 190 \\\\\n1 & 53764.1397 & 0.0010 & $-$0.0073 & 400 \\\\\n2 & 53764.1957 & 0.0007 & $-$0.0146 & 402 \\\\\n3 & 53764.2511 & 0.0006 & $-$0.0225 & 535 \\\\\n4 & 53764.3255 & 0.0016 & $-$0.0114 & 345 \\\\\n7 & 53764.5218 & 0.0011 & $-$0.0050 & 43 \\\\\n8 & 53764.5815 & 0.0010 & $-$0.0085 & 52 \\\\\n9 & 53764.6420 & 0.0011 & $-$0.0114 & 61 \\\\\n11 & 53764.7765 & 0.0003 & $-$0.0035 & 135 \\\\\n12 & 53764.8409 & 0.0004 & $-$0.0024 & 137 \\\\\n13 & 53764.9058 & 0.0004 & $-$0.0008 & 133 \\\\\n14 & 53764.9707 & 0.0004 & 0.0008 & 120 \\\\\n15 & 53765.0315 & 0.0012 & $-$0.0016 & 42 \\\\\n16 & 53765.0984 & 0.0009 & 0.0020 & 97 \\\\\n17 & 53765.1591 & 0.0003 & $-$0.0007 & 214 \\\\\n18 & 53765.2227 & 0.0004 & $-$0.0004 & 197 \\\\\n19 & 53765.2869 & 0.0003 & 0.0006 & 193 \\\\\n23 & 53765.5426 & 0.0002 & 0.0030 & 169 \\\\\n24 & 53765.6074 & 0.0002 & 0.0045 & 188 \\\\\n25 & 53765.6687 & 0.0004 & 0.0025 & 64 \\\\\n27 & 53765.7982 & 0.0001 & 0.0054 & 135 \\\\\n28 & 53765.8604 & 0.0001 & 0.0044 & 135 \\\\\n29 & 53765.9231 & 0.0001 & 0.0038 & 135 \\\\\n30 & 53765.9855 & 0.0001 & 0.0029 & 134 \\\\\n31 & 53766.0484 & 0.0006 & 0.0025 & 64 \\\\\n32 & 53766.1121 & 0.0003 & 0.0029 & 76 \\\\\n33 & 53766.1743 & 0.0003 & 0.0017 & 145 \\\\\n34 & 53766.2385 & 0.0004 & 0.0027 & 140 \\\\\n42 & 53766.7449 & 0.0002 & 0.0027 & 94 \\\\\n43 & 53766.8074 & 0.0001 & 0.0019 & 127 \\\\\n44 & 53766.8706 & 0.0002 & 0.0018 & 121 \\\\\n45 & 53766.9335 & 0.0002 & 0.0014 & 122 \\\\\n46 & 53766.9956 & 0.0002 & 0.0002 & 107 \\\\\n63 & 53768.0702 & 0.0003 & $-$0.0013 & 255 \\\\\n64 & 53768.1324 & 0.0002 & $-$0.0024 & 393 \\\\\n65 & 53768.1955 & 0.0002 & $-$0.0026 & 419 \\\\\n66 & 53768.2587 & 0.0002 & $-$0.0026 & 417 \\\\\n67 & 53768.3223 & 0.0002 & $-$0.0023 & 333 \\\\\n68 & 53768.3866 & 0.0002 & $-$0.0014 & 106 \\\\\n74 & 53768.7653 & 0.0003 & $-$0.0024 & 116 \\\\\n75 & 53768.8290 & 0.0002 & $-$0.0020 & 117 \\\\\n76 & 53768.8909 & 0.0004 & $-$0.0034 & 117 \\\\\n77 & 53768.9539 & 0.0002 & $-$0.0037 & 106 \\\\\n78 & 53769.0191 & 0.0007 & $-$0.0018 & 53 \\\\\n80 & 53769.1449 & 0.0006 & $-$0.0025 & 30 \\\\\n81 & 53769.2077 & 0.0005 & $-$0.0031 & 33 \\\\\n82 & 53769.2748 & 0.0004 & 0.0007 & 20 \\\\\n84 & 53769.3993 & 0.0002 & $-$0.0014 & 129 \\\\\n85 & 53769.4626 & 0.0003 & $-$0.0014 & 144 \\\\\n86 & 53769.5259 & 0.0003 & $-$0.0014 & 144 \\\\\n87 & 53769.5891 & 0.0003 & $-$0.0015 & 144 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453764.0837 + 0.063297 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J1025 (2006) (continued).}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n93 & 53769.9692 & 0.0005 & $-$0.0011 & 43 \\\\\n94 & 53770.0338 & 0.0005 & 0.0002 & 89 \\\\\n95 & 53770.0970 & 0.0009 & 0.0000 & 78 \\\\\n97 & 53770.2257 & 0.0018 & 0.0022 & 77 \\\\\n98 & 53770.2854 & 0.0006 & $-$0.0014 & 261 \\\\\n99 & 53770.3491 & 0.0027 & $-$0.0010 & 108 \\\\\n105 & 53770.7347 & 0.0005 & 0.0047 & 45 \\\\\n106 & 53770.7976 & 0.0005 & 0.0044 & 66 \\\\\n107 & 53770.8635 & 0.0016 & 0.0070 & 92 \\\\\n108 & 53770.9233 & 0.0005 & 0.0035 & 65 \\\\\n109 & 53770.9879 & 0.0009 & 0.0048 & 46 \\\\\n110 & 53771.0466 & 0.0039 & 0.0002 & 137 \\\\\n111 & 53771.1150 & 0.0004 & 0.0053 & 195 \\\\\n112 & 53771.1778 & 0.0004 & 0.0048 & 194 \\\\\n113 & 53771.2407 & 0.0004 & 0.0044 & 193 \\\\\n114 & 53771.3039 & 0.0008 & 0.0043 & 193 \\\\\n121 & 53771.7517 & 0.0005 & 0.0091 & 57 \\\\\n122 & 53771.8117 & 0.0014 & 0.0057 & 79 \\\\\n123 & 53771.8797 & 0.0006 & 0.0105 & 65 \\\\\n124 & 53771.9424 & 0.0007 & 0.0099 & 51 \\\\\n127 & 53772.1339 & 0.0006 & 0.0115 & 242 \\\\\n128 & 53772.1954 & 0.0004 & 0.0096 & 237 \\\\\n129 & 53772.2566 & 0.0008 & 0.0075 & 138 \\\\\n141 & 53773.0222 & 0.0011 & 0.0136 & 24 \\\\\n142 & 53773.0864 & 0.0007 & 0.0144 & 14 \\\\\n158 & 53774.0871 & 0.0040 & 0.0024 & 56 \\\\\n159 & 53774.1543 & 0.0014 & 0.0064 & 90 \\\\\n160 & 53774.2209 & 0.0005 & 0.0097 & 134 \\\\\n161 & 53774.2833 & 0.0005 & 0.0088 & 135 \\\\\n173 & 53775.0398 & 0.0005 & 0.0057 & 21 \\\\\n174 & 53775.1067 & 0.0007 & 0.0093 & 233 \\\\\n175 & 53775.1704 & 0.0008 & 0.0097 & 250 \\\\\n176 & 53775.2300 & 0.0007 & 0.0060 & 218 \\\\\n177 & 53775.2919 & 0.0009 & 0.0046 & 134 \\\\\n188 & 53775.9848 & 0.0013 & 0.0012 & 12 \\\\\n189 & 53776.0482 & 0.0011 & 0.0013 & 237 \\\\\n190 & 53776.1181 & 0.0009 & 0.0079 & 336 \\\\\n191 & 53776.1781 & 0.0009 & 0.0046 & 230 \\\\\n192 & 53776.2426 & 0.0008 & 0.0059 & 142 \\\\\n193 & 53776.3006 & 0.0013 & 0.0005 & 133 \\\\\n205 & 53777.0572 & 0.0031 & $-$0.0024 & 81 \\\\\n206 & 53777.1187 & 0.0015 & $-$0.0042 & 134 \\\\\n207 & 53777.1802 & 0.0016 & $-$0.0060 & 133 \\\\\n208 & 53777.2431 & 0.0017 & $-$0.0065 & 133 \\\\\n209 & 53777.3080 & 0.0062 & $-$0.0048 & 99 \\\\\n223 & 53778.1895 & 0.0057 & $-$0.0095 & 33 \\\\\n232 & 53778.7589 & 0.0008 & $-$0.0097 & 65 \\\\\n233 & 53778.8201 & 0.0012 & $-$0.0118 & 66 \\\\\n234 & 53778.8824 & 0.0014 & $-$0.0129 & 66 \\\\\n235 & 53778.9464 & 0.0011 & $-$0.0122 & 63 \\\\\n249 & 53779.8286 & 0.0021 & $-$0.0161 & 65 \\\\\n250 & 53779.8939 & 0.0012 & $-$0.0141 & 64 \\\\\n251 & 53779.9557 & 0.0017 & $-$0.0156 & 56 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J153616$-$0839.1}\\label{obj:asas1536}\n\n ASAS J153616$-$0839.1 (hereafter ASAS J1536) is a dwarf nova detected\nby ASAS-3 on 2004 February 2 ($V = 11.54$). A prediscovery observation by\nK. Haseda on 2004 January 31 ($m_{\\rm pg} = 11.2$) was reported\n(vsnet-alert 7986, 7987; see also \\cite{sch04asas1536}).\nThe object showed a relatively smooth fading until February 7, then\nfollowed by a $\\sim$ 0.2 mag rise associated with prominent superhumps.\nThe object underwent four post-superoutburst rebrightenings\n(figure \\ref{fig:asas1536lc}).\n\n The times of superhump maxima are listed in table \\ref{tab:asas1536oc2004}.\nThere was a clear stage A--B transition around $E=30$.\nThe $P_{\\rm dot}$ of the stage B was $+2.4(2.1) \\times 10^{-5}$.\nWe know little information whether the object had already developed\nsuperhumps or early superhumps before the start of our observation.\nWe, however, adopted this value as the representative period derivative\nof this system since the object is likely a WZ Sge-type dwarf nova with\nmultiple rebrightenings and a rise associated with prominent superhumps\ncan be better interpreted as a signature of emergence of ordinary\nsuperhumps (cf. \\cite{pat98egcnc}). Following this interpretation,\nthe epoch of our observation corresponds to the middle plateau stage of the\nsuperoutburst rather than its final stage. We present a representative\naveraged light curve of superhumps (figure \\ref{fig:asas1536shpdm}).\n\n The object showed a weaker superhump signal during the rebrightening\nand post-superoutburst stages (figure \\ref{fig:asas1536latepdm}).\nThe period, 0.06473(1) d, appears to be longer than the $P_{\\rm SH}$\nduring the superoutburst plateau, analogous to other WZ Sge-type\ndwarf novae (subsection \\ref{sec:latestage}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig182.eps}\n \\end{center}\n \\caption{Light curve of ASAS J1536 (2004).\n The filled circles, open circles and a cross represent CCD observations\n used here and ASAS-3 $V$ data, and Haseda's prediscovery photographic\n observation, respectively.}\n \\label{fig:asas1536lc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig183.eps}\n \\end{center}\n \\caption{Ordinary superhumps in ASAS J1536 (2004) after BJD 2453043\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas1536shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig184.eps}\n \\end{center}\n \\caption{Superhumps in ASAS J1536 (2004) during the rebrightenings\n and post-superoutburst stage.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:asas1536latepdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J1536 (2004).}\\label{tab:asas1536oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53041.3165 & 0.0019 & $-$0.0206 & 189 \\\\\n15 & 53042.3057 & 0.0009 & $-$0.0017 & 200 \\\\\n16 & 53042.3627 & 0.0024 & $-$0.0094 & 85 \\\\\n30 & 53043.2831 & 0.0005 & 0.0053 & 89 \\\\\n31 & 53043.3509 & 0.0006 & 0.0084 & 71 \\\\\n39 & 53043.8620 & 0.0079 & 0.0020 & 10 \\\\\n42 & 53044.0604 & 0.0005 & 0.0064 & 115 \\\\\n43 & 53044.1220 & 0.0003 & 0.0032 & 106 \\\\\n45 & 53044.2550 & 0.0003 & 0.0068 & 204 \\\\\n46 & 53044.3178 & 0.0005 & 0.0050 & 205 \\\\\n54 & 53044.8268 & 0.0026 & $-$0.0036 & 20 \\\\\n58 & 53045.0914 & 0.0004 & 0.0024 & 133 \\\\\n59 & 53045.1546 & 0.0003 & 0.0008 & 125 \\\\\n61 & 53045.2840 & 0.0005 & 0.0008 & 205 \\\\\n62 & 53045.3527 & 0.0006 & 0.0048 & 163 \\\\\n69 & 53045.8043 & 0.0023 & 0.0036 & 16 \\\\\n70 & 53045.8644 & 0.0073 & $-$0.0009 & 20 \\\\\n73 & 53046.0600 & 0.0003 & 0.0005 & 125 \\\\\n74 & 53046.1224 & 0.0006 & $-$0.0017 & 81 \\\\\n76 & 53046.2592 & 0.0009 & 0.0057 & 191 \\\\\n77 & 53046.3184 & 0.0008 & 0.0002 & 189 \\\\\n78 & 53046.3816 & 0.0010 & $-$0.0013 & 57 \\\\\n82 & 53046.6400 & 0.0006 & $-$0.0016 & 59 \\\\\n84 & 53046.7845 & 0.0029 & 0.0134 & 16 \\\\\n85 & 53046.8407 & 0.0086 & 0.0050 & 19 \\\\\n89 & 53047.0923 & 0.0005 & $-$0.0022 & 106 \\\\\n90 & 53047.1578 & 0.0003 & $-$0.0014 & 118 \\\\\n92 & 53047.2875 & 0.0008 & $-$0.0011 & 219 \\\\\n93 & 53047.3481 & 0.0009 & $-$0.0051 & 176 \\\\\n98 & 53047.6728 & 0.0010 & $-$0.0039 & 42 \\\\\n100 & 53047.8029 & 0.0049 & $-$0.0031 & 16 \\\\\n101 & 53047.8652 & 0.0062 & $-$0.0055 & 18 \\\\\n108 & 53048.3228 & 0.0007 & $-$0.0008 & 111 \\\\\n115 & 53048.7757 & 0.0093 & $-$0.0007 & 13 \\\\\n116 & 53048.8331 & 0.0169 & $-$0.0080 & 16 \\\\\n138 & 53050.2659 & 0.0010 & 0.0017 & 151 \\\\\n139 & 53050.3257 & 0.0015 & $-$0.0032 & 159 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453041.3371 + 0.0646895 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{ASAS J160048$-$4846.2}\\label{obj:asas1600}\n\n \\citet{ima06asas1600} and \\citet{soe09asas1600} reported a detailed report\nof the 2005 superoutburst. We further analyzed the data in combination\nwith the AAVSO observations. The times of superhump maxima are\nlisted in table \\ref{tab:asas1600oc2005}. The result basically confirmed\nthe analysis by \\citet{soe09asas1600}. The maxima for $E \\ge 243$\nwere humps observed during the rebrightening. Since the $O-C$'s of these\nhumps were not on a smooth extension of the stage C superhumps, these\nhumps are less likely persisting superhumps.\n\n\\begin{table}\n\\caption{Superhump maxima of ASAS J1600 (2005).}\\label{tab:asas1600oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53533.4285 & 0.0011 & $-$0.0240 & 147 \\\\\n1 & 53533.4925 & 0.0006 & $-$0.0250 & 147 \\\\\n2 & 53533.5648 & 0.0007 & $-$0.0176 & 147 \\\\\n8 & 53533.9619 & 0.0009 & $-$0.0101 & 107 \\\\\n9 & 53534.0332 & 0.0008 & $-$0.0038 & 111 \\\\\n10 & 53534.0990 & 0.0009 & $-$0.0029 & 90 \\\\\n13 & 53534.2960 & 0.0003 & $-$0.0006 & 145 \\\\\n14 & 53534.3632 & 0.0002 & 0.0016 & 147 \\\\\n15 & 53534.4283 & 0.0003 & 0.0017 & 147 \\\\\n16 & 53534.4932 & 0.0002 & 0.0017 & 145 \\\\\n17 & 53534.5604 & 0.0002 & 0.0040 & 147 \\\\\n18 & 53534.6229 & 0.0004 & 0.0016 & 84 \\\\\n28 & 53535.2765 & 0.0001 & 0.0058 & 146 \\\\\n29 & 53535.3418 & 0.0002 & 0.0062 & 146 \\\\\n30 & 53535.4064 & 0.0001 & 0.0058 & 147 \\\\\n31 & 53535.4711 & 0.0002 & 0.0056 & 146 \\\\\n32 & 53535.5359 & 0.0002 & 0.0054 & 147 \\\\\n45 & 53536.3752 & 0.0003 & 0.0005 & 86 \\\\\n46 & 53536.4410 & 0.0002 & 0.0014 & 146 \\\\\n47 & 53536.5059 & 0.0002 & 0.0014 & 132 \\\\\n48 & 53536.5699 & 0.0003 & 0.0005 & 95 \\\\\n59 & 53537.2848 & 0.0002 & 0.0011 & 148 \\\\\n60 & 53537.3490 & 0.0002 & 0.0004 & 148 \\\\\n61 & 53537.4139 & 0.0002 & 0.0003 & 148 \\\\\n62 & 53537.4787 & 0.0002 & 0.0002 & 144 \\\\\n63 & 53537.5452 & 0.0004 & 0.0017 & 117 \\\\\n73 & 53538.1946 & 0.0003 & 0.0018 & 123 \\\\\n74 & 53538.2590 & 0.0003 & 0.0012 & 144 \\\\\n75 & 53538.3240 & 0.0003 & 0.0013 & 147 \\\\\n76 & 53538.3890 & 0.0003 & 0.0014 & 140 \\\\\n77 & 53538.4533 & 0.0003 & 0.0008 & 146 \\\\\n78 & 53538.5195 & 0.0003 & 0.0020 & 146 \\\\\n79 & 53538.5843 & 0.0006 & 0.0019 & 87 \\\\\n89 & 53539.2362 & 0.0003 & 0.0044 & 144 \\\\\n90 & 53539.3009 & 0.0004 & 0.0042 & 144 \\\\\n91 & 53539.3654 & 0.0003 & 0.0038 & 144 \\\\\n92 & 53539.4313 & 0.0004 & 0.0047 & 144 \\\\\n93 & 53539.4970 & 0.0004 & 0.0055 & 144 \\\\\n104 & 53540.2136 & 0.0004 & 0.0078 & 147 \\\\\n105 & 53540.2786 & 0.0004 & 0.0079 & 147 \\\\\n106 & 53540.3421 & 0.0003 & 0.0064 & 147 \\\\\n107 & 53540.4072 & 0.0003 & 0.0065 & 147 \\\\\n108 & 53540.4723 & 0.0004 & 0.0067 & 147 \\\\\n109 & 53540.5376 & 0.0003 & 0.0071 & 132 \\\\\n119 & 53541.1813 & 0.0018 & 0.0014 & 90 \\\\\n120 & 53541.2491 & 0.0005 & 0.0042 & 147 \\\\\n121 & 53541.3134 & 0.0005 & 0.0036 & 146 \\\\\n122 & 53541.3777 & 0.0004 & 0.0031 & 146 \\\\\n123 & 53541.4407 & 0.0005 & 0.0010 & 147 \\\\\n124 & 53541.5058 & 0.0005 & 0.0013 & 146 \\\\\n125 & 53541.5711 & 0.0007 & 0.0016 & 111 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453533.4525 + 0.064936 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of ASAS J1600 (2005). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n135 & 53542.2184 & 0.0008 & $-$0.0004 & 144 \\\\\n136 & 53542.2824 & 0.0006 & $-$0.0014 & 122 \\\\\n137 & 53542.3457 & 0.0004 & $-$0.0031 & 147 \\\\\n138 & 53542.4114 & 0.0005 & $-$0.0022 & 147 \\\\\n139 & 53542.4741 & 0.0008 & $-$0.0045 & 147 \\\\\n140 & 53542.5399 & 0.0008 & $-$0.0037 & 147 \\\\\n182 & 53545.2514 & 0.0016 & $-$0.0194 & 86 \\\\\n243 & 53549.2366 & 0.0043 & 0.0046 & 106 \\\\\n244 & 53549.2939 & 0.0027 & $-$0.0030 & 128 \\\\\n245 & 53549.3520 & 0.0033 & $-$0.0098 & 115 \\\\\n246 & 53549.4149 & 0.0022 & $-$0.0118 & 73 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{CTCV J0549$-$4921}\\label{obj:j0549}\n\n The identification of this object (hereafter CTCV J0549) as an SU UMa-type\ndwarf nova was reported by \\citet{ima08fltractcv0549}. As in KK Tel\n\\citep{kat03v877arakktelpucma}, \\citet{ima08fltractcv0549} failed to\nidentify the correct $P_{\\rm SH}$ and $P_{\\rm dot}$ due to the large\nvariation in $P_{\\rm SH}$. In table \\ref{tab:j0549oc2006}, we listed\nupdated times of superhump maxima, measured from the data reported in\n\\citet{ima08fltractcv0549}. Following the stage A period evolution\n($E \\le 1$), the $P_{\\rm SH}$ varied strongly as in UV Gem and KK Tel.\nThe identified periods are given in table \\ref{tab:perlist}.\nAfter an examination of ASAS-3 light curve \\citep{ASAS3}, we detected\na number of outbursts (table \\ref{tab:j0549out}). The object appears\nto be more active than inferred by \\citet{ima08fltractcv0549}.\nThe typical length of supercycle is 750--800 d.\n\n\\begin{table}\n\\caption{Superhump maxima of CTCV J0549 (2006).}\\label{tab:j0549oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53828.2560 & 0.0017 & $-$0.0251 & 188 \\\\\n1 & 53828.3308 & 0.0027 & $-$0.0349 & 183 \\\\\n23 & 53830.2389 & 0.0004 & 0.0126 & 105 \\\\\n24 & 53830.3275 & 0.0005 & 0.0166 & 123 \\\\\n35 & 53831.2610 & 0.0002 & 0.0197 & 193 \\\\\n36 & 53831.3448 & 0.0004 & 0.0189 & 99 \\\\\n47 & 53832.2610 & 0.0003 & 0.0048 & 189 \\\\\n48 & 53832.3513 & 0.0010 & 0.0106 & 98 \\\\\n118 & 53838.2499 & 0.0003 & $-$0.0111 & 190 \\\\\n119 & 53838.3334 & 0.0008 & $-$0.0122 & 98 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453828.2811 + 0.084575 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Outbursts of CTCV J0549.}\\label{tab:j0549out}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\nJD$-$2400000 & $V$ max & Duration (d) & Type \\\\\n\\hline\n51952.5 & 13.5 & $>$9 & Super \\\\\n52172.9 & 13.7 & 1 & Normal \\\\\n52578.7 & 14.0 & 1 & Normal \\\\\n53025.6 & 13.6 & $>$10 & Super \\\\\n53489.5 & 13.8 & 1 & Normal \\\\\n53740.6 & 13.6 & 2 & Normal \\\\\n53813.7 & 15.0 & 1 & Normal \\\\\n53830.5 & 13.3 & $>$6 & Super \\\\\n54216.5 & 13.8 & 1 & Normal \\\\\n54301.9 & 13.8 & 1 & Normal \\\\\n54440.7 & 14.3 & 1 & Normal \\\\\n54586.5 & 13.1 & $>$8 & Super \\\\\n54705.9 & 14.4 & 1 & Normal \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{Ha 0242$-$2802}\\label{obj:ha0242}\n\n Ha 0242$-$2802 (hereafter Ha 0242) was discovered as a CV selected\nby H$\\alpha$ emission \\citep{how02shortPCV}. \\citet{wou04CV4} presented\ntime-resolved photometry in quiescence and established its eclipsing\nnature. \\citet{mas05ha0242} reported phase-resolved spectroscopy.\nWe observed the 2006 superoutburst and established its SU UMa-type\nnature. The times of superhump maxima, measured from observations\noutside the eclipses, are listed in table \\ref{tab:ha0242oc2006}.\nDue to the overlapping eclipses, it is difficult to clearly determine\nthe period variation. The mean $P_{\\rm SH}$ with the PDM method\nwas 0.07709(2) d (figure \\ref{fig:ha0242shpdm}), 3.3 \\% longer than\nthe $P_{\\rm orb}$ (updated using eclipse timings in \\cite{kra06ha0242}).\nThis $P_{\\rm SH}$ was adopted in table \\ref{tab:perlist}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig185.eps}\n \\end{center}\n \\caption{Superhumps in Ha 0242 (2002). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:ha0242shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of Ha 0242 (2006).}\\label{tab:ha0242oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53742.3224 & 0.0023 & $-$0.0047 & 102 \\\\\n8 & 53742.9480 & 0.0028 & 0.0048 & 166 \\\\\n9 & 53743.0219 & 0.0016 & 0.0017 & 128 \\\\\n29 & 53744.5569 & 0.0041 & $-$0.0035 & 28 \\\\\n30 & 53744.6442 & 0.0012 & 0.0068 & 47 \\\\\n31 & 53744.7095 & 0.0022 & $-$0.0050 & 26 \\\\\n42 & 53745.5612 & 0.0006 & $-$0.0005 & 53 \\\\\n43 & 53745.6392 & 0.0005 & 0.0006 & 59 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453742.3271 + 0.077013 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSSp J013701.06$-$091234.9}\\label{obj:j0137}\n\n This object (hereafter SDSS J0137) was extensively studied by\n\\citet{ima06j0137}. We have reanalyzed the data and obtained improved\nand newly measured times of superhump maxima (table \\ref{tab:j0137oc2003}).\nThe $P_{\\rm dot}$ for $E \\le 98$ (before the remarkable period\nshortening as described in \\cite{ima06j0137})\nwas $+2.3(1.7) \\times 10^{-5}$.\n\n The 2009 superoutburst was detected during its rising stage\n(vsnet-alert 10994). Only the stage C superhumps were recorded\n(table \\ref{tab:j0137oc2009}). The mean superhump period with the\nPDM method was 0.056443(8) d. We adopted this value rather than the one\nfrom the times of maxima because of fragmentary visibility of superhumps\ndue to the unfavorable seasonal condition. The relatively low frequency\nof superoutburst (once in three to five years) appears to be\nconfirmed.\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0137 (2003--2004).}\\label{tab:j0137oc2003}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52996.8751 & 0.0007 & $-$0.0022 & 64 \\\\\n1 & 52996.9288 & 0.0005 & $-$0.0051 & 164 \\\\\n2 & 52996.9846 & 0.0008 & $-$0.0059 & 134 \\\\\n8 & 52997.3246 & 0.0001 & $-$0.0056 & 129 \\\\\n9 & 52997.3819 & 0.0002 & $-$0.0049 & 128 \\\\\n10 & 52997.4397 & 0.0004 & $-$0.0037 & 86 \\\\\n18 & 52997.8883 & 0.0010 & $-$0.0080 & 59 \\\\\n19 & 52997.9478 & 0.0003 & $-$0.0051 & 127 \\\\\n20 & 52998.0052 & 0.0005 & $-$0.0043 & 107 \\\\\n21 & 52998.0612 & 0.0004 & $-$0.0049 & 89 \\\\\n37 & 52998.9728 & 0.0005 & 0.0009 & 101 \\\\\n38 & 52999.0291 & 0.0005 & 0.0006 & 100 \\\\\n53 & 52999.8745 & 0.0035 & $-$0.0031 & 41 \\\\\n54 & 52999.9370 & 0.0005 & 0.0027 & 57 \\\\\n55 & 52999.9940 & 0.0009 & 0.0032 & 38 \\\\\n67 & 53000.6751 & 0.0015 & 0.0049 & 61 \\\\\n71 & 53000.9011 & 0.0004 & 0.0044 & 96 \\\\\n72 & 53000.9591 & 0.0006 & 0.0058 & 136 \\\\\n73 & 53001.0153 & 0.0005 & 0.0055 & 159 \\\\\n74 & 53001.0708 & 0.0005 & 0.0043 & 154 \\\\\n96 & 53002.3202 & 0.0002 & 0.0083 & 119 \\\\\n97 & 53002.3770 & 0.0002 & 0.0085 & 126 \\\\\n98 & 53002.4356 & 0.0007 & 0.0104 & 75 \\\\\n106 & 53002.8862 & 0.0005 & 0.0082 & 77 \\\\\n107 & 53002.9404 & 0.0004 & 0.0058 & 90 \\\\\n108 & 53002.9965 & 0.0004 & 0.0053 & 75 \\\\\n109 & 53003.0512 & 0.0009 & 0.0033 & 61 \\\\\n125 & 53003.9561 & 0.0004 & 0.0025 & 86 \\\\\n126 & 53004.0132 & 0.0005 & 0.0030 & 80 \\\\\n127 & 53004.0674 & 0.0017 & 0.0006 & 65 \\\\\n131 & 53004.2942 & 0.0003 & 0.0009 & 128 \\\\\n132 & 53004.3502 & 0.0002 & 0.0004 & 102 \\\\\n166 & 53006.2671 & 0.0009 & $-$0.0076 & 41 \\\\\n195 & 53007.9059 & 0.0005 & $-$0.0105 & 93 \\\\\n197 & 53008.0251 & 0.0020 & $-$0.0045 & 29 \\\\\n231 & 53009.9404 & 0.0015 & $-$0.0139 & 83 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452996.8773 + 0.056611 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0137 (2009).}\\label{tab:j0137oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54867.9004 & 0.0038 & $-$0.0099 & 35 \\\\\n18 & 54868.9285 & 0.0009 & 0.0017 & 36 \\\\\n36 & 54869.9520 & 0.0006 & 0.0087 & 111 \\\\\n53 & 54870.9071 & 0.0008 & 0.0038 & 49 \\\\\n124 & 54874.9091 & 0.0017 & $-$0.0038 & 53 \\\\\n160 & 54876.9456 & 0.0020 & $-$0.0004 & 35 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454867.9103 + 0.056473 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J031051.66$-$075500.3}\\label{obj:j0310}\n\n This object (hereafter SDSS J0310) is a CV selected\nduring the course of the SDSS \\citep{szk03SDSSCV2}.\nB. Monard detected an outburst in 2004 July and reported the presence\nof superhumps (vsnet-alert 8236, 8239). We analyzed the observation\nof this superoutburst. The best superhump period based on the first\nthree nights was 0.06866(6) d (figure \\ref{fig:j0310shpdm}),\nsupporting the identification by D. Nogami (vsnet-alert 8240).\nThe times of superhump maxima based in this\nperiod identification are listed in table \\ref{tab:j0310oc2004}.\nWe obtained a global $P_{\\rm dot}$ of\n$+2.0(2.7) \\times 10^{-5}$, which is probably a mixture of different stages\nof period evolution. The object underwent another superoutburst\nin 2009 January--February (vsnet-alert 10995).\nFurther observations are absolutely needed to better qualify the period\nevolution.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig186.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J0310 (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0310shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0310 (2004).}\\label{tab:j0310oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53198.5967 & 0.0009 & 0.0031 & 154 \\\\\n1 & 53198.6602 & 0.0012 & $-$0.0020 & 98 \\\\\n14 & 53199.5511 & 0.0086 & $-$0.0034 & 83 \\\\\n15 & 53199.6279 & 0.0013 & 0.0048 & 155 \\\\\n44 & 53201.6086 & 0.0023 & $-$0.0050 & 154 \\\\\n49 & 53201.9664 & 0.0066 & 0.0097 & 73 \\\\\n78 & 53203.9367 & 0.0019 & $-$0.0105 & 137 \\\\\n160 & 53209.5801 & 0.0116 & 0.0047 & 87 \\\\\n161 & 53209.6427 & 0.0084 & $-$0.0013 & 134 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453198.5936 + 0.068637 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J033449.86$-$071047.8}\\label{obj:j0334}\n\n SDSS J033449.86$-$071047.8 (hereafter SDSS J0334) is a CV selected\nduring the course of the SDSS \\citep{szk07SDSSCV6}, who reported\nthe classification as a dwarf nova and an orbital period of 0.079 d.\nThe 2009 outburst was detected by H. Maehara (vsnet-alert 10967).\nThe detection of superhumps qualified this object as an SU UMa-type\ndwarf nova (vsnet-alert 10973). The best superhump period determined\nfrom the observations was 0.07485(3) d (figure \\ref{fig:j0334shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0334oc2009}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig187.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J0334 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0334shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0334 (2009).}\\label{tab:j0334oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54856.0144 & 0.0009 & $-$0.0041 & 160 \\\\\n1 & 54856.0945 & 0.0024 & 0.0012 & 89 \\\\\n12 & 54856.9133 & 0.0015 & $-$0.0025 & 73 \\\\\n13 & 54856.9924 & 0.0014 & 0.0019 & 207 \\\\\n14 & 54857.0689 & 0.0023 & 0.0036 & 127 \\\\\n39 & 54858.9403 & 0.0014 & 0.0056 & 136 \\\\\n40 & 54859.0062 & 0.0022 & $-$0.0032 & 166 \\\\\n52 & 54859.9067 & 0.0024 & $-$0.0000 & 145 \\\\\n53 & 54859.9821 & 0.0015 & 0.0006 & 189 \\\\\n54 & 54860.0531 & 0.0037 & $-$0.0031 & 113 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454856.0185 + 0.074773 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J074640.62$+$173412.8}\\label{obj:j0746}\n\n SDSS J074640.62$+$173412.8 (hereafter SDSS J0746) is a CV selected\nduring the course of the SDSS \\citep{szk06SDSSCV5}, who suggested the\ndwarf nova-type classification based on its variability.\nJ. Shears reported an outburst of this object in 2009 January\n(cvnet-outburst 2949). The detection of superhumps led to a classification\nas an SU UMa-type dwarf nova (vsnet-alert 11069).\nThe mean superhump period with the PDM method was 0.066761(15) d\n(figure \\ref{fig:j0746shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0746oc2009}.\nThere was a stage B--C transition around $E=78$. Excluding $E=30$,\nwe obtained $P_{\\rm dot}$ = $+9.3(2.5) \\times 10^{-5}$, fairly common\nfor this $P_{\\rm SH}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig188.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J0746 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0746shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0746 (2009).}\\label{tab:j0746oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54874.9304 & 0.0011 & 0.0039 & 49 \\\\\n1 & 54874.9954 & 0.0019 & 0.0021 & 70 \\\\\n2 & 54875.0599 & 0.0015 & $-$0.0001 & 42 \\\\\n30 & 54876.9158 & 0.0063 & $-$0.0127 & 42 \\\\\n31 & 54876.9944 & 0.0026 & $-$0.0009 & 70 \\\\\n32 & 54877.0607 & 0.0017 & $-$0.0013 & 257 \\\\\n33 & 54877.1304 & 0.0015 & 0.0016 & 292 \\\\\n34 & 54877.1928 & 0.0023 & $-$0.0027 & 119 \\\\\n76 & 54880.0014 & 0.0027 & 0.0031 & 232 \\\\\n77 & 54880.0711 & 0.0016 & 0.0061 & 314 \\\\\n78 & 54880.1387 & 0.0020 & 0.0069 & 182 \\\\\n90 & 54880.9367 & 0.0068 & 0.0042 & 64 \\\\\n91 & 54880.9988 & 0.0033 & $-$0.0005 & 56 \\\\\n92 & 54881.0658 & 0.0019 & $-$0.0003 & 42 \\\\\n93 & 54881.1409 & 0.0018 & 0.0081 & 60 \\\\\n94 & 54881.1859 & 0.0044 & $-$0.0136 & 71 \\\\\n138 & 54884.1366 & 0.0039 & 0.0008 & 99 \\\\\n139 & 54884.1979 & 0.0044 & $-$0.0046 & 74 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454874.9265 + 0.066734 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J081207.63$+$131824.4}\\label{obj:j0812}\n\n SDSS J081207.63$+$131824.4 (hereafter SDSS J0812) is a CV selected\nduring the course of the SDSS \\citep{szk07SDSSCV6}. The 2008 superoutburst\ndetected by K. Itagaki \\citep{yam08j0812cbet1536} led to the classification\nas a long-$P_{\\rm orb}$ SU UMa-type dwarf nova.\nThe mean superhump period with the PDM method was 0.08432(1) d\n(figure \\ref{fig:j0812shpdm}). The times of superhump\nmaxima are listed in table \\ref{tab:j0812oc2008}. We obtained a global\n$P_{\\rm dot}$ of $-24.0(5.2) \\times 10^{-5}$, a value similar to\nthe one in UV Gem having a similar $P_{\\rm SH}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig189.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J0812 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0812shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0812 (2008).}\\label{tab:j0812oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54751.2800 & 0.0002 & $-$0.0146 & 333 \\\\\n35 & 54754.2365 & 0.0036 & $-$0.0002 & 75 \\\\\n36 & 54754.3234 & 0.0006 & 0.0027 & 154 \\\\\n47 & 54755.2555 & 0.0004 & 0.0101 & 299 \\\\\n48 & 54755.3309 & 0.0008 & 0.0014 & 188 \\\\\n59 & 54756.2661 & 0.0015 & 0.0120 & 216 \\\\\n60 & 54756.3402 & 0.0010 & 0.0020 & 120 \\\\\n71 & 54757.2698 & 0.0008 & 0.0070 & 319 \\\\\n83 & 54758.2727 & 0.0023 & 0.0012 & 88 \\\\\n95 & 54759.2586 & 0.0018 & $-$0.0217 & 103 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454751.2946 + 0.084059 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSSp J082409.73$+$493124.4}\\label{obj:j0824}\n\n SDSSp J082409.73$+$493124.4 (hereafter SDSS J0824) is a CV selected\nduring the course of the SDSS \\citep{szk02SDSSCVs} (see \\cite{boy08j0824}\nfor the history of observation).\n\\citet{boy08j0824} reported the detection of superhumps with a mean\nperiod of 0.06954(5). \\citet{boy08j0824} interpreted an apparent phase\ntransition in the late course of the superoutburst as being the transition\nto late superhumps. Their data, however, had a gap in the middle stage\nof the superoutburst. Our own observations happened to fill the gap.\nWe used a combined data set by ours and\nfrom the AAVSO database, the latter including the partial data in\n\\citet{boy08j0824}. We used the data common to the AAVSO database\nand those in \\citet{boy08j0824} to determine the systematic difference\nbetween our measurements and those by \\citet{boy08j0824}.\n\n Table \\ref{tab:j0824oc2007} lists combined times of superhump maxima,\nafter adding a systematic difference of 0.0035 d to \\citet{boy08j0824}.\nThe entire data now clearly show a sharp transition from the stage B\nwith a slightly positive $P_{\\rm dot}$ to the stage C after $E = 110$\n(figure \\ref{fig:j0824reboc}).\nThe phase discontinuity reported in \\citet{boy08j0824} reflected this\nperiod variation rather than a transition to late superhumps.\nThe $P_{\\rm dot}$ of the first segment was $+8.0(2.5) \\times 10^{-5}$.\n\n Another likely superoutburst was observed in 2007 December (J. Shears,\nbaavss-alert 1492), giving a supercycle length of $\\sim$ 300 d.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig190.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps SDSS J0824.\n (Upper): $O-C$ diagram. The values of $O-C$'s are different from\n those listed in table \\ref{tab:j0824oc2007} and were calculated from\n a linear fit for the times of superhumps for $E \\le 110$.\n The curve represents a quadratic fit with $P_{\\rm dot}$\n = $+8.0 \\times 10^{-5}$.\n (Lower): Light curve.}\n \\label{fig:j0824reboc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0824 (2007).}\\label{tab:j0824oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54160.4661 & 0.0012 & 0.0001 & 45 \\\\\n8 & 54161.0272 & 0.0033 & 0.0044 & 101 \\\\\n9 & 54161.0860 & 0.0028 & $-$0.0064 & 102 \\\\\n10 & 54161.1583 & 0.0016 & $-$0.0037 & 103 \\\\\n13 & 54161.3654 & 0.0015 & $-$0.0054 & 108 \\\\\n14 & 54161.4388 & 0.0014 & $-$0.0017 & 118 \\\\\n16 & 54161.5716 & 0.0017 & $-$0.0080 & 102 \\\\\n22 & 54161.9875 & 0.0030 & $-$0.0098 & 79 \\\\\n23 & 54162.0697 & 0.0034 & 0.0028 & 74 \\\\\n43 & 54163.4526 & 0.0020 & $-$0.0064 & 144 \\\\\n44 & 54163.5262 & 0.0016 & $-$0.0025 & 120 \\\\\n45 & 54163.5930 & -- & $-$0.0053 & 0 \\\\\n46 & 54163.6620 & -- & $-$0.0059 & 0 \\\\\n47 & 54163.7360 & -- & $-$0.0015 & 0 \\\\\n48 & 54163.8070 & -- & $-$0.0001 & 0 \\\\\n49 & 54163.8710 & -- & $-$0.0057 & 0 \\\\\n51 & 54164.0257 & 0.0040 & 0.0098 & 69 \\\\\n60 & 54164.6380 & -- & $-$0.0044 & 0 \\\\\n67 & 54165.1351 & 0.0060 & 0.0055 & 79 \\\\\n68 & 54165.1972 & 0.0048 & $-$0.0020 & 62 \\\\\n80 & 54166.0455 & 0.0077 & 0.0109 & 100 \\\\\n82 & 54166.1765 & 0.0095 & 0.0028 & 91 \\\\\n94 & 54167.0201 & 0.0032 & 0.0110 & 95 \\\\\n105 & 54167.7820 & -- & 0.0073 & 0 \\\\\n109 & 54168.0722 & 0.0081 & 0.0191 & 134 \\\\\n110 & 54168.1384 & 0.0035 & 0.0157 & 139 \\\\\n116 & 54168.5491 & 0.0014 & 0.0087 & 23 \\\\\n117 & 54168.6112 & 0.0016 & 0.0012 & 17 \\\\\n118 & 54168.6837 & 0.0013 & 0.0041 & 23 \\\\\n119 & 54168.7518 & 0.0019 & 0.0026 & 21 \\\\\n120 & 54168.8248 & 0.0014 & 0.0060 & 23 \\\\\n121 & 54168.8910 & -- & 0.0026 & 0 \\\\\n123 & 54169.0330 & 0.0064 & 0.0053 & 102 \\\\\n124 & 54169.1109 & 0.0088 & 0.0136 & 102 \\\\\n125 & 54169.1879 & 0.0057 & 0.0211 & 102 \\\\\n128 & 54169.3741 & 0.0018 & $-$0.0016 & 75 \\\\\n129 & 54169.4467 & 0.0013 & 0.0014 & 61 \\\\\n130 & 54169.5127 & 0.0014 & $-$0.0022 & 74 \\\\\n143 & 54170.4116 & 0.0012 & $-$0.0082 & 77 \\\\\n144 & 54170.4823 & 0.0018 & $-$0.0071 & 70 \\\\\n145 & 54170.5499 & 0.0014 & $-$0.0092 & 55 \\\\\n153 & 54171.0994 & 0.0037 & $-$0.0165 & 93 \\\\\n154 & 54171.1851 & 0.0023 & $-$0.0004 & 42 \\\\\n166 & 54171.9979 & 0.0054 & $-$0.0229 & 80 \\\\\n168 & 54172.1408 & 0.0080 & $-$0.0191 & 79 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454160.4659 + 0.069607 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n \\multicolumn{5}{l}{\\phantom{$^{c}$} $N=0$ refers to \\citet{boy08j0824}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSSp J083845.23$+$491055.5}\\label{obj:j0838}\n\n SDSSp J083845.23$+$491055.5 (hereafter SDSS J0838) was discovered\nas a CV having a typical spectrum of a dwarf novae \\citep{szk02SDSSCVs}.\nWe analyzed the AAVSO data during the 2007 October superoutburst\n(cf. baavss-alert 1383, 1386).\nThe times of superhump maxima are listed in table \\ref{tab:j0838oc2007}.\n\n The object underwent another superoutburst in 2009 (baavss-alert\n1944). The observation of this superoutburst finally led to an\nidentification of the superhump period (vsnet-alert 11099).\nThe times of superhump maxima are listed in table \\ref{tab:j0838oc2009}.\nAlthough the identification of the cycle number between $E=2$ (stage B)\nand $E=101$ was rather uncertain, the stage C superhumps with a mean\nperiod of 0.07147(2) d (PDM method, figure \\ref{fig:j0838shpdm}) were\neventually identified.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig191.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J0838 (2009, late stage). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0838shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0838 (2007).}\\label{tab:j0838oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54396.5730 & 0.0008 & 0.0010 & 98 \\\\\n1 & 54396.6432 & 0.0007 & $-$0.0020 & 101 \\\\\n2 & 54396.7194 & 0.0008 & 0.0010 & 57 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454396.5720 + 0.07316 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J0838 (2009).}\\label{tab:j0838oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54884.1135 & 0.0002 & $-$0.0010 & 140 \\\\\n1 & 54884.1829 & 0.0005 & $-$0.0034 & 69 \\\\\n2 & 54884.2575 & 0.0003 & $-$0.0005 & 131 \\\\\n101 & 54891.3654 & 0.0010 & 0.0059 & 51 \\\\\n102 & 54891.4367 & 0.0009 & 0.0055 & 52 \\\\\n103 & 54891.5065 & 0.0010 & 0.0036 & 49 \\\\\n111 & 54892.0825 & 0.0010 & 0.0057 & 140 \\\\\n112 & 54892.1485 & 0.0010 & $-$0.0000 & 151 \\\\\n123 & 54892.9322 & 0.0045 & $-$0.0054 & 90 \\\\\n129 & 54893.3651 & 0.0027 & $-$0.0029 & 51 \\\\\n131 & 54893.5091 & 0.0022 & $-$0.0024 & 53 \\\\\n152 & 54895.0228 & 0.0031 & 0.0049 & 126 \\\\\n153 & 54895.0841 & 0.0038 & $-$0.0055 & 137 \\\\\n154 & 54895.1732 & 0.0040 & 0.0118 & 146 \\\\\n155 & 54895.2169 & 0.0062 & $-$0.0162 & 73 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454884.1145 + 0.071732 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J100515.39$+$191108.0}\\label{obj:j1005}\n\n The 2009 outburst of this object (hereafter SDSS J1005) was reported\nS. Brady (cvnet-outburst 2859), which later turned out to be a\nsuperoutburst. We analyzed the available data of this outburst during\nits late stage and obtained a mean superhump period of 0.07747(2) d\nwith the PDM method (figure \\ref{fig:j1005shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j1005oc2009}.