title
stringlengths 1
149
⌀ | section
stringlengths 1
1.9k
⌀ | text
stringlengths 13
73.5k
|
|---|---|---|
Timeline of the COVID-19 pandemic in Turkey
|
November 2020
|
17 November Recep Tayyip Erdoğan announced new measures to control the spread of the virus. He stated that distant learning would continue until the end of the year, a curfew would be imposed on weekends except between 10:00 am–08:00 pm, restaurants would only provide take-away service, and shopping malls and markets would close at 08:00 pm.
20 November On 20 November, Ministry of Health reinstated the curfew on people age 65 and older and people twenty and younger. On the same day, Minister of Internal Affairs ordered businesses and places of worship to halt indoor activities. Grocery stores and pharmacies have remained open, with legally imposed limits to capacity.
30 November On 30 November, official figures showed that gross domestic product expanded 15.6 per cent compared with the previous quarter, and 6.7 per cent compared with a year earlier.
|
Timeline of the COVID-19 pandemic in Turkey
|
December 2020
|
6 December On 6 December, Ministry of Health Fahrettin Koca announced that 50 million doses of CoronaVac should arrive by the end of February 2021, and 10 million doses of the Pfizer–BioNTech COVID-19 vaccine should start arriving still during December.
|
Timeline of the COVID-19 pandemic in Turkey
|
December 2020
|
7 December On 7 December, Pfizer and BioNTech finalized their submission to the Turkish Medicines and Medical Devices Agency (TMA), which has been reviewing data from the clinical trial on a rolling basis since October. The TMA said it would recommend granting an emergency use authorization if it concluded "that the benefits of the vaccine outweigh its risks in protecting against COVID-19", based on the 2004 law that created the TMA's process.
|
Timeline of the COVID-19 pandemic in Turkey
|
December 2020
|
10 December On 10 December, the seven-day averages for three of the primary metrics (tests, cases, hospitalizations) were at record highs. Earlier in the spring of 2020, during the first COVID-19 surge in the Turkey, the rising death toll reached a peak on 22 April, with a seven-day average of 122 daily deaths. In December, the seven-day average of deaths in Turkey from COVID-19 broke that record, at 255 on 29 December.
|
Timeline of the COVID-19 pandemic in Turkey
|
December 2020
|
13 December On 13 December, TMA pushed back formal assessments of two COVID-19 vaccines, delaying distribution of the Pfizer–BioNTech COVID-19 vaccine and CoronaVac in Turkey to the end of December. The TMA said it planned to give an opinion on the Pfizer–BioNTech COVID-19 vaccine at a meeting on 29 December. TMA has also delayed assessing the rival Moderna vaccine until 12 January.
|
Timeline of the COVID-19 pandemic in Turkey
|
January 2021
|
1 January Turkey detected 15 cases of the UK coronavirus variant on 1 January 2021.
14 January On 14 January 2021, Turkish President Recep Tayyip Erdoğan received the COVID-19 vaccine.
|
Flame (malware)
|
Flame (malware)
|
Flame, also known as Flamer, sKyWIper, and Skywiper, is modular computer malware discovered in 2012 that attacks computers running the Microsoft Windows operating system. The program is used for targeted cyber espionage in Middle Eastern countries.Its discovery was announced on 28 May 2012 by the MAHER Center of the Iranian National Computer Emergency Response Team (CERT), Kaspersky Lab and CrySyS Lab of the Budapest University of Technology and Economics. The last of these stated in its report that Flame "is certainly the most sophisticated malware we encountered during our practice; arguably, it is the most complex malware ever found." Flame can spread to other systems over a local network (LAN). It can record audio, screenshots, keyboard activity and network traffic. The program also records Skype conversations and can turn infected computers into Bluetooth beacons which attempt to download contact information from nearby Bluetooth-enabled devices. This data, along with locally stored documents, is sent on to one of several command and control servers that are scattered around the world. The program then awaits further instructions from these servers.According to estimates by Kaspersky in May 2012, Flame had initially infected approximately 1,000 machines, with victims including governmental organizations, educational institutions and private individuals. At that time 65% of the infections happened in Iran, Israel, Palestine, Sudan, Syria, Lebanon, Saudi Arabia, and Egypt, with a "huge majority of targets" within Iran. Flame has also been reported in Europe and North America. Flame supports a "kill" command which wipes all traces of the malware from the computer. The initial infections of Flame stopped operating after its public exposure, and the "kill" command was sent.Flame is linked to the Equation Group by Kaspersky Lab. However, Costin Raiu, the director of Kaspersky Lab's global research and analysis team, believes the group only cooperates with the creators of Flame and Stuxnet from a position of superiority: "Equation Group are definitely the masters, and they are giving the others, maybe, bread crumbs. From time to time they are giving them some goodies to integrate into Stuxnet and Flame."In 2019, researchers Juan Andres Guerrero-Saade and Silas Cutler announced their discovery of the resurgence of Flame. The attackers used 'timestomping' to make the new samples look like they were created before the 'suicide' command. However, a compilation error included the real compilation date (circa 2014). The new version (dubbed 'Flame 2.0' by the researchers) includes new encryption and obfuscation mechanisms to hide its functionality.
|
Flame (malware)
|
History
|
Flame (a.k.a. Da Flame) was identified in May 2012 by the MAHER Center of the Iranian National CERT, Kaspersky Lab and CrySyS Lab (Laboratory of Cryptography and System Security) of the Budapest University of Technology and Economics when Kaspersky Lab was asked by the United Nations International Telecommunication Union to investigate reports of a virus affecting Iranian Oil Ministry computers. As Kaspersky Lab investigated, they discovered an MD5 hash and filename that appeared only on customer machines from Middle Eastern nations. After discovering more pieces, researchers dubbed the program "Flame" after one of the main modules inside the toolkit [FROG.DefaultAttacks.A-InstallFlame].According to Kaspersky, Flame had been operating in the wild since at least February 2010. CrySyS Lab reported that the file name of the main component was observed as early as December 2007. However, its creation date could not be determined directly, as the creation dates for the malware's modules are falsely set to dates as early as 1994.Computer experts consider it the cause of an attack in April 2012 that caused Iranian officials to disconnect their oil terminals from the Internet. At the time the Iranian Students News Agency referred to the malware that caused the attack as "Wiper", a name given to it by the malware's creator. However, Kaspersky Lab believes that Flame may be "a separate infection entirely" from the Wiper malware. Due to the size and complexity of the program—described as "twenty times" more complicated than Stuxnet—the Lab stated that a full analysis could require as long as ten years.On 28 May, Iran's CERT announced that it had developed a detection program and a removal tool for Flame, and had been distributing these to "select organizations" for several weeks. After Flame's exposure in news media, Symantec reported on 8 June that some Flame command and control (C&C) computers had sent a "suicide" command to infected PCs to remove all traces of Flame.According to estimates by Kaspersky in May 2012, initially Flame had infected approximately 1,000 machines, with victims including governmental organizations, educational institutions and private individuals. At that time the countries most affected were Iran, Israel, the Palestinian Territories, Sudan, Syria, Lebanon, Saudi Arabia, and Egypt.
|
Flame (malware)
|
History
|
A sample of the Flame malware is available at GitHub
|
Flame (malware)
|
Operation
|
Flame is an uncharacteristically large program for malware at 20 megabytes. It is written partly in the Lua scripting language with compiled C++ code linked in, and allows other attack modules to be loaded after initial infection. The malware uses five different encryption methods and an SQLite database to store structured information. The method used to inject code into various processes is stealthy, in that the malware modules do not appear in a listing of the modules loaded into a process and malware memory pages are protected with READ, WRITE and EXECUTE permissions that make them inaccessible by user-mode applications. The internal code has few similarities with other malware, but exploits two of the same security vulnerabilities used previously by Stuxnet to infect systems. The malware determines what antivirus software is installed, then customises its own behaviour (for example, by changing the filename extensions it uses) to reduce the probability of detection by that software. Additional indicators of compromise include mutex and registry activity, such as installation of a fake audio driver which the malware uses to maintain persistence on the compromised system.Flame is not designed to deactivate automatically, but supports a "kill" function that makes it eliminate all traces of its files and operation from a system on receipt of a module from its controllers.Flame was signed with a fraudulent certificate purportedly from the Microsoft Enforced Licensing Intermediate PCA certificate authority. The malware authors identified a Microsoft Terminal Server Licensing Service certificate that inadvertently was enabled for code signing and that still used the weak MD5 hashing algorithm, then produced a counterfeit copy of the certificate that they used to sign some components of the malware to make them appear to have originated from Microsoft. A successful collision attack against a certificate was previously demonstrated in 2008, but Flame implemented a new variation of the chosen-prefix collision attack.
|
Flame (malware)
|
Deployment
|
Like the previously known cyber weapons Stuxnet and Duqu, it is employed in a targeted manner and can evade current security software through rootkit functionality. Once a system is infected, Flame can spread to other systems over a local network or via USB stick. It can record audio, screenshots, keyboard activity and network traffic. The program also records Skype conversations and can turn infected computers into Bluetooth beacons which attempt to download contact information from nearby Bluetooth enabled devices. This data, along with locally stored documents, is sent on to one of several command and control servers that are scattered around the world. The program then awaits further instructions from these servers.Unlike Stuxnet, which was designed to sabotage an industrial process, Flame appears to have been written purely for espionage. It does not appear to target a particular industry, but rather is "a complete attack toolkit designed for general cyber-espionage purposes".Using a technique known as sinkholing, Kaspersky demonstrated that "a huge majority of targets" were within Iran, with the attackers particularly seeking AutoCAD drawings, PDFs, and text files. Computing experts said that the program appeared to be gathering technical diagrams for intelligence purposes.A network of 80 servers across Asia, Europe and North America has been used to access the infected machines remotely.