\nThese superhumps most likely correspond to stage C superhumps.\nJ. Pietz reported a period of 0.0779 d (cvnet-outburst 2866).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig192.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1005 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1005shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1005 (2009).}\\label{tab:j1005oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54838.5679 & 0.0004 & $-$0.0016 & 106 \\\\\n1 & 54838.6471 & 0.0005 & 0.0002 & 140 \\\\\n10 & 54839.3442 & 0.0003 & 0.0007 & 166 \\\\\n16 & 54839.8075 & 0.0008 & $-$0.0005 & 51 \\\\\n17 & 54839.8855 & 0.0004 & 0.0001 & 80 \\\\\n18 & 54839.9622 & 0.0006 & $-$0.0006 & 40 \\\\\n36 & 54841.3606 & 0.0006 & 0.0046 & 112 \\\\\n41 & 54841.7439 & 0.0018 & 0.0009 & 54 \\\\\n42 & 54841.8201 & 0.0007 & $-$0.0003 & 81 \\\\\n43 & 54841.8990 & 0.0007 & 0.0011 & 67 \\\\\n46 & 54842.1303 & 0.0054 & 0.0003 & 56 \\\\\n47 & 54842.2034 & 0.0014 & $-$0.0041 & 142 \\\\\n48 & 54842.2891 & 0.0025 & 0.0043 & 149 \\\\\n49 & 54842.3570 & 0.0025 & $-$0.0052 & 115 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454838.5695 + 0.077404 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J110014.72$+$131552.1}\\label{obj:j1100}\n\n SDSS J110014.72$+$131552.1 (hereafter SDSS J1100) was selected as\na CV during the course of the SDSS \\citep{szk06SDSSCV5}.\nDuring the 2009 outburst detected by the CRTS (vsnet-alert 11188),\nsuperhumps were detected (vsnet-alert 11198, 11202).\nAlthough the short baseline of the observations makes alias selection\nslightly ambiguous, we present the $O-C$'s based on the period of\n0.06757(2) d (PDM method).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig193.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1100 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1100shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1100 (2009).}\\label{tab:j1100oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54940.1283 & 0.0015 & $-$0.0020 & 122 \\\\\n15 & 54941.1459 & 0.0045 & 0.0026 & 71 \\\\\n63 & 54944.3870 & 0.0014 & 0.0024 & 108 \\\\\n64 & 54944.4492 & 0.0027 & $-$0.0030 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454940.1303 + 0.067529 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J122740.83$+$513925.0}\\label{obj:j1227}\n\n SDSS J122740.83$+$513925.0 (hereafter SDSS J1227) was selected as\na high-inclination CV during the course of the SDSS \\citep{szk04SDSSCV3}.\n\\citet{lit08eclCV} reported parameters of eclipses. \\citet{she08j1227}\nreported the detection of superhumps and discussed on the variation of\neclipses during the 2007 superoutburst. Using the times of eclipses\npublished in \\citet{lit08eclCV} and \\citet{she08j1227}, we obtained\nthe following updated ephemeris (equation \\ref{equ:j1227ecl}).\n\n\\begin{equation}\n{\\rm Min(BJD)} = 2453796.2478(4) + 0.06295835(5) E\n\\label{equ:j1227ecl}.\n\\end{equation}\n\n We analyzed the combined data set with ours, AAVSO data, and data\nextracted from figures in \\citet{she08j1227} which were not included\nin ours nor in the AAVSO data.\nThe times of superhump maxima are listed in\ntable \\ref{tab:j1227oc2007}. The first night of the observation\neither corresponded to the stage A or the complex profile disturbed\nthe $O-C$'s. The period appears almost constant for the interval\n$33 \\le E \\le 124$, with a mean $P_{\\rm SH}$ of 0.064552(21) d\nand $P_{\\rm dot}$ = $+2.8(2.5) \\times 10^{-5}$. This $P_{\\rm dot}$\nappears rather unusual for this $P_{\\rm SH}$. The positive $O-C$'s for\n$126 \\le E \\le 129$ may reflect the terminal stage of the stage B,\nwhen the $P_{\\rm SH}$ usually lengthens. This identification seems\nto be supported by the apparent increase of the amplitudes of\nsuperhumps at this epoch. Using the entire interval for\n$33 \\le E \\le 129$, we obtained a mean $P_{\\rm SH}$ of 0.064593(22) d\nand $P_{\\rm dot}$ = $+6.1(2.1) \\times 10^{-5}$. We adopted these\nvalues in table \\ref{tab:perlist}.\nThe fractional superhump excesses for these periods are\n2.5 \\% and 2.6 \\%, respectively.\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1227 (2007).}\\label{tab:j1227oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54256.4358 & 0.0012 & $-$0.0237 & -- \\\\\n1 & 54256.5064 & 0.0021 & $-$0.0178 & -- \\\\\n33 & 54258.6073 & 0.0004 & 0.0114 & 61 \\\\\n34 & 54258.6739 & 0.0003 & 0.0133 & 60 \\\\\n35 & 54258.7354 & 0.0008 & 0.0100 & 58 \\\\\n40 & 54259.0611 & 0.0010 & 0.0120 & 104 \\\\\n61 & 54260.4153 & 0.0032 & 0.0066 & 57 \\\\\n62 & 54260.4762 & 0.0006 & 0.0028 & 37 \\\\\n63 & 54260.5428 & 0.0004 & 0.0047 & 100 \\\\\n77 & 54261.4417 & 0.0012 & $-$0.0028 & 103 \\\\\n78 & 54261.5105 & 0.0007 & 0.0012 & 98 \\\\\n80 & 54261.6421 & 0.0008 & 0.0034 & 31 \\\\\n81 & 54261.7047 & 0.0010 & 0.0012 & 33 \\\\\n82 & 54261.7706 & 0.0009 & 0.0024 & 35 \\\\\n86 & 54262.0316 & 0.0009 & 0.0044 & 49 \\\\\n101 & 54262.9979 & 0.0011 & $-$0.0004 & 81 \\\\\n102 & 54263.0632 & 0.0014 & 0.0002 & 114 \\\\\n111 & 54263.6429 & 0.0016 & $-$0.0028 & 34 \\\\\n112 & 54263.7045 & 0.0016 & $-$0.0059 & 35 \\\\\n113 & 54263.7691 & 0.0024 & $-$0.0060 & 35 \\\\\n114 & 54263.8314 & 0.0034 & $-$0.0085 & 35 \\\\\n123 & 54264.4155 & 0.0026 & $-$0.0070 & 74 \\\\\n124 & 54264.4887 & 0.0006 & 0.0014 & 68 \\\\\n126 & 54264.6177 & 0.0009 & 0.0009 & 41 \\\\\n127 & 54264.6816 & 0.0012 & 0.0001 & 39 \\\\\n128 & 54264.7449 & 0.0010 & $-$0.0014 & 41 \\\\\n129 & 54264.8114 & 0.0026 & 0.0004 & 40 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454256.4595 + 0.064740 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J152419.33$+$220920.0}\\label{obj:j1524}\n\n SDSS J152419.33$+$220920.0 (hereafter SDSS J1524) was suggested to be\na high-inclination CV during the course of the SDSS \\citep{szk09SDSSCV7}.\nThe 2009 outburst of this object was detected by the CRTS (vsnet-alert 11133).\nSubsequent observations established the presence of superhumps and\neclipses (cvnet-outburst 3029).\n\n The times of eclipse minima, measured outside the eclipses as in\nV2051 Oph, are listed in table \\ref{tab:j1524ecl}.\nThe times for $E < 0$ were from the CRTS chance detections of eclipses.\nThe times of these epochs have typical uncertainties of 0.001--0.002 d\n(approximately half duration of the eclipse). The epochs for $E \\ge 0$\nwere determined from time-resolved CCD observations; the typical uncertainty\nof the determination is $\\sim$ 0.001 d or less. The resultant orbital\nephemeris is given in equation \\ref{equ:j1524ecl}.\n\n The times of superhump maxima are listed in table \\ref{tab:j1524oc2009}.\nA stage B--C transition around $E=89$ was clearly detected.\nThe mean $P_{\\rm SH}$ and $P_{\\rm dot}$ during the stage B were\n0.067111(14) d (PDM method, figure \\ref{fig:j1524shpdm})\nand $+8.2(2.6) \\times 10^{-5}$, respectively.\nThe fractional superhump excess for $P_1$ was 2.7 \\%.\n\n\\begin{equation}\n{\\rm Min(BJD)} = 2454921.5937(1) + 0.0653187(1)\n\\label{equ:j1524ecl}.\n\\end{equation}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig194.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1524 (2009) before BJD 2454928.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1524shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Eclipse Minima of SDSS J1524.}\\label{tab:j1524ecl}\n\\begin{center}\n\\begin{tabular}{ccc}\n\\hline\\hline\n$E$ & Minimum$^*$ & $O-C$$^\\dagger$ \\\\\n\\hline\n$-$4528 & 54625.8317 & 0.0012 \\\\\n$-$4283 & 54641.8325 & $-$0.0012 \\\\\n$-$134 & 54912.8405 & $-$0.0005 \\\\\n$-$26 & 54919.8935 & $-$0.0020 \\\\\n0 & 54921.5936 & $-$0.0001 \\\\\n13 & 54922.4421 & $-$0.0008 \\\\\n14 & 54922.5100 & 0.0018 \\\\\n15 & 54922.5743 & 0.0008 \\\\\n16 & 54922.6386 & $-$0.0002 \\\\\n18 & 54922.7697 & 0.0003 \\\\\n19 & 54922.8351 & 0.0004 \\\\\n20 & 54922.9006 & 0.0006 \\\\\n29 & 54923.4880 & 0.0000 \\\\\n30 & 54923.5536 & 0.0003 \\\\\n33 & 54923.7502 & 0.0010 \\\\\n34 & 54923.8151 & 0.0006 \\\\\n35 & 54923.8804 & 0.0005 \\\\\n36 & 54923.9452 & 0.0000 \\\\\n40 & 54924.2054 & $-$0.0011 \\\\\n41 & 54924.2702 & $-$0.0015 \\\\\n43 & 54924.4011 & $-$0.0013 \\\\\n45 & 54924.5342 & 0.0011 \\\\\n46 & 54924.5986 & 0.0002 \\\\\n48 & 54924.7293 & 0.0003 \\\\\n49 & 54924.7933 & $-$0.0011 \\\\\n50 & 54924.8598 & 0.0002 \\\\\n51 & 54924.9250 & 0.0001 \\\\\n58 & 54925.3821 & $-$0.0001 \\\\\n61 & 54925.5785 & 0.0003 \\\\\n74 & 54926.4259 & $-$0.0014 \\\\\n75 & 54926.4927 & 0.0001 \\\\\n76 & 54926.5575 & $-$0.0005 \\\\\n79 & 54926.7539 & 0.0000 \\\\\n80 & 54926.8193 & 0.0001 \\\\\n81 & 54926.8845 & 0.0000 \\\\\n85 & 54927.1457 & $-$0.0001 \\\\\n86 & 54927.2111 & 0.0000 \\\\\n87 & 54927.2768 & 0.0004 \\\\\n105 & 54928.4527 & 0.0005 \\\\\n107 & 54928.5828 & 0.0000 \\\\\n110 & 54928.7792 & 0.0004 \\\\\n111 & 54928.8446 & 0.0005 \\\\\n\\hline\n \\multicolumn{3}{l}{$^*$ BJD$-$2400000.} \\\\\n \\multicolumn{3}{l}{$^\\dagger$ Against equation \\ref{equ:j1524ecl}.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1524 (2009).}\\label{tab:j1524oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54921.6110 & 0.0006 & 0.0018 & 59 \\\\\n13 & 54922.4789 & 0.0005 & $-$0.0016 & 107 \\\\\n14 & 54922.5442 & 0.0005 & $-$0.0034 & 100 \\\\\n15 & 54922.6118 & 0.0006 & $-$0.0028 & 77 \\\\\n17 & 54922.7479 & 0.0005 & $-$0.0008 & 58 \\\\\n18 & 54922.8117 & 0.0003 & $-$0.0040 & 59 \\\\\n19 & 54922.8802 & 0.0005 & $-$0.0025 & 58 \\\\\n20 & 54922.9478 & 0.0004 & $-$0.0019 & 46 \\\\\n27 & 54923.4232 & 0.0019 & 0.0044 & 48 \\\\\n28 & 54923.4835 & 0.0010 & $-$0.0024 & 115 \\\\\n29 & 54923.5508 & 0.0010 & $-$0.0022 & 105 \\\\\n30 & 54923.6210 & 0.0012 & 0.0011 & 54 \\\\\n32 & 54923.7501 & 0.0017 & $-$0.0040 & 58 \\\\\n33 & 54923.8221 & 0.0013 & 0.0011 & 57 \\\\\n34 & 54923.8854 & 0.0009 & $-$0.0026 & 57 \\\\\n35 & 54923.9579 & 0.0014 & 0.0028 & 40 \\\\\n38 & 54924.1618 & 0.0021 & 0.0056 & 52 \\\\\n39 & 54924.2205 & 0.0015 & $-$0.0027 & 63 \\\\\n40 & 54924.2899 & 0.0016 & $-$0.0003 & 125 \\\\\n41 & 54924.3538 & 0.0060 & $-$0.0035 & 32 \\\\\n42 & 54924.4186 & 0.0016 & $-$0.0056 & 54 \\\\\n43 & 54924.4859 & 0.0014 & $-$0.0054 & 61 \\\\\n44 & 54924.5569 & 0.0009 & $-$0.0014 & 117 \\\\\n45 & 54924.6209 & 0.0008 & $-$0.0045 & 76 \\\\\n47 & 54924.7562 & 0.0006 & $-$0.0032 & 62 \\\\\n48 & 54924.8256 & 0.0008 & $-$0.0008 & 69 \\\\\n49 & 54924.8926 & 0.0009 & $-$0.0009 & 68 \\\\\n50 & 54924.9596 & 0.0010 & $-$0.0009 & 57 \\\\\n56 & 54925.3620 & 0.0022 & $-$0.0006 & 30 \\\\\n57 & 54925.4301 & 0.0009 & 0.0005 & 73 \\\\\n58 & 54925.4935 & 0.0007 & $-$0.0032 & 134 \\\\\n59 & 54925.5578 & 0.0013 & $-$0.0059 & 120 \\\\\n72 & 54926.4481 & 0.0022 & 0.0131 & 100 \\\\\n73 & 54926.5103 & 0.0042 & 0.0082 & 100 \\\\\n74 & 54926.5699 & 0.0022 & 0.0008 & 82 \\\\\n77 & 54926.7797 & 0.0020 & 0.0096 & 59 \\\\\n78 & 54926.8433 & 0.0011 & 0.0062 & 60 \\\\\n83 & 54927.1772 & 0.0018 & 0.0049 & 141 \\\\\n84 & 54927.2443 & 0.0021 & 0.0051 & 108 \\\\\n85 & 54927.3113 & 0.0010 & 0.0050 & 125 \\\\\n87 & 54927.4448 & 0.0020 & 0.0045 & 34 \\\\\n88 & 54927.5155 & 0.0009 & 0.0081 & 48 \\\\\n89 & 54927.5798 & 0.0010 & 0.0054 & 53 \\\\\n101 & 54928.3835 & 0.0043 & 0.0048 & 23 \\\\\n102 & 54928.4494 & 0.0018 & 0.0037 & 68 \\\\\n103 & 54928.5143 & 0.0009 & 0.0016 & 85 \\\\\n104 & 54928.5840 & 0.0015 & 0.0042 & 78 \\\\\n107 & 54928.7820 & 0.0010 & 0.0012 & 58 \\\\\n108 & 54928.8481 & 0.0023 & 0.0002 & 57 \\\\\n117 & 54929.4467 & 0.0082 & $-$0.0044 & 58 \\\\\n118 & 54929.5129 & 0.0026 & $-$0.0052 & 37 \\\\\n148 & 54931.5131 & 0.0037 & $-$0.0158 & 50 \\\\\n163 & 54932.5228 & 0.0043 & $-$0.0115 & 48 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454921.6092 + 0.067025 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J155644.24$-$000950.2}\\label{obj:j1556}\n\n SDSS J155644.24$-$000950.2 (hereafter SDSS J1556) was selected as\na dwarf nova during the course of the SDSS \\citep{szk02SDSSCVs}.\n\\citet{wou04CV4} obtained 0.07408(1) d from quiescent orbital humps.\nDuring the 2006 March outburst, H. Maehara reported the detection\nof superhumps (vsnet-alert 9440).\n\n We observed the 2007 superoutburst. A PDM analysis yielded a mean\nsuperhump period of 0.082853(5) d (figure \\ref{fig:j1556shpdm},\nwhich corresponds to the longer one-day alias of \\citet{wou04CV4}.\nBoth PDM analysis and superhump $O-C$ analyses\nsupported this alias selection. Using the one-day alias period 0.08001(1)\ncalculated from \\citet{wou04CV4}, we obtained a reasonable fractional\nsuperhump excess of 3.6 \\%.\n\n The times of superhump maxima are listed in table \\ref{tab:j1556oc2007}.\nThe $O-C$ diagram (figure \\ref{fig:ocsamp}) showed a strong decrease\nin the superhump period.\nThe global $P_{\\rm dot}$ was $-8.7(1.1) \\times 10^{-5}$,\nand was $-6.9(0.8) \\times 10^{-5}$ excluding the initial stage of\ndevelopment (stage A, $E \\le 1$).\nWe consider the latter value as being the representative\nperiod derivative.\n\n Details of these and other observations and discussion will be\npresented in Maehara et al., in preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig195.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1556 (2007). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1556shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1556 (2007).}\\label{tab:j1556oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54311.9945 & 0.0003 & $-$0.0114 & 204 \\\\\n1 & 54312.0754 & 0.0005 & $-$0.0134 & 245 \\\\\n12 & 54313.0013 & 0.0002 & 0.0010 & 256 \\\\\n13 & 54313.0836 & 0.0003 & 0.0004 & 214 \\\\\n24 & 54313.9997 & 0.0002 & 0.0050 & 234 \\\\\n25 & 54314.0794 & 0.0004 & 0.0018 & 182 \\\\\n61 & 54317.0704 & 0.0015 & 0.0096 & 54 \\\\\n72 & 54317.9804 & 0.0005 & 0.0080 & 359 \\\\\n73 & 54318.0629 & 0.0004 & 0.0077 & 311 \\\\\n84 & 54318.9733 & 0.0002 & 0.0066 & 428 \\\\\n85 & 54319.0570 & 0.0005 & 0.0074 & 360 \\\\\n101 & 54320.3751 & 0.0004 & $-$0.0003 & 83 \\\\\n121 & 54322.0285 & 0.0008 & $-$0.0043 & 304 \\\\\n133 & 54323.0182 & 0.0008 & $-$0.0090 & 365 \\\\\n145 & 54324.0123 & 0.0005 & $-$0.0093 & 378 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454312.0059 + 0.082866 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J162718.39$+$120435.0}\\label{obj:j1627}\n\n The 2008 outburst of SDSS J162718.39$+$120435.0 (hereafter SDSS J1627) \nwas detected by S. Brady (cvnet-outburst 2421), which was subsequently\nproven to be a superoutburst (cvnet-outburst 2426). The observations\npresented here are a combination of \\citet{she08j1627} and the\nVSNET Collaboration. The times of superhump maxima\n(table \\ref{tab:j1627oc2008}) indicated a long $P_{\\rm SH}$ with\na strong global period variation of\n$P_{\\rm dot}$ = $-20.0(2.5) \\times 10^{-5}$.\nThe $O-C$ diagram (figure \\ref{fig:lp2})\nwas clearly composed of all stages A--C. The abrupt\nperiod change between stages B and C was also noted in \\citet{she08j1627}.\nThe periods of each segments are listed in table \\ref{tab:perlist}.\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1627.}\\label{tab:j1627oc2008}\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ \\\\\n\\hline\n0 & 54617.7385 & 0.0016 & $-$0.0659 \\\\\n2 & 54617.9384 & 0.0025 & $-$0.0843 \\\\\n6 & 54618.4293 & 0.0047 & $-$0.0303 \\\\\n7 & 54618.5422 & 0.0017 & $-$0.0266 \\\\\n8 & 54618.6593 & 0.0011 & $-$0.0186 \\\\\n9 & 54618.7619 & 0.0007 & $-$0.0252 \\\\\n10 & 54618.8736 & 0.0004 & $-$0.0227 \\\\\n15 & 54619.4453 & 0.0007 & 0.0029 \\\\\n16 & 54619.5581 & 0.0006 & 0.0065 \\\\\n17 & 54619.6670 & 0.0003 & 0.0063 \\\\\n18 & 54619.7794 & 0.0003 & 0.0095 \\\\\n19 & 54619.8891 & 0.0002 & 0.0100 \\\\\n26 & 54620.6590 & 0.0002 & 0.0155 \\\\\n27 & 54620.7679 & 0.0002 & 0.0151 \\\\\n28 & 54620.8776 & 0.0003 & 0.0156 \\\\\n33 & 54621.4239 & 0.0004 & 0.0159 \\\\\n33 & 54621.4241 & 0.0004 & 0.0161 \\\\\n34 & 54621.5389 & 0.0004 & 0.0218 \\\\\n35 & 54621.6439 & 0.0011 & 0.0175 \\\\\n36 & 54621.7584 & 0.0004 & 0.0228 \\\\\n37 & 54621.8668 & 0.0003 & 0.0220 \\\\\n38 & 54621.9815 & 0.0004 & 0.0275 \\\\\n49 & 54623.1727 & 0.0005 & 0.0175 \\\\\n50 & 54623.2884 & 0.0012 & 0.0239 \\\\\n52 & 54623.5010 & 0.0005 & 0.0182 \\\\\n54 & 54623.7199 & 0.0003 & 0.0187 \\\\\n55 & 54623.8292 & 0.0003 & 0.0188 \\\\\n56 & 54623.9345 & 0.0004 & 0.0149 \\\\\n60 & 54624.3742 & 0.0006 & 0.0178 \\\\\n71 & 54625.5686 & 0.0005 & 0.0110 \\\\\n79 & 54626.4409 & 0.0005 & 0.0096 \\\\\n80 & 54626.5494 & 0.0005 & 0.0090 \\\\\n86 & 54627.1992 & 0.0008 & 0.0035 \\\\\n98 & 54628.5042 & 0.0006 & $-$0.0019 \\\\\n109 & 54629.7014 & 0.0005 & $-$0.0059 \\\\\n110 & 54629.8139 & 0.0007 & $-$0.0026 \\\\\n111 & 54629.9205 & 0.0010 & $-$0.0052 \\\\\n117 & 54630.5779 & 0.0009 & $-$0.0030 \\\\\n118 & 54630.6836 & 0.0013 & $-$0.0065 \\\\\n119 & 54630.7940 & 0.0012 & $-$0.0054 \\\\\n120 & 54630.9006 & 0.0010 & $-$0.0080 \\\\\n127 & 54631.6609 & 0.0008 & $-$0.0121 \\\\\n128 & 54631.7746 & 0.0010 & $-$0.0075 \\\\\n149 & 54634.0514 & 0.0099 & $-$0.0239 \\\\\n150 & 54634.1522 & 0.0082 & $-$0.0324 \\\\\n\\hline\n \\multicolumn{4}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{4}{l}{$^{b}$ Against $max = 2454617.8043 + 0.109202 E$.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J170213.26$+$322954.1}\\label{sec:j1702}\\label{obj:j1702}\n\n This object (hereafter SDSS J1702) was discovered as a high-inclination\nCV by \\citet{szk04SDSSCV3}. \\citet{lit06j0702} identified this object\nas an eclipsing CV in the period gap and suggested that it has an\nevolved secondary. \\citet{boy06j1702} observed the 2005 superoutburst\nof this object and established its SU UMa-type nature. We used the\nAAVSO data which includes the data used in \\citet{boy06j1702}.\nUsing the eclipse ephemeris by \\citet{boy06j1702}, we extracted the\ntimes of superhump maxima outside the eclipses (table \\ref{tab:j1702oc2005}).\nAlthough our analysis basically confirmed the $P_{\\rm SH}$, the periods\nbefore $E \\le 20$ and $E \\ge 38$ appears to show a discontinuous change.\nThe mean periods determined with the PDM method were 0.10486(3) d\nbefore BJD 2453652 (figure \\ref{fig:j1702pdma})\nand 0.10546(3) d after BJD 2453652 (figure \\ref{fig:j1702pdmb}),\nrespectively.\nAlthough the timing of $E=38$ maximum was affected by an eclipse,\nthe $O-C$ analysis also supports the same tendency.\nThese periods correspond to fractional superhump excesses of\n4.8 \\% and 5.4 \\%, respectively.\n\nIt is very unusual for such a long $P_{\\rm SH}$-system to show an\nincrease in the $P_{\\rm SH}$ during the middle-to-late stage of\na superoutburst (cf. V725 Aql, subsection \\ref{sec:v725aql}).\nAlthough the effect of the overlapping orbital\nvariation can not be excluded, this object deserves further detailed\nstudy for evolution of superhump periods.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig196.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1702 before BJD 2453652. (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1702pdma}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig197.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J1702 after BJD 2453652. (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1702pdmb}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1702 (2005).}\\label{tab:j1702oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53648.3842 & 0.0003 & 0.0045 & 152 \\\\\n2 & 53648.5926 & 0.0018 & 0.0027 & 14 \\\\\n9 & 53649.3267 & 0.0009 & 0.0014 & 215 \\\\\n18 & 53650.2729 & 0.0002 & 0.0020 & 178 \\\\\n19 & 53650.3820 & 0.0008 & 0.0060 & 93 \\\\\n38 & 53652.3560 & 0.0033 & $-$0.0163 & 39 \\\\\n47 & 53653.3115 & 0.0005 & $-$0.0063 & 263 \\\\\n48 & 53653.4184 & 0.0008 & $-$0.0045 & 105 \\\\\n56 & 53654.2611 & 0.0007 & $-$0.0023 & 146 \\\\\n57 & 53654.3672 & 0.0006 & $-$0.0012 & 204 \\\\\n66 & 53655.3154 & 0.0011 & 0.0014 & 225 \\\\\n85 & 53657.3228 & 0.0038 & 0.0125 & 85 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453648.3797 + 0.105066 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSSp J173008.38$+$624754.7}\\label{obj:j1730}\n\n SDSSp J173008.38+624754.7 (hereafter SDSS J1730) was selected as\na dwarf nova during the course of the SDSS \\citep{szk02SDSSCVs}.\n\\citet{szk02SDSSCVs}\nobtained an orbital period of 117(5) m (0.081(3) d) from radial-velocity\nstudy, which made the object a good candidate for an SU UMa-type dwarf nova.\n\n We observed the 2001 October superoutburst, soon after the discovery\nannouncement of this object, 2002 February-March and 2004 March\nsuperoutbursts.\nWe first analyzed the best sampled superoutburst in 2004\n(table \\ref{tab:j1730oc2004}). The mean $P_{\\rm SH}$ and the global\n$P_{\\rm dot}$ was 0.07948(2) d and $-7.7(3.5) \\times 10^{-5}$.\nThis $P_{\\rm dot}$ was likely from a stage B--C transition around\n$E=10$. The mean periods before and after this epoch were\n0.08007(24) d and 0.07946(2) d, respectively.\n\nThe times of superhump maxima for the 2001 superoutburst are listed in\ntable \\ref{tab:j1730oc2001}.\nThe last two superhumps ($E = 108$ and $E = 109$) have large\n$O-C$'s. These superhumps may have been traditional late superhumps,\nor the period had largely changed before these observations.\nWe disregarded these maxima and obtained a mean\n$P_{\\rm SH}$ of 0.07941(10) d, which likely reflects stage C superhumps.\n\n The 2002 February-March superoutburst (table \\ref{tab:j1730oc2002})\nwas probably observed during the stage C. The mean $P_{\\rm SH}$\nwas 0.07939(5) d, with an insignificant $P_{\\rm dot}$ of\n$+2.0(3.5) \\times 10^{-5}$.\n\n We derived a mean supercycle of 109(1) d from the times of these four\nsuperoutbursts and the 2002 September one.\n\n The variation of superhump period has generally been small\nin this system. In conjunction with the long superhump period,\nthe object resembles BF Ara and HV Aur. The shortness of the cycle length\nof normal outbursts (9--10 d) and supercycle also resembles\nBF Ara (cf. \\cite{kat03bfara}).\nThe lack of period variation, though, may be a result of the lack\nof observations during the early stage (cf. the 2004 superoutburst).\nThis possibility should be resolved by future observations.\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1730 (2004).}\\label{tab:j1730oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53082.5597 & 0.0005 & $-$0.0042 & 34 \\\\\n1 & 53082.6414 & 0.0004 & $-$0.0020 & 26 \\\\\n5 & 53082.9597 & 0.0002 & $-$0.0016 & 155 \\\\\n6 & 53083.0432 & 0.0004 & 0.0024 & 83 \\\\\n7 & 53083.1241 & 0.0006 & 0.0038 & 201 \\\\\n8 & 53083.2008 & 0.0005 & 0.0010 & 158 \\\\\n9 & 53083.2791 & 0.0004 & $-$0.0001 & 196 \\\\\n13 & 53083.5965 & 0.0010 & $-$0.0006 & 21 \\\\\n30 & 53084.9505 & 0.0004 & 0.0022 & 159 \\\\\n31 & 53085.0284 & 0.0004 & 0.0006 & 158 \\\\\n50 & 53086.5388 & 0.0005 & 0.0008 & 65 \\\\\n51 & 53086.6178 & 0.0007 & 0.0004 & 61 \\\\\n61 & 53087.4123 & 0.0011 & 0.0000 & 54 \\\\\n62 & 53087.4894 & 0.0007 & $-$0.0024 & 72 \\\\\n63 & 53087.5716 & 0.0005 & 0.0004 & 46 \\\\\n64 & 53087.6498 & 0.0024 & $-$0.0009 & 25 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453082.5639 + 0.079481 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1730 (2001).}\\label{tab:j1730oc2001}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52205.3181 & 0.0004 & 0.0021 & 71 \\\\\n1 & 52205.4009 & 0.0004 & 0.0053 & 74 \\\\\n8 & 52205.9567 & 0.0010 & 0.0038 & 173 \\\\\n20 & 52206.9088 & 0.0009 & 0.0003 & 177 \\\\\n21 & 52206.9873 & 0.0010 & $-$0.0007 & 173 \\\\\n35 & 52208.0953 & 0.0010 & $-$0.0075 & 171 \\\\\n85 & 52212.0865 & 0.0124 & 0.0024 & 23 \\\\\n86 & 52212.1341 & 0.0234 & $-$0.0295 & 130 \\\\\n108 & 52213.9347 & 0.0072 & 0.0194 & 129 \\\\\n109 & 52213.9994 & 0.0025 & 0.0044 & 120 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452205.3160 + 0.079624 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J1730 (2002).}\\label{tab:j1730oc2002}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 52326.2335 & 0.0010 & 0.0081 & 143 \\\\\n1 & 52326.3031 & 0.0021 & $-$0.0016 & 150 \\\\\n26 & 52328.2777 & 0.0093 & $-$0.0118 & 119 \\\\\n50 & 52330.1936 & 0.0010 & $-$0.0013 & 228 \\\\\n51 & 52330.2749 & 0.0007 & 0.0007 & 280 \\\\\n52 & 52330.3621 & 0.0035 & 0.0085 & 219 \\\\\n115 & 52335.3449 & 0.0017 & $-$0.0103 & 290 \\\\\n139 & 52337.2672 & 0.0024 & 0.0067 & 321 \\\\\n140 & 52337.3410 & 0.0094 & 0.0011 & 259 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2452326.2254 + 0.079390 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J210014.12$+$004446.0}\\label{obj:j2100}\n\n This object (hereafter SDSS J2100) was selected as a CV during the\ncourse of the SDSS \\citet{szk04SDSSCV3}.\n\\citet{tra05j2100} reported the detection of\nsuperhumps with a period of 0.08746(8) d on two consecutive nights\nduring the 2003 superoutburst.\nWe observed the earliest stage of the 2007 superoutburst. Assuming\nthat the first epoch observation was taken during the stage A\ndevelopment, we assigned $E$ for superhumps (table \\ref{tab:j2100oc2007}).\nThe mean period for $44 \\le E \\le 56$ was 0.08696(15) d.\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J2100 (2007).}\\label{tab:j2100oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54318.2574 & 0.0021 & $-$0.0027 & 180 \\\\\n44 & 54322.1570 & 0.0038 & 0.0063 & 78 \\\\\n45 & 54322.2459 & 0.0024 & 0.0068 & 46 \\\\\n56 & 54323.2014 & 0.0033 & $-$0.0104 & 77 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454318.2601 + 0.088423 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{SDSS J225831.18$-$094931.7}\\label{obj:j2258}\n\n SDSS J225831.18$-$094931.7 (hereafter SDSS J2258) was selected as\na CV during the course of the SDSS \\citep{szk03SDSSCV2}.\nThe SU UMa-type nature was established during\nthe 2004 June superoutburst (vsnet-alert 8162; the reported period of\n0.045 d referred to a half of $P_{\\rm SH}$). During its superoutburst\nin 2005 August, H. Maehara established a long $P_{\\rm SH}$ of 0.083 d\n(vsnet-campaign-dn 4489).\n\n The times of superhump maxima during the 2008 superoutburst are\nlisted in table \\ref{tab:j2258oc2008}. This outburst was apparently\ndetected during its late stage, since the object already started fading\nrapidly after six days. The mean superhump period with the PDM method\nwas 0.08607(2) d (figure \\ref{fig:j2258shpdm}), which most likely\nrefers to $P_2$, with an almost zero\n$P_{\\rm dot}$ of $+1.5(2.1) \\times 10^{-5}$.\nThe maxima for $82 \\le E \\le 93$ refer to the post-superoutburst stage.\nThere was no apparent indication of a phase shift around the termination\nof the superoutburst.\n\n The times of superhump maxima during the 2004 superoutburst\nare also given (table \\ref{tab:j2258oc2004}). The 2004 superoutburst\nwas caught during its final stage. The 2005 observation is omitted\nbecause it was a single-night observation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig198.eps}\n \\end{center}\n \\caption{Superhumps in SDSS J2258 (2004). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j2258shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J2258 (2004).}\\label{tab:j2258oc2004}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53159.5243 & 0.0004 & $-$0.0031 & 368 \\\\\n1 & 53159.6148 & 0.0007 & 0.0015 & 211 \\\\\n12 & 53160.5599 & 0.0006 & 0.0016 & 379 \\\\\n13 & 53160.6464 & 0.0008 & 0.0023 & 290 \\\\\n20 & 53161.2446 & 0.0023 & $-$0.0008 & 145 \\\\\n23 & 53161.5019 & 0.0073 & $-$0.0012 & 224 \\\\\n24 & 53161.5887 & 0.0012 & $-$0.0003 & 380 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453159.5274 + 0.085900 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\begin{table}\n\\caption{Superhump maxima of SDSS J2258 (2008).}\\label{tab:j2258oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54788.9460 & 0.0004 & 0.0023 & 178 \\\\\n1 & 54789.0298 & 0.0004 & $-$0.0001 & 260 \\\\\n11 & 54789.8849 & 0.0019 & $-$0.0064 & 77 \\\\\n12 & 54789.9817 & 0.0003 & 0.0042 & 389 \\\\\n13 & 54790.0657 & 0.0004 & 0.0021 & 423 \\\\\n23 & 54790.9250 & 0.0004 & $-$0.0000 & 309 \\\\\n24 & 54791.0122 & 0.0003 & 0.0011 & 820 \\\\\n25 & 54791.0971 & 0.0013 & $-$0.0002 & 286 \\\\\n34 & 54791.8713 & 0.0023 & $-$0.0013 & 87 \\\\\n35 & 54791.9586 & 0.0005 & $-$0.0001 & 260 \\\\\n36 & 54792.0410 & 0.0010 & $-$0.0038 & 187 \\\\\n46 & 54792.9068 & 0.0011 & 0.0005 & 122 \\\\\n47 & 54792.9962 & 0.0012 & 0.0038 & 162 \\\\\n58 & 54793.9362 & 0.0007 & $-$0.0037 & 289 \\\\\n59 & 54794.0250 & 0.0016 & $-$0.0011 & 123 \\\\\n82 & 54796.0086 & 0.0022 & 0.0013 & 64 \\\\\n92 & 54796.8730 & 0.0034 & 0.0043 & 55 \\\\\n93 & 54796.9520 & 0.0015 & $-$0.0029 & 81 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454788.9438 + 0.086141 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J004226.5$+$421537}\\label{obj:j0042}\n\n This object (hereafter OT J0042) was discovered by K. Itagaki\nas a possible nova in M31 which reached a peak magnitude of 14.5\naround 2008 November 28.6 UT (=M31N 2008-11b, \\cite{ita08j0042cbet1588}).\nMulticolor photometry by S. Kiyota suggested that this object is\na foreground dwarf nova rather than a nova in M31 (vsnet-alert 10747).\nThe object was indeed spectroscopically confirmed as a dwarf nova\n\\citep{kas08j0042cbet1611}.\n\n Until 2008 December 7, early superhumps were present (vsnet-alert\n10747, 10763, 10786). The mean period of early superhumps was\n0.05550(2) d (figure \\ref{fig:j0042eshpdm}).\n\n On December 10, ordinary superhump emerged (cvnet-outburst 2801,\nvsnet-alert 10818). The times of superhump maxima are listed in\ntable \\ref{tab:j0042oc2008}. The mean $P_{\\rm SH}$ determined\nwith the PDM method was 0.05687(2) d (figure \\ref{fig:j0042shpdm}).\nThe $P_{\\rm dot}$ was slightly positive, $+4.0(1.8) \\times 10^{-5}$.\nThe fractional superhump excess is 2.5(1) \\%, which is slightly\nlarge for a WZ Sge-type dwarf nova. Since the amplitudes of\nearly superhumps and ordinary superhumps were low, these period\ndeterminations may have been affected by non-ideal photometric\nconditions and the fractional superhump excess needs to be treated\nwith caution.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig199.eps}\n \\end{center}\n \\caption{Early superhumps in OT J0042 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0042eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig200.eps}\n \\end{center}\n \\caption{Ordinary superhumps in OT J0042 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0042shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0042 (2008).}\\label{tab:j0042oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54810.9649 & 0.0033 & 0.0052 & 43 \\\\\n1 & 54811.0200 & 0.0016 & 0.0034 & 128 \\\\\n2 & 54811.0747 & 0.0044 & 0.0013 & 98 \\\\\n3 & 54811.1324 & 0.0034 & 0.0021 & 78 \\\\\n4 & 54811.1963 & 0.0031 & 0.0091 & 43 \\\\\n34 & 54812.8911 & 0.0023 & $-$0.0029 & 30 \\\\\n35 & 54812.9431 & 0.0040 & $-$0.0077 & 28 \\\\\n36 & 54813.0008 & 0.0063 & $-$0.0069 & 30 \\\\\n37 & 54813.0675 & 0.0029 & 0.0029 & 40 \\\\\n70 & 54814.9424 & 0.0034 & 0.0004 & 30 \\\\\n71 & 54814.9984 & 0.0041 & $-$0.0005 & 95 \\\\\n72 & 54815.0529 & 0.0017 & $-$0.0030 & 136 \\\\\n73 & 54815.1110 & 0.0014 & $-$0.0017 & 119 \\\\\n74 & 54815.1668 & 0.0032 & $-$0.0028 & 112 \\\\\n89 & 54816.0244 & 0.0020 & 0.0014 & 67 \\\\\n90 & 54816.0657 & 0.0023 & $-$0.0142 & 18 \\\\\n158 & 54819.9633 & 0.0039 & 0.0148 & 30 \\\\\n160 & 54820.0728 & 0.0027 & 0.0105 & 127 \\\\\n161 & 54820.1130 & 0.0021 & $-$0.0061 & 112 \\\\\n162 & 54820.1708 & 0.0087 & $-$0.0053 & 61 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454810.9596 + 0.056892 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J011306.7$+$215250}\\label{obj:j0113}\n\n This object (=CSS080922:011307$+$215250, hereafter OT J0113)\nwas discovered by the Catalina Real-time Transient Survey\n(CRTS, \\cite{dra08atel1734}).\\footnote{\n $<$http:\/\/nesssi.cacr.caltech.edu\/catalina\/$>$.\n For the information of the individual Catalina CVs, see\n $<$http:\/\/nesssi.cacr.caltech.edu\/catalina\/AllCV.html$>$.\n}\nH. Maehara detected superhumps and identified this object as\na long-$P_{\\rm SH}$ SU UMa-type dwarf nova (vsnet-alert 10539).\nThe observation was performed during the last stage of the superoutburst\n(table \\ref{tab:j0113oc2008}). The cycle count is based on period\ndetermination in \\citet{sha09v466andj0113}.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0113 (2008).}\\label{tab:j0113oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54732.1975 & 0.0007 & 0.0016 & 187 \\\\\n21 & 54734.1751 & 0.0040 & $-$0.0017 & 93 \\\\\n22 & 54734.2694 & 0.0032 & $-$0.0016 & 129 \\\\\n43 & 54736.2535 & 0.0040 & 0.0016 & 51 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454732.1959 + 0.094325 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J021110.2$+$171624}\\label{obj:j0211}\n\n This object (=CSS080130:021110$+$171624, hereafter OT J0211) was\ndiscovered by the CRTS in 2008 January (\\cite{djo08atel1416}; \\cite{CRTS};\ncvnet-discussion 1106). \nThe detection of superhumps\nled to a classification as an SU UMa-type dwarf nova\n(cvnet-discussion 1109). \\citet{djo08atel1416} reported spectroscopic\nconfirmation as a CV.\n\n We observed the 2008 November superoutburst (vsnet-alert 10663)\nand established the superhump period of 0.08164(6) d with the PDM method\n(figure \\ref{fig:j0211shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0211oc2008}.\nThe object appears to have a relatively short supercycle of\n$\\sim$280 d, typical for an SU UMa-type dwarf nova with a long\n$P_{\\rm SH}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig201.eps}\n \\end{center}\n \\caption{Superhumps in OT J0211 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0211shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0211.}\\label{tab:j0211oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54775.0286 & 0.0046 & 0.0006 & 89 \\\\\n1 & 54775.1098 & 0.0011 & 0.0001 & 129 \\\\\n12 & 54776.0016 & 0.0037 & $-$0.0062 & 53 \\\\\n13 & 54776.0932 & 0.0009 & 0.0038 & 227 \\\\\n14 & 54776.1728 & 0.0013 & 0.0018 & 87 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454775.0281 + 0.081643 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J023839.1$+$355648}\\label{sec:j0238}\\label{obj:j0238}\n\n This object (=CSS081026:023839$+$355648, hereafter OT J0238)\nwas discovered by the CRTS.\nH. Maehara suggested that this object may be a WZ Sge-type dwarf nova\n(vsnet-alert 10628). Superhumps were later detected (vsnet-alert 10667,\nfigure \\ref{fig:j0238shpdm}).\nA reanalysis of the early data confirmed the presence of early superhumps\n(vsnet-alert 10686), confirming the suggested\nclassification of the object as a WZ Sge-type dwarf nova with the\nshortest known $P_{\\rm SH}$.\n\\citet{shu08j0238} observed the same outburst and reported \nperiods of 0.0531 d and 0.0537 d for early and ordinary superhumps.