|
Flame (malware)
|
Origin
|
On 19 June 2012, The Washington Post published an article claiming that Flame was jointly developed by the U.S. National Security Agency, CIA and Israel's military at least five years prior. The project was said to be part of a classified effort code-named Olympic Games, which was intended to collect intelligence in preparation for a cyber-sabotage campaign aimed at slowing Iranian nuclear efforts.According to Kaspersky's chief malware expert, "the geography of the targets and also the complexity of the threat leaves no doubt about it being a nation-state that sponsored the research that went into it." Kaspersky initially said that the malware bears no resemblance to Stuxnet, although it may have been a parallel project commissioned by the same attackers.
|
Flame (malware)
|
Origin
|
After analysing the code further, Kaspersky later said that there is a strong relationship between Flame and Stuxnet; the early version of Stuxnet contained code to propagate via USB drives that is nearly identical to a Flame module that exploits the same zero-day vulnerability.Iran's CERT described the malware's encryption as having "a special pattern which you only see coming from Israel". The Daily Telegraph reported that due to Flame's apparent targets—which included Iran, Syria, and the West Bank—Israel became "many commentators' prime suspect". Other commentators named China and the U.S. as possible perpetrators. Richard Silverstein, a commentator critical of Israeli policies, claimed that he had confirmed with a "senior Israeli source" that the malware was created by Israeli computer experts. The Jerusalem Post wrote that Israel's Vice Prime Minister Moshe Ya'alon appeared to have hinted that his government was responsible, but an Israeli spokesperson later denied that this had been implied. Unnamed Israeli security officials suggested that the infected machines found in Israel may imply that the virus could be traced to the U.S. or other Western nations. The U.S. has officially denied responsibility.A leaked NSA document mentions that dealing with Iran's discovery of FLAME is an NSA and GCHQ jointly-worked event.
|
International Student Congress Of (bio)Medical Sciences
|
International Student Congress Of (bio)Medical Sciences
|
The International Student Congress Of (bio)Medical Sciences, also known as ISCOMS, is an annually held student congress on biomedical sciences. The primary aim of ISCOMS is getting medical students acquainted with research and its many elements.
750 participants from 60 countries attended the 25th edition of ISCOMS in 2018. The 26th edition of ISCOMS will take place from 3–7 June 2019 and the abstract submission is open from October 29, 2018 till February 7, 2019.
|
International Student Congress Of (bio)Medical Sciences
|
History
|
ISCOMS started as a congress for medical students in Groningen, named "Studenten Congres Geneeskunde". In 2003, the Student Congres Geneeskunde changed to an international congress with the name International Student Congress of Medicine. In 2004 the name was changed to ISCOMS. In 2010, the name was changed to the International Student Congress Of (bio)Medical Sciences, to show that it is a congress for students in all biomedical fields.
|
International Student Congress Of (bio)Medical Sciences
|
Location
|
ISCOMS takes place at the University Medical Center Groningen (UMCG) in the Netherlands. It is one of the largest hospitals in the world, offering supraregional tertiary care to the northern part of the Netherlands. The medical center employs almost 17,000 people, numbers almost 1400 beds and is affiliated with the University of Groningen.
|
International Student Congress Of (bio)Medical Sciences
|
Congress structure
|
The congress is for (bio)medical students who are interested in research. Students may be either presenting or non-presenting participants. If a participant wants to present their research, they are required to submit their abstract beforehand. A strict selection procedure takes place and only the best students are invited to present their research at ISCOMS.
|
International Student Congress Of (bio)Medical Sciences
|
Congress structure
|
When accepted, participants are divided into different session in which they present their research. This may be either through a poster presentation, or an oral presentation where students can present their research by means of a slideshow presentation. In both sessions other students and professionals from the UMCG listen and discuss the research. Thirdly, there is a plenary session: the eight best abstracts will be presented in the primary lecture hall of the UMCG.
|
International Student Congress Of (bio)Medical Sciences
|
Congress structure
|
The congress also holds pre-course masterclasses about research skills, and a great variety of workshops during the congress days on practical skills. Besides that ISCOMS offers keynote lectures from renowned scientist presenting their research to the participants.