\nWe used the combined data set with ours and \\citet{shu08j0238},\nafter selecting the best-quality segment, and refined the period\nof early superhumps to be 0.05281(6) d (figure \\ref{fig:j0238eshpdm}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig202.eps}\n \\end{center}\n \\caption{Ordinary superhumps in OT J0238 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0238shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig203.eps}\n \\end{center}\n \\caption{Early superhumps in OT J0238 (2008) before BJD 2454769.5.\n (Upper): PDM analysis.\n The alias selection was based on $P_{\\rm SH}$.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0238eshpdm}\n\\end{figure}\n\n The times of superhump maxima are listed in table \\ref{tab:j0238oc2008}.\nThe $O-C$ diagram clearly consists of A--C stages. The $P_{\\rm dot}$\nfor the stage B ($67 \\le E \\le 350$, disregarding $E=347$)\nwas $+2.0(0.2) \\times 10^{-5}$. The duration of the stage A\n(52 $P_{\\rm SH}$ or longer) is longer than those of typical SU UMa-type\ndwarf novae (20--30 $P_{\\rm SH}$). This might be a signature of slow\nevolution of superhumps in this system.\n\n The details will be presented by Maehara et al., in preparation.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0238 (2008).}\\label{tab:j0238oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54772.4407 & 0.0023 & $-$0.0347 & 22 \\\\\n1 & 54772.5024 & 0.0016 & $-$0.0266 & 28 \\\\\n2 & 54772.5582 & 0.0007 & $-$0.0245 & 27 \\\\\n3 & 54772.6087 & 0.0020 & $-$0.0277 & 25 \\\\\n19 & 54773.4863 & 0.0011 & $-$0.0089 & 24 \\\\\n32 & 54774.1946 & 0.0016 & 0.0016 & 25 \\\\\n37 & 54774.4622 & 0.0020 & 0.0009 & 21 \\\\\n50 & 54775.1666 & 0.0006 & 0.0075 & 110 \\\\\n51 & 54775.2196 & 0.0006 & 0.0068 & 133 \\\\\n52 & 54775.2751 & 0.0006 & 0.0087 & 88 \\\\\n67 & 54776.0801 & 0.0007 & 0.0085 & 110 \\\\\n68 & 54776.1354 & 0.0011 & 0.0101 & 118 \\\\\n69 & 54776.1896 & 0.0007 & 0.0107 & 19 \\\\\n70 & 54776.2396 & 0.0006 & 0.0070 & 22 \\\\\n71 & 54776.2947 & 0.0006 & 0.0085 & 28 \\\\\n72 & 54776.3480 & 0.0007 & 0.0080 & 22 \\\\\n73 & 54776.4018 & 0.0007 & 0.0082 & 21 \\\\\n74 & 54776.4552 & 0.0006 & 0.0079 & 22 \\\\\n75 & 54776.5091 & 0.0007 & 0.0082 & 22 \\\\\n91 & 54777.3662 & 0.0006 & 0.0064 & 19 \\\\\n92 & 54777.4206 & 0.0006 & 0.0072 & 23 \\\\\n93 & 54777.4725 & 0.0004 & 0.0053 & 24 \\\\\n94 & 54777.5256 & 0.0005 & 0.0048 & 21 \\\\\n95 & 54777.5826 & 0.0009 & 0.0082 & 15 \\\\\n107 & 54778.2241 & 0.0023 & 0.0055 & 13 \\\\\n108 & 54778.2773 & 0.0009 & 0.0050 & 17 \\\\\n109 & 54778.3303 & 0.0009 & 0.0044 & 18 \\\\\n110 & 54778.3824 & 0.0008 & 0.0028 & 12 \\\\\n114 & 54778.6007 & 0.0013 & 0.0065 & 12 \\\\\n115 & 54778.6509 & 0.0014 & 0.0029 & 8 \\\\\n127 & 54779.2962 & 0.0008 & 0.0041 & 39 \\\\\n145 & 54780.2584 & 0.0024 & 0.0002 & 99 \\\\\n146 & 54780.3128 & 0.0016 & 0.0009 & 45 \\\\\n147 & 54780.3642 & 0.0016 & $-$0.0014 & 56 \\\\\n164 & 54781.2831 & 0.0015 & 0.0050 & 33 \\\\\n165 & 54781.3313 & 0.0008 & $-$0.0005 & 41 \\\\\n166 & 54781.3868 & 0.0015 & 0.0014 & 20 \\\\\n167 & 54781.4351 & 0.0019 & $-$0.0039 & 12 \\\\\n186 & 54782.4608 & 0.0029 & 0.0019 & 13 \\\\\n187 & 54782.5170 & 0.0031 & 0.0044 & 11 \\\\\n188 & 54782.5629 & 0.0034 & $-$0.0033 & 15 \\\\\n189 & 54782.6141 & 0.0011 & $-$0.0059 & 10 \\\\\n197 & 54783.0494 & 0.0096 & 0.0001 & 80 \\\\\n198 & 54783.0909 & 0.0033 & $-$0.0120 & 105 \\\\\n199 & 54783.1512 & 0.0021 & $-$0.0055 & 112 \\\\\n200 & 54783.2075 & 0.0018 & $-$0.0028 & 99 \\\\\n201 & 54783.2606 & 0.0013 & $-$0.0034 & 113 \\\\\n216 & 54784.0712 & 0.0054 & 0.0021 & 110 \\\\\n217 & 54784.1159 & 0.0068 & $-$0.0069 & 107 \\\\\n256 & 54786.2136 & 0.0009 & $-$0.0025 & 16 \\\\\n257 & 54786.2657 & 0.0013 & $-$0.0042 & 9 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454772.4753 + 0.053675 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\addtocounter{table}{-1}\n\\begin{table}\n\\caption{Superhump maxima of OT J0238 (2008). (continued)}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max & error & $O-C$ & $N$ \\\\\n\\hline\n258 & 54786.3234 & 0.0017 & $-$0.0001 & 10 \\\\\n259 & 54786.3771 & 0.0038 & $-$0.0000 & 13 \\\\\n260 & 54786.4285 & 0.0018 & $-$0.0023 & 11 \\\\\n261 & 54786.4835 & 0.0036 & $-$0.0010 & 14 \\\\\n301 & 54788.6365 & 0.0019 & 0.0050 & 16 \\\\\n310 & 54789.1212 & 0.0025 & 0.0066 & 92 \\\\\n311 & 54789.1727 & 0.0014 & 0.0045 & 112 \\\\\n312 & 54789.2210 & 0.0024 & $-$0.0010 & 132 \\\\\n313 & 54789.2781 & 0.0046 & 0.0025 & 56 \\\\\n329 & 54790.1421 & 0.0047 & 0.0077 & 114 \\\\\n330 & 54790.1946 & 0.0024 & 0.0065 & 115 \\\\\n331 & 54790.2408 & 0.0035 & $-$0.0009 & 114 \\\\\n347 & 54791.0835 & 0.0024 & $-$0.0170 & 39 \\\\\n348 & 54791.1658 & 0.0035 & 0.0116 & 150 \\\\\n349 & 54791.2073 & 0.0025 & $-$0.0006 & 153 \\\\\n350 & 54791.2693 & 0.0085 & 0.0077 & 100 \\\\\n384 & 54793.0858 & 0.0038 & $-$0.0007 & 70 \\\\\n404 & 54794.1400 & 0.0025 & $-$0.0201 & 97 \\\\\n405 & 54794.1981 & 0.0036 & $-$0.0156 & 65 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J032912.3$+$125018}\\label{obj:j0329}\n\n This object (also known as VS 0329$+$1250; hereafter OT J0329)\nwas discovered by \\citet{skv06j0329cbet701}.\nThe detection of superhumps led to a classification as an SU UMa-type\ndwarf nova \\citep{waa06j0329cbet701}.\n\\citet{sha07j0329} reported a superhump period of 0.053394(7) d,\nthe shortest record at that time among ordinary SU UMa-type dwarf novae.\nWe used a combination of the photometric data by \\citet{sha07j0329}\nand AAVSO observations and obtained times of superhump maxima\n(table \\ref{tab:j0329oc2006}; the times for superhumps were systematically\ndifferent from those by \\citet{sha07j0329} due to the difference in\nthe method for determining the maxima).\nThe mean $P_{\\rm SH}$ with the PDM method was 0.053388(4) d\n(figure \\ref{fig:j0329shpdm}).\nThe $P_{\\rm dot}$ was $+2.8(0.3) \\times 10^{-5}$\n($E \\le 139$, figure \\ref{fig:j0329oc}),\nconfirming the positive $P_{\\rm dot}$ reported in \\citet{sha07j0329}.\nAlthough there appears to have been a transition to stage C after $E=139$,\nwe could not measure $P_2$ because of the lack of observations.\n\n According to the CRTS, this object\n(=CSS081025:032912$+$125018) has a magnitude of 21 in quiescence and\nexperienced two further faint outbursts. The relatively small outburst\namplitude for an extremely short $P_{\\rm SH}$ and the presence of relatively\nfrequent (approximately once per year) outbursts, combined with\nthe relatively large $P_{\\rm dot}$,\nwould place the object as a member of OT J0557\n(group ``X'' in \\cite{uem09j0557}, though the $P_{\\rm dot}$ is larger\nin OT J0557) rather than an extreme WZ Sge-type dwarf nova.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig204.eps}\n \\end{center}\n \\caption{Superhumps in OT J0329 (2006). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0329shpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig205.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps OT J0329 (2006).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($E \\le 139$, thin curve). Late-stage humps with\n large errors were omitted.\n (Lower): Light curve.}\n \\label{fig:j0329oc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0329 (2006).}\\label{tab:j0329oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54035.4296 & 0.0006 & 0.0017 & 27 \\\\\n1 & 54035.4833 & 0.0007 & 0.0019 & 28 \\\\\n2 & 54035.5343 & 0.0003 & $-$0.0005 & 44 \\\\\n3 & 54035.5889 & 0.0004 & 0.0008 & 60 \\\\\n4 & 54035.6429 & 0.0004 & 0.0013 & 94 \\\\\n5 & 54035.6964 & 0.0004 & 0.0014 & 124 \\\\\n6 & 54035.7498 & 0.0003 & 0.0014 & 64 \\\\\n7 & 54035.8032 & 0.0004 & 0.0014 & 66 \\\\\n8 & 54035.8570 & 0.0004 & 0.0018 & 70 \\\\\n26 & 54036.8163 & 0.0003 & $-$0.0002 & 58 \\\\\n44 & 54037.7764 & 0.0003 & $-$0.0015 & 104 \\\\\n45 & 54037.8306 & 0.0002 & $-$0.0006 & 112 \\\\\n46 & 54037.8845 & 0.0002 & $-$0.0002 & 79 \\\\\n47 & 54037.9369 & 0.0003 & $-$0.0012 & 56 \\\\\n48 & 54037.9900 & 0.0002 & $-$0.0015 & 57 \\\\\n62 & 54038.7377 & 0.0003 & $-$0.0015 & 56 \\\\\n63 & 54038.7914 & 0.0003 & $-$0.0012 & 56 \\\\\n64 & 54038.8449 & 0.0003 & $-$0.0011 & 57 \\\\\n65 & 54038.8977 & 0.0003 & $-$0.0017 & 57 \\\\\n66 & 54038.9526 & 0.0006 & $-$0.0003 & 33 \\\\\n75 & 54039.4305 & 0.0016 & $-$0.0029 & 30 \\\\\n76 & 54039.4858 & 0.0008 & $-$0.0010 & 52 \\\\\n77 & 54039.5417 & 0.0010 & 0.0014 & 52 \\\\\n78 & 54039.5931 & 0.0012 & $-$0.0006 & 41 \\\\\n79 & 54039.6460 & 0.0009 & $-$0.0011 & 41 \\\\\n80 & 54039.7009 & 0.0010 & 0.0004 & 61 \\\\\n81 & 54039.7528 & 0.0006 & $-$0.0011 & 62 \\\\\n82 & 54039.8045 & 0.0009 & $-$0.0029 & 64 \\\\\n83 & 54039.8587 & 0.0007 & $-$0.0020 & 59 \\\\\n95 & 54040.5010 & 0.0007 & $-$0.0006 & 87 \\\\\n96 & 54040.5541 & 0.0006 & $-$0.0009 & 74 \\\\\n99 & 54040.7159 & 0.0008 & 0.0006 & 75 \\\\\n100 & 54040.7690 & 0.0006 & 0.0003 & 111 \\\\\n101 & 54040.8232 & 0.0007 & 0.0011 & 55 \\\\\n120 & 54041.8362 & 0.0014 & $-$0.0005 & 38 \\\\\n121 & 54041.8929 & 0.0010 & 0.0028 & 57 \\\\\n138 & 54042.8018 & 0.0016 & 0.0037 & 66 \\\\\n139 & 54042.8544 & 0.0015 & 0.0029 & 56 \\\\\n263 & 54049.4722 & 0.0083 & $-$0.0018 & 34 \\\\\n264 & 54049.5433 & 0.0070 & 0.0160 & 24 \\\\\n266 & 54049.6205 & 0.0083 & $-$0.0136 & 20 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454035.4280 + 0.053407 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J040659.8$+$005244}\\label{obj:j0406}\n\n This object (hereafter OT J0406) was discovered by K. Itagaki\n\\citep{yam08j0406cbet1463}. Subsequent observations confirmed the\nSU UMa-type nature of the object (vsnet-alert 10422).\nThe mean superhump period with the PDM method was 0.07992(2) d\n(figure \\ref{fig:j0406shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0406oc2008}.\nThe period was almost constant with $P_{\\rm dot}$ = $+2.8(3.4) \\times 10^{-5}$.\nThe outburst may have been detected during its late course, and\nthe lack of period variation may be attributed to stage C superhumps.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig206.eps}\n \\end{center}\n \\caption{Superhumps in OT J0406 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0406shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0406 (2008).}\\label{tab:j0406oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54687.3825 & 0.0004 & 0.0005 & 151 \\\\\n11 & 54688.2619 & 0.0008 & 0.0005 & 350 \\\\\n24 & 54689.2989 & 0.0009 & $-$0.0018 & 193 \\\\\n36 & 54690.2605 & 0.0007 & 0.0005 & 167 \\\\\n61 & 54692.2591 & 0.0013 & 0.0003 & 138 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454687.3820 + 0.079947 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J055718$+$683226}\\label{obj:j0557}\n\n This object was discovered by \\citet{klo06j0557cbet777} and was\nextensively studied by \\citet{uem09j0557}. We present a supplementary\nanalysis using the combined data with \\citet{uem09j0557} and the\nAAVSO data (table \\ref{tab:j0557oc2006}).\nThe $P_{\\rm dot}$ for $E \\le 110$ (stage B) was\n$+9.0(2.1) \\times 10^{-5}$. The relatively large $P_{\\rm dot}$\nwith a very short $P_{\\rm SH}$ strengthens the similarity to V844 Her,\nas suggested by \\citet{uem09j0557}.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0557 (2006).}\\label{tab:j0557oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54087.2836 & 0.0005 & $-$0.0005 & 155 \\\\\n1 & 54087.3365 & 0.0009 & $-$0.0011 & 95 \\\\\n15 & 54088.0832 & 0.0005 & $-$0.0017 & 99 \\\\\n16 & 54088.1373 & 0.0006 & $-$0.0010 & 99 \\\\\n17 & 54088.1868 & 0.0012 & $-$0.0049 & 99 \\\\\n19 & 54088.2976 & 0.0006 & $-$0.0009 & 111 \\\\\n20 & 54088.3487 & 0.0005 & $-$0.0032 & 100 \\\\\n34 & 54089.0971 & 0.0009 & $-$0.0022 & 106 \\\\\n35 & 54089.1478 & 0.0009 & $-$0.0049 & 132 \\\\\n36 & 54089.2019 & 0.0010 & $-$0.0041 & 140 \\\\\n37 & 54089.2561 & 0.0010 & $-$0.0033 & 105 \\\\\n38 & 54089.3088 & 0.0007 & $-$0.0039 & 144 \\\\\n39 & 54089.3628 & 0.0005 & $-$0.0033 & 177 \\\\\n40 & 54089.4162 & 0.0010 & $-$0.0034 & 80 \\\\\n41 & 54089.4709 & 0.0013 & $-$0.0021 & 55 \\\\\n42 & 54089.5255 & 0.0014 & $-$0.0009 & 63 \\\\\n43 & 54089.5765 & 0.0007 & $-$0.0032 & 121 \\\\\n49 & 54089.8967 & 0.0019 & $-$0.0033 & 60 \\\\\n50 & 54089.9555 & 0.0012 & 0.0021 & 101 \\\\\n51 & 54090.0055 & 0.0011 & $-$0.0013 & 100 \\\\\n52 & 54090.0576 & 0.0042 & $-$0.0026 & 100 \\\\\n54 & 54090.1670 & 0.0031 & 0.0001 & 30 \\\\\n74 & 54091.2388 & 0.0019 & 0.0041 & 42 \\\\\n91 & 54092.1382 & 0.0026 & $-$0.0039 & 167 \\\\\n92 & 54092.1956 & 0.0086 & 0.0001 & 65 \\\\\n97 & 54092.4736 & 0.0037 & 0.0112 & 44 \\\\\n98 & 54092.5204 & 0.0022 & 0.0045 & 43 \\\\\n99 & 54092.5738 & 0.0031 & 0.0046 & 79 \\\\\n100 & 54092.6371 & 0.0014 & 0.0145 & 35 \\\\\n109 & 54093.1147 & 0.0048 & 0.0116 & 110 \\\\\n110 & 54093.1708 & 0.0051 & 0.0143 & 113 \\\\\n143 & 54094.9264 & 0.0021 & 0.0082 & 93 \\\\\n144 & 54094.9808 & 0.0026 & 0.0092 & 67 \\\\\n180 & 54096.8984 & 0.0044 & 0.0050 & 62 \\\\\n183 & 54097.0587 & 0.0062 & 0.0051 & 111 \\\\\n185 & 54097.1442 & 0.0075 & $-$0.0161 & 112 \\\\\n257 & 54100.9959 & 0.0024 & $-$0.0081 & 100 \\\\\n258 & 54101.0637 & 0.0040 & 0.0063 & 57 \\\\\n259 & 54101.1063 & 0.0025 & $-$0.0045 & 88 \\\\\n260 & 54101.1477 & 0.0021 & $-$0.0165 & 42 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454087.2842 + 0.053385 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J074727.6$+$065050}\\label{obj:j0747}\n\n This object (hereafter OT J0747) was discovered by K. Itagaki\n\\citep{yam08j0747cbet1216}. Soon after the discovery announcement\nand spectroscopic confirmation, this object was proposed to be a\ngood candidate for a WZ Sge-type dwarf nova (vsnet-alert 9832).\nThe detection of superhumps and later repeated rebrightenings\nconfirmed this suggestion. The outburst behavior was very similar\nto those of EG Cnc or UZ Boo (figure \\ref{fig:j0747lc}).\nThe post-superoutburst observations indicated that the final fading\nwas on a smooth extension of the quiescence during the rebrightening\nphase, as in SDSS J0804 (for the implication, see \\cite{kat09j0804}).\n\n The times of superhump maxima during the main superoutburst are\nlisted in table \\ref{tab:j0747oc2008}.\nThe detection of the outburst was 11 d after the maximum ($V = 11.4$)\nretrospectively measured with ASAS-3. The stage of early superhumps\nand early development of the ordinary superhumps were not recorded.\nThe $P_{\\rm dot}$ during the plateau stage was $+4.0(0.8) \\times 10^{-5}$\n($E \\le 109$). \\citet{she09j0747} reported $P_{\\rm dot}$ of\n$+4.4(0.9) \\times 10^{-5}$ using a slightly different set of observations.\n\n After removing the global trend of the outburst (the method is the\nsame as in \\cite{kat09j0804}), PDM analyses yielded mean superhump\nperiods of 0.060750(7) d during the superoutburst\n(figure \\ref{fig:j0747mainpdm})\nand 0.060771(3) d during the rebrightening phase\n(figure \\ref{fig:j0747rebpdm}).\nThe superhump period during the rebrightening phase is 0.3 \\% longer\nthan that during the superoutburst plateau.\nThis behavior follows the general tendency in WZ Sge-type dwarf novae\n(subsection \\ref{sec:latestage}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,70mm){fig207.eps}\n \\end{center}\n \\caption{Light curve of the 2008 superoutburst of OT J0747.\n The filled circles and filled squares represent CCD observations\n used here and ASAS-3 $V$ data, respectively.}\n \\label{fig:j0747lc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig208.eps}\n \\end{center}\n \\caption{Superhumps in OT J0747 during the superoutburst plateau\n (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0747mainpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig209.eps}\n \\end{center}\n \\caption{Superhumps in OT J0747 during the rebrightening phase (2008).\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0747rebpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0747 (2008).}\\label{tab:j0747oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54486.5762 & 0.0017 & 0.0016 & 6 \\\\\n1 & 54486.6361 & 0.0006 & 0.0007 & 8 \\\\\n2 & 54486.6980 & 0.0004 & 0.0019 & 7 \\\\\n3 & 54486.7587 & 0.0009 & 0.0019 & 8 \\\\\n4 & 54486.8186 & 0.0010 & 0.0010 & 8 \\\\\n7 & 54487.0016 & 0.0005 & 0.0019 & 154 \\\\\n8 & 54487.0616 & 0.0002 & 0.0011 & 338 \\\\\n9 & 54487.1224 & 0.0007 & 0.0012 & 170 \\\\\n16 & 54487.5446 & 0.0034 & $-$0.0018 & 20 \\\\\n18 & 54487.6691 & 0.0006 & 0.0013 & 8 \\\\\n20 & 54487.7896 & 0.0012 & 0.0003 & 6 \\\\\n21 & 54487.8474 & 0.0017 & $-$0.0027 & 6 \\\\\n24 & 54488.0330 & 0.0007 & 0.0008 & 68 \\\\\n25 & 54488.0928 & 0.0004 & $-$0.0001 & 114 \\\\\n26 & 54488.1540 & 0.0004 & 0.0003 & 114 \\\\\n31 & 54488.4583 & 0.0011 & 0.0009 & 91 \\\\\n32 & 54488.5150 & 0.0013 & $-$0.0031 & 95 \\\\\n40 & 54489.0066 & 0.0009 & 0.0026 & 56 \\\\\n41 & 54489.0653 & 0.0005 & 0.0006 & 125 \\\\\n42 & 54489.1229 & 0.0005 & $-$0.0025 & 111 \\\\\n43 & 54489.1846 & 0.0005 & $-$0.0016 & 113 \\\\\n44 & 54489.2463 & 0.0005 & $-$0.0006 & 114 \\\\\n45 & 54489.3052 & 0.0006 & $-$0.0024 & 110 \\\\\n52 & 54489.7309 & 0.0008 & $-$0.0018 & 58 \\\\\n53 & 54489.7911 & 0.0005 & $-$0.0024 & 76 \\\\\n54 & 54489.8517 & 0.0007 & $-$0.0025 & 81 \\\\\n55 & 54489.9134 & 0.0024 & $-$0.0015 & 76 \\\\\n62 & 54490.3446 & 0.0020 & 0.0045 & 58 \\\\\n63 & 54490.3991 & 0.0012 & $-$0.0017 & 64 \\\\\n64 & 54490.4592 & 0.0010 & $-$0.0024 & 63 \\\\\n68 & 54490.7028 & 0.0006 & $-$0.0017 & 42 \\\\\n69 & 54490.7627 & 0.0005 & $-$0.0026 & 58 \\\\\n70 & 54490.8245 & 0.0014 & $-$0.0015 & 57 \\\\\n73 & 54491.0071 & 0.0008 & $-$0.0011 & 174 \\\\\n74 & 54491.0708 & 0.0014 & 0.0020 & 121 \\\\\n75 & 54491.1264 & 0.0014 & $-$0.0033 & 113 \\\\\n76 & 54491.1893 & 0.0016 & $-$0.0011 & 115 \\\\\n77 & 54491.2520 & 0.0013 & 0.0009 & 85 \\\\\n83 & 54491.6146 & 0.0011 & $-$0.0009 & 26 \\\\\n84 & 54491.6774 & 0.0017 & 0.0012 & 23 \\\\\n85 & 54491.7383 & 0.0022 & 0.0014 & 23 \\\\\n86 & 54491.8001 & 0.0021 & 0.0024 & 29 \\\\\n87 & 54491.8590 & 0.0014 & 0.0006 & 34 \\\\\n88 & 54491.9183 & 0.0011 & $-$0.0009 & 30 \\\\\n92 & 54492.1609 & 0.0024 & $-$0.0011 & 78 \\\\\n105 & 54492.9571 & 0.0014 & 0.0055 & 173 \\\\\n106 & 54493.0142 & 0.0010 & 0.0019 & 173 \\\\\n108 & 54493.1374 & 0.0019 & 0.0035 & 62 \\\\\n109 & 54493.1957 & 0.0018 & 0.0012 & 41 \\\\\n122 & 54493.9844 & 0.0006 & 0.0003 & 51 \\\\\n123 & 54494.0423 & 0.0009 & $-$0.0025 & 56 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454486.5746 + 0.060733 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J080714.2$+$113812}\\label{obj:j0807}\n\n This object (hereafter OT J0807) was discovered by K. Itagaki\nand was suggested to be a candidate WZ Sge-type dwarf nova\n(vsnet-newvar 2602, vsnet-alert 9721, 9731). The object was soon\nconfirmed to exhibit superhumps. The outburst was associated with an\nunusual rebrightening following a one-day dip near the termination\nof the superoutburst (vsnet-alert 9745, 9746, figure \\ref{fig:j0807oc}).\nThe mean superhump period with the PDM method was 0.060818(10) d\n(figure \\ref{fig:j0807shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j0807oc2007}.\nJudging from the light curve and the variation of the amplitude of\nsuperhumps, the outburst was probably detected during its\nmiddle-to-late course. The stage of early superhumps, if the object\nis indeed a WZ Sge-type dwarf nova, and early development of\nthe ordinary superhumps thus were not recorded. The table includes\nthe maxima during the rebrightening ($E = 218, 219$).\nThe break in the $O-C$ diagram most likely reflected a transition\nto the stage C.\nWe determined a relatively large $P_{\\rm dot}$ = $+9.5(4.8) \\times 10^{-5}$\nfor the earlier phase ($E \\le 89$). This behavior of period variation\nis similar to those observed in the stage B of short-period SU UMa-type\ndwarf novae or some WZ Sge-type dwarf novae.\nMore detailed analysis will be reported by Maehara et al., in preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig210.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps OT J0807 (2007).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($E \\le 89$, thin curve)\n (Lower): Light curve. Large dots are our CCD observations and open\n squares are Itagaki's CCD observations.}\n \\label{fig:j0807oc}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig211.eps}\n \\end{center}\n \\caption{Superhumps in OT J0807 (2007). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0807shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0807 (2007).}\\label{tab:j0807oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54424.9170 & 0.0003 & $-$0.0049 & 113 \\\\\n1 & 54424.9763 & 0.0003 & $-$0.0064 & 113 \\\\\n4 & 54425.1594 & 0.0014 & $-$0.0056 & 90 \\\\\n5 & 54425.2201 & 0.0004 & $-$0.0057 & 368 \\\\\n6 & 54425.2808 & 0.0005 & $-$0.0058 & 373 \\\\\n7 & 54425.3422 & 0.0005 & $-$0.0052 & 296 \\\\\n16 & 54425.8931 & 0.0006 & $-$0.0012 & 111 \\\\\n17 & 54425.9525 & 0.0009 & $-$0.0026 & 102 \\\\\n18 & 54426.0110 & 0.0005 & $-$0.0049 & 108 \\\\\n22 & 54426.2538 & 0.0012 & $-$0.0053 & 220 \\\\\n23 & 54426.3192 & 0.0013 & $-$0.0006 & 116 \\\\\n26 & 54426.5005 & 0.0014 & $-$0.0017 & 121 \\\\\n27 & 54426.5581 & 0.0012 & $-$0.0048 & 123 \\\\\n28 & 54426.6250 & 0.0013 & 0.0013 & 105 \\\\\n29 & 54426.6828 & 0.0013 & $-$0.0017 & 116 \\\\\n37 & 54427.1660 & 0.0072 & $-$0.0047 & 106 \\\\\n38 & 54427.2294 & 0.0010 & $-$0.0021 & 66 \\\\\n39 & 54427.2906 & 0.0006 & $-$0.0016 & 80 \\\\\n54 & 54428.2073 & 0.0013 & 0.0034 & 321 \\\\\n55 & 54428.2763 & 0.0069 & 0.0116 & 345 \\\\\n56 & 54428.3218 & 0.0024 & $-$0.0037 & 267 \\\\\n70 & 54429.1825 & 0.0030 & 0.0062 & 129 \\\\\n71 & 54429.2575 & 0.0046 & 0.0204 & 131 \\\\\n72 & 54429.3205 & 0.0035 & 0.0226 & 123 \\\\\n89 & 54430.3462 & 0.0033 & 0.0150 & 37 \\\\\n153 & 54434.2262 & 0.0013 & 0.0052 & 123 \\\\\n154 & 54434.2872 & 0.0024 & 0.0054 & 123 \\\\\n155 & 54434.3496 & 0.0018 & 0.0071 & 132 \\\\\n169 & 54435.2044 & 0.0022 & 0.0111 & 147 \\\\\n170 & 54435.2615 & 0.0025 & 0.0073 & 204 \\\\\n187 & 54436.2838 & 0.0052 & $-$0.0036 & 54 \\\\\n218 & 54438.1507 & 0.0030 & $-$0.0208 & 188 \\\\\n219 & 54438.2086 & 0.0027 & $-$0.0237 & 175 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454424.9219 + 0.060778 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J081418.9$-$005022}\\label{obj:j0814}\n\n This object (=CSS080409:081419$-$005022, hereafter OT J0814) was\ndiscovered by the CRTS (\\cite{dra08atel1479}; \\cite{CRTS}; vsnet-alert 10038).\nASAS-3 detected a new outburst in 2008 October\n(vsnet-alert 10594), during which superhumps were detected\n(vsnet-alert 10603, 10630). Due to the short visibility of the object,\nit was difficult to uniquely determine $P_{\\rm SH}$. We adopted the\nmost likely period (0.0763 d) that best express all the recorded superhumps.\nThe times of superhump maxima are listed in table \\ref{tab:j0814oc2008}.\nThere was likely a stage B--C transition.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0814 (2008).}\\label{tab:j0814oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54759.5713 & 0.0008 & $-$0.0041 & 116 \\\\\n1 & 54759.6459 & 0.0009 & $-$0.0058 & 95 \\\\\n79 & 54765.6153 & 0.0007 & 0.0148 & 149 \\\\\n101 & 54767.2901 & 0.0066 & 0.0116 & 81 \\\\\n141 & 54770.3126 & 0.0022 & $-$0.0166 & 91 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454759.5754 + 0.076268 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J084555.1$+$033930}\\label{obj:j0845}\n\n This object (hereafter OT J0845) was discovered by K. Itagaki\n(\\cite{yam08j0845cbet1225}; \\cite{hon08j0845cbet1229}).\nThe mean superhump period with the PDM method was 0.06036(2) d\n(figure \\ref{fig:j0845shpdm}, excluding the first night).\nThe times of superhump maxima are listed in table \\ref{tab:j0845oc2008}.\nThe observation on the first night ($E = 0$) apparently caught the\nevolutionary stage of superhumps (cf. vsnet-alert 9847). We used\n$E > 0$ data and obtained $P_{\\rm dot}$ = $+6.7(3.4) \\times 10^{-5}$.\nThe object is likely a large-amplitude\nSU UMa-type dwarf nova rather than a typical WZ Sge-type star\n(vsnet-alert 9852).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig212.eps}\n \\end{center}\n \\caption{Superhumps in OT J0845 (2008) after BJD 2454491.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0845shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J0845 (2008).}\\label{tab:j0845oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54487.1018 & 0.0032 & $-$0.0004 & 100 \\\\\n66 & 54491.0961 & 0.0007 & 0.0023 & 208 \\\\\n67 & 54491.1548 & 0.0006 & 0.0006 & 114 \\\\\n68 & 54491.2181 & 0.0009 & 0.0034 & 110 \\\\\n69 & 54491.2735 & 0.0015 & $-$0.0017 & 105 \\\\\n99 & 54493.0894 & 0.0016 & $-$0.0001 & 168 \\\\\n100 & 54493.1443 & 0.0013 & $-$0.0057 & 114 \\\\\n167 & 54497.2036 & 0.0043 & 0.0016 & 52 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454487.1022 + 0.060478 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J090239.7$+$052501}\\label{obj:j0902}\n\n OT J090239.7$+$052501 (=CSS080304:090240$+$052501, hereafter OT J0902)\nis a transient discovered by the CRTS \\citet{CRTS}.\nThe object had a blue SDSS counterpart with $g = 23.17$, $g-r = +0.07$\n(vsnet-alert 9945). Spectroscopic observation of the outbursting\nobject revealed the presence of a broad He\\textsc{II} emission lines\n\\citep{djo08j0902atel1411} which is suggestive of a WZ Sge-type\noutburst in a high-inclination system (vsnet-alert 9948;\n\\cite{ima06tss0222}). Early superhumps were subsequently detected\n(vsnet-alert 9953, 9955, 9963). The object was still in outburst\n27 d after the outburst detection (vsnet-alert 10011).\nAlthough we did not observe ordinary superhumps, we include this\nobject for improving the statistics of WZ Sge-type dwarf novae.\nThe mean period of early superhumps was 0.05652(3) d\n(figure \\ref{fig:j0902eshpdm}).\nUemura and Arai (vsnet-alert 9963) independently obtained the same\nperiod.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig213.eps}\n \\end{center}\n \\caption{Early superhumps in OT J0902 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j0902eshpdm}\n\\end{figure}\n\n\\subsection{OT J102146.4$+$234926}\\label{obj:j1021}\n\n This object (also called Var Leo 06, hereafter OT J1021) was discovered\nby \\citet{chr06j1021cbet746} in the course of the Catalina Sky Survey\n(CSS). \\citet{gol07j1021} and \\citet{uem08j1021} reported the detection\nof superhumps and classified the object as a WZ Sge-type dwarf nova.\nWe reanalyzed the data for OT J1021 in \\citet{uem08j1021} in combination\nwith the AAVSO data, and determined the superhump maxima\nduring the plateau stage and the rebrightening stage (table\n\\ref{tab:j1021oc2006}). The maxima can be well expressed by a single\nperiod of 0.056295(10) d without a phase shift (figure \\ref{fig:j1021oc}).\nThis lack of a phase shift, as well as the smooth continuation of\nthe general fading trend before and after the ``dip'', the dip\nphenomenon in this object can be better understood as a temporary\ncooling of the disk, and the plateau stage of the main superoutburst\nand the ``rebrightening'' comprise a continuous entity, rather than\nthe complete termination of a superoutburst and a newly triggered\nsuperoutburst (see e.g. discussion for AL Com \\cite{nog97alcom}).\nA similar phenomenon was also observed in 1RXS J0232\n(subsection \\ref{sec:j0232}).\n\nThe $O-C$ apparently showed a break around $E = 240$ (corresponding\nto a stage B--C transition), rather than a phase shift as\nshown in \\citet{uem08j1021}. The mean period and $P_{\\rm dot}$\nfor $E \\le 240$ were 0.056312(12) d and $0.4(0.8) \\times 10^{-5}$,\nrespectively. The period after the transition was 0.056043(65),\nwhich is probably identical to the newly appeared period of\n0.055988(15) d during the fading tail \\citep{uem08j1021}.\nAlthough \\citet{uem08j1021} attributed this period to a candidate\norbital period, the above behavior agrees with a transition to\na shorter superhump period, generally seen in SU UMa-type dwarf novae.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,90mm){fig214.eps}\n \\end{center}\n \\caption{$O-C$ of superhumps OT J1021 (2006).\n (Upper): $O-C$ diagram. The $O-C$ values were against the mean period\n for the stage B ($E \\le 240$, thin curve).\n (Lower): Light curve.}\n \\label{fig:j1021oc}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1021.}\\label{tab:j1021oc2006}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54060.8730 & 0.0022 & 0.0008 & 9 \\\\\n1 & 54060.9295 & 0.0015 & 0.0009 & 36 \\\\\n2 & 54060.9839 & 0.0006 & $-$0.0010 & 60 \\\\\n3 & 54061.0404 & 0.0013 & $-$0.0007 & 29 \\\\\n6 & 54061.2101 & 0.0292 & 0.0000 & 62 \\\\\n7 & 54061.2688 & 0.0024 & 0.0024 & 118 \\\\\n8 & 54061.3233 & 0.0017 & 0.0007 & 134 \\\\\n18 & 54061.8857 & 0.0008 & 0.0002 & 56 \\\\\n19 & 54061.9407 & 0.0007 & $-$0.0012 & 58 \\\\\n20 & 54061.9963 & 0.0007 & $-$0.0019 & 58 \\\\\n31 & 54062.6037 & 0.0098 & $-$0.0136 & 40 \\\\\n36 & 54062.8980 & 0.0006 & $-$0.0009 & 58 \\\\\n37 & 54062.9526 & 0.0007 & $-$0.0025 & 58 \\\\\n38 & 54063.0103 & 0.0009 & $-$0.0011 & 58 \\\\\n48 & 54063.5648 & 0.0137 & $-$0.0096 & 41 \\\\\n49 & 54063.6244 & 0.0049 & $-$0.0063 & 34 \\\\\n59 & 54064.2022 & 0.0038 & 0.0086 & 121 \\\\\n60 & 54064.2617 & 0.0184 & 0.0117 & 91 \\\\\n77 & 54065.2186 & 0.0063 & 0.0117 & 217 \\\\\n79 & 54065.3171 & 0.0030 & $-$0.0025 & 108 \\\\\n83 & 54065.5470 & 0.0028 & 0.0023 & 33 \\\\\n84 & 54065.5997 & 0.0026 & $-$0.0013 & 42 \\\\\n85 & 54065.6595 & 0.0061 & 0.0022 & 28 \\\\\n165 & 54070.1562 & 0.0034 & $-$0.0047 & 66 \\\\\n167 & 54070.2676 & 0.0246 & $-$0.0059 & 57 \\\\\n169 & 54070.3840 & 0.0027 & $-$0.0021 & 68 \\\\\n184 & 54071.2239 & 0.0097 & $-$0.0066 & 72 \\\\\n185 & 54071.2833 & 0.0021 & $-$0.0035 & 193 \\\\\n186 & 54071.3601 & 0.0021 & 0.0170 & 204 \\\\\n226 & 54073.6041 & 0.0010 & 0.0092 & 21 \\\\\n227 & 54073.6527 & 0.0030 & 0.0016 & 24 \\\\\n237 & 54074.2217 & 0.0014 & 0.0076 & 167 \\\\\n238 & 54074.2761 & 0.0012 & 0.0057 & 317 \\\\\n239 & 54074.3338 & 0.0038 & 0.0071 & 235 \\\\\n240 & 54074.3796 & 0.0019 & $-$0.0034 & 94 \\\\\n255 & 54075.2282 & 0.0015 & 0.0008 & 364 \\\\\n256 & 54075.2808 & 0.0014 & $-$0.0029 & 300 \\\\\n257 & 54075.3391 & 0.0012 & $-$0.0009 & 159 \\\\\n261 & 54075.5717 & 0.0040 & 0.0065 & 24 \\\\\n262 & 54075.6275 & 0.0017 & 0.0061 & 24 \\\\\n279 & 54076.5723 & 0.0114 & $-$0.0062 & 32 \\\\\n280 & 54076.6343 & 0.0019 & $-$0.0005 & 67 \\\\\n297 & 54077.5843 & 0.0027 & $-$0.0075 & 7 \\\\\n298 & 54077.6318 & 0.0029 & $-$0.0163 & 10 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454060.8722 + 0.056295 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J102637.0$+$475426}\\label{obj:j1026}\n\n This object (hereafter OT J1026) was discovered by K. Itagaki\n\\citep{yam09j1026cbet1644}. The SU UMa-type nature of this object was\nimmediately clarified (vsnet-alert 10882). The object soon started fading,\nindicating that the outburst was caught during its final stage.\nA PDM analysis of the entire data set yielded a period of 0.06752(9) d\n(figure \\ref{fig:j1026shpdm}).\nThis period presumably corresponds to $P_2$. The times of superhump\nmaxima are given in table \\ref{tab:j1026oc2009}.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig215.eps}\n \\end{center}\n \\caption{Superhumps in OT J1026 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1026shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1026 (2009).}\\label{tab:j1026oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54835.1783 & 0.0137 & $-$0.0180 & 40 \\\\\n1 & 54835.2703 & 0.0018 & 0.0064 & 72 \\\\\n2 & 54835.3407 & 0.0026 & 0.0092 & 61 \\\\\n28 & 54837.0918 & 0.0051 & 0.0034 & 28 \\\\\n29 & 54837.1526 & 0.0035 & $-$0.0034 & 40 \\\\\n30 & 54837.2300 & 0.0039 & 0.0065 & 67 \\\\\n32 & 54837.3608 & 0.0019 & 0.0021 & 39 \\\\\n46 & 54838.2987 & 0.0076 & $-$0.0061 & 71 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454835.1963 + 0.067575 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J102842.9$-$081927}\\label{obj:j1028}\n\n This transient (=CSS090331:102843$-$081927, hereafter OT J1028)\nwas detected by the CRTS. The object soon turned out to be\nan ultrashort-period SU UMa-type dwarf nova (vsnet-alert 11149, 11158, 11164).\nAn unusual $V-J$ color was reported (vsnet-alert 11163).\nA spectroscopic observation clarified its hydrogen-rich nature\n(vsnet-alert 11166), suggesting that the object is similar to V485 Cen\nand EI Psc.\n\n The times of superhump maxima are listed in table \\ref{tab:j1028oc2009}.\nThe outburst was apparently observed during the relatively late stage\nand the following decline phase. Although we included times of maxima\nafter BJD 2454928 (decline phase) because of the continued detection\nof the periodicity after the decline, this part of the data suffered from\nthe low signal-to-noise ratio. We thus restricted to $E \\le 59$ for\ndetermining parameters, yielding a marginally positive\n$P_{\\rm dot}$ = $+11.6(8.5) \\times 10^{-5}$.\nA PDM analysis of the same interval yielded a period of 0.038147(14) d\n(figure \\ref{fig:j1028shpdm}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig216.eps}\n \\end{center}\n \\caption{Superhumps in OT J1028 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1028shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1028 (2009).}\\label{tab:j1028oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54922.9883 & 0.0016 & 0.0015 & 56 \\\\\n1 & 54923.0247 & 0.0009 & $-$0.0001 & 72 \\\\\n2 & 54923.0621 & 0.0011 & $-$0.0009 & 72 \\\\\n3 & 54923.0995 & 0.0010 & $-$0.0015 & 72 \\\\\n4 & 54923.1380 & 0.0008 & $-$0.0012 & 72 \\\\\n28 & 54924.0535 & 0.0021 & 0.0002 & 43 \\\\\n29 & 54924.0918 & 0.0020 & 0.0005 & 119 \\\\\n30 & 54924.1280 & 0.0010 & $-$0.0014 & 120 \\\\\n31 & 54924.1655 & 0.0025 & $-$0.0020 & 119 \\\\\n32 & 54924.2069 & 0.0017 & 0.0012 & 110 \\\\\n52 & 54924.9632 & 0.0058 & $-$0.0042 & 42 \\\\\n53 & 54925.0118 & 0.0038 & 0.0063 & 71 \\\\\n54 & 54925.0446 & 0.0015 & 0.0010 & 71 \\\\\n55 & 54925.0860 & 0.0009 & 0.0043 & 72 \\\\\n56 & 54925.1237 & 0.0016 & 0.0039 & 71 \\\\\n57 & 54925.1616 & 0.0014 & 0.0037 & 72 \\\\\n58 & 54925.1983 & 0.0034 & 0.0023 & 70 \\\\\n59 & 54925.2356 & 0.0008 & 0.0015 & 67 \\\\\n134 & 54928.0912 & 0.0022 & 0.0005 & 62 \\\\\n135 & 54928.1210 & 0.0051 & $-$0.0079 & 68 \\\\\n159 & 54929.0377 & 0.0060 & $-$0.0053 & 50 \\\\\n188 & 54930.1368 & 0.0054 & $-$0.0108 & 52 \\\\\n189 & 54930.1747 & 0.0066 & $-$0.0110 & 66 \\\\\n213 & 54931.0986 & 0.0017 & $-$0.0013 & 64 \\\\\n214 & 54931.1529 & 0.0071 & 0.0150 & 46 \\\\\n240 & 54932.1301 & 0.0032 & 0.0019 & 58 \\\\\n423 & 54939.1023 & 0.0029 & 0.0037 & 44 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454922.9868 + 0.038089 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J111217.4$-$353829}\\label{obj:j1112}\n\n This object (hereafter OT J1112) was detected\nby ``Pi of the Sky'' and its dwarf nova-type\nnature was confirmed (vsnet-alert 9764, 9767, 9769, 9770, 9771).\nThe detection of early superhumps and ordinary superhumps led to\na classification of a typical WZ Sge-type dwarf nova (vsnet-alert\n9775, 9806). The presence of He\\textsc{II} and C\\textsc{IV}\nemission lines in the spectrum was also very similar to WZ Sge\n(vsnet-alert 9782).\nThe times of superhump maxima are listed are in table \\ref{tab:j1112oc2007}.