Moreover, ISCOMS offers an extensive social programme, where all the participants have the opportunity to get to know each other and the ISCOMS organising committees. Finally, there is a post-congress tour visiting parts of the Netherlands.
|
International Student Congress Of (bio)Medical Sciences
|
Keynote Speakers
|
Nobel Prize laureates who have given a keynote lecture during one of the previous ISCOMS editions.
|
International Student Congress Of (bio)Medical Sciences
|
Healthy Ageing
|
‘Healthy Ageing’ is the primary focus of research, patient care, and education & training within the University of Groningen and the University Medical Center Groningen. Knowing that ageing of the population poses an increasing burden on society, and that associated disabilities and diseases incur increasing economic, healthcare, infrastructural and personal costs that tax national societies heavily, stimulation of a healthy lifestyle is a key in order to deal with this societal challenge. Therefore, ISCOMS continues to emphasize the importance of ‘Healthy Ageing’. It is well known that lifestyles, nutritional patterns, the amount of exercise, and the use of medication are all factors that affect the development of health. However, the influences of these factors and the way they relate to each other is still unclear. As such, ISCOMS is proud to contribute to the gaining of new knowledge.
|
International Student Congress Of (bio)Medical Sciences
|
Organisational structure
|
The organisation of ISCOMS consists of (bio)medical students from the University of Groningen. There are nine Executive Board members and 21 committee members. Committees include the Scientific Programme, Hosting and Logistics, International Contacts, Sponsors and Fundraising, Public Relations, and Research and Development.
|
International Student Congress Of (bio)Medical Sciences
|
ISCOMS Research Fellowships (IRF)
|
ISCOMS is more than just a congress; it also incorporates several different projects. The ISCOMS Research Fellowships (IRF) is such a project and is unique in Europe and has become an integral part of the experience. It provides a starting point for students to pursue a career in medical sciences, broaden their scientific network, increase the range of their knowledge and amplify their experience with research by giving 25 enthusiastic and talented students the opportunity to join a research group in the University Medical Center Groningen. During a challenging two-week period, chosen students will work on their own individual project and for some this may transcend into a chance to conduct a long-term PhD project in Groningen.
|
International Student Congress Of (bio)Medical Sciences
|
Partners
|
The official partners of the ISCOMS are: Leiden International Medical Student Conference (LIMSC) International Federation of Medical Students' Associations the Netherlands (IFMSA-NL) Zagreb International Medical Summit (ZIMS) European Medical Students' Association (EMSA) Asian Medical Students' Association (AMSA) Young European Scientists meeting Porto (YES-meeting) International Medical Students' Congress Novi Sad (IMSCNS) International Conference for Healthcare and Medical Students (ICHAMS)
|
Folding endurance
|
Folding endurance
|
In paper testing, folding endurance is defined as the logarithm (to the base of ten) of the number of double folds that are required to make a test piece break under standardized conditions: F = log10 d,where F is the folding endurance and d the number of double folds.
|
Folding endurance
|
Folding endurance
|
Folding endurance is especially applicable for papers used for maps, bank notes, archival documents, etc. The direction of the grain in relation to the folding line, the type of fibres used, the fibre contents, the calliper of the test piece, etc., as well as which type of folding tester that is used affect how many double folds a test piece can take.
|
Folding endurance
|
Folding endurance
|
Folding endurance must not be confused with the related term fold number.
|
Folding endurance
|
Standards on folding endurance
|
ISO 5626: Paper – Determination of folding endurance.
TAPPI Test Method T 511: Folding endurance of paper (MIT tester).
TAPPI Test Method T 423: Folding endurance of paper (Schopper type tester).
|
Nesbitt's inequality
|
Nesbitt's inequality
|
In mathematics, Nesbitt's inequality states that for positive real numbers a, b and c, ab+c+ba+c+ca+b≥32.
It is an elementary special case (N = 3) of the difficult and much studied Shapiro inequality, and was published at least 50 years earlier.
There is no corresponding upper bound as any of the 3 fractions in the inequality can be made arbitrarily large.
|
Nesbitt's inequality
|
Proof
|
First proof: AM-HM inequality By the AM-HM inequality on (a+b),(b+c),(c+a) ,(a+b)+(a+c)+(b+c)3≥31a+b+1a+c+1b+c.
Clearing denominators yields ((a+b)+(a+c)+(b+c))(1a+b+1a+c+1b+c)≥9, from which we obtain 2a+b+cb+c+2a+b+ca+c+2a+b+ca+b≥9 by expanding the product and collecting like denominators. This then simplifies directly to the final result.
Second proof: Rearrangement Suppose a≥b≥c , we have that 1b+c≥1a+c≥1a+b define x→=(a,b,c) y→=(1b+c,1a+c,1a+b) The scalar product of the two sequences is maximum because of the rearrangement inequality if they are arranged the same way, call y→1 and y→2 the vector y→ shifted by one and by two, we have: x→⋅y→≥x→⋅y→1 x→⋅y→≥x→⋅y→2 Addition yields our desired Nesbitt's inequality.
Third proof: Sum of Squares The following identity is true for all a,b,c: ab+c+ba+c+ca+b=32+12((a−b)2(a+c)(b+c)+(a−c)2(a+b)(b+c)+(b−c)2(a+b)(a+c)) This clearly proves that the left side is no less than 32 for positive a, b and c.
Note: every rational inequality can be demonstrated by transforming it to the appropriate sum-of-squares identity, see Hilbert's seventeenth problem.