\nThe change in the superhump period was very small,\n$P_{\\rm dot}$ = $+0.5(0.3) \\times 10^{-5}$, similar to WZ Sge\nitself. The mean periods of early and ordinary superhumps,\ndetermined with the PDM method, were\n0.05847(2) d (figure \\ref{fig:j1112eshpdm}) and\n0.058965(9) d (figure \\ref{fig:j1112shpdm}),\nrespectively. This $P_{\\rm SH}$ is adopted in table \\ref{tab:perlist}.\nThe fractional superhump excess was estimated to be 0.8(1) \\%,\nalso very typical for a WZ Sge-type dwarf nova.\nMore detailed analysis will be presented in Maehara et al.,\nin preparation.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig217.eps}\n \\end{center}\n \\caption{Early superhumps in OT J1112 (2007). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1112eshpdm}\n\\end{figure}\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig218.eps}\n \\end{center}\n \\caption{Ordinary superhumps in OT J1112 (2007). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1112shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1112 (2007--2008).}\\label{tab:j1112oc2007}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54475.3297 & 0.0027 & $-$0.0009 & 124 \\\\\n16 & 54476.2778 & 0.0010 & 0.0030 & 281 \\\\\n82 & 54480.1717 & 0.0008 & 0.0023 & 61 \\\\\n83 & 54480.2255 & 0.0019 & $-$0.0029 & 96 \\\\\n84 & 54480.2868 & 0.0009 & $-$0.0007 & 233 \\\\\n85 & 54480.3474 & 0.0019 & 0.0009 & 303 \\\\\n116 & 54482.1778 & 0.0010 & 0.0020 & 61 \\\\\n117 & 54482.2350 & 0.0014 & 0.0002 & 61 \\\\\n118 & 54482.2934 & 0.0007 & $-$0.0004 & 61 \\\\\n119 & 54482.3517 & 0.0008 & $-$0.0011 & 51 \\\\\n218 & 54488.1932 & 0.0080 & $-$0.0016 & 39 \\\\\n219 & 54488.2539 & 0.0028 & 0.0001 & 61 \\\\\n220 & 54488.3062 & 0.0014 & $-$0.0066 & 60 \\\\\n221 & 54488.3695 & 0.0024 & $-$0.0023 & 33 \\\\\n253 & 54490.2588 & 0.0019 & $-$0.0014 & 130 \\\\\n254 & 54490.3219 & 0.0042 & 0.0028 & 112 \\\\\n269 & 54491.2046 & 0.0021 & 0.0003 & 36 \\\\\n270 & 54491.2656 & 0.0036 & 0.0023 & 108 \\\\\n287 & 54492.2705 & 0.0014 & 0.0040 & 135 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454475.3306 + 0.059010 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J130030.3$+$115101}\\label{obj:j1300}\n\n This transient (=CSS080702:130030$+$115101, hereafter OT J1300)\nwas detected by the CRTS.\nIndependent detections by ASAS-3 suggested a superoutburst of an SU UMa-type\ndwarf nova (vsnet-alert 10300). Five days after the maximum, the object\nshowed superhumps (vsnet-alert 10311).\nThe mean superhump period with the PDM method was 0.06440(2) d\n(figure \\ref{fig:j1300shpdm})\nThe times of superhump maxima are listed in table \\ref{tab:j1300oc2008}.\nThe epoch $E = 0$ corresponded\nto a growing stage of superhumps. Disregarding this epoch, we obtained\n$P_{\\rm dot}$ = $+14.4(1.5) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig219.eps}\n \\end{center}\n \\caption{Superhumps in OT J1300 (2008) after BJD 2454653.9.\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1300shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1300 (2008).}\\label{tab:j1300oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54653.0315 & 0.0007 & $-$0.0016 & 120 \\\\\n14 & 54653.9374 & 0.0012 & 0.0027 & 44 \\\\\n15 & 54653.9998 & 0.0003 & 0.0007 & 108 \\\\\n16 & 54654.0645 & 0.0008 & 0.0011 & 88 \\\\\n77 & 54657.9847 & 0.0013 & $-$0.0069 & 51 \\\\\n93 & 54659.0198 & 0.0039 & $-$0.0021 & 43 \\\\\n108 & 54659.9915 & 0.0010 & 0.0037 & 80 \\\\\n109 & 54660.0547 & 0.0014 & 0.0024 & 50 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454653.0331 + 0.064396 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J144011.0$+$494734}\\label{obj:j1440}\n\n This transient (=CSS090530:144011$+$494734, hereafter OT J1440) was\ndetected by the CRTS.\nThe detection of superhumps confirmed the SU UMa-type classification\n(vsnet-outburst 10297, vsnet-alert 11283).\nThe mean superhump period with the PDM method was 0.06471(5) d\n(figure \\ref{fig:j1440shpdm})\nThe times of superhump maxima are listed in table \\ref{tab:j1440oc2009}.\nAlthough there was a clear break in the $O-C$ diagram between $E=1$ and\n$E=15$, it was unclear whether this break is attributed to stage A--B or\nstage B--C transition. We adopted the latter interpretation because the\nperiod was almost constant after the break.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig220.eps}\n \\end{center}\n \\caption{Superhumps in OT J1440 (2009).\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1440shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1440 (2009).}\\label{tab:j1440oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54983.0238 & 0.0031 & $-$0.0045 & 69 \\\\\n1 & 54983.0935 & 0.0121 & 0.0003 & 64 \\\\\n15 & 54984.0043 & 0.0016 & 0.0025 & 188 \\\\\n16 & 54984.0689 & 0.0011 & 0.0023 & 224 \\\\\n22 & 54984.4581 & 0.0005 & 0.0021 & 92 \\\\\n23 & 54984.5209 & 0.0009 & $-$0.0001 & 101 \\\\\n24 & 54984.5867 & 0.0006 & 0.0009 & 74 \\\\\n37 & 54985.4313 & 0.0013 & 0.0018 & 73 \\\\\n38 & 54985.4918 & 0.0007 & $-$0.0027 & 106 \\\\\n39 & 54985.5566 & 0.0009 & $-$0.0027 & 104 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454983.0283 + 0.064899 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J144341.9$-$175550}\\label{obj:j1443}\n\n This transient (=CSS090418:144342$-$175550, hereafter OT J1443) was\ndetected by the CRTS.\nThe detection of superhumps confirmed the SU UMa-type classification\n(vsnet-alert 11193, 11195, 11196, 11199, 11219). The times of superhump\nmaxima are listed in table \\ref{tab:j1443oc2009}.\nThanks to the early detection of the outburst, all stages A--C were\nrecorded. The $P_{\\rm dot}$ during the stage B was\n$+11.0(1.3) \\times 10^{-5}$ ($12 \\le E \\le 112$).\nOther parameters are listed in table \\ref{tab:perlist}.\nThe mean $P_{\\rm SH}$ over the entire superoutburst was 0.072065(10) d\n(PDM method, figure \\ref{fig:j1443shpdm}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig221.eps}\n \\end{center}\n \\caption{Superhumps in OT J1443 (2009). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1443shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1443 (2009).}\\label{tab:j1443oc2009}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54940.1823 & 0.0024 & $-$0.0308 & 134 \\\\\n1 & 54940.2643 & 0.0019 & $-$0.0209 & 151 \\\\\n12 & 54941.0808 & 0.0009 & 0.0025 & 42 \\\\\n13 & 54941.1551 & 0.0009 & 0.0047 & 179 \\\\\n14 & 54941.2256 & 0.0004 & 0.0031 & 75 \\\\\n15 & 54941.2986 & 0.0009 & 0.0040 & 43 \\\\\n26 & 54942.0921 & 0.0004 & 0.0044 & 58 \\\\\n27 & 54942.1640 & 0.0004 & 0.0042 & 72 \\\\\n28 & 54942.2359 & 0.0004 & 0.0040 & 74 \\\\\n29 & 54942.3077 & 0.0003 & 0.0037 & 74 \\\\\n30 & 54942.3790 & 0.0004 & 0.0029 & 60 \\\\\n54 & 54944.1074 & 0.0004 & 0.0009 & 74 \\\\\n55 & 54944.1785 & 0.0005 & $-$0.0001 & 75 \\\\\n56 & 54944.2504 & 0.0004 & $-$0.0003 & 74 \\\\\n57 & 54944.3236 & 0.0007 & 0.0008 & 48 \\\\\n68 & 54945.1178 & 0.0006 & 0.0019 & 152 \\\\\n69 & 54945.1862 & 0.0006 & $-$0.0017 & 261 \\\\\n70 & 54945.2608 & 0.0021 & 0.0007 & 146 \\\\\n95 & 54947.0691 & 0.0012 & 0.0066 & 119 \\\\\n110 & 54948.1540 & 0.0005 & 0.0100 & 115 \\\\\n111 & 54948.2340 & 0.0011 & 0.0178 & 120 \\\\\n112 & 54948.3033 & 0.0018 & 0.0150 & 71 \\\\\n123 & 54949.0852 & 0.0011 & 0.0038 & 141 \\\\\n124 & 54949.1598 & 0.0010 & 0.0064 & 246 \\\\\n125 & 54949.2346 & 0.0010 & 0.0090 & 184 \\\\\n137 & 54950.0927 & 0.0010 & 0.0019 & 151 \\\\\n138 & 54950.1625 & 0.0009 & $-$0.0003 & 314 \\\\\n139 & 54950.2310 & 0.0015 & $-$0.0040 & 260 \\\\\n151 & 54951.0961 & 0.0060 & $-$0.0040 & 319 \\\\\n152 & 54951.1674 & 0.0009 & $-$0.0048 & 393 \\\\\n153 & 54951.2305 & 0.0034 & $-$0.0139 & 209 \\\\\n165 & 54952.1111 & 0.0063 & 0.0015 & 314 \\\\\n166 & 54952.1698 & 0.0037 & $-$0.0119 & 242 \\\\\n179 & 54953.1123 & 0.0021 & $-$0.0066 & 180 \\\\\n180 & 54953.1803 & 0.0021 & $-$0.0107 & 285 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454940.2131 + 0.072099 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J163120.9$+$103134}\\label{obj:j1631}\n\n This transient (=CSS080505:163121$+$103134, hereafter OT J1631) was\ndiscovered by the CRTS \\citep{CRTS}.\nSoon after the discovery announcement, past outbursts from ASAS-3 records\nand the ROSAT identification were noticed (cvnet-discussion 1136,\nvsnet-alert 10159). The detection of superhump led to secure classification\nof this object. \\citet{mah08atel1520} presented a spectroscopical\nconfirmation as a CV.\nThe mean superhump period with the PDM method was 0.064129(5) d\n(figure \\ref{fig:j1631shpdm}).\nThe times of superhump maxima are listed in\ntable \\ref{tab:j1631oc2008}. The $O-C$ diagram showed a clear positive\nperiod derivative ($E \\le 96$) before a transition to the stage C,\nbehavior typical for this superhump period (cf. figure \\ref{fig:octrans}).\nWe obtained $P_{\\rm dot}$ = $+12.5(1.3) \\times 10^{-5}$ for the stage B.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig222.eps}\n \\end{center}\n \\caption{Superhumps in OT J1631 (2008).\n (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1631shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1631 (2008).}\\label{tab:j1631oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54592.4052 & 0.0004 & 0.0062 & 247 \\\\\n1 & 54592.4679 & 0.0005 & 0.0048 & 246 \\\\\n2 & 54592.5331 & 0.0014 & 0.0059 & 135 \\\\\n16 & 54593.4275 & 0.0004 & 0.0024 & 218 \\\\\n17 & 54593.4905 & 0.0005 & 0.0012 & 200 \\\\\n18 & 54593.5549 & 0.0006 & 0.0014 & 103 \\\\\n27 & 54594.1302 & 0.0012 & $-$0.0005 & 66 \\\\\n28 & 54594.1947 & 0.0012 & $-$0.0001 & 67 \\\\\n31 & 54594.3860 & 0.0006 & $-$0.0013 & 184 \\\\\n32 & 54594.4492 & 0.0005 & $-$0.0022 & 201 \\\\\n33 & 54594.5102 & 0.0006 & $-$0.0054 & 156 \\\\\n46 & 54595.3437 & 0.0009 & $-$0.0056 & 122 \\\\\n47 & 54595.4096 & 0.0009 & $-$0.0039 & 204 \\\\\n48 & 54595.4725 & 0.0011 & $-$0.0052 & 205 \\\\\n63 & 54596.4348 & 0.0009 & $-$0.0049 & 84 \\\\\n64 & 54596.5012 & 0.0012 & $-$0.0027 & 76 \\\\\n65 & 54596.5619 & 0.0060 & $-$0.0061 & 52 \\\\\n77 & 54597.3381 & 0.0012 & 0.0004 & 105 \\\\\n78 & 54597.4012 & 0.0024 & $-$0.0006 & 182 \\\\\n79 & 54597.4648 & 0.0011 & $-$0.0011 & 193 \\\\\n80 & 54597.5281 & 0.0020 & $-$0.0020 & 175 \\\\\n81 & 54597.5935 & 0.0010 & $-$0.0007 & 70 \\\\\n89 & 54598.1132 & 0.0010 & 0.0058 & 126 \\\\\n90 & 54598.1716 & 0.0083 & 0.0001 & 86 \\\\\n91 & 54598.2398 & 0.0013 & 0.0042 & 137 \\\\\n94 & 54598.4314 & 0.0011 & 0.0033 & 83 \\\\\n95 & 54598.4930 & 0.0008 & 0.0008 & 82 \\\\\n96 & 54598.5581 & 0.0025 & 0.0018 & 47 \\\\\n109 & 54599.3918 & 0.0009 & 0.0017 & 72 \\\\\n110 & 54599.4507 & 0.0009 & $-$0.0036 & 81 \\\\\n125 & 54600.4145 & 0.0034 & $-$0.0019 & 76 \\\\\n137 & 54601.1945 & 0.0030 & 0.0084 & 185 \\\\\n138 & 54601.2497 & 0.0010 & $-$0.0005 & 135 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454592.3989 + 0.064140 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J191443.6$+$605214}\\label{obj:j1914}\n\n This transient (hereafter OT J1914) was detected by K. Itagaki\n\\citep{yam08j1914cbet1535}. The SU UMa-type nature of this object\nwas soon established (vsnet-alert 10558).\nThe mean superhump period during the entire plateau phase was\n0.071292(14) d (PDM method, figure \\ref{fig:j1914shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j1914oc2008}.\nA stage B--C transition was recorded around $E = 82$.\nThe mean $P_{\\rm SH}$ and $P_{\\rm dot}$ during the stage B were\n0.07134(3) d and $+9.7(2.6) \\times 10^{-5}$, respectively.\n\\citet{boy09j1914} reported $P_{\\rm dot}$ = $+3.4(2.0) \\times 10^{-5}$\nusing a slightly different treatment and data set.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig223.eps}\n \\end{center}\n \\caption{Superhumps in OT J1914 (2008, plateau phase). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1914shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1914.}\\label{tab:j1914oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54743.0965 & 0.0021 & $-$0.0093 & 128 \\\\\n1 & 54743.1697 & 0.0023 & $-$0.0073 & 64 \\\\\n40 & 54745.9467 & 0.0013 & $-$0.0050 & 152 \\\\\n41 & 54746.0178 & 0.0012 & $-$0.0050 & 136 \\\\\n68 & 54747.9442 & 0.0013 & 0.0003 & 291 \\\\\n69 & 54748.0183 & 0.0010 & 0.0032 & 285 \\\\\n70 & 54748.0888 & 0.0011 & 0.0026 & 215 \\\\\n72 & 54748.2343 & 0.0006 & 0.0058 & 54 \\\\\n73 & 54748.3078 & 0.0012 & 0.0082 & 23 \\\\\n74 & 54748.3753 & 0.0016 & 0.0045 & 26 \\\\\n82 & 54748.9491 & 0.0010 & 0.0091 & 203 \\\\\n83 & 54749.0172 & 0.0015 & 0.0060 & 182 \\\\\n84 & 54749.0870 & 0.0013 & 0.0048 & 147 \\\\\n87 & 54749.3001 & 0.0019 & 0.0044 & 25 \\\\\n88 & 54749.3682 & 0.0039 & 0.0013 & 26 \\\\\n91 & 54749.5881 & 0.0012 & 0.0077 & 16 \\\\\n100 & 54750.2198 & 0.0017 & $-$0.0008 & 28 \\\\\n101 & 54750.2931 & 0.0006 & 0.0013 & 49 \\\\\n105 & 54750.5809 & 0.0025 & 0.0045 & 15 \\\\\n111 & 54751.0003 & 0.0021 & $-$0.0030 & 154 \\\\\n112 & 54751.0633 & 0.0065 & $-$0.0111 & 31 \\\\\n116 & 54751.3613 & 0.0014 & 0.0023 & 25 \\\\\n117 & 54751.4338 & 0.0024 & 0.0036 & 25 \\\\\n119 & 54751.5767 & 0.0030 & 0.0043 & 16 \\\\\n124 & 54751.9109 & 0.0029 & $-$0.0173 & 54 \\\\\n125 & 54752.0113 & 0.0058 & 0.0119 & 42 \\\\\n126 & 54752.0664 & 0.0054 & $-$0.0041 & 29 \\\\\n138 & 54752.9118 & 0.0041 & $-$0.0125 & 131 \\\\\n139 & 54752.9948 & 0.0031 & $-$0.0007 & 302 \\\\\n140 & 54753.0569 & 0.0030 & $-$0.0097 & 91 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454743.1058 + 0.071148 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J195951.3$+$224232}\\label{obj:j1959}\n\n This object (also called Var Vul 05, hereafter OT J1959)\nwas discovered by J. Hanisch (vsnet-alert 8629; \\cite{ren05j1959iauc8591}).\nSubsequent observations\nconfirmed the presence of superhumps (cvnet-outburst 543, vsnet-alert\n8640). The large outburst amplitude ($\\sim$ 8 mag, vsnet-alert 8654)\nmakes the object an excellent candidate for a WZ Sge-type dwarf nova.\n\n The object underwent another recorded outburst in 2008 April.\\footnote{\n$<$http:\/\/tech.groups.yahoo.com\/group\/VarVul05\/message\/98$>$.\n} The recurrence time may be an order of $\\sim$ 1000 d.\n\nWe adopted a mean superhump period of 0.05990(3) d\n(figure \\ref{fig:j1959shpdm}). Although there was some hint of\ndouble-wave modulations suggesting early superhumps, the large amplitude\nof the modulations and the epoch of the observation ($>$ 6 d after\nthe outburst detection) suggest the identification of these humps\nas ordinary superhumps.\nThe times of superhump maxima are listed in table \\ref{tab:j1959oc2005}.\nThe resultant $P_{\\rm dot}$ is virtually zero, $-0.7(5.2) \\times 10^{-5}$.\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig224.eps}\n \\end{center}\n \\caption{Superhumps in OT J1959 (2005). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j1959shpdm}\n\\end{figure}\n\nAlthough this object is provisionally listed as a WZ Sge-type\nobject based on its apparently large outburst amplitude\nand the long outburst duration (table \\ref{tab:wztab}),\nthis object might resemble a borderline object such as BC UMa\nand RZ Leo. Future detection of early superhumps and accurate determination\nof $P_{\\rm dot}$ are desired.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J1959 (2005).}\\label{tab:j1959oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53606.3830 & 0.0012 & 0.0004 & 37 \\\\\n1 & 53606.4448 & 0.0017 & 0.0024 & 26 \\\\\n2 & 53606.4991 & 0.0023 & $-$0.0033 & 33 \\\\\n44 & 53609.0202 & 0.0156 & 0.0012 & 42 \\\\\n45 & 53609.0786 & 0.0020 & $-$0.0003 & 53 \\\\\n68 & 53610.4518 & 0.0022 & $-$0.0052 & 36 \\\\\n69 & 53610.5220 & 0.0058 & 0.0051 & 20 \\\\\n93 & 53611.9546 & 0.0012 & $-$0.0003 & 96 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453606.3825 + 0.059919 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J213122.4$-$003937}\\label{obj:j2131}\n\n This transient (hereafter OT J2131) was detected by K. Itagaki\n\\citep{yam08j1631cbet1631}. Subsequent observations confirmed\nthe SU UMa-type nature of this object (vsnet-alert 10830).\nSince the individual observations were not long enough, we could not\nuniquely select the superhump period among one-day aliases\n(e.g. 0.069 d, as in vsnet-alert 10830).\nIn table \\ref{tab:j2131oc2008}, we list epochs based on the base period\nof 0.06463(3) d, a candidate superhump period.\nThis selection of the alias needs to be verified by future observations.\n\n\\begin{table}\n\\caption{Superhump maxima of OT J2131 (2008).}\\label{tab:j2131oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54819.8932 & 0.0028 & $-$0.0020 & 179 \\\\\n15 & 54820.8670 & 0.0024 & 0.0030 & 84 \\\\\n16 & 54820.9282 & 0.0042 & $-$0.0004 & 119 \\\\\n62 & 54823.8993 & 0.0011 & $-$0.0006 & 245 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454819.8951 + 0.064593 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{OT J213701.8$+$071446}\\label{obj:j2137}\n\n This transient (hereafter OT J2137) was detected by K. Itagaki\n(vsnet-alert 10670, 10671). The object was soon confirmed to be\nan SU UMa-type dwarf nova in the period gap (vsnet-alert 10674, 10677).\nThe mean superhump period during the entire observation with the PDM\nmethod was 0.097762(14) d (figure \\ref{fig:j2137shpdm}).\nThe times of superhump maxima are listed in table \\ref{tab:j2137oc2008}.\nThere was an apparent transition in the period between $E=0$ and $E=5$.\nAfter $E=5$, the superhump period was almost constant\n($P_{\\rm SH}$ = 0.09768(3) d, $P_{\\rm dot}$ = $+2.3(4.7) \\times 10^{-5}$).\nSince the object faded 6 d after this transition (vsnet-obs 62796),\nwe probably observed the stage C superhumps, which could explain the\nlack of period variation. The object underwent a rebrightening\n(vsnet-alert 10708) 5 d after the fading. Such a rebrightening is\nrare in a long-$P_{\\rm SH}$ system. The object may resemble V725 Aql\nin its period evolution of superhumps and in the presence of\na rebrightening (\\cite{uem01v725aql}; subsection \\ref{sec:v725aql}).\n\n\\begin{figure}\n \\begin{center}\n \\FigureFile(88mm,110mm){fig225.eps}\n \\end{center}\n \\caption{Superhumps in OT J2137 (2008). (Upper): PDM analysis.\n (Lower): Phase-averaged profile.}\n \\label{fig:j2137shpdm}\n\\end{figure}\n\n\\begin{table}\n\\caption{Superhump maxima of OT J2137.}\\label{tab:j2137oc2008}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 54778.0721 & 0.0003 & $-$0.0067 & 171 \\\\\n5 & 54778.5693 & 0.0019 & 0.0019 & 37 \\\\\n6 & 54778.6678 & 0.0007 & 0.0027 & 46 \\\\\n10 & 54779.0583 & 0.0002 & 0.0023 & 184 \\\\\n20 & 54780.0345 & 0.0003 & 0.0012 & 142 \\\\\n43 & 54782.2815 & 0.0074 & 0.0005 & 48 \\\\\n50 & 54782.9661 & 0.0005 & 0.0010 & 404 \\\\\n51 & 54783.0585 & 0.0011 & $-$0.0043 & 194 \\\\\n53 & 54783.2597 & 0.0008 & 0.0014 & 95 \\\\\n60 & 54783.9419 & 0.0012 & $-$0.0004 & 462 \\\\\n61 & 54784.0404 & 0.0009 & 0.0004 & 236 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2454778.0788 + 0.097726 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\subsection{TSS J022216.4$+$412260}\\label{obj:j0222}\n\n The 2005 superoutburst of this WZ Sge-type dwarf nova was described\nin \\citet{ima06tss0222}. We used the data used in \\citet{ima06tss0222} and\ndetermined times of superhump maxima during the plateau phase\n(table \\ref{tab:j0222oc2005}).\nThe superhumps were likely growing before $E = 37$. We used the segment\nlater than this epoch and obtained\n$P_{\\rm dot}$ = $+2.2(1.5) \\times 10^{-5}$.\n\n\\begin{table}\n\\caption{Superhump maxima of TSS J0222 (2005).}\\label{tab:j0222oc2005}\n\\begin{center}\n\\begin{tabular}{ccccc}\n\\hline\\hline\n$E$ & max$^a$ & error & $O-C^b$ & $N^c$ \\\\\n\\hline\n0 & 53695.1319 & 0.0022 & $-$0.0009 & 52 \\\\\n1 & 53695.1905 & 0.0052 & 0.0021 & 61 \\\\\n14 & 53695.9146 & 0.0041 & 0.0035 & 61 \\\\\n20 & 53696.2345 & 0.0028 & $-$0.0103 & 88 \\\\\n37 & 53697.1953 & 0.0010 & 0.0054 & 105 \\\\\n38 & 53697.2488 & 0.0017 & 0.0033 & 88 \\\\\n74 & 53699.2534 & 0.0072 & 0.0064 & 58 \\\\\n88 & 53700.0250 & 0.0017 & $-$0.0003 & 117 \\\\\n89 & 53700.0771 & 0.0014 & $-$0.0039 & 110 \\\\\n90 & 53700.1366 & 0.0018 & $-$0.0000 & 88 \\\\\n91 & 53700.1910 & 0.0015 & $-$0.0011 & 82 \\\\\n92 & 53700.2465 & 0.0015 & $-$0.0013 & 71 \\\\\n104 & 53700.9131 & 0.0038 & $-$0.0019 & 66 \\\\\n125 & 53702.0762 & 0.0024 & $-$0.0063 & 141 \\\\\n126 & 53702.1392 & 0.0024 & 0.0010 & 198 \\\\\n127 & 53702.1980 & 0.0116 & 0.0043 & 126 \\\\\n128 & 53702.2416 & 0.0054 & $-$0.0077 & 34 \\\\\n159 & 53703.9711 & 0.0047 & $-$0.0017 & 83 \\\\\n160 & 53704.0376 & 0.0052 & 0.0092 & 109 \\\\\n195 & 53705.9712 & 0.0075 & $-$0.0031 & 81 \\\\\n196 & 53706.0327 & 0.0036 & 0.0028 & 57 \\\\\n197 & 53706.0861 & 0.0032 & 0.0006 & 59 \\\\\n\\hline\n \\multicolumn{5}{l}{$^{a}$ BJD$-$2400000.} \\\\\n \\multicolumn{5}{l}{$^{b}$ Against $max = 2453695.1328 + 0.055598 E$.} \\\\\n \\multicolumn{5}{l}{$^{c}$ Number of points used to determine the maximum.} \\\\\n\\end{tabular}\n\\end{center}\n\\end{table}\n\n\\section{Conclusion}\\label{sec:conclusion}\n\n We systematically surveyed period variations of superhumps in\nSU UMa-type dwarf novae based on newly obtained data and past\npublications. We found:\n\n\\begin{itemize}\n\\item In well-observed systems, the $O-C$ diagram of superhump maxima \nare usually composed of three distinct stages: early evolutionary\nstage with a longer superhump period (stage A), middle stage with\nsystematically varying periods (stag B), and final stage with\na shorter superhump period (stage C).\n\\item During the stage B, the period derivative is strongly correlated\nto the orbital period, or, more likely, to the mass ratio of the system.\nPreviously reported anomalously large period derivatives in EI Psc and\nV485 Cen were not confirmed.\n\\item Upon transition to stage C, the superhump period generally decreases\nby 0.5--1.0 \\%.\n\\item We generally did not find strong evidence that period derivatives\nvary between different superoutburst of the same object. No apparent\ncorrelation with the presence of a precursor outburst was recorded.\n\\item The superhump period at the start of stage B is close to that\nin the stage C. The fractional superhump excesses of these periods\nare strongly correlated to the orbital period, or the mass ratio.\nThis period is slightly shorter than that expected for the precession\nrate of single-particle dynamical 3:1 resonance.\n\\item In systems with positive period derivatives, the maximum period\nat the end of stage B has a limit correlated to the mass ratio.\nWe interpret that the lengthening of the period is a result of outward\npropagation of the eccentricity wave and this upper limit of the period\ncorresponds to the radius near the tidal truncation.\n\\item We interpreted that stage C superhumps are rejuvenized excitation\nof 3:1 resonance when the superhumps in the outer disk is effectively\nquenched.\n\\item Traditional phase reversal in ``late superhumps'' was not\nrecorded in many systems. We suggested that some of these observations\nmisinterpreted stage C superhumps.\n\\item In some systems, particularly WZ Sge-type dwarf novae and analogous\nsystems, long-enduring superhump signals were recorded\nduring the post-superoutburst stage. The $O-C$ analysis suggests that\nthese superhumps evolved from superhumps in the stages B or C.\nThe periods of these persisting superhumps are usually longer than the\nperiods of superhumps during the main superoutburst by $0.2-0.5$ \\%.\n\\item The period variation in systems with long superhump periods\n vary from system to system. Some systems show a very large decrease\nin the superhump period. While some systems show a stepwise decrease\nas in short-period systems, some systems show a more continuous change.\n\\item Some long-period systems apparently lack period variations,\nand there is even a hint of positive period derivatives in systems\nwith very infrequent outbursts. The superoutbursts in these systems\nresemble those of short-period systems in the frequent presence of\na rebrightening.\n\\item The positive period derivatives appears to be confirmed in\nER UMa-type dwarf novae. In ER UMa itself, the stage C superhumps\nseem to appear earlier than in other SU UMa-type dwarf nova accompanied\nby a phase $\\sim$0.5 offset.\n\\item In WZ Sge-type dwarf novae, period derivatives are an excellent\nfunction of the fractional superhump excess or the mass-ratio.\n\\item In WZ Sge-type dwarf novae, the type of rebrightening is correlated\nwith the period variation. Superoutbursts with multiple rebrightenings\nor with a long-lasting rebrightening tend to have smaller period\nderivatives while superoutbursts with a single rebrightening tend to\nhave larger period derivatives.\n\\item The superhumps of at least one outburst of a black-hole X-ray binary\n(KV UMa) exhibited the same evolutionary sequence as in SU UMa-type\ndwarf novae, although the degree of period variation was an order\nof magnitude smaller.\n\\item We refined the empirical relations between the fractional superhump\nexcess and the mass ratio, and the fractional superhump excess and\nthe superhump period.\n\\end{itemize}\n\n The present survey has clarified the relation between general behavior of\nperiod variation of superhumps and the system mass ratio (or the superhump\nperiod). Although this would seem to indicate that SU UMa-type dwarf\nnovae are ``single parameter systems'' regarding the period variation\nof superhumps, the difference in behavior between different objects\nwith nearly equal superhump periods or mass ratios is much larger than\nthe variation within the same system. This suggests the presence of\na mechanism causing diversity in different systems; questions whether\nthis diversity is related to outburst characteristics, or to the condition\nof the accretion disk, need to be answered by future investigations.\nThere have also been indications of unusual development of superhumps in\nseveral systems, making future observations of superhumps in even\nwell-observed objects still attractive. The early emergence of the\nstage C superhumps in ER UMa-type dwarf novae and some other systems,\nand the superhumps in WZ Sge-type dwarf novae, particularly the late-stage\nhumps and transient enhancement of orbital humps, are still poorly understood.\nThe study presents an alternative idea to the traditional picture of\ndecreasing superhump period due to the shrinkage of the accretion disk\nfrom the radius of the 3:1 resonance, which anticipates novel theoretical\nprogress in understanding the superhump phenomenon.\n\n\\vskip 3mm\n\nThis work was supported by the Grant-in-Aid for the Global COE Program\n``The Next Generation of Physics, Spun from Universality and Emergence''\nfrom the Ministry of Education, Culture, Sports, Science and Technology\n(MEXT) of Japan.\nThis work was partly supported by a Grant-in-Aid from the \nMinistry of Education, Culture, Sports, Science and Technology \nof Japan (19740104).\nPart of this work is supported by a Research Fellowship of\nthe Japan Society for the Promotion of Science for Young Scientists (AI).\nThe authors are grateful to observers of VSNET Collaboration and\nVSOLJ observers who supplied vital data. We also benefited from\nthe data by Martin Nicholson, Achim Sucker, Paulo Cacella,\nT. Kryachko and his colleagues, Doug West, Oksana I. Dudka,\nand Masayuki Moriyama.\nWe acknowledge with thanks the variable star\nobservations from the AAVSO International Database contributed by\nobservers worldwide and used in this research.\nThis work is deeply indebted to outburst detections and announcement\nby a number of variable star observers worldwide, including participants of\nCVNET, BAA VSS alert and AVSON networks. \nWe are grateful to Allen W. Shafter for providing observations of\nOT J0329, and Artur Rutkowski for providing the times of superhump\nmaxima for DI UMa.\nThe CCD operation of the Bronberg Observatory is partly sponsored by\nthe Center for Backyard Astrophysics.\nThe CCD operation by Peter Nelson is on loan from the AAVSO,\nfunded by the Curry Foundation.\nP. Schmeer's observations were made with the Iowa Robotic Observatory,\nand he wishes to thank Robert Mutel and his students.\nWe are grateful to the Catalina Real-time Transient Survey\nteam for making their real-time\ndetection of transient objects available to the public, and providing\ntimes of eclipses for SDSS J1524.\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\nIn pulsed radar systems, pulse compression technology\\cite{farnett1990pulse}\\cite{mahafza2002radar} has been commonly used to obtain high pulse energy, large bandwidth, and improved range resolution. Through the use of a matched filter receiver, the returned signal reflected by a target goes through a filter matched to the reverse and conjugate version of the transmitted pulse. Then the echo signal is compressed into a short pulse which is shown in the matched filter output along with the well-known maximum SNR. However, the matched filter output also has undesired range sidelobes if the pulses are not carefully chosen. The range sidelobes of a strong target may mask main the peak of a weak target near the strong target. Therefore, low range sidelobes are desirable when dealing with multi-targets. \n\nIn order to obtain these low range sidelobes, phase coding is usually used in radar for digital pulse compression. For a phase coded waveform, it is phase coded by a unimodular code or sequence. The matched filter output of a phase coded waveform is controlled by an aperiodic auto-correlation function of a code (sequence).\nFor bi-phase codes, the Barker code is a famous code whose aperiodic auto-correlation function has low sidelobes with only one element amplitude value. In addition, polyphase codes proposed by Heimiller\\cite{heimiller1961phase} and Chu\\cite{chu1972polyphase} also have low sidelobes of aperiodic auto-correlation functions. However, it is impossible to achieve zero sidelobes of an aperiodic auto-correlation with one unimodular sequence\\cite{pezeshki2008doppler}. This has resulted in the use of Golay complementary pairs in phase coding.\n\n In radar, Golay waveforms phase coded by Golay pairs are coherently transmitted, and the returned signals are also coherently processed through the matched filter. Then the sum of the matched filter outputs has no range sidelobes since Golay pairs have an impulse-like aperiodic autocorrelation function. But the Golay pairs are sensitive to Doppler effects which result from the moving targets. In other words, as the inter-pulse Doppler shift changes the phase of the complementary waveforms, the matched filter outputs' sum of complementary waveforms have fairly high range sidelobes. In order to solve this problem, some methods for constructing Doppler resilient waveforms have been proposed. These existing construction methods fall into two categories.\n \n The first category only concerns the transmission of the basic Golay waveforms. The transmission is determined by space-time codes. Examples of these codes that play a key role in constructing Doppler resilient Golay waveforms (pulse train) are first-order Reed-M{\\\"u}ller codes\\cite{suvorova2007doppler}, Prouhet\u2013Thue\u2013Morse (PTM) sequences\\cite{pezeshki2008doppler}, oversampled PTM sequences\\cite{chi2009range}, generalized PTM sequences\\cite{tang2014construction}, and equal sums of powers (ESP) sequences\\cite{nguyen2016doppler}. The first-order Reed-M{\\\"u}ller codes decrease the range sidelobes (less than -60dB) at a specific Doppler value (e.g., 0.25 rad). PTM sequences can almost clear range sidelobes (which are approximately equal to -80dB) near zero Doppler (i.e., $[-0.1,0.1]$ in rad). The oversampled PTM sequences can also almost clear range sidelobes not only near zero Doppler but also in all rational Doppler shifts (in rad). The generalized PTM sequence is generally used for a complementary set, but it is also compatible with the traditional PTM sequence when only a complementary pair is considered. Therefore, the generalized PTM sequence for a complementary waveform set can almost clear range sidelobes near zero Doppler. The ESP sequence has almost the same Doppler resilient performance compared to a PTM sequence. In fact, ESP and PTM are closely related to the solutions of the Prouhet-Tarry-Escott (PTE) problem. However, ESP sequences need two antennas to transmit the Golay waveforms in some pulse repetition intervals (PRIs) that will result in inter-waveform interferences. \n \n The second category focuses on not only the transmission of the basic Golay waveforms but also the coefficients of the receiver filter. The pulse weighing technology is similar to traditional time-domain window design. In the windowing method, the coefficients of the matched filters are determined from known time-domain windows such as the rectangular window, B-spline windows, the triangular window, Hann and Hamming windows, which can achieve range sidelobe suppression. However, when Doppler effects are present, these well-known traditional windows cannot be directly used to suppress the sidelobes down to a very low level. Wu $et$ $al.$\\cite{wu2020range} jointly considered the coefficients of the receiver and a given window function (e.g., Hamming and rectangular windows) with the higher-order Doppler null and max-SNR constraints, so that the traditional window function can be indirectly used to suppress the range sidelobes in a given Doppler interval. Generally, these known windows are not suitable for Doppler resilience. Dang $et\\, al$. \\cite{dang2011coordinating}\\cite{dang2014signal}\\cite{dang2020coordinating} proposed the binomial design (BD) that puts binomial coefficients as the coefficients of the receiver filter, and alternatively transmits Golay waveforms at the transmitter. The BD method has a relatively large Doppler resilient interval, in which range sidelobes are suppressed down to almost zero. \n \n\n\nSo in this paper, the construction of Doppler resilient complementary waveforms based on a null space approach is proposed. \nThe main contributions of this paper are listed as follows:\n\\begin{itemize}\n \\item For the defined ambiguity function \\cite{dang2020coordinating}, it is proved theoretically that there exists a totally Doppler resilient type ambiguity function, as well as the delay resilient type ambiguity function, under certain conditions by solving a linear system and finding the null space. \n\\item A Doppler resilient transmission waveform based on Golay pairs which can suppress the range sidelobes in a specified Doppler interval of interest, or even overall Doppler interval, is designed. Here, the design problem is formulated as a linear system with one key term which results in range sidelobes. \n\\item By forcing the above key term in the formulated linear system to zero, the linear system can be solved to obtain a null space. From the null space, the characteristic vector to control the transmission of basic Golay waveforms, and the coefficients of the receiver filter, in the intervals of interest or the entire Doppler interval, are extracted. \n\\item Based on the derived null space, a complex optimization problem, which is non-convex and non-concave in nature, is formulated for maximizing the signal-to-noise ratio (SNR). A heuristic coordinated descent (HCD) algorithm is proposed to obtain a sub-optimal solution of the formulated optimization problem, where the null space is taken as a means to transform the problem into a simpler one, i.e, finding the coefficients of a linear combination of null space basis vectors.\n\\item The above characteristic vector in the transmission waveform, and the coefficients of the receiver filter, when applied to fully polarimetric radar systems, can achieve nearly perfect Doppler resilient performance and fully suppress the inter-antenna interference.\n\\item The delay resilient problems are also investigated and solved by using the frequency-domain phase coding, also based on the null space algorithm. In fact, the null space algorithm is used to obtain the frequency-domain characteristic vector, and also the coefficients of the frequency-domain filter at the receiver. \\end{itemize}\n\n\\subsection{Notation}\nThe superscripts $(\\cdot)^{T},(\\cdot)^{*}$ and $(\\cdot)^{H}$ denote transpose, complex conjugate, and conjugate transpose, respectively. In addition, `$\\circ$' denotes the Hadamard product and $\\mathrm{Null}(\\mathbf{E})$ denotes null space of matrix $\\mathbf{E}$. \n\n\n\n\n \\section{Signal Model}\n\\subsection{Time-Domain Signal Model}\nA pair of biphase sequences $\\mathbf{x}$ and $\\mathbf{y}$ is called Golay pair or complementary pair if\n\\begin{eqnarray}\n\tC_\\mathbf{x}[k]+C_\\mathbf{y}[k]=2L\\delta_k, \\,\\, k=-L+1,\\cdots,0,\\cdots, L-1\n\\end{eqnarray}\nwhere $C_\\mathbf{x}[k]$ is the auto-correlation function of $\\mathbf x$ at lag $k$, $\\delta_k$ is the Kronecker delta function, and $\\mathbf{x}=[x[0],x[1],\\cdots,x[L-1]]^T$, $\\mathbf{y}=[y[0],y[1],\\cdots,y[L-1]]^T$.\n\n\nIn the signal model, the basic Golay complementary waveforms $s_x(t)$ and $s_y(t)$ are phase coded by the Golay complementary pair $(\\mathbf{x},\\mathbf{y})$\\cite{chi2009range,dang2011coordinating,dang2014signal}, i.e.,\n\\begin{eqnarray}\n\ts_x(t)=\\sum_{l=0}^{L-1}x[l]u(t-lT_c),\\,\\, s_y(t)=\\sum_{l=0}^{L-1}y[l]u(t-lT_c),\n\\end{eqnarray}\nwhere $u(t)$ is a unit-energy baseband pulse shape, and $T_c$ is the chip length.\n\nLet the vector $\\mathbf{p}=[p_0,p_1,\\cdots,p_{N-1}]^T$ be the characteristic vector to control the transmission of basic Golay waveforms $s_x(t)$ and $s_y(t)$, where $N$ is the number of pulses and $p_n=1$ or $-1$. If $p_n=1$, $s_x(t)$ is transmitted, otherwise $s_y(t)$ is transmitted. Thus the characteristic vector $\\mathbf{p}$ and the basic Golay waveforms, $s_x(t)$ and $s_y(t)$ constitute the Golay transmission waveform or complementary waveform, $Z_p(t)$, i.e.,\n\\begin{eqnarray}\n\tZ_{P}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}\\left[\\left(1+p_{n}\\right) s_{x}(t-n T)+\\left(1-p_{n}\\right) s_{y}(t-n T)\\right],\\label{eq:Zp}\n\\end{eqnarray}\nwhere $T$ denotes the pulse repetition interval (PRI). \n\nLet the input to the matched filter be $Z_P (t) e^{j\\nu t}$, where $\\nu=2\\pi f_d$, and $f_d$ is the Doppler shift in Hz. Also, $Z_P (t) e^{j\\nu t}$ passes through the linear filter with impulse response $Z_{W}^*(-t)$, where\n\\begin{eqnarray}\n\\begin{split}\n\tZ_{W}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}w_n^*&\\left[\\left(1+p_{n}\\right) s_{x}(t-n T)\\right.\\\\\n\t&\\left.+\\left(1-p_{n}\\right) s_{y}(t-n T)\\right],\\label{eq:Zw}\n\t\\end{split}\n\\end{eqnarray}\n$w_n\\in \\mathbb{C}$ is the coefficient of receiver filter and $\\mathbf{w} = [w_0,w_1,\\cdots,w_{N-1}]^T$.\n\nThen the output, i.e., the cross-ambiguity function is given by\n\\begin{eqnarray}\n\t\\chi_{P, W}(\\tau, \\nu)=\\int_{-\\infty}^{+\\infty} Z_{P}(t) Z_{W}^{*}(t-\\tau) \\mathrm{e}^{j \\nu t} d t.\\label{eq:chiPW}\n\\end{eqnarray}\n\n\nThe radar parameters (such as chip length $T_c$ and PRI $T$) are chosen to ensure that $L T_c$ is much less than $T$ and $\\nu T$ is almost equal to zero.\nAfter carefully choosing the radar parameters, the center lobe of $\\chi_{P, W}(\\tau, \\nu)$ depends on the discrete cross ambiguity function\\cite{wu2020range}\\cite{dang2020coordinating}\n\\begin{equation}\n\t\\begin{aligned} \\mathcal{A}_{P, W}(k, \\theta) &=\\frac{1}{2}\\left[C_{x}[k]+C_{y}[k]\\right] \\sum_{n=0}^{N-1} w_n e^{j n \\theta} \\\\ &+\\frac{1}{2}\\left[C_{x}[k]-C_y[k]\\right] \\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}, \\end{aligned}\\label{eq:APW}\n\\end{equation}\nwhere $\\theta = \\nu T = 2\\pi f_d T$ is the Doppler shift in radians.\n\nThe first part of (\\ref{eq:APW}) only determines the shape of $\\mathcal{A}_{P, W}(0, \\theta)$ since the Golay complementary pair ($\\mathbf{x}$,$\\mathbf{y})$ makes the first formula of (\\ref{eq:APW}) vanish at nonzero $k$. However, the second part of (\\ref{eq:APW}) determines the range sidelobes around the Doppler shift $\\theta$, in which the choices of $p_n$ and $w_n$ are important. In \\cite{dang2020coordinating}\\cite{wu2020range}, two performance metrics (i.e., Doppler resilience and SNR) are chosen to judge the Doppler resilient complementary waveform specified by $\\{\\mathbf{p}, \\mathbf{w}\\}$.\n\n\n\n\\subsection{Frequency-Domain Pulse Amplitude Modulation (PAM) Signal Model}\nThe frequency-domain PAM waveforms for $\\mathbf{x}$ and $\\mathbf{y}$ are given by \\cite{pezeshki2009sidelobe}\\cite{wang2019range}\n\\begin{eqnarray}\n\t\\hat{x}(\\omega) = \\sum_{l=0}^{L-1}x[l]\\Omega(\\omega-lW_c),\\,\\,\n\t\\hat{y}(\\omega) = \\sum_{l=0}^{L-1}y[l]\\Omega(\\omega-lW_c),\n\\end{eqnarray}\nwhere $W_c$ denotes the subcarrier spacing and $\\Omega(\\omega)$ denotes the subcarrier complex amplitude.\n\nThen the transmitted frequency PAM pulse train is expressed as\n\\begin{eqnarray}\n\\hat{z}_{\\mathcal{P}} (\\omega) = \\sum_{n=0}^{N-1}p_n\\hat{x}(\\omega-nW_0)+(1-p_n)\\hat{y}(\\omega-nW_0),\n\\end{eqnarray}\nand the impluse response of the filter in the frequency domain is $\\hat{z}_{\\mathcal{Q}} (-\\omega)$, where\n\\begin{eqnarray}\n\\hat{z}_{\\mathcal{Q}} (\\omega) = \\sum_{n=0}^{N-1}w_n^*[p_n\\hat{x}(\\omega-nW_0)+(1-p_n)\\hat{y}(\\omega-nW_0)],\n\\end{eqnarray}\t\nwhere $W_0$ is the frequency-domain PRI, where $W_0\\gg W_c$.\n\nThen the cross ambiguity function of $\\hat{z}_\\mathcal{P}(\\omega)$ and $\\hat{z}_\\mathcal{Q}(\\omega)$ is given by\n\\begin{eqnarray}\n\\chi_{P,W}^f (\\nu,\\tau) = \\int_{-\\infty}^{+\\infty} \\hat{z}_\\mathcal{P}(\\omega) \\hat{z}_\\mathcal{Q}^*(\\omega-\\nu)e^{-j\\tau \\omega}d\\omega.\n\\end{eqnarray}\nAfter applying the inverse continuous-time Fourier transform, the transmitted frequency domain PAM waveform $\\hat{z}_{\\mathcal{P}} (\\omega)$ is an OFDM waveform in the time-domain:\n\n\n\\begin{eqnarray}\n\\begin{split}\nZ_\\mathcal{P} (t) &= \\frac{1}{2 \\pi} \\sum_{n=0}^{N-1} \\sum_{l=0}^{L-1}( p_n {x}[l]+(1-p_n){y}[l]) \\\\\n& \\quad \\cdot e^{j(nW_0+lW_c)t}\\hat{\\Omega}(t), \\label{eq: ZpOFDM}\n\\end{split}\n\\end{eqnarray}\nand similarly the inverse Fourier transform of $\\hat{z}_{\\mathcal{Q}} (\\omega)$ is given by\n\\begin{eqnarray}\\label{eq: ZqODFM}\n\\begin{split}\nZ_\\mathcal{Q} (t) &= \\frac{1}{2 \\pi} \\sum_{n=0}^{N-1} \\sum_{l=0}^{L-1}w_n( p_n {x}[l]\\\\\n&{}\\quad+(1-p_n){y}[l]) e^{j(nW_0+lW_c)t}\\hat{\\Omega}(t),\n\\end{split}\n\\end{eqnarray}\nwhere $\\hat{\\Omega}(t) = \\mathcal{F}^{-1} \\left\\{2\\pi \\Omega(\\omega) \\right\\}$ and $\\mathcal{F}^{-1} $ denotes the inverse Fourier transform.\n\nThe discrete ambiguity function based on $\\chi_{P,W}^f(\\nu,\\tau)$ is given by\n\\begin{equation}\n\\begin{aligned}\n\\mathcal{B}_{P,W}(i,\\alpha)=& \\frac{1}{2}\\left[C_{\\hat{x}}[i]+C_{\\hat{y}}[i]\\right] \\sum_{n=0}^{N-1} w_n e^{j n \\alpha} \\\\\n&+\\frac{1}{2}\\left[C_{\\hat{x}}[i]-C_{\\hat{y}}[i]\\right] \\sum_{n=0}^{N-1}(-1)^{p_n} w_n e^{j n \\alpha},\n\\end{aligned}\\label{eq:BPW}\n\\end{equation}\nwhere $\\alpha = \\tau W_0$ is the time shift.\n\n\\section{Doppler\/delay resilience based windowing}\n\\subsection{Doppler Resilience}\n\n\\emph{Definition 1:}\nThe ambiguity function $\\mathcal{A}_{P, W}(k, \\theta)$ is a Doppler resilient type if the following conditions hold:\n\\begin{eqnarray}\n\t |\\mathcal{A}_{P, W}(0,\\theta)|> 0, \\quad \\theta\\in \\Theta,\\label{eq:purpose}\n\\end{eqnarray}\t\nand\n\\begin{eqnarray}\n\t |\\mathcal{A}_{P, W}(k, \\theta)\/\\mathcal{A}_{P, W}(0, \\theta)|\\leq \\eta, \\quad k\\neq 0, \\,\\,\\theta\\in \\Theta,\\label{eq:D2}\n\\end{eqnarray}\t\nwhere $\\Theta=[0,D_I]$ is the specified Doppler interval of interest, $D_I$ is a positive real number, and $\\eta$ is a very small positive real number.\n\n\nWe will show that the range sidelobes may almost vanish around the specified Doppler interval of interest $\\Theta = [0,D_I]$ , and maintain $|\\mathcal{A}(0,\\theta)|\\neq 0$. The best case is that $\\eta$ in (\\ref{eq:D2}) is totally equal to zero such that the discrete ambiguity function satisfies the following equation\n\\begin{eqnarray}\n\t\\mathcal{A}_{P, W}(k, \\theta)=\\mathcal{A}_{P, W}(0,\\theta)\\delta_k, \\quad \\theta\\in \\Theta\\label{eq:purpose}.\n\\end{eqnarray}\n\n\n\\emph{Definition 2:}\nThe ambiguity function is a totally Doppler resilient type for $\\theta\\in \\Theta$ if \n\\begin{eqnarray}\n\t\\mathcal{A}_{P, W}(k, \\theta)=\\mathcal{A}_{P, W}(0,\\theta)\\delta_k,\\,\\, \\theta\\in \\Theta,\n\\end{eqnarray}\nwhere $|\\mathcal{A}_{P, W}(0,\\theta)|> 0$.\n\n\nTo make analyzing the ambiguity function much easier, a Doppler Vandermonde matrix $\\mathbf{E}$ is proposed as follows:\n\\begin{eqnarray}\n\\mathbf{E} =\n\\left[\\begin{matrix}\n e^{j0\\theta_0}& e^{j1\\theta_0}&e^{j2\\theta_0}&\\cdots&e^{j(N-1)\\theta_0} \\\\\n e^{j0\\theta_1}& e^{j1\\theta_1}&e^{j2\\theta_1}&\\cdots&e^{j(N-1)\\theta_1} \\\\\n \\vdots&\\vdots&\\vdots&\\vdots&\\vdots\\\\\n e^{j0\\theta_{M-1}}& e^{j1\\theta_{M-1}}&e^{j2\\theta_{M-1}}&\\cdots&e^{j(N-1)\\theta_{M-1}} \\\\\n\\end{matrix}\\right].\\label{eq:E}\n\\end{eqnarray}\nwhere $\\Theta_{\\Delta} = \\{\\theta_0,\\theta_1,\\cdots,\\theta_{M-1}\\}$ and $\\Theta_{\\Delta}\\subset \\Theta$. \n\n\n\n\n\\emph{Proposition 1:}\n\tIf $(\\mathbf{x},\\mathbf{y})$ is a Golay pair, then the discrete ambiguity function defined in (\\ref{eq:APW}) can be rewritten as\n\t\\begin{eqnarray}\n\t\t\\mathcal{A}_{P,W} (k,\\theta)= \t\\left\\{\n\t\t\\begin{aligned}\n\t\t\t&\\frac{1}{2}(C_{\\mathbf{x}}(k)-C_{\\mathbf{y}}(k))\\sum_{n=0}^{N-1}p_n w_n e^{jn\\theta}, &\\,\\, k\\neq0,\\\\\n\t\t\t&L\\sum_{n=0}^{N-1}w_n e^{jn\\theta}, &\\,\\, k= 0.\n\t\t\t\\end{aligned}\n\t\t\\right.\n\t\\end{eqnarray}\n\n\n\\begin{proof}\n When $k\\neq 0$, since $(\\mathbf{x},\\mathbf{y})$ is a Golay pair, then $C_{\\mathbf{x}}[k]+C_{\\mathbf{y}}[k]=0$, so that \n \\begin{equation}\n \t\\mathcal{A}_{P,W} (k,\\theta)=\\frac{1}{2}(C_{\\mathbf{x}}(k)-C_{\\mathbf{y}}(k))\\sum_{n=0}^{N-1}p_n w_n e^{jn\\theta}.\n \\end{equation}\n When $k= 0$, $C_{\\mathbf{x}}(0)=C_{\\mathbf{y}}(0)=L$, and then it holds that\n \\begin{equation}\n \t\\mathcal{A}_{P,W} (k,\\theta)=L\\sum_{n=0}^{N-1}w_n e^{jn\\theta}.\n \\end{equation}\t\n \\end{proof}\n\n\\emph{Remark 1:}\n$\\frac{1}{2}(C_{\\mathbf{x}}(k)-C_{\\mathbf{y}}(k))\\sum_{n=0}^{N-1}p_n w_n e^{jn\\theta}$ denotes the range sidelobes, which we should clear.\n\n \n\n\n\n\n\n\\emph{Lemma 1:}\n\tLet $z_n= p_n w_n$, $n=0,1,2,\\cdots,N-1$. Then $|\\mathcal{A}_{P,W}(k,\\theta)|$ is bounded by $| f_{\\mathbf{z}}(\\theta)|$, i.e.,\n\t\\begin{equation}\n\t\t\\begin{aligned} \n\t\t\t|\\mathcal{A}_{P,W}(k,\\theta)| \\leq L |f_{\\mathbf{z}}(\\theta)|, \\quad k\\neq 0,\n\t\t\\end{aligned}\n\t\\end{equation}\n\twhere the key term $f_{\\mathbf{z}}(\\theta)$ is given by\n\t\\begin{eqnarray}\n\t\tf_{\\mathbf{z}}(\\theta)= \t\\sum_{n=0}^{N-1} z_n e^{j n \\theta}.\n\t\\end{eqnarray}\n\\begin{proof}\n\tSince $|C_{\\mathbf{x}}(k)|\\leq L$ and $|C_{\\mathbf{y}}(k)|\\leq L$ , then \n\\begin{eqnarray}\n\t\t\\frac{1}{2}|C_{\\mathbf{x}}(k)-C_{\\mathbf{y}}(k)|\\leq L,\\,\\, \\mathrm{for\\,\\, all}\\,\\, k\\in [-(L-1),L-1].\n\\end{eqnarray}\nWhen $k\\neq 0$, we have\n\t\t\\begin{equation}\n\t\t\\begin{aligned} \n\t\t|\\mathcal{A}_{P,W}(k,\\theta)| \t&=|\\frac{1}{2}\\left[C_{x}(k)-C_{y}(k)\\right] \\sum_{n=0}^{N-1}z_n e^{j n \\theta}| \\\\\n\t\t\t&\\leq \t|\\frac{1}{2}\\left[C_{x}(k)-C_{y}(k)\\right] ||\\sum_{n=0}^{N-1}z_n e^{j n \\theta}| \\\\\n\t\t\t&=L|\\sum_{n=0}^{N-1}z_n e^{j n \\theta}|\\\\\n\t\t\t&=L|f_{\\mathbf{z}}(\\theta)|.\n\t\t\\end{aligned}\n\t\\end{equation}\n\\end{proof}\n\tFrom lemma 1, we konw that range sidelobes can be controlled by $f_{\\mathbf{z}}(\\theta)$. Therefore, clearing the range sidelobes means $f_{\\mathbf{z}}(\\theta)=0$. \n\n\\emph{Lemma 2:}\n\t$\tf_{\\mathbf{z}}(\\theta)=0$, $\\theta\\in\\Theta_{\\Delta}$\n\tif and only if \n\t$$ \\mathbf{z}=[z_0,z_1,z_2,\\cdots,z_{N-1}]^T\\in \\mathrm{Null}(\\mathbf{E}),$$ where $z_n = p_n w_n$.\n\n\\begin{proof}\n$\tf_{\\mathbf{z}}(\\theta)=0$, $\\theta\\in\\Theta_{\\Delta}$ iff\n\t\\begin{eqnarray}\n\t\t\\sum_{n=0}^{N-1} z_n e^{j n \\theta}=0, \\quad \\mathrm{for\\,\\, all\\,}\\theta \\in \\Theta.\\label{eq:obj1}\n\t\\end{eqnarray}\ni.e.,\n\t\\begin{eqnarray}\n\\left[\\begin{matrix}\n \\sum_{n=0}^{N-1} z_n e^{j n \\theta_0}\\\\\n \\sum_{n=0}^{N-1} z_n e^{j n \\theta_1}\\\\\n \\vdots\\\\\n \\sum_{n=0}^{N-1} z_n e^{j n \\theta_{M-1}}\n\\end{matrix}\\right]\t=\\bf 0,\n\\end{eqnarray}\n\n\\begin{eqnarray}\n\\implies\t\\mathbf{E}\\mathbf{z}=\\bf 0.\n\\end{eqnarray}\n\tIn other words, $\\mathbf{z} \\in \\mathrm{Null}(\\mathbf{E})$.\n\\end{proof}\n\n\n\n\n\\emph{Theorem 1:}\n\tIf $\\mathbf{p}$ and $\\mathbf{w}$ satisfy $\\mathbf{w} \\neq \\mathbf{0}$, $\\mathbf{w} \\notin \\mathrm{Null}(\\mathbf{E})$ and $\\mathbf{p}\\circ \\mathbf{w} \\in \\mathrm{Null}(\\mathbf{E})$,\n\t the ambiguity function $\\mathcal{A}_{P,W}(k,\\theta)$ is a totally Doppler resilient type ambiguity function, i.e.,\n\t\\begin{eqnarray}\n\t\t\\mathcal{A}_{P,W}(k,\\theta) = 0, \\quad \\quad k\\neq 0, \\,\\, \\theta \\in \\Theta_{\\Delta}.\n\t\\end{eqnarray}\n\t\n\n\\begin{proof}\n\tThis is easily obtained from Lemma 1 and Lemma 2.\n\\end{proof}\n\nBased on Theorem 1, the range sidelobes in $\\Theta_{\\Delta}$ will vanish. However, the Doppler interval of interest $\\Theta=[0,D_I]$ or the overall Doppler interval $[0,\\pi]$ is truely focused, within which the range sidelobes are suppressed. In other words, we hope the range sidelobes of the ambiguity function $\\mathcal{A}_{P,W}(k,\\theta)$ can be no more than -90dB in the Doppler interval of interest $[0,D_I]$. \n\n\\emph{Proposition 2:}\n\tIn the Doppler interval of interest $[0,D_I]$, the discrete Doppler shifts can be chosen as $\\theta_m = m D_I\/(M-1)$, $m=0,1,\\cdots,M-1$. If $f_\\mathbf{z}(\\theta_m)=0$, $\\theta_m=0,1,\\cdots,M-1$, then the range sidelobes of $\\mathcal{A}_{P,W}(k,\\theta)$ can be suppressed for all $\\theta \\in [0,D_I]$, i.e., $\\mathcal{A}_{P,W}(k,\\theta)\\rightarrow 0$.\n\n\nAfter solving the linear system $\\mathbf{Ez}=\\bf 0$, we find the null space of $\\mathbf{E}$. Then $\\mathbf{p}$ and $\\mathbf{w}$ can be found based on $\\text{Null}(\\mathbf{E})$. Supposed that $\\hat{\\mathbf{z}} \\in \\text{Null}(\\mathbf{E})$, then $\\mathbf{p}$ and $\\mathbf{w}$ are solved as follows:\n\\begin{equation}\np_n=\n\\left\\{\n \\begin{array}{lr}\n +1, & \\text{if} \\quad \\mathrm{Re}\\{\\hat{\\mathbf{z}}\\}\\geq 0, \\\\\n -1, & \\text{if} \\quad \\mathrm{Re}\\{\\hat{\\mathbf{z}}\\}< 0,\\\\\n \\end{array}\n\\right.\\label{eq:p}\n\\end{equation}\n\n\\begin{equation}\nw_n=\n\\left\\{\n \\begin{array}{lr}\n +\\hat{z}_n, & \\text{if} \\quad \\mathrm{Re}\\{\\hat{\\mathbf{z}}\\}\\geq 0, \\\\\n -\\hat{z}_n, & \\text{if} \\quad \\mathrm{Re}\\{\\hat{\\mathbf{z}}\\}< 0.\\\\\n \\end{array}\n\\right.\\label{eq:w}\n\\end{equation}\t\t\nIt is easy to verify that $\\mathbf{w} \\neq \\mathbf{0}$, $\\mathbf{w} \\notin \\mathrm{Null}(\\mathbf{E})$. Then we design an algorithm for finding $\\mathbf{p}$ and $\\mathbf{w}$ in algorithm 1.\n\\begin{algorithm}[htb]\n\\setstretch{1.5}\n\\caption{Null space (NS) algorithm for obtaining $\\mathbf{p}$ and $\\mathbf{w}$:}\n\\label{alg:Framwork}\n\\begin{algorithmic}[1]\n\\STATE Input $N$, $D_I$, and $\\theta_m= m D_I\/(M-1)$, \\\\\n$m=0,1,\\cdots, M-1$. Here, $M = N-1$.\n\\STATE Generate matrix $\\mathbf{E}$ shown in (\\ref{eq:E}).\n\\STATE Compute the null space of $\\mathbf{E}$, i.e., $\\text{Null}(\\mathbf{E})$.\n\\STATE Select a solution from $\\text{Null}(\\mathbf{E})$, called $\\hat{\\mathbf{z}}$.\n\\STATE Obtain $\\mathbf{p}$ and $\\mathbf{w}$ as (\\ref{eq:p}) and (\\ref{eq:w})\n\\end{algorithmic}\n\\end{algorithm}\n\n\\emph{Remark 2:}\n\tIn the practical operations of Algorithm 1, we use the MATLAB instruction ``null(E)'' to obtain the basis vectors (which can span the null space). Then we select a solution from $\\mathrm{Null}(\\mathbf{E})$. Usually, we can select the basis vector as our solution. If SNR is considered, we should carefully choose the vector by some algorithms which is also introduced in this paper.\n\n\\emph{Remark 3:}\n\tThe number $M$ of the discrete Doppler shifts $\\theta_m$ $(m=0,1,\\cdots,M-1)$ is limited by the number of pulses $N$. This fact results from the solutions of the linear equations, i.e, if $M 0, \\quad \\alpha \\in \\Gamma,\\label{eq:purpose}\n\\end{eqnarray}\t\nand\n\\begin{eqnarray}\n\t |\\mathcal{B}_{P, W}(i, \\alpha)\/\\mathcal{B}_{P, W}(i, 0)|\\leq \\eta, \\quad i\\neq 0, \\,\\,\\alpha\\in \\Gamma,\\label{eq:purpose}\n\\end{eqnarray}\t\nwhere $\\Gamma=[0,T_I]$ is the delay interval of interest, $T_I$ is a positive real number, and $\\eta$ is a very small positive real number.\n\n\n\\emph{Definition 4:}\nThe ambiguity function $\\mathcal{B}_{P, W}(i,\\alpha)$ is a totally delay resilient type for $\\theta\\in \\Theta$ if \n\\begin{eqnarray}\n\t\\mathcal{B}_{P, W}(i, \\alpha)=\\mathcal{B}_{P, W}(i,0)\\delta_i,\n\\end{eqnarray}\nwhere $|\\mathcal{B}_{P, W}(i,0)|> 0$.\n\n\nIn order to simplify the analysis of the ambiguity function, a delay Vandermonde matrix $\\mathbf{T}$ is proposed as follows:\n\\begin{eqnarray}\n\\mathbf{T} =\n\\left[\\begin{matrix}\n e^{j0\\alpha_0}& e^{j1\\alpha_0}&e^{j2\\alpha_0}&\\cdots&e^{j(N-1)\\alpha_0} \\\\\n e^{j0\\alpha_1}& e^{j1\\alpha_1}&e^{j2\\alpha_1}&\\cdots&e^{j(N-1)\\alpha_1} \\\\\n \\vdots&\\vdots&\\vdots&\\vdots&\\vdots\\\\\n e^{j0\\alpha_{M-1}}& e^{j1\\alpha_{M-1}}&e^{j2\\alpha_{M-1}}&\\cdots&e^{j(N-1)\\alpha_{M-1}} \\\\\n\\end{matrix}\\right].\\label{eq:T}\n\\end{eqnarray}\nwhere $\\Gamma_{\\Delta} = \\{\\alpha_0,\\alpha_1,\\cdots,\\alpha_{M-1}\\}$, and $\\Gamma_{\\Delta}\\subset \\Gamma=[0,T_I]$. \n\n\n\n\n\\emph{Lemma 3:}\n\tThe first term of $\\mathcal{B}_{P,W}(i,\\alpha)$ in (\\ref{eq:BPW}) is a delta function for any given $\\theta \\in \\Theta$, i.e.,\n\t\\begin{equation}\n\t\\begin{aligned} \\frac{1}{2}\\left[C_{x}[i]+C_{y}[i]\\right] \\sum_{n=0}^{N-1} w_n e^{j n \\alpha} = L(\\sum_{n=0}^{N-1} w_n e^{j n \\alpha})\\delta_i,\n\t\\end{aligned}\n\t\\end{equation}\nif and only if $\\mathbf{w} \\neq \\mathbf{0}$ and $\\mathbf{w} \\notin \\mathrm{Null}(\\mathbf{T})$.\n\n\n\\emph{Lemma 4:}\n\tThe second term of $\\mathcal{B}_{P,W}(i,\\alpha)$ in (\\ref{eq:BPW}) is zero for all given $\\alpha \\in \\Gamma_{\\Delta}$, i.e.,\n\t\\begin{equation}\n\t\\begin{aligned} \\frac{1}{2}\\left[C_{x}(i)-C_{y}(i)\\right] \\sum_{n=0}^{N-1}p_n w_n e^{j n \\alpha} = 0,\n\t\\end{aligned}\n\t\\end{equation}\n\tif and only if $\\mathbf{p}\\circ \\mathbf{w} \\in \\mathrm{Null}(\\mathbf{T})$.\n\\begin{proof}\nSince $C_{\\mathbf{x}}(i)-C_{\\mathbf{y}}(i)\\neq 0$, when $k\\neq 0$,then the following equation should hold:\n\t\\begin{eqnarray}\n\t\t\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\alpha}=0, \\quad \\mathrm{for\\,\\, all\\,}\\alpha \\in \\Gamma_{\\Delta},\n\t\\end{eqnarray}\ni.e.,\n\\begin{eqnarray}\n\t\\mathbf{T}\\mathbf{z}=\\bf 0,\n\\end{eqnarray}\nwhere $\\mathbf{z} = [z_0,z_1,\\cdots,z_{N-1}]^T$, $z_n = p_n w_n$, $n=0,1,\\cdots,N-1$,\n$\\theta_m \\in \\Theta$, $m=0,1,\\cdots,M-1$.\n\tIn other words, $\\mathbf{p}\\circ \\mathbf{w} \\in \\mathrm{Null}(\\mathbf{E})$.\n\\end{proof}\n\n\\emph{Theorem 2:}\n\tIf $\\mathbf{p}$ and $\\mathbf{w}$ satisfy $\\mathbf{w} \\neq \\mathbf{0}$, $\\mathbf{w} \\notin \\mathrm{Null}(\\mathbf{T})$ and $\\mathbf{p}\\circ \\mathbf{w} \\in \\mathrm{Null}(\\mathbf{T})$,\n\tthen the ambiguity function $\\mathcal{A}_{P,W}(k,\\theta)$ is a totally delay resilient type ambiguity function, i.e., \n\t\t\\begin{eqnarray}\n\t\t\\mathcal{B}_{P,W}(i,\\alpha) = 0, \\quad \\quad k\\neq 0, \\,\\, \\theta \\in \\Gamma_{\\Delta}.\n\t\\end{eqnarray}\n\n\n\\subsection{Signal-to-Noise Ratio (SNR)}\nThe SNR\\cite{dang2011coordinating,dang2014signal,dang2020coordinating} is described as\n\\begin{eqnarray}\n\t\\mathrm{SNR} = \\frac{L\\sigma_b^2}{N_0}\\frac{\\|\\mathbf{w}\\|_1^2}{\\|\\mathbf{w}\\|_2^2},\\label{eq:SNR}\n\\end{eqnarray}\nwhere $\\sigma_b^2$ is the power of the target and $N_0$ is the power spectral density (PSD) of the white noise\\cite{dang2020coordinating}. We can maximize the SNR by maximizing $\\|\\mathbf{w}\\|_1^2\/ \\|\\mathbf{w}\\|_2^2$ under some constraints. For the constraints, the Doppler resilience constraint should be still satisfied, i.e.,\n\\begin{eqnarray}\n\\mathbf{E}\\mathbf{z}=\\mathbf{0},\t\n\\end{eqnarray}\nwhere $\\mathbf{z} = \\mathbf{p}\\circ \\mathbf{w}$, $p_n \\in \\{1,-1\\}$. Then the optimization is proposed as follows:\n\\begin{equation}\n\\begin{array}{ll}\n\t\\displaystyle \\max_{\\mathbf{w},\\mathbf{p}}\\, & \\frac{\\|\\mathbf{w}\\|_1^2}{\\|\\mathbf{w}\\|_2^2}\\\\\n\t s.t. & \\bf{Ez} = \\mathbf{0}\\\\\n\t\\quad & \\mathbf{z} = \\mathbf{p}\\circ \\mathbf{w}\\\\\n\t\\quad & p_n \\in \\{1,-1\\} .\n\t\\end{array}\\label{opt:SNR}\n\\end{equation}\nThis optimization problem (\\ref{opt:SNR}) is a challenging optimization problem because it contains binary variables $p_n$ and complex-valued variables $z_n$. Besides, the objective function in (\\ref{opt:SNR}) is not a concave function and the constraint set is not a convex set either.\n\nBecause of the difficulty of the proposed optimization problem, we have to transform the complex style into a much simpler form. We will analyze the constraint set first. Suppose $\\mathbf{z}_1, \\mathbf{z}_2, \\cdots,\\mathbf{z}_U \\in \\mathrm{Null}(\\mathbf{E})$, and $\\bm{\\lambda} = [\\lambda_1,\\lambda_2,\\cdots,\\lambda_{U}]^T$ is an arbitrary vector with real number elements, then \n\\begin{eqnarray}\n\\mathbf{Z}\\bm \\lambda \\in \\mathrm{Null}(\\mathbf{E}).\n\\end{eqnarray}\ni.e.,\n\\begin{eqnarray}\n\t\\mathbf{E}(\\mathbf{Z}\\bm \\lambda) = \\mathbf{0}.\n\\end{eqnarray}\nwhere $\\mathbf{Z} = [\\mathbf{z}_1\\,\\, \\mathbf{z}_2 \\,\\, \\cdots \\,\\, \\mathbf{z}_U]$.\nMoreover, for the second and third constraint, it is easy to verify that \n\\begin{eqnarray}\n\t\\|\\mathbf{Z}\\bm \\lambda\\| = \\|\\mathbf{p}\\circ\\mathbf{w}\\|=\\|\\mathbf{w}\\|,\n\\end{eqnarray}\nwhere $\\|\\cdot\\|$ means either $\\|\\cdot\\|_1$ or $\\|\\cdot\\|_2$.\n\nTherefore, the procedure for solving the optimization problem (\\ref{opt:SNR}) can be transformed into two steps:\n\\begin{itemize}\n\t\\item {\\bf{Step 1}}. Solve the following \n\t\\begin{eqnarray}\n\t\\max_{\\bm \\lambda}\\, \\frac{\\|\\mathbf{Z}\\bm{\\lambda}\\|_1^2}{\\|\\mathbf{Z}\\bm{\\lambda}\\|_2^2}.\\label{opt:SNR1}\n\\end{eqnarray}\n\n \\item {\\bf{Step 2}}. Implement (\\ref{eq:p}) and (\\ref{eq:w}).\n\\end{itemize}\n\\subsection{First Algorithm for SNR}\nThe optimization problem (\\ref{opt:SNR1}) is still a difficult problem, since its objective function is not concave. In order to solve it, two algorithms are proposed. The first algorithm is a simpler one, where the constraint set related to the first algorithm is limited to a much smaller set than that to the second algorithm. The second algorithm is slightly more difficult than the first algorithm, but the second one can find a better solution. So the first algorithm will be introduced first. Before introducing the first algorithm, a theorem will be proposed.\n\n\\emph{Theorem 3:} Let $\\lambda_u$ be nonnegative real number with $\\sum_{u=1}^{U}\\lambda_u=1$, then\n\\begin{eqnarray}\n\\max_{\\lambda_u} {\\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1}= \\max_u\\{\\|\\mathbf{z}_u\\|_1\\}, u=1,2,\\cdots,U.\n\\end{eqnarray}\n\n\n\\begin{proof}\t\nAccording to the triangle inequality of norm, i.e.,\n\\begin{eqnarray}\n \\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1\\leq \\sum_{u=1}^{U}\\lambda_u \\|\\mathbf{z}_u\\|_1,\n\\end{eqnarray}\nthen \n\\begin{eqnarray}\n\\begin{split}\n\\max_{\\lambda_u} \\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1 &\\leq \\max_{\\lambda_u} \\sum_{u=1}^{U}\\lambda_u \\|\\mathbf{z}_u\\|_1\\\\\n&=\\max_{u}\\{\\|\\mathbf{z}_u\\|_1\\}.\\label{ineq:right}\n\\end{split}\n\\end{eqnarray}\n\n \nSince $\\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1 = \\|\\mathbf{z}_u\\|$, when $\\lambda_u=1$, $u = 1,2,\\cdots,U$, then \n\\begin{eqnarray}\n\t\\|\\mathbf{z}_v\\|_1 \\leq \\max_{\\lambda_u}{\\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1}, \n\\end{eqnarray}\n\\begin{eqnarray}\n\t\\implies \\max_u\\{\\|\\mathbf{z}_u\\|_1\\} \\leq \\max_{\\lambda_u}{\\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1}.\\label{ineq:left}\n\\end{eqnarray}\n\nBased on (\\ref{ineq:right}) and (\\ref{ineq:left}), we can get \n\\begin{eqnarray}\n\\max_{\\lambda_u} {\\|\\sum_{u=1}^{U}\\lambda_u \\mathbf{z}_u\\|_1}= \\max_u\\{\\|\\mathbf{z}_u\\|_1\\}, u=1,2,\\cdots,U.\n\\end{eqnarray}\n\\end{proof}\n\nAs regards the first method, $\\lambda_u$ should be limited by $\\lambda_u\\geq 0$ and $\\sum_{u=1}^{U}\\lambda_u=1$. Based on this fact, Theorem 3 implies that $\\bm\\lambda$ has only one nonzero element, i.e.,1, and the other elements are zeros, which means that the elements of $\\bm \\lambda$ should be limited to $\\sum_{u=1}^{U}\\lambda_u=1$ and $\\lambda_u\\in\\{0, 1\\}$. Without loss of generality, assume $\\mathbf{z}_1,\\mathbf{z}_2,\\cdots, \\mathbf{z}_U$ are normalized, i.e., $\\|\\mathbf{z}_1\\|_2, \\|\\mathbf{z}_2\\|_2, \\cdots,\\|\\mathbf{z}_U\\|_2$ are equal to 1, then we get\n\\begin{eqnarray}\n\t\\|\\mathbf{Z}\\bm \\lambda\\|_2 = 1.\n\\end{eqnarray}\nTherefore, the optimization problem (\\ref{opt:SNR1}) is equivalent to \n\\begin{eqnarray}\n\t\\max_{\\bm \\lambda}\\, \\|\\mathbf{Z}\\bm{\\lambda}\\|_1^2\\label{opt:SNR2}\n\\end{eqnarray}\nWithout loss of generality, we assume $\\|\\mathbf{z}_1\\|_1\\geq \\|\\mathbf{z}_2\\|_1\\geq \\cdots,\\|\\mathbf{z}_U\\|_1$. Again, based on Theorem 3, the optimal solution to (\\ref{opt:SNR2}) is\n\n\n\\begin{equation}\n\t\\lambda_u=\\left\\{\\begin{array}{ll}\n1, &\\mathrm{if}\\,\\, u=1\\\\\n0, &\\mathrm{otherwise}.\\\\\n\\end{array}\n\\right.\n\\end{equation} \n\n\nLet $\\hat{\\mathbf{z}}=\\mathbf{z}_1$, then $\\mathbf{p}$ and $\\mathbf{w}$ can be obtained from (\\ref{eq:p}) and (\\ref{eq:w}).\n\n\n\\begin{algorithm}[htb]\n\\setstretch{1.5}\n\\caption{Basis selection (BS) method in null space:}\n\\label{alg:Framwork}\n\\begin{algorithmic}[1]\n\\STATE $\\mathbf{z}_1, \\mathbf{z}_2, \\cdots,\\mathbf{z}_U \\in \\mathrm{Null}(\\mathbf{E})$ are the basis vectors.\n\\STATE Compute $\\|\\mathbf{z}_1\\|_1, \\|\\mathbf{z}_2\\|_1, \\cdots,\\|\\mathbf{z}_U\\|_1$.\n\\STATE if $\\|\\mathbf{z}_u\\|_1$ is the largest one, choose $\\mathbf{z}_u$.\n\\end{algorithmic}\n\\end{algorithm}\n\n\\subsection{Second Algorithm for SNR}\nAlthough the first proposed algorithm has a low computational complexity, it has a very limited performance because the elements of $\\bm \\lambda$ are restricted to the set $\\{0,1\\}$. In order to improve the performance, here we proposed a second method -- termed a Heuristic Coordinated Descent (HCD) method where the binary constraint on $\\bm \\lambda$ is removed and $\\bm \\lambda\\in \\mathbb{C}^U$. HCD can be viewed as a relatively effective method to deal with the non-convex optimization problem with a much larger constraint set. \n\nGenerally speaking, the Coordinate Descent (CD) algorithms\\cite{wright2015coordinate} are iterative methods. The most common CD algorithm is by fixing other elements of the variable vector and obtaining the new iteration point by minimizing (maximizing) the objective function with respect to a single element of variable vector. In other words, when an optimization problem was considered, i.e.,\n\\begin{equation}\n\t\\min_{\\bm x\\in \\mathbb{C}^N} f(\\bm x),\n\\end{equation}\nthen the CD algorithm starts with some initial vector $\\bm{x}^{(0)}=(x_0^{(0)},x_1^{(0)},\\cdots,x_{N-1}^{(0)})$ and repeats the following iteration\n\\begin{eqnarray}\n\t\\begin{aligned}\nx_{0}^{(k)} & = \\underset{x_{0}}{\\operatorname{argmin}} f\\left(x_{0},\\, x_{1}^{(k-1)},\\, x_{2}^{(k-1)},\\, \\cdots,\\, x_{N-1}^{(k-1)}\\right), \\\\\nx_{1}^{(k)} & = \\underset{x_{1}}{\\operatorname{argmin}} f\\left(x_{0}^{(k)},\\, x_{1},\\, x_{2}^{(k-1)},\\, \\cdots,\\, x_{N-1}^{(k-1)}\\right), \\\\\nx_{2}^{(k)} & = \\underset{x_{2}}{\\operatorname{argmin}} f\\left(x_{0}^{(k)},\\, x_{1}^{(k)},\\, x_{2}, \\cdots,\\, x_{N-1}^{(k-1)}\\right), \\\\\n& \\vdots \\\\\nx_{N-1}^{(k)} & =\\underset{x_{N-1}}{\\operatorname{argmin}} f\\left(x_{0}^{(k)}, x_{1}^{(k)}, x_{2}^{(k)}, \\cdots,\\, x_{N-1}\\right),\n\\end{aligned}\\label{proc:cd1}\n\\end{eqnarray}\nwhere $k = 1,2,3,\\cdots$.\n\nSince the objective value of (\\ref{opt:SNR1}) is always no less than 0, maximizing it is equivalent to minimizing the reciprocal, i.e.,\n\\begin{eqnarray}\n\t\\min_{\\bm \\lambda}\\, \\frac{\\|\\mathbf{Z}\\bm{\\lambda}\\|_2^2}{\\|\\mathbf{Z}\\bm{\\lambda}\\|_1^2}.\\label{opt:SNR3}\n\\end{eqnarray}\n\n In the optimization problem (\\ref{opt:SNR3}), the objective function is still a non-convex function, so that it is difficult for us to obtain the global optimal solution. Based on these difficulties, a heuristic Coordinated Descent (HCD) is proposed. \n \n The algorithm is based on the CD algorithm. It also starts with some initial vector $\\bm{\\lambda}^{(0)}=(\\lambda_1^{(0)},\\lambda_2^{(0)},\\cdots,\\lambda_n^{(0)})$ and then repeats the procedure as (\\ref{proc:cd1}). However, the difference between the HCD and the general CD is that the HCD will revert to the $(k-1)$-th state if the objective value of $k$-th state is higher than the one from the previous iteration. For details, the following formula shows the $k$-th itertation of $u$-th element: \n\\begin{eqnarray}\n\\begin{aligned}\n\\lambda_{u}^{(k)} & = \\underset{\\lambda_{u}}{\\operatorname{argmin}}\\,\\, f\\left(\\lambda_{1}^{(k)}, \\lambda_{2}^{(k)}, \\cdots,\\lambda_{u-1}^{(k)},\\lambda_{u},\\lambda_{u+1}^{(k)}, \\cdots, \\lambda_{U}^{(k)}\\right), \\\\\n\\end{aligned}\\label{proc:cd1}\n\\end{eqnarray}\n and then $\\lambda_u^{(k)}$ will revert to $\\lambda_u^{(k-1)}$ if \n \\begin{eqnarray}\n \\begin{split}\n &f\\left(\\lambda_{1}^{(k)}, \\lambda_{2}^{(k)}, \\cdots,\\lambda_{u-1}^{(k)},\\lambda_{u}^{(k)},\\lambda_{u+1}^{(k)}, \\cdots, \\lambda_{U}^{(k)}\\right)\\\\\n &\\geq f\\left(\\lambda_{1}^{(k)}, \\lambda_{2}^{(k)}, \\cdots,\\lambda_{u-1}^{(k-1)},\\lambda_{u}^{(k)},\\lambda_{u+1}^{(k)}, \\cdots, \\lambda_{U}^{(k)}\\right).\\\\\\label{ineq:g}\n \\end{split}\n \\end{eqnarray}\n The second difference is that HCD generates many initial vectors. For every initial vector, we repeat the iteration procedure and obtain a solution when it satisfies the stop criteria. For all these initial vectors, we have many solutions from which we can choose the best solution that has the smallest objective value. \n The algorithm is summarized in algorithm 3. \n \n\\begin{algorithm}[htb]\n\\setstretch{1.5}\n\\caption{Heuristic Coordinated Descent (HCD) in null space:}\n\\label{alg:Framwork}\n\\begin{algorithmic}[]\n\\STATE for $i = 1: I$\\\\\n\\STATE \\quad randomized initial vectors $\\bm \\lambda^{(0)}$ \\\\\n\\STATE \\quad for $k = 1:K$\\\\\n\\STATE \\quad \\quad for $u = 1:U$\\\\\n\\quad\\quad \\quad Compute $\\lambda_{u}^{(k)}$ as (\\ref{proc:cd1})\\\\\n\\quad\\quad \\quad if (\\ref{ineq:g}) satisfies, then $\\lambda_{u}^{k-1} = \\lambda_{u}^{k-1}$.\\\\\n\\quad\\quad \\quad if $\\|\\bm \\lambda^{(k)}-\\bm \\lambda^{(k-1)} \\|_2\\leq \\varepsilon$; $\\hat{\\bm \\lambda}_i = \\bm \\lambda^{(k)}$; end\\\\\n\\quad\\quad end $u$\\\\\n\\quad end $k$\\\\\n\\STATE end $i$\\\\\n\\STATE choose $\\hat{\\bm \\lambda_i}$ as the best $\\bm \\lambda$ such that (\\ref{opt:SNR3}) minimized.\n\\end{algorithmic}\n\\end{algorithm}\n \n\n\n\n\n\n\n\n\\section{Windowing for Fully Polarimetric Radar Systems}\n\nThe fully polarimetric radar systems can transmit and receive on two orthogonal polarizations at the same time. The use of two orthogonal polarizations increases the degrees of freedom and can result in significant improvement in detection performance.\n\nTwo pulse trains $Z_{VP}(t)$ and $Z_{HP}(t)$, transmitted simultaneously from vertical polarization and horizontal polarization, are written by\n\\begin{eqnarray}\n\tZ_{VP}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}\\left[\\left(1+p_{n}\\right) s_{x}(t-n T)-\\left(1-p_{n}\\right) \\tilde{s}_{y}(t-n T)\\right],\n\\end{eqnarray}\nand\n\\begin{eqnarray}\n\tZ_{HP}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}\\left[\\left(1-p_{n}\\right) \\tilde{s}_{x}(t-n T)+\\left(1+p_{n}\\right) s_{y}(t-n T)\\right],\n\\end{eqnarray}\nwhere $\\tilde{\\cdot}$ means reversal, i.e.,\n\\begin{eqnarray}\n\t\\tilde{s}_x(t)=\\sum_{l=0}^{L-1}x[L-1-l]u(t-lT_c),\\\\ \\tilde{s}_y(t)=\\sum_{l=0}^{L-1}y[L-1-l]u(t-lT_c).\n\\end{eqnarray}\nIn the proposed transmission mode, two orthogonal polarizations have different waveforms in a PRI. For example, if $s_x(t)$ (or $-\\tilde{s}_{y}(t)$) is transmitted from vertical polarization, then $s_y(t)$ (or $\\tilde{s}_{x}(t)$) is transmitted from horizontal polarization. Besides, this mode also contains the famous Alamouti time-space coding when two different waveforms are transmitted in the adjoint two PRIs . For example, in the $n$-th PRI, horizontal polarization and horizontal polarization transmit $s_x(t)$ and $s_y(t)$ respectively; in the $(n+1)$-th PRI, vertical polarization and horizontal polarization transmit $s_y(t)$ and $\\tilde{s}_x(t)$ respectively, which constitudes the famous Alamouti matrix\n\\begin{equation}\n\t\\left[\\begin{matrix}\ns_x(t)\t& -\\tilde{s}_y(t)\\\\\ns_y(t) & \\tilde{s}_x(t)\n\\end{matrix}\\right],\n\\end{equation}\nwhich can eliminate polarization interference when the target is static. For a Doppler shift resulting in polarization interference, a moving target is considered with a Doppler shift $\\omega$ in Hz.\n\nFor the vertical polarization antenna, the returned signal is given by\n\\begin{eqnarray}\n\tR_V(t) = (h_{VV}Z_{VP}(t)+h_{VH}Z_{HP}(t))e^{j \\omega t}.