Fourth proof: Cauchy–Schwarz Invoking the Cauchy–Schwarz inequality on the vectors ⟨a+b,b+c,c+a⟩,⟨1a+b,1b+c,1c+a⟩ yields ((b+c)+(a+c)+(a+b))(1b+c+1a+c+1a+b)≥9, which can be transformed into the final result as we did in the AM-HM proof.
Fifth proof: AM-GM Let x=a+b,y=b+c,z=c+a . We then apply the AM-GM inequality to obtain the following 6.
because 6.
Substituting out the x,y,z in favor of a,b,c yields 2a+b+cb+c+a+b+2ca+b+a+2b+cc+a≥6 2ab+c+2ca+b+2ba+c+3≥6 which then simplifies to the final result.
|
Nesbitt's inequality
|
Proof
|
Sixth proof: Titu's lemma Titu's lemma, a direct consequence of the Cauchy–Schwarz inequality, states that for any sequence of n real numbers (xk) and any sequence of n positive numbers (ak) , ∑k=1nxk2ak≥(∑k=1nxk)2∑k=1nak . We use the lemma on (xk)=(1,1,1) and (ak)=(b+c,a+c,a+b) . This gives, 1b+c+1c+a+1a+b≥322(a+b+c) This results in, a+b+cb+c+a+b+cc+a+a+b+ca+b≥92 i.e., ab+c+bc+a+ca+b≥92−3=32 Seventh proof: Using homogeneity As the left side of the inequality is homogeneous, we may assume a+b+c=1 . Now define x=a+b , y=b+c , and z=c+a . The desired inequality turns into 1−xx+1−yy+1−zz≥32 , or, equivalently, 1x+1y+1z≥9/2 . This is clearly true by Titu's Lemma.
|
Nesbitt's inequality
|
Proof
|
Eighth proof: Jensen inequality Define S=a+b+c and consider the function f(x)=xS−x . This function can be shown to be convex in [0,S] and, invoking Jensen inequality, we get aS−a+bS−b+cS−c3≥S/3S−S/3.
A straightforward computation yields ab+c+bc+a+ca+b≥32.
Ninth proof: Reduction to a two-variable inequality By clearing denominators, ab+c+ba+c+ca+b≥32⟺2(a3+b3+c3)≥ab2+a2b+ac2+a2c+bc2+b2c.
It now suffices to prove that x3+y3≥xy2+x2y for (x,y)∈R+2 , as summing this three times for (x,y)=(a,b),(a,c), and (b,c) completes the proof.
As x3+y3≥xy2+x2y⟺(x−y)(x2−y2)≥0 we are done.
|
Prehomogeneous vector space
|
Prehomogeneous vector space
|
In mathematics, a prehomogeneous vector space (PVS) is a finite-dimensional vector space V together with a subgroup G of the general linear group GL(V) such that G has an open dense orbit in V. Prehomogeneous vector spaces were introduced by Mikio Sato in 1970 and have many applications in geometry, number theory and analysis, as well as representation theory. The irreducible PVS were classified by Sato and Tatsuo Kimura in 1977, up to a transformation known as "castling". They are subdivided into two types, according to whether the semisimple part of G acts prehomogeneously or not. If it doesn't then there is a homogeneous polynomial on V which is invariant under the semisimple part of G.
|
Prehomogeneous vector space
|
Setting
|
In the setting of Sato, G is an algebraic group and V is a rational representation of G which has a (nonempty) open orbit in the Zariski topology. However, PVS can also be studied from the point of view of Lie theory: for instance, in Knapp (2002), G is a complex Lie group and V is a holomorphic representation of G with an open dense orbit. The two approaches are essentially the same, and the theory has validity over the real numbers. We assume, for simplicity of notation, that the action of G on V is a faithful representation. We can then identify G with its image in GL(V), although in practice it is sometimes convenient to let G be a covering group.
|
Prehomogeneous vector space
|
Setting
|
Although prehomogeneous vector spaces do not necessarily decompose into direct sums of irreducibles, it is natural to study the irreducible PVS (i.e., when V is an irreducible representation of G). In this case, a theorem of Élie Cartan shows that G ≤ GL(V)is a reductive group, with a centre that is at most one-dimensional. This, together with the obvious dimensional restriction dim G ≥ dim V,is the key ingredient in the Sato–Kimura classification.
|
Prehomogeneous vector space
|
Castling
|
The classification of PVS is complicated by the following fact. Suppose m > n > 0 and V is an m-dimensional representation of G over a field F. Then: (G×SL(n),V⊗Fn) is a PVS if and only if (G×SL(m−n),V∗⊗Fm−n) is a PVS.The proof is to observe that both conditions are equivalent to there being an open dense orbit of the action of G on the Grassmannian of n-planes in V, because this is isomorphic to the Grassmannian of (m-n)-planes in V*.