\\label{eq:RV}\n\\end{eqnarray}\nAlso, similarly, for the horizental polarization antenna, the returned signal is given by\n\\begin{eqnarray}\n\tR_H(t) = (h_{HV}Z_{VP}(t)+h_{HH}Z_{HP}(t))e^{j \\omega t},\\label{eq:RH}\n\\end{eqnarray}\nwhere $h_{VH}$ denotes the scattering coefficient into the vertical polarization channel from a horizontally polarized incident field\\cite{pezeshki2008doppler}. Note that $h_{VV}$, $h_{VH}$, $h_{HV}$, $h_{HH}$ constitute a scattering matrix \\begin{equation}\n\\mathbf{H}=\\left[\\begin{matrix}\nh_{VV} & h_{VH}\\\\\nh_{HV} & h_{HH}\n\\end{matrix}\t\n\\right].\\label{eq:output1}\n\\end{equation}\n\n\n\nAt the receiver with two polarization antennas, each antenna has two responses of matched filters, i.e., $Z_{VW}^*(-t)$ and $Z_{HW}^*(-t)$, where\n\\begin{eqnarray}\n\\begin{split}\n\tZ_{VW}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}w_n &\\left[\\left(1+p_{n}\\right) s_{x}(t-n T)\\right.\\\\\n\t &\\left.-\\left(1-p_{n}\\right) \\tilde{s}_{y}(t-n T)\\right],\\label{eq:ZVW}\n\\end{split}\n\\end{eqnarray}\nand\n\\begin{eqnarray}\n\\begin{split}\n\tZ_{HW}(t)=\\frac{1}{2} \\sum_{n=0}^{N-1}w_n &\\left[\\left(1-p_{n}\\right) \\tilde{s}_{x}(t-n T)\\right.\\\\\n\t&\\left.+\\left(1+p_{n}\\right) s_{y}(t-n T)\\right].\\label{eq:ZHW}\n\t\\end{split}\n\\end{eqnarray}\n\nThe returned signals go through the matched filters then the outputs of the matched filters are given by\n\\begin{equation}\n\\mathbf{U}(\\tau)=\\left[\\begin{matrix}\n\\mathbf{RZ}_{11}(\\tau) & \\mathbf{RZ}_{12}(\\tau)\\\\\n\\mathbf{RZ}_{21}(\\tau) & \\mathbf{RZ}_{22}(\\tau)\n\\end{matrix}\t\n\\right]\\label{eq:output1}\n\\end{equation}\nwhere\n\\begin{eqnarray}\n\t\\mathbf{RZ}_{11}(\\tau)=\\int_{-\\infty}^{+\\infty} R_V(t) Z_{HW}^{*}(t-\\tau) d t,\\label{eq:RZ11}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n\t\\mathbf{RZ}_{12}(\\tau)=\\int_{-\\infty}^{+\\infty} R_V(t) Z_{VW}^{*}(t-\\tau) d t,\\label{eq:RZ12}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n\t\\mathbf{RZ}_{21}(\\tau)=\\int_{-\\infty}^{+\\infty} R_H(t) Z_{HW}^{*}(t-\\tau) d t,\\label{eq:RZ21}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n\t\\mathbf{RZ}_{22}(\\tau)=\\int_{-\\infty}^{+\\infty} R_H(t) Z_{VW}^{*}(t-\\tau) d t.\\label{eq:RZ22}\n\\end{eqnarray}\n\n\nAfter substituting $R_V(t)$ of (\\ref{eq:RV}) into (\\ref{eq:RZ11}) and (\\ref{eq:RZ12}), and bringing $R_H(t)$ of (\\ref{eq:RH}) into (\\ref{eq:RZ21}) and (\\ref{eq:RZ22}), then we get the following proposition.\n\n\\emph{Proposition 3:}\n\tThe output matrix $\\mathbf{U}(\\tau)$ in (\\ref{eq:output1}) can be transformed into\n\t\\begin{equation}\n\\mathbf{U}(\\tau)=\n\\left[\\begin{matrix}\nh_{VV} & h_{VH}\\\\\nh_{HV} & h_{HH}\n\\end{matrix}\t\n\\right]\n\\left[\\begin{matrix}\n\\chi_{VP,VW}(\\tau,\\omega) & \\chi_{VP,HW}(\\tau,\\omega)\\\\\n\\chi_{HP,VW}(\\tau,\\omega) & \\chi_{HP,HW}(\\tau,\\omega)\n\\end{matrix}\t\n\\right].\\label{eq:output2}\n\\end{equation}\t\n\nIn (\\ref{eq:output2}), the cross ambiguity function $\\chi_{a,b}(\\tau,\\omega)$ is defined as\n\\begin{eqnarray}\n\t\\chi_{a,b}(\\tau, \\omega)=\\int_{-\\infty}^{+\\infty} Z_{a}(t) Z_{b}^{*}(t-\\tau) \\mathrm{e}^{j \\omega t} d t,\n\\end{eqnarray}\nwhere $a = VP \\,\\, \\mathrm{or} \\,\\, HP$ and $b = VW\\,\\, \\mathrm{or}\\,\\, HW$.\n\nBased on the transform from (\\ref{eq:chiPW}) to (\\ref{eq:APW}), the discrete cross ambiguity function $\\chi_{VP,VW}(k,\\theta)$ is given by\n\\begin{equation}\n\t\\begin{aligned} \\mathcal{A}_{VP, VW}(k, \\theta) &=\\frac{1}{2}\\left[C_{x}(k)+C_{y}(k)\\right] \\sum_{n=0}^{N-1} w_n e^{j n \\theta} \\\\ &+\\frac{1}{2}\\left[C_{x}(k)-C_{y}(k)\\right] \\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}. \\end{aligned}\\label{eq:AVPVW}\n\\end{equation}\n\nSimilarily, the discrete cross ambiguity function $\\chi_{VP,VW}(k,\\theta)$ is given by\n\\begin{equation}\n\t\\begin{aligned} \\mathcal{A}_{HP, HW}(k, \\theta) &=\\frac{1}{2}\\left[C_{x}(k)+C_{y}(k)\\right] \\sum_{n=0}^{N-1} w_n e^{j n \\theta} \\\\ &-\\frac{1}{2}\\left[C_{x}(k)-C_{y}(k)\\right] \\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}.\\end{aligned}\\label{eq:AHPHW}\n\\end{equation}\n\nAlso, the discrete cross ambiguity function $\\chi_{VP,HW}(k,\\theta)$ is given by\n\\begin{eqnarray}\n\t&\\mathcal{A}_{VP, HW}(k, \\theta)=\\frac{1}{2}\\left[C_{xy}(k)-C_{\\tilde{y}\\tilde{x}}(k)\\right] \\displaystyle\\sum_{n=0}^{N-1} w_n e^{j n \\theta} \\nonumber\\\\\n\t&\\qquad\\qquad\\qquad\\quad+\\frac{1}{2}\\left[C_{xy}(k)+C_{\\tilde{y}\\tilde{x}}(k)\\right] \\displaystyle\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}\\\\\n\t&\\qquad\\quad= C_{xy}(k)\t\\displaystyle\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}, \\label{AVPHW}\t\t\t\n\\end{eqnarray}\nand the discrete cross ambiguity function $\\chi_{HP,VW}(k,\\theta)$ is given by\n\\begin{eqnarray}\n\t&\\mathcal{A}_{HP, VW}(k, \\theta)=\\frac{1}{2}\\left[-C_{\\tilde{x}\\tilde{y}}(k)+C_{yx}(k)\\right] \\displaystyle\\sum_{n=0}^{N-1} w_n e^{j n \\theta} \\nonumber\\\\\n\t&\\qquad\\qquad\\qquad\\quad+\\frac{1}{2}\\left[C_{\\tilde{x}\\tilde{y}}(k)+C_{yx}(k)\\right] \\displaystyle\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}\\\\\n\t&\\qquad\\quad= C_{yx}(k)\t\\displaystyle\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}. \\label{eq:AHPVW}\t\t\t\n\\end{eqnarray}\n\n\\emph{Proposition 4:}\n\tAfter discretization, the output matrix $\\mathbf{U}(\\tau)$ in (\\ref{eq:output2}) can be transformed into\n\t\\begin{equation}\n\\mathbf{U}(\\tau)=\n\\left[\\begin{matrix}\nh_{VV} & h_{VH}\\\\\nh_{HV} & h_{HH}\n\\end{matrix}\t\n\\right]\n\\left[\\begin{matrix}\n\\mathcal{A}_{VP,VW}(k,\\theta) & \\mathcal{A}_{VP,HW}(k,\\theta)\\\\\n\\mathcal{A}_{HP,VW}(k,\\theta) & \\mathcal{A}_{HP,HW}(k,\\theta)\n\\end{matrix}\t\n\\right].\\label{eq:output3}\n\\end{equation}\t\n\n\nFrom Proposition 4, to obtain the scattering coefficients, two conditions must be satisfied:\n\\begin{itemize}\n\t\\item the range sidelobes of $\\mathcal{A}_{VP,VW}(k,\\theta) $ and $\\mathcal{A}_{HP,HW}(k,\\theta)$ should be reduced to zero.\n\t\\item $\\mathcal{A}_{VP,HW}(k,\\theta)$ and $\\mathcal{A}_{HP,VW}(k,\\theta)$ should be equal to zero.\n\\end{itemize}\n\n\nThe range sidelobes of $\\mathcal{A}_{VP,VW}(k,\\theta) $ and $\\mathcal{A}_{HP,HW}(k,\\theta)$ arise from the second terms of (\\ref{eq:AVPVW}) and (\\ref{eq:AHPHW}) , i.e.,\n\\begin{eqnarray}\n\t\\frac{1}{2}\\left[C_{x}(k)-C_{y}(k)\\right] \\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}.\n\\end{eqnarray}\nBesides, $\\mathcal{A}_{VP,HW}(k,\\theta)$ and $\\mathcal{A}_{HP,VW}(k,\\theta)$ depend on\n\\begin{eqnarray}\n\tC_{xy}(k)\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta} \\,\\,\\mathrm{or}\\,\\,\n\tC_{yx}(k)\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}.\n\\end{eqnarray}\nIn summary, $\\mathcal{A}_{VP,VW}(k,\\theta) $, $\\mathcal{A}_{HP,HW}(k,\\theta)$, $\\mathcal{A}_{VP,HW}(k,\\theta)$ and $\\mathcal{A}_{HP,VW}(k,\\theta)$ are determined by\n\\begin{eqnarray}\n\t\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}.\n\\end{eqnarray}\nTherefore, to obtain the scattering coefficients, the following equation must hold:\n\\begin{eqnarray}\n\t\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}=0, \\quad \\mathrm{for\\,\\, all\\,}\\theta \\in \\Theta.\n\\end{eqnarray}\n\\emph{Theorem 4:}\nThe range sidelobes of $\\mathcal{A}_{VP,VW}(k,\\theta)$ are vanished and the value of $\\mathcal{A}_{VP, HW}(k, \\theta)$ is zero if and only if\n\t\\begin{eqnarray}\n\t\t\\sum_{n=0}^{N-1} p_{n} w_n e^{j n \\theta}=0, \\quad \\mathrm{for\\,\\, all\\,}\\theta \\in \\Theta.\\label{eq:obj2}\n\t\\end{eqnarray}\n\n\n\n\nSince (\\ref{eq:obj2}) is the same as (\\ref{eq:obj1}), then to solve (\\ref{eq:obj1}) or (\\ref{eq:obj2}) to obtain $\\mathbf{p}$ and $\\mathbf{w}$, we can use Algorithm 1.\n\n\n\\section{Numerical Results and Discussions}\nIn this section, numerical examples are given to verify the results in Sections III and IV. Also, the proposed null space (NS) Doppler resilient scheme and the binomial design (BD) scheme are verified and discussed.\n\n\\emph{Remark 4:}\n\tIn some figures, \"Amb fcn\" is the abbreviation of the ambiguity function.\n\n\n\\subsection{Doppler Resilience in an Interested Doppler Interval for a Single Antenna System}\nAt first, to show the performance which flexibly suppresses the range sidelobes in the Doppler interval of interest based on the proposed null space algorithm, the specified Doppler interval of interest is given by $\\theta \\in [0,2]$. In each continuous Doppler interval, the sampling resolution is $D_I\/(M-1)$, where $D_I=2$ and $M=N-1$. Besides, the number of pulses is $N = 48$. Based on the null space algorithm (algorithm 1), matrix $\\mathbf{E}$ is generated as (\\ref{eq:E}), thus the null space of $\\mathbf{E}$ can be calculated, and $\\mathbf{p}$, $\\mathbf{w}$ are also easily obtained based on Algorithm 1. Besides, the Golay pair is length-64 and is given by\n\\begin{eqnarray}\n\\begin{split}\n&\t\\mathbf{x} = [ 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1,\\\\\n&\\quad\\quad 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, \\\\\n&\\quad\\quad 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, \\\\\n&\\quad\\quad -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1 ],\n\\end{split}\\label{eq:GCPx}\n\\end{eqnarray}\n\n\\begin{eqnarray}\n\\begin{split}\n &\t \\mathbf{y} = [ 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, \\\\\n &\\quad\\quad\t 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, \\\\\n &\\quad\\quad\t 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, \\\\\n &\\quad\\quad\t -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1 ].\n\\end{split}\\label{eq:GCPy}\n\\end{eqnarray}\n\n\n Fig. \\ref{fig1} shows the value of $p_n$ along the PRI $n$ and the modulus of coefficients along the PRI $n$. Then the complementary transmission waveform $Z_P(t)$ in (\\ref{eq:Zp}) is determined by $p_n$, and $Z_W(t)$ in (\\ref{eq:Zw}) is determined by $p_n$ and $w_n$.\n \n\nFig. \\ref{fig2} shows two ambiguity functions (\\ref{eq:APW}) under $\\theta \\in [0,2]$ with $N=48$ based on algorithm 1 and \\cite{chi2009range}, respectively. In Fig. \\ref{fig2}(a) which is based on Algorithm 1, the sidelobes within the Doppler interval of interest are obviously lower than the sidelobes outside the Doppler interval of interest. Moreover, in Fig. \\ref{fig2}(a), although $[0,2]$ is considerd, the range sidelobes are still very low within $[0,2.4]$. In Fig. \\ref{fig2}(b), based on the oversampled-PTM sequence in \\cite{chi2009range}, the ambiguity function has higer range sidelobes than those shown in Fig. \\ref{fig2}(a).\n\n\\begin{figure}[htbp]\n\\centering\n\\subfigure[The value of $p_n$ ]{\n\\begin{minipage}{7cm}\n\\centering\n\\includegraphics[width=1\\linewidth]{pic\/fig1a.eps}\\\\\n\\end{minipage}\n}\n\\subfigure[The modulus of the coefficients of the receiver filter]{\n\\begin{minipage}{7cm}\n\\centering\n\\includegraphics[width=1\\linewidth]{pic\/fig1b.eps}\n\\end{minipage}\n}\n\\caption{The value of $p_n$ along the PRI $n$ and the modulus of $w_n$ along the PRI $n$.}\n\\label{fig1}\n\\end{figure}\n\n\n\\begin{figure}[htbp]\n\\centering\n\\subfigure[AF for the Doppler interval of interest based on Algorithm 1.]{\n\\begin{minipage}{8cm}\n\\centering\n\\includegraphics[width=8cm]{pic\/fig2a.eps}\\\\\n\\end{minipage}\n}\n\\subfigure[AF for the Doppler interval of interest based on \\cite{chi2009range} and\\cite{chi2010complementary}.]{\n\\begin{minipage}{8cm}\n\\centering\n\\includegraphics[width=8cm]{pic\/fig2b.eps}\n\\end{minipage}\n}\n\\caption{Comparison between (a) AF for the Doppler interval of interest based on algorithm 1, and (b)AF for the Doppler interval of interest based on \\cite{chi2009range} and \\cite{chi2010complementary}.}\n\\label{fig2}\n\\end{figure}\n\n\n\n\n\\subsection{Doppler Resilience in the Overall Doppler Interval for a Single Antenna System}\n\nWe will now discuss the Doppler resilience in the overall Doppler interval $[0,\\pi)$. \n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/gHHN50.eps}\n}\n\\caption{ AF for overall Doppler interval $[0,\\pi)$ based on Algorithm 1.}\n\\label{fig3}\n\\end{figure}\n\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/BigHHN50.eps}\n}\n\\caption{AF for all Doppler interval $[0,\\pi)$ based on the binomial design.}\n\\label{pic:BigHHN50}\n\\end{figure}\n\nFig. \\ref{fig3} shows an ambiguity function (\\ref{eq:APW}) in the overall Doppler area $ [0,\\pi]$ with $N=48$ based on Algorithm 1. For the whole Doppler area, the range sidelobes are lower than -90dB which is an ultra low level. \n\nFig. \\ref{pic:BigHHN50} is an ambiguity function (\\ref{eq:APW}) in the overall Doppler area $ [0,\\pi]$ with $N=48$ based on Binomial design, which is a baseline of Fig. \\ref{fig3}. In Fig. \\ref{pic:BigHHN50}, the range sidelobes gradually increase when the Doppler shift is larger than about 2.2 rad.\n\nFrom Fig. \\ref{fig3} and Fig. \\ref{pic:BigHHN50}, it is obvious that the Doppler resilience based on the proposed method is significantly better than that of the BD method in the overall Doppler interval $ [0,\\pi]$.\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/APW.eps}\n}\n\\caption{Doppler profile.}\n\\label{pic:APW}\n\\end{figure}\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/PRSL.eps}\n}\n\\caption{Peak range sidelobe level. }\n\\label{pic:PRSL}\n\\end{figure}\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/SNRfig.eps}\n}\n\\caption{$\\|\\mathbf{w}\\|_1^2\/\\|\\mathbf{w}\\|_2^2$ versus the number of pulses $N$. }\n\\label{pic:SNR}\n\\end{figure}\n\n\nFig. \\ref{pic:APW} and Fig. \\ref{pic:PRSL} show the Doppler profile and peak range sidelobe level (PRSL), respectively. From Fig. \\ref{pic:APW}, it is observed that the null space (NS) method keeps the mainlobes at a high level but the BD method gradually loses the mainlobe when the Doppler shift increases. From Fig. \\ref{pic:PRSL}, BD also has low sidelobes as well as NS when the Doppler shift is not very big, but when the Doppler increases to a high value, the BD has a high sidelobe level. Besides, from Fig. \\ref{pic:PRSL}, the NS has an overall low sidelobe level compared with BD. Moreover, the two figures indicate that the NS method has better Doppler resilience in the overall Doppler interval $[0,\\pi]$.\n\nFig. \\ref{pic:SNR} shows that the value of $\\|\\mathbf{w}\\|_1^2\/\\|\\mathbf{w}\\|_2^2$ increases when the pulse number $N$ increases. It is obvious that the proposed two methods have a significantly higher SNR than BD. Besides, for the two proposed methods, the heuristic coordinated descent (HCD) slightly outperforms basis selection (BS).\n\n\\subsection{Doppler Resilience for Fully Polarimetric Radar Systems}\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/AFHVin.eps}\n}\n\\caption{AF for the intersted Doppler interval about polarimetry interference based on NS.}\n\\label{pic:AFHVin}\n\\end{figure}\n\n\n\nBased on the analysis in section IV, the transmission scheme is proposed in (\\ref{eq:ZVW}) and (\\ref{eq:ZHW}). For the vertical polarization antenna (V-antenna), the candidate Golay waveform is $s_x(t)$ and $-\\tilde{s}_y(t)$. For the horizontal polarization antenna (H-antenna), the candidate Golay waveforms are $s_y(t)$ and $\\tilde{s}_x(t)$. If $s_x(t)$ is transmitted at the V-antenna, then at the same time, $s_y(t)$ should be transmitted. Similarly, if $-\\tilde{s}_y(t)$ is transmitted at the V-antenna, then at the same time, $\\tilde{s}_x(t)$ should be transmitted. It is noted that here the pulse number $N$ is still 48, and the Golay pair is shown in (\\ref{eq:GCPx}) and (\\ref{eq:GCPy}). \n\n\n\n\nTo verify the flexible Doppler resilience in fully polarimetric radar systems, the Doppler area is chosen as before, i.e, $\\theta \\in [0,2]$. $\\mathbf{p}$ and $\\mathbf{w}$ are generated via the null space method. After plotting the ambiguity functions $\\mathcal{A}_{VP, VW}(k, \\theta)$ and $\\mathcal{A}_{HP, HW}(k, \\theta)$, it is shown that they have the same shape as Fig. \\ref{fig2}. Besides, the ambiguity functions $\\mathcal{A}_{VP, HW}(k, \\theta)$ and $\\mathcal{A}_{HP, VW}(k, \\theta)$ also have the same shape (shown in Fig. \\ref{pic:AFHVin}). From Fig. \\ref{pic:AFHVin}, it is observed the values of $\\mathcal{A}_{VP, HW}(k, \\theta)$ or $\\mathcal{A}_{HP, VW}(k, \\theta)$ in dB are of a very low level (no more than -90dB) in the interested Doppler area, i.e., $\\theta\\in [0,2]$. In summary, the range sidelobes and polarimetry interferences are flexibly controlled in the interested Doppler area.\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/gHVN50.eps}\n}\n\\caption{AF for the overall Doppler interval about polarimetry interference based on NS.}\n\\label{pic:gHVN50}\n\\end{figure}\n\n\\begin{figure}[htbp]\n\\centering\n{\n\\includegraphics[width=0.8\\columnwidth]{pic\/BigHVN50.eps}\n}\n\\caption{ AF for the overall Doppler interval about polarimetry interference based on BD.}\n\\label{pic:BigHVN50}\n\\end{figure}\n\nNow, the Doppler resilience in the overall Doppler area $[0,\\pi]$ is also investigated. After plotting the ambiguity functions $\\mathcal{A}_{VP, VW}(k, \\theta)$ and $\\mathcal{A}_{HP, HW}(k, \\theta)$, it is shown that they have the same shape as Fig. \\ref{fig3}. Besides, the ambiguity functions $\\mathcal{A}_{VP, HW}(k, \\theta)$ and $\\mathcal{A}_{HP, VW}(k, \\theta)$ also have the same shape (shown in Fig. \\ref{pic:gHVN50}). From Fig. \\ref{pic:gHVN50}, it is observed the values of $\\mathcal{A}_{VP, HW}(k, \\theta)$ or $\\mathcal{A}_{HP, VW}(k, \\theta)$ in dB are no more than -90dB, which means that polarimetry interferences are clearly vanished in overall Doppler area $[0,\\pi]$.\n\nThirdly, Fig. \\ref{pic:BigHVN50} is a cross ambiguity function generated by BD. It also has excellent low function values, but the values increase when the Doppler shift is bigger than 1 rad, so that it has worse polarimetry interferences as the Doppler increases. \n\n \\subsection{Discussion}\n Based on the above numerical examples, in which the Doppler resilience is good no matter what the Doppler interval of interest or the overall Doppler interval $[0,\\pi)$, one may ask why do we consider the Doppler interval of interest. In fact, a tradeoff exists between the number of pulses $N$ and the Doppler interval. \n \n If the number of pulses $N$ is too small or the Doppler interval is too big, then $\\mathbf{E}$ is a tall matrix which may have full column rank for which the linear system is inconsistent\\footnote{It is easy to verify that $\\mathbf{E}$ is full rank if $M>N$ and $\\theta_{m_1}\\not\\equiv\\theta_{m_2}(\\mathrm{mod}2\\pi)$, where $m_1,m_2\\in \\{0,1,\\cdots,M-1\\}$ and $m_1\\neq m_2$. }, so that Algorithm 1 cannot find any solution of the linear system, i.e., $\\mathbf{Null}(\\mathbf{E})=\\varnothing$. Therefore, It makes sense to consider the Doppler interval of interest. \n \n Moreover. if the Doppler interval of interest $[0,D_I]$ is given, then the range sidelobes can be suppressed better if the number $M$ of the discrete Doppler shifts $\\theta_m \\in [0,D_I]$ increases. However, the number $M$ of the discrete Doppler shifts is limited by the number of pulses $N$. This constraint is to ensure the existence of a solution for the addressed linear equations. According to the theory of solutons of linear equations, $\\mathbf{Ez}=\\mathbf{0}$ has infinite nontrivial solutions if $M14.7$,\n while LBLs have $log\\nu_{peak}<14.7$. In addition, \\citet{Pado95} found that LBLs and HBLs can also be divided by using the ratio of X-ray flux at 1 keV (in units of $erg$ $cm^{-2}$ $s^{-1}$) to 5 GHz radio flux density (in units of Janskys). The criterion is $f_{x}\/f_{r}\\sim10^{-11}$, corresponding to the broad\nband spectral index (from radio 5 GHz to X-ray 1 keV) $\\alpha_{rx}\\simeq0.75$.\nHBLs have the broad band spectral index of $\\alpha_{rx}\\leq0.75$, and LBLs have the spectral index of $\\alpha_{rx}> 0.75$ \\citep{Giom95,Ma07,Mei02,Urry95}. For two different subclasses of BL\nLacs objects, the SEDs have been investigated by a number of authors\n\\citep[e.g.,][]{Bao08,Chen06,Pado95,Giom90,Niep06}. \\citet{Pado95}\nand \\citet{Giom90} found that two subclasses occupy different regions on\nthe $\\alpha_{ro}$ - $\\alpha_{ox}$ plane. \\citet{Pado95} also found\nthere exist the correlations between the minimum soft X-ray flux and\nthe radio flux, and also the correlations between radio and optical fluxes for the\nsubsample of HBLs, but not for that of LBLs. \\citet{Niep06} found\nthat there is a negative correlation between the luminosity and\nthe synchrotron peak frequency $\\nu_{peak}$ at radio and optical band,\nwhereas the correlation turns slightly positive in X-ray\n\\citep{Niep06}. \\citet{Fan12} and \\citet{Lyu14} found that HBLs have different properties from LBLs. \\citet{Yan14} found that the one-zone synchrotron self-Compton (SSC) model can successfully fit the SEDs of HBLs, but fails to explain the SEDs of LBLs. In addition, \\citet{Bao08} found that two subclasses of BL Lacs objects are unified.\n\nBL Lacs objects and FSRQs are grouped together under the\ndenomination of blazars, which eliminates the somewhat ambiguous\nissue of strength of the emission lines as a classification\ncriterion. However, there are some differences in the individual\nemission properties among different blazar subclasses. The\nrelationship among different kinds of balzars can promote our\nperception of the fundamental properties of blazars. Therefore, it\nis imperative to investigate the connection among FSRQs, LBLs, and\nHBLs.\n\nThe relationship between of BL Lacs objects and FSRQs has been\ndiscussed by a number of authors\n\\citep[e.g.,][]{Coma97,Foss98,Ghis98,Ghis09,Li10,Samb96,Xie01,Xie04a,Xie04b,Xie06,Xie07,Xie08,Zhen07},\nwho assembled the SED of many radio, X-ray, and $\\gamma$-ray\nselected blazars. \\citet{Foss98} studied the SEDs of a combined\nblazar sample, and found that the SEDs properties of these\nsubclasses present a remarkable continuity and a systematic trend as\na function of source luminosity, which suggests that the parameter\ndescribing the blazar continua is likely to be the source\nluminosity. Based on the first Fermi sample, \\citet{Ghis09} found\nthat FSRQs and BL Lacs objects occupy separate regions, and obey a\nspectral sequence. However, \\citet{Ant05} found that there are selection\neffects for the \"blazars sequence\" reported by \\citet{Foss98} and\n\\citet{Ghis98}. Some literatures show that HBLs have different properties from FSRQs, but LBLs are similar to FSRQs \\citep[e.g.][]{Chen13,Fan12,Li10,Lyu14}.\nHowever, \\citet{Li10} and \\citet{Chen13} also found that their whole sample suggest the unified\nscheme of blazars. \\citet{Coma97} discovered\nthat there is a significant anticorrelation between X-ray and\n$\\gamma$-ray spectral indices, and also between the broadband spectral\nindices $\\alpha_{ro}$ and $\\alpha_{x\\gamma}$ of BL Lacs objects and\nFSRQs. The correlation between the broadband spectral indices\nobtained by \\citet{Coma97} implied that there is a different shape in\noverall energy distributions from radio to $\\gamma$-ray energies\nbetween BL Lacs objects and FSRQs. \\citet{Samb96} and \\citet{Xie04a}\nfound that three kinds of blazars have different SEDs, but follow a\ncontinuous spectral sequence.\n\nIn this paper, we will study the distributions of luminosities and the\nradio-optical-X-ray SEDs of SDSS blazars, and connections among\nLBLs, HBLs, and FSRQs. A detailed explanation of the sample is given\nin Sec. 2. The distributions of luminosity are presented in Sec. 3.\nThe broad band spectral energy distribution is given in Sec. 4. In Sec\n5, discussions and conclusions are presented.\n\n\\section{The Sample of SDSS Blazars}\nThe Sloan Digital Sky Survey (SDSS) is one of the most ambitious and\ninfluential surveys in the history of astronomy. \\citet{Plot08} have\ndrawn a large sample of 501 BL Lacs objects candidates from the\ncombination of SDSS Data Release 5 (SDSS DR5) optical spectroscopy, and the\nFaint Images of the Radio Sky at Twenty-Centimeters (FIRST) radio\nsurvey. \\citet{Plot10} have presented a sample of 723 optically selected BL Lac candidates from the SDSS Data Release\n7 (SDSS DR7) spectroscopic database. Based on the large radio (the NRAO VLA Sky Survey, ATCA catalogue of compact PMN sources), ROSAT All Sky Survey (RASS), the SDSS Data Release 4 (SDSS DR4) and 2dF survey data, \\citet{Turr07} presented a Radio-Optical-X-ray catalog built at ASDC (ROXA) including 816 objects, among which 510 are confirmed blazars. In addition, \\citet{Chen09} have also presented a\nsample including 118 Non-thermal jet-dominated FSRQs from SDSS Data Release 3 (SDSS DR3), X-ray quasar sample with\nFIRST and GB6 radio catalogues. Based on the sample of\n\\citet{Plot08,Plot10}, \\citet{Turr07} and \\citet{Chen09}, we compiled a large\nsample of 606 blazars, including 292 FSRQs and 314 BL Lacs. All the objects of the sample have matches in RASS and measured redshifts.\nIn our sample, the three-band luminosities\n($L_{r}$, $L_{o}$, and $L_{x}$) and the broad-band spectral indices\n$\\alpha_{ro}$, $\\alpha_{rx}$, and $\\alpha_{ox}$ were\ngiven by the literatrues \\citep{Chen09,Plot08,Plot10,Turr07}.\nThe luminosities $L_{r}$, $L_{o}$, and $L_{x}$ are the specific\nluminosities (per unit frequency) at 5GHz, 5000${\\AA}$, and 1keV,\nrespectively. $\\alpha_{ro}$ is the two-point spectral indices\nbetween 5 GHz and 5000${\\AA}$, $\\alpha_{rx}$ is the two-point\nspectral indices between 5 GHz and 1 keV, and $\\alpha_{ox}$ is the\ntwo-point spectral indices between 5000${\\AA}$ and 1 keV.\n\nAs discussed in section 1, BL Lacs objects can be divided into HBLs\nand LBLs, based on the radio-X-ray spectral index $\\alpha_{rx}$\nbetween 5 GHz and 1 keV. According to literatures\n\\citep{Giom95,Ma07,Mei02,Plot08,Urry95}, most BL Lacs objects with\n$\\alpha_{rx}\\leq0.75$ are HBLs, and most BL Lacs objects with\n$\\alpha_{rx}>0.75$ are LBLs. Therefore, for investigating the\nrelation among different blazar subclasses, we adopt\n$\\alpha_{rx}=0.75$ as a rough value to divise HBLs and LBLs for the\nSDSS BL Lacs objects \\citep{Giom95,Ma07,Mei02,Urry95}. Based on this\ncriterion, there are 270 HBLs and 44 LBLs in our sample.\n\n\\section{Distributions of luminosity of blazars}\n\\citet{Foss98} studied the SEDs of a combined blazar sample, and\nfound that the source luminosity is the characteristic parameter describing the blazar\ncontinua. On the basis of the first Fermi sample, \\citet{Ghis09}\nhave found BL Lacs objects are harder and less luminous than FSRQs.\n\\citet{Ghis98} found that HBLs are sources with the lowest intrinsic\npower and the weakest external radiation field, LBLs are\nintrinsically more powerful than HBLs, and FSRQs represent the most\npowerful blazars.\n\nThus, we computed the distributions of radio (at 5GHz), optical (at\n5000${\\AA}$) and X-ray (at 1 keV) luminosities for three subclasses\nof blazars. Figure 1-3 give the distribution of luminositices for\nthree kinds of blazars, and all the luminositices are K-corrected to the\nsource rest frame \\citep{Chen09,Plot08,Plot10,Turr07}. The distributions of radio,\noptical and X-ray luminosities are plotted in Figure 1, 2, and 3,\nrespectively.\n\nFrom Figure 1, one can find that FSRQs have larger radio\nluminosities than BL Lacs objects, while the radio luminosities of\nLBLs are more powerful than that of HBLs. This suggests that the\nradio luminosities of the three kinds of blazars, from FSRQs to LBLs\nto HBLs, are decreasing, which is consistent with the argument\nreported by \\citet{Ghis98}. In Figure 2, we can note that the\noptical luminosities of FSRQs are larger than that of BL Lacs\nobjects, while HBLs have similar optical luminosities to that of\nLBLs. Correspondingly, the X-ray luminosities of HBLs are systematically lower than\nFSRQs, but larger than LBLs (see Figure 3).\n\nThe distributions presented in Figure 1, 2, and 3 show that the\nluminosity is an important parameter to distinguish FSRQs and BL\nLacs objects. A tendency of luminosities from FSRQs to BL Lacs objects is revealed from the distributions of\nluminosities. The distributions of luminosities for three kinds of\nblazars presented from Figure 1-3 are consistent with the results\nreported by \\citet{Foss98} and \\citet{Ghis98}. On the other hand,\none can note that all the distributions are continuous in properties\nbetween HBLs and LBLs, and as well as between FSRQs and BL Lacs\nobjects, which is in good agreement with the previous arguments\nabout the continuum of blazars \\citep{Foss98,Ghis98,Xie04a,Coma97,Samb96}.\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig1.eps}\n \\caption{Distributions of radio luminosity at 5 GHz for three kinds of blazars of our sample.\n\\label{fig1}}\n\\end{figure}\n\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig2.eps}\n \\caption{Distributions of optical luminosity at 5000${\\AA}$ for three kinds of blazars of our sample.\n\\label{fig2}}\n\\end{figure}\n\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig3.eps}\n \\caption{Distributions of X-ray luminosity at 1 keV for three kinds of blazars of our sample.\n \\label{fig3}}\n\\end{figure}\n\n\n\\section{Broad band spectral energy distribution of blazars}\nSearching the connection among different blazar subclasses is very\nsignificant, because it can substantially promote our understanding\nabout the fundamental nature of blazars. The relationship among\ndifferent blazars has been discussed in literatures with a\nunified scheme and a spectral sequence for blazars\n\\citep{Foss98,Ghis98,Samb96,Xie04a}. For investigating the\nrelationship among different subclasses of blazars, we will analyze\nthe relationship among the HBLs,\n LBLs, and FSRQs on the basis of the broad band spectral index\n$\\alpha_{ro}$, $\\alpha_{rx}$, and $\\alpha_{ox}$.\n\n\\subsection{Diagram of $\\alpha_{rx}$ versus $\\alpha_{ro}$}\n\nHere, we investigated the relationship between the broad band spectral indices $\\alpha_{rx}$ and $\\alpha_{ro}$ for the whole sample. The plot is shown in Figure 4.\nFigure 4 shows that there is a\ngood correlation between $\\alpha_{rx}$ and $\\alpha_{ro}$ for the whole sample. A linear\nregression analysis equation for all sample is written as\n\\begin{equation}\n\\alpha_{rx}=(0.64\\pm 0.03)\\alpha_{ro}+(0.43\\pm0.01),\n\\label{eq:Lebseque1}\n\\end{equation}\nwith a correlation coefficient $r=0.70$, and a chance\nprobability $p<10^{-4}$.\nMoreover, we also studied the relationship between $\\alpha_{rx}$ and $\\alpha_{ro}$ for the FSRQs and LBLs sample. We obtained\n\n\\begin{equation}\n\\alpha_{rx}=(0.42\\pm 0.02)\\alpha_{ro}+(0.59\\pm0.01),\n\\label{eq:Lebseque2}\n\\end{equation}\nwith a correlation coefficient $r=0.70$, and a chance\nprobability $p<10^{-4}$. The correlation analysis suggests that there is a linear correlation between $\\alpha_{rx}$ and $\\alpha_{ro}$ for the whole sample, and as well as for the FSRQs+LBLs sample. This provides evidence for the\nunified scheme reported by \\citet{Foss98} and \\citet{Ghis98}.\n\nIn addition, Figure 4 shows that the majority of FSRQs and LBLs mix\ntogether, which suggests that they have similar spectral properties.\nHowever, Figure 4 also reveals that the distribution of HBLs in\n$\\alpha_{rx}$ versus $\\alpha_{ro}$ diagram is different from that of FSRQs\nand LBLs. This indicates that HBLs have different spectral properties\nfrom FSRQs and LBLs. The results are consistent with the reported results of\n\\citet{Xie04a}, who found that HBLs and LBLs locate in different\nregions in the $\\alpha_{ox}-\\alpha_{x\\gamma}$ plane, but LBLs and FSRQs\noccupy the same region in $\\alpha_{ox}-\\alpha_{x\\gamma}$ plane. In addition, our results also agree with that reported by \\citet{Fan12} and \\citet{Lyu14}.\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig4.eps}\n \\caption{The relationship between the broadband spectral indices $\\alpha_{ro}$ and $\\alpha_{rx}$ for the sources in our sample.\n \\label{fig4}}\n\\end{figure}\n\n\\subsection{Diagram of $\\alpha_{rx}$ versus $\\alpha_{ox}$}\n\nIn Figure 5, $\\alpha_{rx}$ versus $\\alpha_{ox}$ is plotted for our\nSDSS blazar sample. We can find that the distribution of three kinds\nof blazars revealed from Figure 5 is similar to that of Figure 4. For the whole sample, Figure 5 shows a significant correlation between $\\alpha_{rx}$\nand $\\alpha_{ox}$, and the linear regression analysis yields\n\\begin{equation}\n\\alpha_{rx}=(0.30\\pm 0.01)\\alpha_{ox}+(0.36\\pm0.02),\n\\label{eq:Lebseque3}\n\\end{equation}\nwith a correlation coefficient $r=0.62$ and a chance\nprobability $p<10^{-4}$. Moreover, Figure 5 shows that there is a weak correlation between $\\alpha_{rx}$\nand $\\alpha_{ox}$ for the FSRQs and LBLs sample, and the linear\nregression analysis equation is\n\n\\begin{equation}\n\\alpha_{rx}=(0.07\\pm 0.02)\\alpha_{ox}+(0.71\\pm0.03),\n\\label{eq:Lebseque4}\n\\end{equation}\nwith a correlation coefficient $r=0.17$ and a chance\nprobability $p=0.0016$. In Figure 5, one can note that the\nmajority of FSRQs and LBLs also occupy the same region, but HBLs\noccupy a separate distinct region, which is also consistent with\nprevious results.\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig5.eps}\n \\caption{The relationship between the broadband spectral indices $\\alpha_{ox}$ and $\\alpha_{rx}$ for the sources in our sample.\n \\label{fig5}}\n\\end{figure}\n\n\\subsection{Diagram of $\\alpha_{ox}$ versus $\\alpha_{ro}$}\nBased on the broad band spectral index $\\alpha_{ox}$ versus $\\alpha_{ro}$, we investigated the relationships between $\\alpha_{ox}$ and $\\alpha_{ro}$. Figure 6 plots $\\alpha_{ox}$ versus $\\alpha_{ro}$. A linear\nregression analysis shows that there is a weak or even no correlation between\n$\\alpha_{ox}$ and $\\alpha_{ro}$ ($r=-0.11$ and $p=0.054$) for whole sample. This\nindependent relation is obviously inconsistent with the foregoing\ncorrelation revealed from Figure 4 and Figure 5. However, the correlation\nis significant when considering FSRQs and LBLs sample and the the linear\nregression analysis equation is\n\\begin{equation}\n\\alpha_{ox}=(0.87\\pm 0.07)\\alpha_{ro}+(1.75\\pm0.04),\n\\label{eq:Lebseque6}\n\\end{equation}\nwhere the correlation coefficient is $r=-0.56$ and the chance\nprobability is $p<10^{-4}$. This suggests that HBLs are different from FSRQs, but LBLs are similar to FSRQs.\n In addition, Figure 6 also shows that most of the FSRQs and LBLs\nlocate the same region in $\\alpha_{ox}$ -$\\alpha_{ro}$ plot, but\nHBLs occupy a separate distinct region in $\\alpha_{ox}$ versus\n$\\alpha_{ro}$ plane. This is consistent with the distribution shown in Figure 4 and Figure 5. This supports the foregoing results: FSRQs and LBLs have similar\nspectral properties, but HBLs have distinct spectral properties.