|
Prehomogeneous vector space
|
Castling
|
(In the case that G is reductive, the pair (G,V) is equivalent to the pair (G, V*) by an automorphism of G.) This transformation of PVS is called castling. Given a PVS V, a new PVS can be obtained by tensoring V with F and castling. By repeating this process, and regrouping tensor products, many new examples can be obtained, which are said to be "castling-equivalent". Thus PVS can be grouped into castling equivalence classes. Sato and Kimura show that in each such class, there is essentially one PVS of minimal dimension, which they call "reduced", and they classify the reduced irreducible PVS.
|
Prehomogeneous vector space
|
Classification
|
The classification of irreducible reduced PVS (G,V) splits into two cases: those for which G is semisimple, and those for which it is reductive with one-dimensional centre. If G is semisimple, it is (perhaps a covering of) a subgroup of SL(V), and hence G×GL(1) acts prehomogenously on V, with one-dimensional centre. We exclude such trivial extensions of semisimple PVS from the PVS with one-dimensional center. In other words, in the case that G has one-dimensional center, we assume that the semisimple part does not act prehomogeneously; it follows that there is a relative invariant, i.e., a function invariant under the semisimple part of G, which is homogeneous of a certain degree d.
|
Prehomogeneous vector space
|
Classification
|
This makes it possible to restrict attention to semisimple G ≤ SL(V) and split the classification as follows: (G,V) is a PVS; (G,V) is not a PVS, but (G×GL(1),V) is.However, it turns out that the classification is much shorter, if one allows not just products with GL(1), but also with SL(n) and GL(n). This is quite natural in terms of the castling transformation discussed previously. Thus we wish to classify irreducible reduced PVS in terms of semisimple G ≤ SL(V) and n ≥ 1 such that either: (G×SL(n),V⊗Fn) is a PVS; (G×SL(n),V⊗Fn) is not a PVS, but (G×GL(n),V⊗Fn) is.In the latter case, there is a homogeneous polynomial which separates the G×GL(n) orbits into G×SL(n) orbits.
|
Prehomogeneous vector space
|
Classification
|
This has an interpretation in terms of the grassmannian Grn(V) of n-planes in V (at least for n ≤ dim V). In both cases G acts on Grn(V) with a dense open orbit U. In the first case the complement Grn(V)-U has codimension ≥ 2; in the second case it is a divisor of some degree d, and the relative invariant is a homogeneous polynomial of degree nd.
|
Prehomogeneous vector space
|
Classification
|
In the following, the classification list will be presented over the complex numbers.
General examples * Strictly speaking, we must restrict to n ≤ (dim V)/2 to obtain a reduced example.
Irregular examples Type 1 10 16 Type 2 Sp(2m,C)×SO(3,C)onC2m⊗C3 Both of these examples are PVS only for n=1.
Remaining examples The remaining examples are all type 2. To avoid discussing the finite groups appearing, the lists present the Lie algebra of the isotropy group rather than the isotropy group itself.
Here 14 denotes the space of 3-forms whose contraction with the given symplectic form is zero.
|
Prehomogeneous vector space
|
Proofs
|
Sato and Kimura establish this classification by producing a list of possible irreducible prehomogeneous (G,V), using the fact that G is reductive and the dimensional restriction. They then check whether each member of this list is prehomogeneous or not.
|
Prehomogeneous vector space
|
Proofs
|
However, there is a general explanation why most of the pairs (G,V) in the classification are prehomogeneous, in terms of isotropy representations of generalized flag varieties. Indeed, in 1974, Richardson observed that if H is a semisimple Lie group with a parabolic subgroup P, then the action of P on the nilradical p⊥ of its Lie algebra has a dense open orbit. This shows in particular (and was noted independently by Vinberg in 1975) that the Levi factor G of P acts prehomogeneously on := p⊥/[p⊥,p⊥] . Almost all of the examples in the classification can be obtained by applying this construction with P a maximal parabolic subgroup of a simple Lie group H: these are classified by connected Dynkin diagrams with one distinguished node.
|
Prehomogeneous vector space
|
Applications
|
One reason that PVS are interesting is that they classify generic objects that arise in G-invariant situations. For example, if G=GL(7), then the above tables show that there are generic 3-forms under the action of G, and the stabilizer of such a 3-form is isomorphic to the exceptional Lie group G2.
Another example concerns the prehomogeneous vector spaces with a cubic relative invariant. By the Sato-Kimura classification, there are essentially four such examples, and they all come from complexified isotropy representations of hermitian symmetric spaces for a larger group H (i.e., G is the semisimple part of the stabilizer of a point, and V is the corresponding tangent representation).
|
Prehomogeneous vector space
|
Applications
|
In each case a generic point in V identifies it with the complexification of a Jordan algebra of 3 x 3 hermitian matrices (over the division algebras R, C, H and O respectively) and the cubic relative invariant is identified with a suitable determinant. The isotropy algebra of such a generic point, the Lie algebra of G and the Lie algebra of H give the complexifications of the first three rows of the Freudenthal magic square.
|
Prehomogeneous vector space
|
Applications
|
Other Hermitian symmetric spaces yields prehomogeneous vector spaces whose generic points define Jordan algebras in a similar way.
The Jordan algebra J(m−1) in the last row is the spin factor (which is the vector space Rm−1 ⊕ R, with a Jordan algebra structure defined using the inner product on Rm−1). It reduces to J2(R),J2(C),J2(H),J2(O) for m= 3, 4, 6 and 10 respectively.
The relation between hermitian symmetric spaces and Jordan algebras can be explained using Jordan triple systems.
|
Obstacles to troop movement
|
Obstacles to troop movement
|
Obstacles to troop movement represent either natural, human habitat originated, constructed, concealed obstacles, or obstructive impediments to movement of military troops and their vehicles, or to their visibility. By impeding strategic, operational or tactical manoeuvre, the obstacle represents an added barrier between opposing combat forces, and therefore prevent achievement of objectives and goals specified in the operational planning schedule. The constructed obstacles are used as an aid to defending a position or area as part of the general defensive plan of the commander. The obstacles that originate from the human habitat can be converted by troops into constructed obstacles by either performing additional construction, or executing demolitions to obstruct movement over the transport network, to create a choke point, or to deny traversing of an area to the enemy. The natural obstacles can be used defensively by securing a more difficult to breach defensive position by for example securing a flank on terrain that is deemed impossible to traverse, thus denying the enemy an ability to close into combat range of direct fire weapons.
|
Obstacles to troop movement
|
Role of obstacles
|
Obstacles are used in combat operations to create choke points, deny mobility corridors and avenue of approach to positions, to enhance field of fire for direct fire weapons, or to protect key tactical terrain features to the enemy.
|
Obstacles to troop movement
|
Types of obstacles
|
Natural obstacles Natural obstacles are represented by those terrain features that for which few troops and their vehicles have capability to traverse. They include water obstacles, or areas of poor drainage such as lakes, rivers, swamps and marshes. The former two can be crossed by amphibious vehicles capable of swimming, or vehicles capable of deep wading after preparation, or by constructing a water crossing, and thus creating an easily targeted choke point. Soil and rock can also represent mobility obstacles if the soil is too soft and unable to support the weight of the military vehicles, or the terrain is fractured by cliffs, or large boulders that make organised movement impossible. While soft soil is relative to vehicle ground pressure, there is little that can be done to negotiate very rocky terrain or cliffs except by using specially trained light infantry troops. Vegetation such as jungles or dense forests can also represent obstacles to movement, in some cases even to light infantry troops. Some natural obstacles can be a result of climatic or soil activity such as deep snow that by covering all terrain makes safe traversing difficult and slow, or landslides that may create an obstruction suddenly despite previously clear route reconnaissance report.
|
Obstacles to troop movement
|
Types of obstacles
|
Habitat obstacles While human habitat had, since early construction of roads, sought to create ways of negotiating terrain faster, the human activity on the landscape can create obstacles in its own right. Artificial lakes and ponds, canals, and areas of agricultural cultivation, particularly those that are water-intensive such as rice-paddy fields create obstacles often more difficult than the natural equivalents. Mining activity creates quarries, and the building of roads, rail roads and dams also involve construction of cuts and fills. Seeded tree-line windbreaks, hedgerows, stone walls and plantation forests also disrupt mobility, particularly of vehicles. Lastly the urban areas in themselves represent obstacles by offering elevated firing positions and canyon-like choke points by forcing the opponent to advance through the streets.
|
Obstacles to troop movement
|
Types of obstacles
|
Constructed obstacles Constructed obstacles are those prepared by military engineering troops, often combat engineers, by either using materials to construct impediments to foot and vehicle-borne troops, or by using demolition methods, or excavation such as an abatis, to create obstacles from natural materials and terrain in specific location in accordance with the overall plan of operations. Sometimes such obstacles can be created intentionally or unintentionally through effects of artillery fire cratering. Buildings demolished due to combat or aerial bombing become very effective obstacles as rubble represents difficult to negotiate and irregular piles of building materials.
|
Obstacles to troop movement
|
Types of obstacles
|
Concealed obstacles Concealed obstacles are used with the intention of not only preventing movement of enemy troops, but also causing casualties during attempted movement. Although one of the oldest forms of obstacle use, this became far deadlier with the invention of the mine warfare, and more so with air-delivered scattered submunition minelets that can create an instant minefield.