\n\n\n\n\n\n\\begin{figure}\n\\includegraphics [width=5in, angle=0]{fig6.eps}\n \\caption{The relationship between the broadband spectral indices $\\alpha_{ro}$ and $\\alpha_{ox}$ for the sources in our sample.\n \\label{fig6}}\n\\end{figure}\n\n\n\\subsection{Summary}\nAs noted above, from Figure 4 and 5, there is a strong correlation\nbetween $\\alpha_{rx}$ and $\\alpha_{ro}$, and as well as between\n$\\alpha_{rx}$ versus $\\alpha_{ox}$ for the whole sample, which provides some more\nevidence for the conclusion reported\nby \\citet{Foss98} and \\citet{Ghis98}. Namely, there is a unified\nscheme for blazars. On the other hand, from Figure 4, 5, and 6, one\ncan note that there are also some different distributions from the\nblazar sequence reported by \\citet{Foss98} and \\citet{Ghis98}. In\nthe color-color diagram, HBLs and FSRQs occupy seperated regions,\nwhile the LBLs and FSRQs mix together, which is consistent with that\nreported in some\nliteratures \\citep[e.g.][]{Chen13,Fan12,Li10,Lyu14,Xie04a}. This suggests that FSRQs and LBLs have a\nsimilar property, but HBLs have a distinct property.\n\n\\section{Discussion and Conclusions}\nBased on the Slew survey, the 1-Jy samples of BL Lacs and the 2-Jy\nsample of FSRQs, \\citet{Foss98} studied the systematics of the SEDs of blazars using data\nfrom the radio to the $\\gamma$-ray band, and found that three\ndifferent kinds of blazars follow an almost continuous spectral\nsequence: from FSRQs through LBLs to HBLs. \\citet{Ghis08} revisited the so called \"blazar sequence\", and proposed that the power of the jet and the SED of its emission are linked to the two main parameters of the accretion process. This similar trend was also\nobtained by other authors\n\\citep[e.g.][]{Xie04a,Samb96,Ghis98,Bott02,Mara08} who found that similar\nphysical processes operate in three kinds of blazars.\nHowever, \\citet{Ant05}\nfound that there are selection effects for the\n\"blazars sequence\". Moreover, some authors found that HBLs do not\nfollow the blazars sequence \\citep[e.g.][]{Chen13,Fan12,Giom05,Li10,Pado03,Pado07} .\n\nIn this paper, we computed the distributions of the radio (at 5\nGHz), optical (at 5000 ${\\AA}$), and X-ray (at 1 keV) luminosities.\nThe luminosities distributions reveal that it is an important\nparameter to distinguish FSRQs and BL Lacs objects, and the\ndistributions are continuous for three kinds of blazars. The\nluminosities of FSRQs are lager than that of BL Lacs objects, which\nis in good agreement with the arguments reported by other authors\n\\citep{Abdo09a,Foss98,Ghis98,Samb96}. The distributions of radio\nluminosity support the blazars sequence reported by \\citet{Foss98}\nand \\citet{Ghis98}. However, the distributions of optical and X-ray\nluminosities do not support the sequence.\n\n\nThe broadband energy distribution shows that three kinds of blazars have\ndifferent spectral properties. It also shows that most FSRQs and LBLs mix together in the color-color\ndiagram (see Figure 4, 5, and 6), which is consistent with previous\nresults \\citep{Fan12,Li10,Samb96,Xie04a,Zhen07}. This suggests that they\nhave similar spectral properties, which provides some more evidence for the conclusion of unified\nscheme. However, the location of HBLs is separate with that of FSRQs\nand LBLs in the color-color diagram, which reveals that HBLs have\ndifferent SEDs from FSRQs and LBLs. This suggests that the results\nfrom SDSS sample do not support the so called \"blazar sequence\",\nwhich is consistent with the results reported by the other authors\n\\citep{Ant05,Fan12,Chen13,Li10,Pado03,Pado07,Zhan12}. The spectral\nsequence obtained by \\citet{Foss98} may be related to the selection\neffects, because the sample used by \\citet{Foss98} are classic, high\nflux limit surveys in the radio and X-ray \\citep{Ant05}. Our sample\nused in the paper is a large sample including 606 blazars, which\nwould result in a unbiased view of blazar spectral properties.\nMoreover, Figure 7 gives the relations between the redshift and spectral\nindices. Figure 7 shows that the spectral indices is independent of\nredshift, which suggests that the selection effects of our sample\nare weak.\n\n\n\\citet{Ghis98} suggested the level of cooling is different for different subclasses of blazars. FSRQs suffer stronger cooling, and synchrotron emission peaks at much lower frequency. However, the cooling is less important for HBLs, and the energetic particles can produce synchrotron and inverse Compton (IC) emission up to high frequency. The level of cooling of FSRQs stronger than the one of HBLs may be due to the external radiation field \\citep{Ghis98}. \\citet{Geor01} suggested that the radiating jet plasma in weak sources is outside the broad line scattering region (BLR), while it is within in the power source. This implies that the location of emitting region between HBLs and FSRQs might be very different \\citep{Cost09}. The jet energy of FSRQs would dissipate within the BLR, leading that the high energy electrons in the jet will suffer greater cooling \\citep{Chen11}. \\citet{Ghis10} suggested that the $\\gamma$-ray emission from FSRQs is likely from the Compton scattering of an external radiation source, while for HBLs SSC is able to provide a good fit to the $\\gamma$-ray emission. In addition, based on the physical properties of relativistic jets, \\citet{Yan14} found that the one-zone SSC model can successfully fit the SEDs of HBLs, but fails to explain the SEDs of LBLs. Moreover, they also suggest that the ratios of the Compton to the synchrotron peak energy fluxes of LBLs are greater than those of HBLs and IBLs, and then LBLs are Compton dominated \\citep{Yan14}. This suggests that there is an external radiation field for LBLs. Therefore, the levels of cooling of FSRQs and LBLs is stronger than HBLs, which lead that the synchrotron emission peaks of FSRQs and LBLs is lower than ones of HBLs. \\citet{Abdo10} found FSRQs and LBLs are the low synchrotron peaked\nblazars, while HBLs are high synchrotron peaked\nblazars. \\citet{Fan12} suggest that if the synchrotron peak frequency moves to the lower frequency, then the IC peak frequency may also move to the lower frequency. Thus, the X-ray of LBLs and FSRQs are from the combination of synchrotron emission and the IC emission, while the X-ray of HBLs are from the\nsynchrotron emission of very high energy electrons \\citep{Abdo10,Fan12}.\nIn addition, the different SEDs between HBLs, FSRQs, and LBLs may be\nrelated to the different intrinsical environments around the\nblazar's nucleus. The intrinsical environments of FSRQs and HBLs have\na clear, physics difference: the environment of HBLs is \"cleaner\"\nthan that of FSRQs \\citep{Cost09}. The central regions of FSRQs are rich in gas and dust, which would lead to a high accretion rate onto the central supermassive black hole \\citep{Bott02}. Moreover, the material would efficiently\nreprocess and scatter the accretion disk radiation. This would\nlead to the observed strong optical emission lines in the\nBLR and to a high energy density of the\nexternal soft-photon field in the jet \\citep{Bott02}.\n\n\n\n\n\n\n\n\n\n\nAlthough HBLs have different SEDs from FSRQs and LBLs, the\nsignificant correlation revealed from Figure 4 and 5 suggests that\nthere is a unified scheme for whole sample, which is consistent with the previous conclusion\nreported by other authors\n\\citep{Coma97,Foss98,Ghis98,Li10,Samb96,Xie01,Xie04a}. This hints\nthat there is a similar physical processes operating in all objects.\nIn the case of the blazar-type sources where the emission is usually\nassociated with a stream of relativistic jet, the overall spectrum\nis determined by the energy spectrum of the electrons as well as by\nthe variation of the physics quantities along the jet\n\\citep{Bege84}. HBLs, LBLs, and FSRQs have a significant correlation\nin the color-color diagram (see Figure 4 and 5), which implies that\nsimilar physical processes operate in all objects under a range of\nintrinsic physics conditions or beaming parameter. On the other\nhand, the difference among three subclasses of blazars, revealed\nfrom color-color diagram (see Figure 4, 5, and 6), should be\nattributed to the different level of cooling and the intrinsical different environments around the blazars\nnucleus for different subclasses blazars, which lead to\ndifferent optical and X-ray spectra for different kinds of blazars.\n\n\\begin{figure}\n \\includegraphics [width=5.5in, angle=0]{fig7.eps}\n \\caption{Relations between redshift and spectral indices.\n \\label{fig7}}\n\\end{figure}\n\n\n\\normalem\n\\begin{acknowledgements}\nWe are grateful to the anonymous referee for useful comments. We are grateful for the help from Liang Chen. This research has made use of the SDSS database.\nThis work\nis supported by the National Natural Science Foundation of China\n(10878013), and the Natural Science Foundation of Yunnan Province\n(2011FZ081, 2012FD055, 2013FB063), and the Program for Innovative\nResearch Team (in Science and Technology) in University of Yunnan\nProvince (IRTSTYN), and Science Research Foundation of Yunnan\nEducation Department of China (2012Y316), and the Young Teachers\nProgram of Yuxi Nurmal University. In addition, the work of Yunguo Jiang is supported by the NNSFC with Number 11403015.\n\\end{acknowledgements}\n\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\nThe lack of right-handed neutrino states $N_j$ is an intriguing feature of the Standard Model (SM). Their presence is not strictly required, unlike for the other SM fermions, as we only observe neutrinos through their left-handed SM interactions, and the small but finite masses could be understood with the active left-handed states $\\nu_\\ell$ only, assuming their Majorana nature. This does not mean that right-handed neutrinos do not exist, though: Because they would be \\emph{sterile}, i.e., uncharged under the SM gauge interactions, they participate only in the Yukawa interaction $-y_\\nu^{\\ell j} \\bar L_\\ell\\cdot H N_j$ with a left-handed lepton doublet and the Higgs doublet. If small, $y_\\nu \\sim m_\\nu \/ v \\lesssim 10^{-12}$ ($v = 174$~GeV), this would generate light \\emph{Dirac} neutrino masses $m_\\nu \\lesssim 0.1$~eV seen in oscillations and constrained by absolute mass searches such as tritium decay and cosmological observations.\n\nThe introduction of sterile, right-handed neutrino states opens up the possibility of \\emph{lepton number violation}. Whereas total lepton number is an accidental symmetry in the SM, sterile neutrinos can have a \\emph{Majorana} mass term, $-\\frac{1}{2}M^{ij} \\bar N_i^C N_j$, violating lepton number by two units, unless it is explicitly forbidden by an additional symmetry beyond the SM gauge ones. Such a Majorana mass term is fairly unconstrained from a theoretical point of view, as it is not connected to the SM electroweak symmetry breaking. It can in principle have any scale from eV and below to scales far above the SM. \n\nWith both the Yukawa and a heavy sterile Majorana mass term present, the neutrino spectrum consists of three (mostly) active light neutrinos and two or more (mostly) sterile neutrinos, all having Majorana character. This is the celebrated \\emph{seesaw mechanism} (of type 1), connecting the light neutrino masses to the heavy Majorana mass scale $m_N$ as $|m_\\nu| \\sim (y_\\nu v)^2\/m_N = |V_{\\ell N}|^2m_N$, applicable if $y_\\nu v \\ll m_N$. Here, $|V_{\\ell N}| = y_\\nu v\/m_N$ is the active-sterile mixing strength. Its main phenomenological consequence is that it generates suppressed charged and neutral current interactions between the sterile state $N$ and a SM charged lepton or neutrino of flavour $\\ell = e,\\mu,\\tau$. The lightness of active neutrinos can thus be explained by either making the sterile neutrinos heavy or the Yukawa coupling weak. The admixture of a sterile neutrino with an active one, $N^\\text{mass} \\sim N - V_{\\ell N} \\nu_\\ell$, is in either case small,\n\\begin{align}\n |V_{\\ell N}| = \\sqrt{\\frac{m_\\nu}{m_N}} \n \\lesssim 10^{-6} \\sqrt{\\frac{100~\\text{GeV}}{m_N}}.\n\\end{align}\n\nThere is a third way of keeping the active neutrinos light: If lepton number were to be conserved in the sterile neutrino sector, no light masses are generated. This is not only achieved in the limits $m_N\\to 0$ and $m_N\\to\\infty$ but also if pairs of sterile states form Dirac particles themselves. By violating lepton number symmetry slightly, e.g., through a Majorana mass $\\mu \\ll m_N$, light neutrino masses are generated, $|m_\\nu| \\sim (y_\\nu v\/m_N)^2 \\mu = |V_{\\ell N}|^2 \\mu$, while the heavy sterile neutrinos form quasi-Dirac pairs with a small mass splitting $\\Delta m_N \\sim \\mu$. This concept applies to extended scenarios such as the \\emph{inverse seesaw mechanism} where the scale of lepton number breaking $\\mu$ is decoupled from the heavy neutrino mass $m_N$.\n\nThis proceedings report is based on our paper comparing the sensitivity of direct searches with that of neutrinoless double beta ($0\\nu\\beta\\beta$) decay~\\cite{Bolton:2019pcu}. It utilizes a phenomenological pa\\-ra\\-metrization describing the general mixing of two heavy sterile neutrino states with one generation of active neutrino where the purely Majorana and Dirac scenarios can be understood as limiting cases.\n\n\\section{Current Constraints and Future Sensitivities}\nWe briefly describe the different classes of probes. For details we refer the reader to our paper~\\cite{Bolton:2019pcu}, its accompanying website \\url{www.sterile-neutrino.org} and other recent literature~\\cite{Abdullahi:2022jlv}. We concentrate on the mixing strength $|V_{eN}|$ of a heavy sterile neutrino with electron flavour as this is the one relevant for $0\\nu\\beta\\beta$ decay. Current constraints on $|V_{eN}|$ as a function of the heavy sterile neutrino mass $m_N$ are shown in Fig.~\\ref{fig:current}, over the broad mass range $0.1~\\text{eV} < m_N < 10$~TeV. The diagonal line labelled \\textbf{Seesaw} indicates the mixing strength expected in canonical seesaw, $m_\\nu = |V_{eN}|^2 m_N$, generating a light neutrino mass $m_\\nu = 0.05$~eV. Reaching it may be considered the ultimate goal for sterile neutrino searches, though, both larger (e.g., in inverse seesaw models) and smaller (where other contributions dominate the generation of light masses) mixing strengths are possible.\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\includegraphics[width=0.79\\textwidth]{figures\/VeNsq_constraints}\n\t\\caption{Current constraints on the active-sterile mixing strength $|V_{eN}|$ as a function of the sterile neutrino mass $m_N$. Adapted from the companion paper, with detailed descriptions of the various probes therein and in the accompanying website \\url{www.sterile-neutrino.org}.}\n\t\\label{fig:current}\n\\end{figure}\nIt may be surprising that sterile neutrinos, having no inherent gauge charges, are constrained from so many directions, but the active-sterile mixing causes the sterile neutrinos to participate in charged-current and neutral-current SM interactions, albeit suppressed by~$|V_{\\ell N}|$. As opposed to the light active neutrinos, heavy sterile neutrinos can decay, either promptly or with a macroscopic proper decay length,\n\\begin{align}\n L_N \\approx 25~\\text{mm}\n \\cdot\\frac{10^{-10}}{|V_{\\ell N}|^2}\n \\cdot\\left(\\frac{10~\\text{GeV}}{m_N}\\right)^2,\n\\end{align}\nwhere this approximation is roughly valid for $1~\\text{GeV} \\lesssim m_N \\lesssim m_W$. This improves detectability and especially the \\emph{long-lived particle (LLP)} signature, in combination with high intensity production mechanisms, allows probing sterile neutrinos with very small mixing strengths, close to the canonical seesaw floor. If a heavy sterile neutrino were to be discovered near this line, it would most likely be of Majorana nature. Most probes, such as direct searches, where sterile neutrinos are produced on-shell, are sensitive to both Majorana and Dirac neutrinos. Only those probes relying on a total lepton number violating signal require a Majorana sterile neutrino, c.f. Fig.~\\ref{fig:future}, where corresponding limits are highlighted in red.\n\n\\begin{figure}[t!]\n\t\\centering\n\t\\includegraphics[width=0.79\\textwidth]{figures\/VeNsq_future}\n\t\\caption{As Fig.~\\ref{fig:current}, but showing the projected sensitivities of future searches (open curves), including $0\\nu\\beta\\beta$ decay, over the existing constraints (shaded regions). The region in light blue is disallowed for both Dirac and Majorana sterile neutrinos whereas the region in light red applies only for Majorana neutrinos. The $0\\nu\\beta\\beta$ decay sensitivities are for a heavy sterile Majorana (red) and quasi-Dirac neutrino (teal) for the half-life $T^{0\\nu}_{1\/2} = 10^{28}$~yr in $^{76}$Ge. Adapted from the companion paper, with detailed descriptions of the various probes therein and in the accompanying website \\url{www.sterile-neutrino.org}.}\n\t\\label{fig:future}\n\\end{figure}\nThe strong reach of high-luminosity, displaced-vertex searches is especially apparent in Fig.~\\ref{fig:future}, which shows sensitivities of proposed experiments (open curves) in comparison with current constraints (shaded regions).\n\n\\subsection{High-energy Colliders}\nSterile neutrinos are produced in high-energy collisions through charged and neutral currents such as $pp\\to W^+\\to e^+ N$ and $pp\\to Z\\to \\nu N$. For example, the proposed \\textbf{FCC-ee} will be a powerful $Z$ factory with low background for displaced vertices in a large detector volume. \n\n\\subsection{Meson Decays and Beam-Dump Experiments}\nLikewise, beam-dump experiments and meson factories produce a large number of mesons that subsequently decay to heavy sterile neutrinos, e.g., $K^+ \\to e^+ N$. The most sensitive direct limits are currently from \\textbf{NA62} and the long baseline neutrino oscillation experiment \\textbf{T2K}, exploiting this route in existing facilities. Future searches such as \\textbf{SHiP} can be purpose-built with optimized LLP detectors. \n\n\\subsection{Beta Decays and Nuclear Processes}\nSterile neutrinos mixing with electron-flavour and masses $m_N \\lesssim 1$~MeV can be produced in nuclear beta decays and other weak nuclear processes. They will suppress the rate and can produce a detectable kink in the decay spectrum. Strong advancements in such searches are expected, with the recent BeEST experiment~\\cite{Friedrich:2020nze} improving previous limits by almost two orders of magnitude ({\\boldmath$^7$}\\textbf{Be}). Future searches by the same collaboration and, e.g., the \\textbf{HUNTER} proposal~\\cite{Martoff:2021vxp} aim to go below the region disfavoured by cosmological considerations, probing a parameter space where the sterile neutrino can be a viable Dark Matter candidate.\n\n\\subsection{Active-Sterile Neutrino Oscillations}\nSterile neutrinos can be produced through oscillations with the active states. Persistent anomalies around the squared mass difference $\\Delta m_{14}^2 = m_N^2 - m_\\nu^2 \\approx 1~\\text{eV}^2$ hint at the presence of a sterile neutrino around this scale. Interpreted conservatively, oscillation experiments provide constraints on light eV-scale sterile neutrinos. Heavier sterile neutrinos can also be probed through the resulting deficit of active neutrinos detected, though this requires a very good understanding of the absolute neutrino flux. For DUNE, this is indicated by the contour labelled \\textbf{DUNE Indirect}~\\cite{Carbajal:2022zlp}. \n\n\\subsection{Electroweak Precision Data and Indirect Laboratory Constraints}\nLikewise, any mixing with sterile neutrinos means that the active neutrino mixing matrix itself is non-unitary. This is visible in charged current and neutral current processes, altering electroweak precision data (\\textbf{EWPD}) observables.\n\n\\subsection{Cosmological and Astrophysical Constraints}\nSterile neutrinos are produced in the early universe through scattering or oscillation. If decaying at times later than $\\sim 1$~s, they affect the abundance of primordial elements in big bang nucleosynthesis (\\textbf{BBN}). Decays of longer-lived sterile neutrinos will inject radiation degrees of freedom, i.e., light active neutrinos, which are strongly constrained. Furthermore, the loop-induced decay $N\\to\\nu\\gamma$ is detectable in astrophysical \\textbf{X-ray} observations. Quasi-stable sterile neutrinos will act as Dark Matter and must not overclose the universe (\\textbf{CMB+BAO+}{\\boldmath$H_0$}). Taken at face value, such considerations disfavour much of the parameter space $m_N \\lesssim 1$~GeV accessible in laboratory experiments. They can be relaxed in extended scenarios, e.g., where sterile neutrinos decay to a dark sector modifying their lifetime.\n\n\\subsection{Neutrinoless Double Beta Decay}\n\\label{sec:0vbb}\n\nThe most sensitive probe of the Majorana nature of light active neutrinos is $0\\nu\\beta\\beta$ decay~\\cite{Agostini:2022zub}. Observing this rare nuclear process in select isotopes such as $^{76}\\text{Ge} \\to {}^{76}\\text{Se} + e^- e^-$, is only possible if total lepton number is violated. It would prove that the light active neutrinos are Majorana fermions. In addition, $0\\nu\\beta\\beta$ decay is sensitive to other exotic sources of lepton number violation, typically at or below the $\\mathcal{O}(10)$~TeV scale~\\cite{Doi:1981,Cirigliano:2017djv,Graf:2018ozy,Deppisch:2020ztt}. \n\nThis includes the exchange of sterile neutrinos. In particular, $0\\nu\\beta\\beta$ decay is highly sensitive to heavy Majorana neutrinos. In this case, the decay half-life $T_{1\/2}^{0\\nu}$ for $m_N \\gtrsim 100$~MeV is approximately given by\n\\begin{align}\n\\label{eq:0vbb:half-life-heavy}\n\t\\frac{10^{28}~\\text{yr}}{T_{1\/2}^{0\\nu}} \\approx \\left(\\frac{|V_{eN}|^2}{10^{-9}}\\cdot\\frac{1~\\text{GeV}}{m_N}\\right)^2.\n\\end{align}\nFor lighter sterile neutrinos, $m_N \\lesssim 100$~MeV, the rate is proportional to $m_N^2$,\n\\begin{align}\n\\label{eq:0vbb:half-life-light}\n\t\\frac{10^{28}~\\text{yr}}{T_{1\/2}^{0\\nu}} \\approx \\left(\\frac{|V_{eN}|^2}{10^{-9}}\\cdot\\frac{m_N}{15~\\text{MeV}}\\right)^2,\n\\end{align}\nThe above approximations use nuclear matrix elements for the isotope $^{76}$Ge~\\cite{Deppisch:2020ztt}. The behaviour changes around the nuclear momentum scale $\\approx 100$~MeV of $0\\nu\\beta\\beta$ decay, and at the crossover the momentum dependence should be accounted for more carefully~\\cite{Babic:2018ikc,Dekens:2020ttz}. \n\nThe above sensitivities are normalized with respect to the half-life $T^{0\\nu}_{1\/2}(^{76}\\text{Ge}) = 10^{28}$~yr. This is the projected sensitivity of LEGEND-1000~\\cite{Zsigmond:2020bfx}, one among a range of proposed experiments~\\cite{Agostini:2022zub} mainly aiming to probe the light active Majorana neutrino parameter space for an inverted mass ordering. Current experimental limits are of the order $T^{0\\nu}_{1\/2} \\gtrsim 10^{26}$~yr~\\cite{PhysRevLett.117.082503,GERDA:2020xhi}.\n\nIn Fig.~\\ref{fig:future}, the future sensitivity to Majorana sterile neutrinos is given by the red band labelled {\\boldmath$0\\nu\\beta\\beta~(N)$}, where the width indicates the theoretical uncertainty from nuclear matrix elements. This includes the potential quenching of the axial nuclear coupling strength~\\cite{Deppisch:2016rox}. \n\nFuture $0\\nu\\beta\\beta$ decay experiments can reach sensitivities $|V_{eN}|^2 \\approx 2\\times 10^{-10}$ to $10^{-9}$, in the regime $10~\\text{MeV}\\lesssim m_N \\lesssim 1$~GeV. This is in the range expected for the canonical seesaw with $m_N \\approx 100$~MeV, and also comparable to future direct searches in this mass window such as \\textbf{PIONEER}~\\cite{PIONEER:2022yag} and \\textbf{DUNE}. \n\nFor masses and mixing outside this range, the nominal sensitivity to heavy sterile Majorana neutrinos is still strong, but as mentioned above, the light masses naturally require that sterile neutrinos are quasi-Dirac states with an associated small mass splitting that suppresses $0\\nu\\beta\\beta$ decay. For example, with a pair of quasi-Dirac sterile neutrino states of average mass $m_N$ and relative mass splitting $\\delta_N = \\Delta m_N\/m_N$, Eq.~\\eqref{eq:0vbb:half-life-heavy} is modified to \n\\begin{align}\n\t\\label{eq:0vbb:half-life-heavy-quasi-dirac}\n\t\\frac{10^{28}~\\text{yr}}{T_{1\/2}^{0\\nu}} \n\t\\approx \\left(\\frac{\\delta_N}{10^{-2}}\n\t\\cdot\\frac{|V_{eN}|^2}{10^{-7}}\n\t\\cdot\\frac{1~\\text{GeV}}{m_N}\\right)^2.\n\\end{align}\nLarger masses $m_N \\gtrsim 10$~GeV and splittings are in principle possible but they require a fine-tuned cancellation of the induced loop contribution to the light neutrino masses~\\cite{Mitra:2011qr,Lopez-Pavon:2012yda,Bolton:2019pcu}. Direct searches looking for lepton number conserving signals do not have such a suppression and they can probe purely Dirac-type sterile neutrinos.\n\nThe above discussion assumes that the sterile neutrino contribution saturates the $0\\nu\\beta\\beta$ decay sensitivity, but other mechanisms may be present. Most directly, the light active neutrinos (if Majorana) will induce the effective $0\\nu\\beta\\beta$ mass $m_{\\beta\\beta}$ that destructively interferes with sterile neutrinos for $m_N \\lesssim 100$~MeV if these participate in the seesaw mechanism. For $m_N \\ll 100$~MeV, light and heavy neutrino contributions will cancel to zero in this case.\n\nThe effect of all three types of suppression is indicated in Fig.~\\ref{fig:future} by the teal band labelled {\\boldmath$0\\nu\\beta\\beta~(N_1, N_2)$}: A quasi-Dirac sterile neutrino nature with $\\delta = 10^{-2}$ leads to an overall reduction of sensitivity with respect to the red Majorana band, the interference with the light active neutrino contribution (with $m_\\nu = m_{\\beta\\beta} = 10^{-3}$~eV, also indicated by the lower diagonal \\textbf{Seesaw} line) induces a steeper slope for $m_N < 100$~MeV, and strong loop corrections to the light neutrino masses of 10\\% or more are present to the top and right of the line labelled~\\textbf{Loop}.\n\n\\section{Discussion}\nGiven their curious absence from the SM and their importance as the potential origin of the light neutrino masses, it is only right that sterile neutrinos are being probed in a large number of experiments and observations. We have briefly highlighted the main approaches to search for sterile neutrinos in the experimentally accessible range $1~\\text{eV} \\lesssim m_N \\lesssim 10$~TeV. Beyond this regime, we must primarily resort to theoretical considerations, e.g., the stability of the Higgs potential modified by the Yukawa couplings of the sterile neutrinos.\n\nApart from their connection to neutrino masses, sterile neutrinos may play a crucial role in explaining the matter-antimatter asymmetry of the universe through their participation in various \\emph{leptogenesis} scenarios. This provides a major, additional motivation to search for sterile neutrinos, especially in the range $1~\\text{GeV} \\lesssim m_N \\lesssim 100$~GeV.\n\nLastly, sterile neutrinos may have additional interactions beyond the ones induced by the active-sterile mixing, leading to other portals such as transition magnetic moments~\\cite{Bolton:2021pey} or exotic gauge interactions~\\cite{Liu:2022kid,Padhan:2022fak}.\n\n\\section*{Acknowledgments}\nF.F.D. acknowledges support from the UK Science and Technology Facilities Council (STFC) via the Consolidated Grants ST\/P00072X\/1 and ST\/T000880\/1. P.D.B. has received support from the European Union's Horizon 2020 research and innovation programme under the Marie Sk\u0142odowska-Curie grant agreement No. 860881-HIDDeN. The work of B.D. is supported in part by the US Department of Energy under Grant No. DE-SC0017987.\n\n\\section*{References}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}} +{"text":"\\section{Introduction}\n\nEvolutionary diversity optimisation aims to construct a set of diverse solutions that all have high quality but differ with respect to important properties of the solutions. This area of research started by Ulrich and Thiele~\\cite{DBLP:conf\/gecco\/UlrichBZ10,DBLP:conf\/gecco\/UlrichT11} has recently gained significant attention within the evolutionary computation community. It equips practitioners with high quality solutions of variable designs. Furthermore, the methods developed can be used in the context of machine learning and algorithm selection and configuration. Here, evolutionary diversity optimisation is used to evolve a diverse set of instances that can be used for training prediction models that forecast algorithm performance on a newly given instance.\n\nRecent studies in this area of research mainly focused on the diversity measure to be used in the selection process when characterising solutions by underlying features. Differences in feature values as well as weighted combinations of two or more features have been examined in the context of Travelling Salesperson Problem (TSP) instances and images~\\cite{DBLP:conf\/ppsn\/GaoNN16,DBLP:conf\/gecco\/AlexanderKN17}. More recently the use of the discrepancy measure as well as the use of popular indicators from the area of evolutionary multi-objective optimisation have been proposed and evaluated~\\cite{DBLP:journals\/corr\/abs-1802-05448,DBLP:conf\/gecco\/NeumannG0019}. Special mutation operators for creating diverse sets of TSP instances have been investigated in~\\cite{DBLP:conf\/foga\/BossekKN00T19}.\n\nIn this paper, we examine, for the first time, TSP in the context of evolutionary diversity optimisation. Our focus is on the diversity of the tours themselves, not their qualities. The TSP has been subject to a wide range of studies. Various evolutionary algorithms and other heuristic search methods as well as exact solvers have been developed over the years~\\cite{lin1973,helsgaun2000,xie2009,Nagata2013}.\nFurthermore, the TSP has been studied widely in the area of algorithm selection and configuration~(see \\cite{DBLP:journals\/ec\/KerschkeHNT19} for a recent overview on this research area) and a wide range of studies regarding important features of TSP instances and their relation to algorithm performance have been carried out~\\cite{smithmiles2011,kanda2011,mersmann2013,KKBHTLeveragingTSP}. Evolutionary diversity optimisation has so far only been considered for evolving TSP instances~\\cite{DBLP:conf\/ppsn\/GaoNN16,DBLP:journals\/corr\/abs-1802-05448,DBLP:conf\/gecco\/NeumannG0019}, but not for computing a diverse set of high quality tours for a given TSP instance. \n\nIn this paper, we examine ways to evolve a diverse set of high quality TSP tours for a given TSP instance and population size.\nA crucial aspect in our study is how to measure the diversity of a tours population for an effective diversity-driven approach. To establish diversity-oriented evolutionary pressure, we propose two diversity measures: an edge distribution diversity measure and a pairwise dissimilarity measure. We study both measures with respect to their properties in the context of evolutionary diversity optimisation and carry out experimental investigations showing how evolutionary algorithms generate diverse populations using the two measures on unweighted TSP instances where all tours are accepted. Our results for this basic set up shows that these cases can be handled effectively and set the basis for studies on classical TSPlib instances~\\cite{DBLP:journals\/informs\/Reinelt91} where tours are filtered based on qualities.\n\nWe investigate the introduced evolutionary diversity optimisation approach using the two diversity measures on classical instances, and explore the differences in results when using classical $k$-opt operations where $k=2,3,4$ for a wide range of quality thresholds imposed on the tours. Furthermore, we study how the population size which determines the size of the set of tours effects the ability of the evolutionary diversity optimisation approaches to obtain a high diversity score.\n\nThe paper is structured as follows. In Section~\\ref{sec2}, we introduce the Traveling Salesperson Problem in the context of evolutionary diversity optimisation and the algorithms that are part of our investigations. In Section~\\ref{sec3}, we introduce the edge diversity measure and investigate its theoretical properties. Section~\\ref{sec4} introduces the pairwise distance diversity measure along with its theoretical properties. We report on our experimental investigations in Section~\\ref{sec5} and finish with some conclusions.\n\n\\section{Maximising Diversity in TSP}\n\\label{sec2}\n\nThe Traveling Salesperson problem (TSP), one of the best-known $\\mathcal{NP}$-hard combinatorial optimisation problems, can be described as follows: Given a complete graph $G=(V,E)$ with $n = |V|$ cities, $m = n(n-1)\/2 = |E|$ edges and the pairwise distances between the cities, the goal is to compute a tour of minimal length that visits each city exactly once and finally returns to the original city. For the Euclidean TSP all cities lie in the Euclidean plane and the pairwise distances between the cities are determined by the Euclidean metric. Let $V = \\{1, \\ldots, n\\}$. The goal is to find a permutation $\\pi : V \\rightarrow V$ that minimises the cost function \n\\begin{align*}\nc(\\pi) = d(\\pi(n),\\pi(1)) + \\sum_{i=1}^{n-1} d(\\pi(i),\\pi(i+1)), \n\\end{align*}\nwhere $d(i,j)$ is the Euclidean distance between points $i$ and $j$. Note that the Euclidean TSP remains an $\\mathcal{NP}$-hard combinatorial optimisation problem. \n\nIn this paper, we consider diversity optimisation for the Traveling Salesperson Problem. For each TSP instance, our goal is to find a set $P$ of $\\mu = |P|$ tours that is diverse with respect to some diversity measure, while each tour meets a given quality threshold. Let $I$ be an individual (which constitutes a permutation of the given $n$ cities) and\n$c(I)$ be the cost of $I$. The quality threshold is met iff $c(I) \\leq (1 + \\alpha) \\cdot OPT$, where $OPT$ is the value of an optimal tour and $\\alpha>0$ is a parameter that determines the required quality of a desired solution. The quality criterion means that the quality threshold is met iff $I$ is a $(1 + \\alpha)$ approximation of an optimal solution. We assume that the optimal tour is known for a given TSP instance.\n\nIn order to optimise the diversity for the Traveling Salesperson Problem we employ a $(\\mu+1)$-EA that has already been used in the context of evolutionary diversity optimisation~\\cite{DBLP:conf\/ppsn\/GaoNN16,DBLP:conf\/gecco\/AlexanderKN17,DBLP:journals\/corr\/abs-1802-05448,DBLP:conf\/gecco\/NeumannG0019,DBLP:conf\/foga\/BossekKN00T19}. Our approach differs from the previous ones in terms of the considered problem and underlying diversity measure that drives the optimisation approach.\n\nWe use Algorithm~\\ref{alg:ea} to compute a diverse population consisting of TSP tours where each individual\/tour $I$ has to meet a given quality criteria $c(I)$ according to a given threshold. Initially, the population $P$ is generated with $\\mu$ individuals, and exactly one offspring $I'$ is produced in each iteration. If the offspring $I'$ does not satisfy $c(I') \\leq (1+\\alpha)\\cdot OPT$, then it is discarded. Otherwise $I'$ is added to the population. Afterwards, elitist survival selection is performed with respect to a diversity measure $D$. For our investigations, we consider some function indicating overlaps between tours $D \\colon P \\rightarrow \\mathbb{R}$, which should be minimized to improve diversity. Thus, an individual $I \\in P$ is removed such that $D(P\\setminus \\{I\\})$ is minimal among all individuals $J \\in P$.\n\nWe introduce two diversity measures for evolutionary diversity optimisation for TSP, namely an \\emph{edge diversity} (ED) optimisation approach in Section~\\ref{sec3} and a \\emph{pairwise edge distances} (PD) optimisation approach in Section~\\ref{sec4}. We consider vector functions instead of traditional scalar functions, with the hope to capture more nuances in the survival selection mechanism elegantly.\n\nThe edge diversity optimisation approach attempts to maximise population diversity without relying on dissimilarities between tours. Instead, it considers how frequent each edge is present in the population, and aims to equalise these frequencies. The goal is a population of tours containing every edge, each as close to $k$ times as possible for some $k$. The approach makes sense if edges can be considered independent of each other, meaning each edge is present in the population at a frequency independent of that of other edges. This is not true for tours, thus important information may potentially be left out.\n\nOn the other hand, the pairwise edge distances approach considers solely the edge distances between all pairs of tours in the population in terms of overlap. It attempts to simultaneously maximise these distances and equalising them, with an emphasis on pairs with the least distances. In effect, it tries to increase these small distances by moving tours away from their closest tours and possibly closer to further tours, using mutation operators. Consequently, it tends to generally increase the dissimilarities between a tour $I$ and the rest $P\\setminus\\{I\\}$. This helps lessen the clustering phenomenon, where tours in the population form low-diversity clusters.\n\nThe evolutionary diversity algorithm based on edge diversity measure is compared to the evolutionary diversity optimisation approach based on pairwise edge distances measure in two different settings, using simple unconstrained TSP tours and TSPlib instances~\\cite{DBLP:journals\/informs\/Reinelt91} in Section~\\ref{sec5}.\n\n\\begin{algorithm}[tp]\n\\SetKwData{Left}{left}\\SetKwData{This}{this}\\SetKwData{Up}{up}\n\\SetKwInOut{Input}{input}\\SetKwInOut{Output}{output}\n\n{Initialise the population $P$ with $\\mu$ TSP tours such that $c(I) \\leq (1+ \\alpha)\\cdot OPT$ for all $I \\in P$.\\\\\nChoose $I \\in P$ uniformly at random and produce an offspring $I'$ of $I$ by mutation.\\\\ \nIf $c(I') \\leq (1+ \\alpha)\\cdot OPT$, add $I'$ to $P$. \\\\\nIf $|P| = \\mu+1$, remove exactly one individual $I$, where $I=\\arg \\min_{J \\in P} D(P\\setminus \\{J\\})$, from $P$.\\\\\nRepeat steps 2 to 4 until a termination criterion is reached.\\\\\n}\n\\caption{Diversity maximising ($\\mu + 1$)-EA}\n\\label{alg:ea}\n\\end{algorithm}\n\\section{Maximising edge diversity}\n\\label{sec3}\n\nIn this approach, we consider diversity in terms of equal representations of edges by tours in the population, or \\emph{edge diversity}. It takes into account, for each edge, the number of tours containing it, among the $\\mu$ solutions in the population. These numbers are referred to as \\emph{edge counts}. Given a population $P$ and an edge $e \\in E$, we denote by $n(e, P)$ its edge count, which is defined,\n\\begin{align*}\n n(e, P) := \\left|\\{T \\in P \\, | \\, e \\in E(T)\\}\\right| \\in \\{0, \\ldots, \\mu\\}\n\\end{align*}\nwhere $E(T) \\subset E$ is the set of edges used by solution $T$. Then in order to maximise the edge diversity we aim to minimise the vector\n\\begin{align*}\n \\mathcal{N}(P) = \\text{sort}\\left(n(e_1, P), n(e_2, P), \\ldots, n(e_m, P)\\right)\n\\end{align*}\nin the lexicographic order where sorting is performed in descending order. This is based on the idea of maximising genotypic diversity as the mean of pairwise edge distances~\\cite{DiversityPermutation}. Since $\\mu$ is fixed, we change the mean to a sum to simplify the function\n\\begin{align*}\n gtype(P) = \\sum_{T_1\\in P}\\sum_{T_2\\in P}|E(T_1)\\setminus E(T_2)|.\n\\end{align*}\nThe maximum edge distance between two different tours is $n$, so the maximum diversity is $\\mu(\\mu-1)n$. Let $n_i=n(e_i,P)$. There are $n_i$ tours in $P$ sharing edge $e_i$. Therefore, it affects $n_i(n_i-1)\/2$ pair-wise edge distances, reducing each by $1$. Since they can be added up independently across all edges, the diversity measure is then\n\\begin{align*}\n gtype(P) = \\mu(\\mu-1)n+\\sum_{i}n_i-\\sum_in^2_i.\n\\end{align*}\nSince $\\sum_in_i=\\mu n$ is constant, maximising diversity is reduced to minimising $\\sum_in^2_i$. Given $\\sum_in_i$ being constant, the Cauchy\u2013Schwarz inequality implies that $\\sum_in^2_i$ is the smallest when all $n_i$ are as close to being equal to each other as possible. The population with such property minimises $\\mathcal{N}$, meaning\n\\begin{align*}\n \\argmax_P\\{gtype(P)\\} = \\argmin_P\\{\\mathcal{N}(P)\\}.\n\\end{align*}\nFor complete graphs, the optima for $\\mathcal{N}(P)$ can be determined based on the following result, so the maximum diversity can be calculated.\n\\begin{thm}\\label{theo:ed_opt}\nFor every pair of integers $\\mu\\geq1$ and $n\\geq3$, given a complete graph $G=(V,E)$ where $|V|=n$, there is a $\\mu$-size population $P$ of tours such that\n\\[\\max_{e\\in E}\\{n(e,P)\\}-\\min_{e\\in E}\\{n(e,P)\\}\\leq1.\\]\n\\end{thm}\n\\begin{proof}\nWe prove this by defining a way to construct such a population. According to Theorem~1 in \\cite{Alspach1990}, in every complete graph with $n\\geq3$ vertices, there is a set of $h=\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor$ pairwise edge-disjoint Hamiltonian cycles. We denote by $H$ the set of all such Hamiltonian cycles in $G$, and $E(H)$ the set of all edges $H$ contains. We consider 2 cases: $n$ is odd, and $n$ is even.\n\nAssuming $n$ is odd, then $G$ can be decomposed completely into edge-disjoint tours, meaning $E(H)=E$. Let $\\mu=kh+r$ where $r\\in[0,h)$ and $r\\equiv \\mu\\bmod h$. We construct a population $P'$ by adding all tours in $H$, each exactly $k$ times. We then construct $P$ from $P'$ by adding all tours in $L$ for any $L\\subset H$ where $|L|=r$. With this, $n(e,P)=k$ for all $e\\notin E(L)$, and $n(e,P)=k+1$ for all $e\\in E(L)$.\n\nAssuming $n$ is even, then according to \\cite{Alspach1990}, for any perfect matching $M$ in $G$, the sub-graph $G^*=(V,E\\setminus M)$ can be decomposed completely into edge-disjoint tours. This means $E(H)=E\\setminus M$ for some perfect matching $M$ in $G$. Let $T$ be the tour in $G$ that goes through all edges in $M$, $M'=E(T)\\setminus M$ be another perfect matching edge-disjoint with $M$, $H'$ be the set of all edges-disjoint tours in $G'=(V,E\\setminus M')$, and $\\mu=k(h+1)+r$ where $r\\in[0,h]$ and $r\\equiv \\mu\\bmod (h+1)$. We construct $P$ with the following steps:\n\\begin{enumerate}\n \\item Add all tours in $H$, each $\\left\\lfloor\\frac{k+1}{2}\\right\\rfloor$ times\n \\item Add all tours in $H'$, each $\\left\\lfloor\\frac{k}{2}\\right\\rfloor$ times\n \\item Add tour $T$ $k$ times\n \\item Add all tours in $L$ where $L\\subseteq H$ if $k$ is even, or $L\\subseteq H'$ otherwise, such that $|L|=r$.\n\\end{enumerate}\nThe result is a population $P$ such that $|P|=\\mu$. If $k$ is odd, $n(e,P)=k+1$ for all $e\\in E(L)\\cup M'$ and $n(e,P)=k$ otherwise. If $k$ is even and positive, $n(e,P)=k+1$ for all $e\\in E(L)\\cup M$ and $n(e,P)=k$ otherwise. If $k=0$, $n(e,P)=1$ for all $e\\in E(L)$ and $n(e,P)=0$ otherwise.\n\\end{proof}\nAs demonstrated by the proof, a drawback of this approach is that it does not necessarily prevent duplication of tours in $P$ when $\\mu$ is sufficiently large. This is because the sum of $L1$-norm distances is no more sensitive to small distances than large distances. Consequently, the diversity score based on it can still be large when the population consists of low-diversity sub-populations that are highly dissimilar. In other words, this approach is susceptible to clustering.\n\nIn the context of EAs, this approach formulates a survival selection mechanism: removing from the population the individual $I\\in\\argmin_{I\\in P}\\{\\mathcal{N}(P\\setminus\\{I\\})\\}$. For an efficient implementation, we consider an equivalent fitness function for each individual $I\\in P$\n\\[n_P(I)=\\text{sort}\\left((n(e,P))_{e\\in I}\\right)\\]\nwith descending sorting order. The survival selection mechanism then removes $I\\in\\argmax_{I\\in P}\\{n_P(I)\\}$. The equivalence can be shown. Since elements of $\\mathcal{N}(P\\setminus\\{I\\})$ and $n_P(I)$ are in descending order, they can each be uniquely defined by a vector $(m^I_i)_{i=1,\\dots,\\mu}$ and $(n^I_j)_{j=1,\\dots,\\mu}$, respectively, where $m^I_i$ and $n^I_i$ are numbers of elements in $\\mathcal{N}(P\\setminus\\{I\\})$ and $n_P(I)$ equal to $i$, respectively. For $X,Y\\in P$, if $\\mathcal{N}(P\\setminus\\{X\\})<\\mathcal{N}(P\\setminus\\{Y\\})$ lexicographically, then there must be $j\\in[1,\\mu]$ such that $m^X_jn^Y_j$ and $n^X_i=n^Y_i$ for all $i\\in(j,\\mu]$. This implies that $n_P(X)>n_P(Y)$ lexicographically. On the other hand, it is trivial to prove that $\\mathcal{N}(P\\setminus\\{X\\})=\\mathcal{N}(P\\setminus\\{Y\\})$ implies $n_P(X)=n_P(Y)$. This means\n\\[\\argmin_{I\\in P}\\{\\mathcal{N}(P\\setminus\\{I\\})\\}=\\argmax_{I\\in P}\\{n_P(I)\\}.\\]\nWith this method, the survival selection mechanism is consisted of three phases:\n\\begin{enumerate}\n \\item Calculating the edge counts table: $O(\\mu n)$\n \\item Calculating $n_P(I)$ for all $I$: $O(\\mu n\\log n)$\n \\item Finding and removing $I=\\argmax_{I\\in P}\\{n_P(I)\\}$: $O(\\mu n)$\n\\end{enumerate}\nThe complexity of the survival selection is then $O(\\mu n\\log n)$. On the other hand, the mechanism's complexity when using $gtype(P\\setminus\\{I\\})$ as fitness values is $O(\\mu^2n+\\mu^3)$ ($O(\\mu^2n)$ from calculating the edge distances table and $O(\\mu^2)$ from calculating $gtype$ from said table for each tour). Asymptotically speaking, our proposal can be faster per iteration in many cases.\n\n\\section{Equalising pairwise edge distances}\n\\label{sec4}\n\nOne way to remedy the clustering phenomenon is to increase edge distances between highly similar tours, potentially at the cost of decreasing edge distances between highly dissimilar tours. This method essentially equalises the tours' pairwise edge distances. As such, we present another approach that discourages clustering by emphasising uniform pairwise edge distances while maximising diversity. We reformulate the edge distance as edge overlap\n\\begin{align*}\n o_{XY}=|E(X)\\cap E(Y)|=n-|E(X)\\setminus E(Y)|,\\forall X,Y\\in P.\n\\end{align*}\nThe aim is then to minimise the vector\n\\begin{align*}\n \\mathcal{D}(P) = \\text{sort}\\left(\\left(o_{XY}\\right)_{X,Y\\in P}\\right)\n\\end{align*}\nin the lexicographic order where sorting is performed in descending order. This approach simultaneously maximises diversity via minimising $\\sum_{X,Y\\in P}o_{XY}$, while also maximising uniformity via equalising $o_{XY}$. It can be the case that $\\mathcal{D}(P)<\\mathcal{D}(P')$ and $gtype(P)n^Y_j$ and $n^X_i=n^Y_i$ for all $i\\in(j,n]$. This means $d_P(X)>d_P(Y)$. Furthermore, $\\mathcal{D}(P\\setminus\\{X\\})<\\mathcal{D}(P\\setminus\\{Y\\})$ obviously implies $d_P(X)=d_P(Y)$. Intuitively, this implementation removes $I$ that has the smallest edge distance to $P\\setminus\\{I\\}$, defined by the minimum edge distance between $I$ and all tours in $P\\setminus\\{I\\}$. The lexicographic ordering of vectors allows an elegant way to resolve draw cases: comparing the second minimum distances, the third, the fourth and so on. The result is the guaranteed non-increasing edge distance between $I'$ and $P\\setminus\\{I'\\}$ for all other tours $I'$ as well. The consequence is convergence to a solution population, in which each tour is reasonably dissimilar to the rest. This approach aligns closely with the diversity formulated in \\cite{DiversityManyObj}, with edge distance being the dissimilarity metric. Since $\\mu$ is fixed, we introduce an additional normalization factor.\n\\[div(P)=\\sum_{T\\in P}dist(T,P\\setminus\\{T\\})=\\frac{1}{\\mu n}\\sum_{T\\in P}\\min_{X\\in P\\setminus\\{T\\}}\\left\\lbrace|E(T)\\setminus E(X)|\\right\\rbrace.\\]\nNote that the difference between $gtype$ and $div$ is the focus on the minimum edge distances, the two measures would be the same if $min$ were replaced by $sum$ or $mean$. We hypothesise that edge distances uniformity is strongly positively correlated to $div$. This is explored further in Section \\ref{sec5}.\n\n\\section{Experimental investigations}\n\\label{sec5}\n\nWe perform different series of experiments to gain insights into the process of evolving diverse TSP tours. In all experiments our input is a complete graph $G = (V, E)$ with real-valued cost function $w : E \\to \\mathbb{R}^{+}$. We consider 6 variants of algorithm \\ref{alg:ea}, differing in their mutation operators and survival selection mechanisms. The mutation operators are 2-OPT, 3-OPT, 4-OPT, and the survival selection mechanisms are based on the two proposed approaches.\n\n\\subsection{Unconstrained Diversity Optimisation}\nIn this setting our focus is on diverse TSP tours without constraints on tours' qualities. As such, we study our approaches with random initial populations. We experiment with all combinations of $n=\\{50,100,200,500\\}$ and $\\mu=\\{3,10,20,50\\}$. For each $(n,\\mu)$ combination, 30 populations are randomly generated as initial populations for all EA variants, controlling for the initialisation factor. Furthermore, with the established guarantee for optima, a termination criterion is such optima are reached. As for minimising $\\mathcal{D}(P)$, another criterion\n\\[\\max_{X,Y\\in P}\\{o_{XY}\\}-\\min_{X,Y\\in P}\\{o_{XY}\\}\\leq1\\]\nis added forming a bound on the optima.\nAn additional limit of $\\mu n^2$ iterations is imposed on the experiments. Also, since optimal $gtype$ scores can be calculated, we record the scores in percentages for ease of comparison across all settings.\n\nAccording to Tables \\ref{tb:Edge_counts}, \\ref{tb:Pair_dist}, all variants seem to reliably achieve optima in all cases where $\\mu\\leq\\left\\lfloor\\frac{n-1}{2}\\right\\rfloor$, except for 4-OPT variants seemingly stuck in local optima when $n=50$ and $\\mu=20$. In the other hard cases, none ever reached the optima within the time limits. This suggests that when close to the optima, the probability of increasing $gtype$ in an iteration decreases substantially with increasing $\\mu\/n$. Also, in such cases, all variants with 2-OPT mutation operator achieve higher $gtype$ score than those with 3-OPT, which in turn outperform those with 4-OPT. Furthermore, for $(n,\\mu)=(50,20)$, all 2-OPT variants always reaches the optimum, while 3-OPT variants struggle and 4-OPT variants fail entirely. This indicates that large-step mutation operators are prone to being stuck in local optima when the population is close to maximum $gtype$.\n\nAdditionally, minimising $\\mathcal{N}(P)$ and minimising $\\mathcal{D}(P)$ seem to produce the similar final $gtype$ scores within similar numbers of iterations in all cases, given the same mutation operator used. This indicates that minimising $\\mathcal{D}(P)$ also tends to maximise $gtype$ when all tours are accepted. However, in the hard cases, the PD approach achieves somewhat lower $gtype$ scores than ED across all variants. This suggests that the trade-offs between edge diversity and edge distances uniformity are non-trivial near optima.\n\nAnother observation is that with small enough $\\mu\/n$, 2-OPT variants tend to take more iterations than 3-OPT variants, which in turn tend to terminate later than 4-OPT variants. When $\\mu\/n$ is larger than some number, the trend seems to revert. However, the indication for this observation is weak since no statistically significant difference can be seen in many cases.\n\\subsection{Constrained Diversity Optimisation}\nNow we consider TSP instances from the famous TSPlib, specifically eil51, eil76, eil101. For these experiments, we use the provided optimal tour for each instance, initialise $P$ with $\\mu$ copies of it and perform diversity maximisation subject to $c(I) \\leq (1 + \\alpha)\\cdot OPT$ for all $I \\in P$. I.~e., we accept tours only if they deviate in length by a factor of at most $(1+\\alpha)$ from the optimal tour length OPT. We set up the instances for our experiments with $\\mu=\\{5,10,20,50\\}$ and $\\alpha=\\{0.05, 0.2, 0.5, 1.0\\}$. For each instance, we run each algorithm variant 30 times and record the final population. As before, $gtype$ scores are reported in percentages, since these instances involve complete graphs and Theorem~\\ref{theo:ed_opt} applies. In addition, we record $\\varsigma(P)=\\left(\\max_{X,Y\\in P}\\{o_{XY}\\}-\\min_{X,Y\\in P}\\{o_{XY}\\}\\right)\/n$ to observe uniformity in edge distances between tours; lower scores indicate higher uniformity. All scores are averaged over 30 runs.\n\nAccording to Table~\\ref{tb:TSPlib}, $gtype$ scores achieved predictably increase with increasing $\\alpha$, albeit with diminishing return. On the other hand, $\\varsigma$ scores tend to increase with increasing $\\mu$, and dramatically decrease with increasing $\\alpha$. In terms of mutation operators, 2-OPT seems to be the best performer overall, while 3-OPT and 4-OPT perform similar. Furthermore, all things equal, minimising $\\mathcal{N}(P)$ tends to produce slightly higher $gtype$ scores and noticeably lower $\\varsigma$ scores than minimising $\\mathcal{D}(P)$. The PD approach seems to better capitalise on increasing $\\alpha$, improving edge distances uniformity faster. Moreover, the edge distances uniformity of the PD approach's output populations is less susceptible to compromise due to increasing $\\mu$ within this range. These phenomena align with the remark that the ED approach focuses on $gtype$ while the PD approach compromises it for edge distances uniformity.\n\n\n\\begin{table*}[htbp]\n\\renewcommand{\\arraystretch}{1.2845}\n\\renewcommand\\tabcolsep{5.7pt}\n\\caption{Comparison in terms of diversity (gtype) and pairwise edge distances ranges ($\\varsigma$) among all variants of the EA on TSPlib instances. Better values with statistical significance (based on Wilcoxon rank sum tests with 95\\% confidence threshold) between ED and PD are bold-faced.\n}\n\\label{tb:TSPlib}\n\\begin{scriptsize}\n\\begin{tabular}{crrcccccccccccc}\n \\toprule\n\n\\multirow{3}{*}{\\textbf{}}&\\multirow{3}{*}{\\textbf{$\\mu$}} & \\multirow{3}{*}{\\textbf{$\\alpha$}} &\n\\multicolumn{6}{c}{\\bfseries ED} & \\multicolumn{6}{c}{\\bfseries PD}\\\\\n\\cmidrule(l{2pt}r{2pt}){4-9} \\cmidrule(l{2pt}r{2pt}){10-15}\n & & & \\multicolumn{2}{c}{\\bfseries2-OPT} & \\multicolumn{2}{c}{\\bfseries3-OPT}& \\multicolumn{2}{c}{\\bfseries4-OPT}& \\multicolumn{2}{c}{\\bfseries2-OPT} & \\multicolumn{2}{c}{\\bfseries3-OPT}& \\multicolumn{2}{c}{\\bfseries4-OPT} \\\\\n \\cmidrule(l{2pt}r{2pt}){4-5} \\cmidrule(l{2pt}r{2pt}){6-7}\n \\cmidrule(l{2pt}r{2pt}){8-9} \\cmidrule(l{2pt}r{2pt}){10-11}\n \\cmidrule(l{2pt}r{2pt}){12-13} \\cmidrule(l{2pt}r{2pt}){14-15}\n &&&\\textbf{gtype}&\\textbf{$\\varsigma$}&\\textbf{gtype}&\\textbf{$\\varsigma$}&\\textbf{gtype}&\\textbf{$\\varsigma$}&\\textbf{gtype}&\\textbf{$\\varsigma$}&\\textbf{gtype}&\\textbf{$\\varsigma$}&\\textbf{gtype}&\\textbf{$\\varsigma$}\\\\\n\\midrule\n\\multirow{20}{*}[0.5cm]{\\rotatebox[origin=c]{90}{eil51}}&3&0.05&34.27\\%&68.37\\%&36.23\\%&67.78\\%&28.95\\%&74.05\\%&32.07\\%&69.54\\%&35.95\\%&66.14\\%&29.78\\%&71.96\\%\\\\&\n&0.2&70.78\\%&31.83\\%&67.93\\%&35.03\\%&63.68\\%&40.46\\%&71.11\\%&30.20\\%&65.95\\%&35.75\\%&63.12\\%&38.56\\%\\\\&\n&0.5&93.83\\%&8.43\\%&90.85\\%&11.05\\%&90.78\\%&11.37\\%&93.62\\%&\\textbf{7.12\\%}&90.26\\%&11.18\\%&90.37\\%&10.59\\%\\\\&\n&1&99.89\\%&0.13\\%&99.83\\%&0.26\\%&99.80\\%&0.33\\%&99.80\\%&0.33\\%&99.74\\%&0.65\\%&99.76\\%&0.52\\%\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&10&0.05&\\textbf{31.82\\%}&79.67\\%&\\textbf{33.64\\%}&78.43\\%&27.79\\%&82.88\\%&29.37\\%&78.24\\%&31.60\\%&\\textbf{75.95\\%}&27.65\\%&\\textbf{79.61\\%}\\\\&\n&0.2&\\textbf{63.04\\%}&70.39\\%&\\textbf{60.60\\%}&67.12\\%&\\textbf{57.78\\%}&63.40\\%&60.99\\%&\\textbf{44.90\\%}&59.23\\%&\\textbf{47.39\\%}&55.99\\%&\\textbf{51.31\\%}\\\\&\n&0.5&\\textbf{83.14\\%}&30.85\\%&\\textbf{81.34\\%}&36.67\\%&\\textbf{81.29\\%}&37.58\\%&82.00\\%&\\textbf{20.33\\%}&80.12\\%&\\textbf{23.01\\%}&79.87\\%&\\textbf{23.99\\%}\\\\&\n&1&\\textbf{95.06\\%}&10.26\\%&\\textbf{94.14\\%}&11.76\\%&\\textbf{94.19\\%}&11.63\\%&94.57\\%&\\textbf{7.58\\%}&93.30\\%&\\textbf{8.50\\%}&93.16\\%&\\textbf{8.50\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&20&0.05&\\textbf{32.52\\%}&95.23\\%&\\textbf{32.86\\%}&91.37\\%&\\textbf{27.89\\%}&90.85\\%&29.20\\%&\\textbf{82.42\\%}&31.23\\%&\\textbf{79.08\\%}&26.45\\%&\\textbf{83.53\\%}\\\\&\n&0.2&\\textbf{62.32\\%}&92.09\\%&\\textbf{59.98\\%}&91.57\\%&\\textbf{57.46\\%}&91.70\\%&59.30\\%&\\textbf{49.15\\%}&57.84\\%&\\textbf{51.37\\%}&54.53\\%&\\textbf{55.29\\%}\\\\&\n&0.5&\\textbf{80.95\\%}&59.02\\%&\\textbf{79.24\\%}&63.27\\%&\\textbf{79.60\\%}&64.84\\%&79.03\\%&\\textbf{25.29\\%}&77.69\\%&\\textbf{27.84\\%}&77.32\\%&\\textbf{29.08\\%}\\\\&\n&1&\\textbf{92.17\\%}&19.87\\%&\\textbf{91.41\\%}&22.42\\%&\\textbf{91.58\\%}&21.31\\%&90.97\\%&\\textbf{11.83\\%}&90.28\\%&\\textbf{12.42\\%}&90.24\\%&\\textbf{12.75\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&50&0.05&\\textbf{32.66\\%}&100.00\\%&\\textbf{33.23\\%}&100.00\\%&\\textbf{28.01\\%}&100.00\\%&29.81\\%&\\textbf{85.88\\%}&31.75\\%&\\textbf{82.48\\%}&26.93\\%&\\textbf{85.95\\%}\\\\&\n&0.2&\\textbf{63.26\\%}&99.48\\%&\\textbf{61.52\\%}&97.78\\%&\\textbf{58.92\\%}&96.99\\%&59.68\\%&\\textbf{53.59\\%}&58.36\\%&\\textbf{57.12\\%}&55.04\\%&\\textbf{59.80\\%}\\\\&\n&0.5&\\textbf{80.74\\%}&92.35\\%&\\textbf{79.56\\%}&90.59\\%&\\textbf{79.80\\%}&88.76\\%&79.15\\%&\\textbf{29.67\\%}&78.12\\%&\\textbf{32.29\\%}&77.94\\%&\\textbf{33.66\\%}\\\\&\n&1&\\textbf{91.65\\%}&48.95\\%&\\textbf{91.25\\%}&52.68\\%&\\textbf{91.33\\%}&48.37\\%&90.60\\%&\\textbf{15.69\\%}&90.42\\%&\\textbf{15.75\\%}&90.42\\%&\\textbf{16.67\\%}\\\\\\hline\n\\multirow{20}{*}[0.5cm]{\\rotatebox[origin=c]{90}{eil76}}&3&0.05&30.12\\%&71.84\\%&30.06\\%&72.89\\%&24.20\\%&78.60\\%&29.04\\%&71.97\\%&29.80\\%&71.89\\%&24.08\\%&76.97\\%\\\\&\n&0.2&70.23\\%&31.67\\%&63.98\\%&38.90\\%&60.39\\%&42.02\\%&69.05\\%&32.15\\%&63.17\\%&37.76\\%&59.11\\%&42.06\\%\\\\&\n&0.5&94.66\\%&6.49\\%&90.63\\%&11.45\\%&91.05\\%&11.14\\%&94.72\\%&5.88\\%&90.82\\%&\\textbf{9.74\\%}&90.29\\%&10.61\\%\\\\&\n&1&99.91\\%&0.22\\%&99.63\\%&0.57\\%&99.80\\%&0.48\\%&99.90\\%&0.09\\%&99.65\\%&0.53\\%&99.69\\%&0.57\\%\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&10&0.05&\\textbf{28.52\\%}&79.39\\%&\\textbf{29.33\\%}&78.95\\%&23.14\\%&83.60\\%&27.09\\%&78.73\\%&28.35\\%&79.17\\%&22.87\\%&82.59\\%\\\\&\n&0.2&\\textbf{61.56\\%}&57.19\\%&\\textbf{58.62\\%}&56.75\\%&\\textbf{56.01\\%}&60.13\\%&59.57\\%&\\textbf{44.91\\%}&56.41\\%&\\textbf{49.08\\%}&53.67\\%&\\textbf{52.24\\%}\\\\&\n&0.5&\\textbf{84.71\\%}&28.60\\%&\\textbf{81.03\\%}&36.45\\%&\\textbf{81.92\\%}&33.64\\%&82.94\\%&\\textbf{18.99\\%}&79.54\\%&\\textbf{23.07\\%}&79.45\\%&\\textbf{23.90\\%}\\\\&\n&1&\\textbf{95.92\\%}&7.94\\%&\\textbf{94.39\\%}&9.96\\%&\\textbf{94.78\\%}&9.43\\%&95.32\\%&\\textbf{5.83\\%}&93.66\\%&\\textbf{7.72\\%}&93.74\\%&\\textbf{7.72\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&20&0.05&\\textbf{28.74\\%}&88.95\\%&\\textbf{28.85\\%}&88.68\\%&\\textbf{23.69\\%}&88.42\\%&26.96\\%&\\textbf{81.49\\%}&27.38\\%&\\textbf{81.97\\%}&22.25\\%&\\textbf{85.18\\%}\\\\&\n&0.2&\\textbf{61.19\\%}&92.76\\%&\\textbf{58.37\\%}&92.89\\%&\\textbf{56.06\\%}&91.45\\%&58.50\\%&\\textbf{48.29\\%}&55.41\\%&\\textbf{53.16\\%}&52.20\\%&\\textbf{56.67\\%}\\\\&\n&0.5&\\textbf{82.35\\%}&53.90\\%&\\textbf{79.64\\%}&65.39\\%&\\textbf{80.32\\%}&58.68\\%&79.72\\%&\\textbf{23.73\\%}&77.58\\%&\\textbf{26.84\\%}&77.40\\%&\\textbf{28.42\\%}\\\\&\n&1&\\textbf{93.03\\%}&16.10\\%&\\textbf{91.95\\%}&20.04\\%&\\textbf{92.37\\%}&18.11\\%&91.67\\%&\\textbf{10.26\\%}&90.67\\%&\\textbf{11.58\\%}&90.78\\%&\\textbf{11.84\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&50&0.05&\\textbf{28.84\\%}&100.00\\%&\\textbf{28.41\\%}&99.91\\%&\\textbf{23.99\\%}&98.95\\%&27.01\\%&\\textbf{84.47\\%}&27.77\\%&\\textbf{85.09\\%}&22.52\\%&\\textbf{87.28\\%}\\\\&\n&0.2&\\textbf{62.42\\%}&98.95\\%&\\textbf{59.32\\%}&98.73\\%&\\textbf{56.80\\%}&98.07\\%&58.16\\%&\\textbf{52.54\\%}&55.73\\%&\\textbf{56.80\\%}&52.29\\%&\\textbf{60.35\\%}\\\\&\n&0.5&\\textbf{81.53\\%}&86.62\\%&\\textbf{79.74\\%}&90.39\\%&\\textbf{80.35\\%}&88.03\\%&79.05\\%&\\textbf{27.50\\%}&77.21\\%&\\textbf{31.01\\%}&77.08\\%&\\textbf{32.63\\%}\\\\&\n&1&\\textbf{91.73\\%}&42.19\\%&\\textbf{91.18\\%}&46.62\\%&\\textbf{91.39\\%}&38.55\\%&90.32\\%&\\textbf{13.68\\%}&89.84\\%&\\textbf{14.78\\%}&90.02\\%&\\textbf{14.91\\%}\\\\\\hline\n\\multirow{20}{*}[0.5cm]{\\rotatebox[origin=c]{90}{eil101}}&3&0.05&35.84\\%&65.97\\%&\\textbf{36.79\\%}&65.74\\%&31.21\\%&70.99\\%&35.69\\%&65.71\\%&35.49\\%&65.51\\%&30.24\\%&70.69\\%\\\\&\n&0.2&\\textbf{72.61\\%}&29.60\\%&67.50\\%&34.69\\%&65.30\\%&36.40\\%&71.29\\%&29.11\\%&65.56\\%&35.08\\%&63.99\\%&36.83\\%\\\\&\n&0.5&95.03\\%&5.91\\%&91.86\\%&9.64\\%&92.29\\%&9.27\\%&94.72\\%&5.78\\%&91.60\\%&8.98\\%&91.63\\%&9.11\\%\\\\&\n&1&99.79\\%&0.40\\%&99.49\\%&0.76\\%&99.72\\%&0.50\\%&99.81\\%&0.36\\%&99.57\\%&0.66\\%&99.85\\%&\\textbf{0.23\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&10&0.05&31.88\\%&76.27\\%&\\textbf{33.44\\%}&74.19\\%&\\textbf{28.88\\%}&78.88\\%&31.36\\%&\\textbf{73.37\\%}&32.60\\%&\\textbf{72.05\\%}&27.77\\%&\\textbf{76.93\\%}\\\\&\n&0.2&\\textbf{63.70\\%}&49.64\\%&\\textbf{60.78\\%}&54.16\\%&\\textbf{58.69\\%}&55.38\\%&62.44\\%&\\textbf{40.89\\%}&59.29\\%&\\textbf{44.95\\%}&56.49\\%&\\textbf{47.95\\%}\\\\&\n&0.5&\\textbf{85.14\\%}&25.78\\%&\\textbf{82.55\\%}&30.43\\%&\\textbf{82.75\\%}&33.00\\%&83.84\\%&\\textbf{17.52\\%}&81.64\\%&\\textbf{20.20\\%}&80.78\\%&\\textbf{21.55\\%}\\\\&\n&1&\\textbf{96.29\\%}&6.80\\%&\\textbf{95.07\\%}&9.08\\%&\\textbf{95.25\\%}&8.75\\%&95.97\\%&\\textbf{4.95\\%}&94.37\\%&\\textbf{6.77\\%}&94.37\\%&\\textbf{6.86\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&20&0.05&\\textbf{32.80\\%}&85.28\\%&\\textbf{33.52\\%}&85.31\\%&\\textbf{28.74\\%}&85.97\\%&30.58\\%&\\textbf{76.63\\%}&31.78\\%&\\textbf{75.38\\%}&27.21\\%&\\textbf{79.90\\%}\\\\&\n&0.2&\\textbf{63.37\\%}&92.48\\%&\\textbf{60.27\\%}&89.70\\%&\\textbf{58.75\\%}&89.90\\%&60.83\\%&\\textbf{44.36\\%}&58.11\\%&\\textbf{48.91\\%}&55.30\\%&\\textbf{51.16\\%}\\\\&\n&0.5&\\textbf{82.93\\%}&56.17\\%&\\textbf{80.68\\%}&57.49\\%&\\textbf{81.19\\%}&55.68\\%&81.04\\%&\\textbf{21.22\\%}&79.08\\%&\\textbf{24.19\\%}&79.05\\%&\\textbf{25.21\\%}\\\\&\n&1&\\textbf{93.71\\%}&14.98\\%&\\textbf{92.62\\%}&17.99\\%&\\textbf{93.06\\%}&15.91\\%&92.28\\%&\\textbf{9.01\\%}&91.31\\%&\\textbf{10.23\\%}&91.42\\%&\\textbf{10.43\\%}\\\\\\cmidrule(l{2pt}r{2pt}){2-15}\n&50&0.05&\\textbf{34.32\\%}&100.00\\%&\\textbf{33.17\\%}&99.47\\%&\\textbf{28.96\\%}&99.01\\%&30.26\\%&\\textbf{79.44\\%}&31.34\\%&\\textbf{78.75\\%}&26.91\\%&\\textbf{82.71\\%}\\\\&\n&0.2&\\textbf{63.92\\%}&98.48\\%&\\textbf{60.95\\%}&97.92\\%&\\textbf{59.39\\%}&97.66\\%&59.76\\%&\\textbf{48.25\\%}&57.89\\%&\\textbf{52.24\\%}&54.86\\%&\\textbf{55.74\\%}\\\\&\n&0.5&\\textbf{81.65\\%}&86.30\\%&\\textbf{79.96\\%}&90.23\\%&\\textbf{80.51\\%}&85.87\\%&79.34\\%&\\textbf{24.85\\%}&78.20\\%&\\textbf{27.36\\%}&77.85\\%&\\textbf{28.84\\%}\\\\&\n&1&\\textbf{91.58\\%}&34.69\\%&\\textbf{90.88\\%}&45.38\\%&\\textbf{91.20\\%}&36.60\\%&90.01\\%&\\textbf{12.34\\%}&89.60\\%&\\textbf{13.17\\%}&89.80\\%&\\textbf{13.43\\%}\\\\\\hline\n\\end{tabular}\n\\end{scriptsize}\n\\end{table*}\n\n\n\\begin{figure}[t]\n\\centering\n\\begin{subfigure}{0.4\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/uniform_vs_div.eps}\n\\caption{$\\varsigma$ and $div$}\\label{fig:uniform_div_corr}\n\\end{subfigure}\n\\begin{subfigure}{0.4\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/gtype_vs_div.eps}\n\\caption{$gtype$ and $div$}\\label{fig:gtype_div}\n\\end{subfigure}\n\\caption{\nScatter plots of all 8640 runs on the TSPlib instances. Each point corresponds to a final population after one run. The Pearson correlation coefficient between $\\varsigma$ and $div$ is $-0.9815$ with $p<0.0001$.}\n\\end{figure}\nAdditionally, we investigate the correlation between edge distances uniformity and the diversity score $div(P)$. Figure \\ref{fig:uniform_div_corr} shows a strong negative linear correlation between $div(P)$ and $\\varsigma(P)$ across all cases. This suggests that focusing on edge distances uniformity, while maximising $gtype$, is effective in maximising $div$. Combined with earlier observations, we can conclude that the PD approach is much more likely to make a better compromise between maximising $gtype$ and maximising $div$. This is illustrated in Figure~\\ref{fig:gtype_div}, indicating that for each $\\alpha$ value, the PD approach maintains higher $div$ scores across all $\\mu$ values without significantly sacrificing $gtype$ scores.\n\n\\begin{figure}[t]\n\\centering\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_5_ec_2opt.eps}\n\\caption{ED, $\\alpha=0.05$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_20_ec_2opt.eps}\n\\caption{ED, $\\alpha=0.2$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_50_ec_2opt.eps}\n\\caption{ED, $\\alpha=0.5$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_100_ec_2opt.eps}\n\\caption{ED, $\\alpha=1.0$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_5_pd_2opt.eps}\n\\caption{PD, $\\alpha=0.05$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_20_pd_2opt.eps}\n\\caption{PD, $\\alpha=0.2$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_50_pd_2opt.eps}\n\\caption{PD, $\\alpha=0.5$}\n\\end{subfigure}\n\\begin{subfigure}{0.24\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_50_100_pd_2opt.eps}\n\\caption{PD, $\\alpha=1.0$}\n\\end{subfigure}\n\\caption{Visualised edge counts from resulted populations in eil51 cases with $\\mu=50$. The optimal tour is marked with red edges. Darker edges have higher counts.}\n\\label{fig:edge_count}\n\\end{figure}\n\n\\begin{figure*}[htbp]\n\\centering\n\\begin{subfigure}{1\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_10_5_ec_2opt_pop.eps}\n\\caption{ED, $\\alpha=5\\%$}\n\\end{subfigure}\n~\\\\\n\\begin{subfigure}{1\\linewidth}\n\\centering\n\\includegraphics[width=\\linewidth]{images\/eil51_10_5_pd_2opt_pop.eps}\n\\caption{PD, $\\alpha=5\\%$}\n\\end{subfigure}\n~\\\\\n\\begin{subfigure}{1\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_10_20_ec_2opt_pop.eps}\n\\caption{ED, $\\alpha=20\\%$}\n\\end{subfigure}\n~\\\\\n\\begin{subfigure}{1\\linewidth}\n\\centering\n\\includegraphics[width=1\\linewidth]{images\/eil51_10_20_pd_2opt_pop.eps}\n\\caption{PD, $\\alpha=20\\%$}\n\\end{subfigure}\n\\caption{\nVisualised tour populations from resulted populations in eil51 cases with $\\mu=10$ and 2-OPT as mutation operator. Red edges are shared by at least two tours in the population, and blue ones are unique to the tour. Left-to-right is the ascending tour length order.}\n\\label{fig:populations}\n\\end{figure*}\n\nThe visuals in Figure~\\ref{fig:edge_count} show that the PD approach results in fewer zero-count edges than the ED, regardless of $\\alpha$. It also results in higher maximum edge counts than the ED in those cases. This is because minimising $\\mathcal{N}(P)$ flattens the edge counts distribution from the top down with the descending sorting order. The implication is that the counts distribution among the lower end is not guaranteed improvement, especially among the zero-count. On the other hand, minimising $\\mathcal{D}(P)$, while not directly dealing with edge counts, tends to equalise this distribution while relaxing minimising higher count edges. Consequently, higher maximum edge counts are achieved, but fewer edges have high counts and more edges have low non-zero counts. Consequently, individuals are more likely to contain more unique edges (edges with count 1), which is also a mark of highly diverse populations. As Figure~\\ref{fig:populations} shows, with small $\\alpha$, the populations generated by the ED approach tend to contain duplicated tours and tours without unique edges. In contrast, tours produced by the PD approach tend to exhibit more uniqueness and stand out from the rest.\n\n\n\\section{Conclusion}\nEvolutionary diversity optimisation aims to generate a set of diverse solutions where all solutions meet given quality criteria. We have introduced and examined for the first time evolutionary diversity optimisation for a classical combinatorial optimisation problems. We introduced two diversity measures that can be used for the Traveling Salesperson Problem and evaluated their performance when used for simple population-based elitist evolutionary algorithms. The results show that both measures can be optimized well in the unconstrained case where all tours meet the quality criterion. Furthermore, our investigations for TSPlib instances point out the increase in terms of diversity that can be obtained when relaxing the quality constraint determined by the required approximation ratio. We also highlighted some differences between populations generated by these two approaches.\n\nThe focus of this paper has been on the introduced diversity measures for diversity optimisation of the TSP and their performance in simple population-based elitist evolutionary algorithms.\nFor future research, it would be interesting to incorporate these measures into state of the art evolutionary algorithms for the TSP and evaluate their performance.\n\n\\section*{Acknowledgment}\nThis work has been supported by the Australian Research Council (ARC) through grant DP190103894.\n\n\\bibliographystyle{unsrt}\n","meta":{"redpajama_set_name":"RedPajamaArXiv"}}