Obstructive obstacles Obstructive obstacles are used primarily to deny terrain visibility to the enemy, thus creating uncertainty in targeting friendly troops. Although ancient in use as tar smoke pots, modern smoke screens are temporary and are used as a tactical measure during manoeuvring, often when a unit is performing a position change.
|
Obstacles to troop movement
|
Obstacle negotiation
|
Ground troops prefer to deal with physical obstacles by circumventing them as rapidly as possible, thus avoiding becoming stationary targets to the enemy direct and indirect fire weapons, and aircraft. Where this is not possible, in modern warfare the most expedient measures taken against constructed or urban obstacles are to either use armoured vehicles, preferably tanks, to remove the obstacle, or to demolish them by firing High Explosive munitions at them. Where combat engineers are present, they can perform this using their specialist skills and tools or vehicles. In the case of natural obstacles, specialist engineering equipment is usually required to negotiate the obstacle, commonly bridging or pontoons. The solution to obstacle bridging had at the strategic level created new forms of warfare and employment of troops in the amphibious operations, and later the airborne operations. At the operational level the use of helicopters in airmobile operations offers a vertical option to negotiating obstacles, often of considerable extent such as mountain passes or extensive areas of impossible vegetation.
|
Payment terminal
|
Payment terminal
|
A payment terminal, also known as a point of sale (POS) terminal, credit card machine, PIN pad, EFTPOS terminal (or by the older term as PDQ terminal which stands for "Process Data Quickly"), is a device which interfaces with payment cards to make electronic funds transfers. The terminal typically consists of a secure keypad (called a PINpad) for entering PIN, a screen, a means of capturing information from payments cards and a network connection to access the payment network for authorization.
|
Payment terminal
|
Payment terminal
|
A payment terminal allows a merchant to capture required credit and debit card information and to transmit this data to the merchant services provider or bank for authorization and finally, to transfer funds to the merchant. The terminal allows the merchant or their client to swipe, insert or hold a card near the device to capture the information. They are often connected to point of sale systems so that payment amounts and confirmation of payment can be transferred automatically to the merchant's retail management system. Terminals can also be used in stand alone mode, where the merchant keys the amount into the terminal before the customer present their card and personal identification number (PIN).
|
Payment terminal
|
Payment terminal
|
The majority of card terminals today transmit data over cellular network connections and Wi-Fi. Legacy terminals communicate over standard telephone line or Ethernet connections. Some also have the ability to cache transactional data to be transmitted to the gateway processor when a connection becomes available; the major drawback to this is that immediate authorization is not available at the time the card was processed, which can subsequently result in failed payments. Wireless terminals transmit card data using Bluetooth, Wi-Fi, cellular, or even satellite networks in remote areas and onboard airplanes.
|
Payment terminal
|
Payment terminal
|
Prior to the development of payment terminals, merchants would capture card information manually using ZipZap machines. The development of payment terminals was led by the advantage of efficiency by decreased transaction processing times and immediate authorisation of payments. In terms of security, terminals provide end to end card data encryption and auditing functions. Nevertheless, there have been some cases of POS pin pad malware. There have also been incidence of skimming at card terminals and this led to the move away from using the magnetic strip to capture information using EMV standards.
|
Payment terminal
|
History
|
Prior to the development of payment terminals, merchants would use manual imprinters (also known as ZipZap machines) to capture the information from the embossed information on a credit card onto a paper slip with carbon-paper copies. These paper slips had to be taken to the bank for processing. This was a cumbersome and time-consuming process.
Point of sale terminals emerged in 1979, when Visa introduced a bulky electronic data capturing terminal which was the first payment terminal. In the same year magnetic stripes were added to credit cards for the first time. This allowed card information to be captured electronically and led to the development of payment terminals.
One of the first companies to produce dedicated payment terminals was Verifone. It started in 1981 in Hawaii as a small electronic company. In 1983 they introduced the ZON terminal series, which would become the standard for modern payment terminals.
|
Payment terminal
|
History
|
Hungarian-born George Wallner in Sydney, Australia, founded rival Hypercom in 1978 and in 1982 started producing dedicated payment terminals. It went on to dominate the Oceania region. The company signed a deal with American Express to provide its terminals to them in the US. To consolidate the deal, Hypercom moved its head office from Australia to Arizona in the US. It then faced head-to-head competition with VeriFone on its home market.Over a decade later in 1994, Lipman Electronic Engineering, Ltd. was established in Israel. Lipman manufactured the Nurit line of processing terminals. Because of Verifone's already firm place in the payment processing industry when Lipman was established, Lipman targeted an untapped niche in the processing industry. While, Lipman holds about a 10% share in wired credit card terminals, they are the undisputed leader, with more than 95% share in wireless processing terminals in the late 1990s.
|
Payment terminal
|
History
|
Verifone would later acquire both of these major rivals, acquiring Lipman in 2006 and the payment part of the Hypercom business including its brand in 2011.
|
Payment terminal
|
History
|
In 1980, Jean-Jacques Poutrel and Michel Malhouitre established Ingenico in France and developed their first payment terminal in 1984. Its Barcelona-based R&D unit would lead the development of payment terminals for the next decade. Ingenico, through a number of acquisitions, would dominate the European market for payment terminals for a number of years. They acquired French based Bull and UK based De La Rue payment terminal activity as well as German Epos in 2001.Initially, information was captured from the magnetic strip on the back of the card, by swiping the card through the terminal. In the late 1990s, this started to be replaced by smart cards where an electronic chip was embedded in the card. This was done for added security and required the card to be inserted into the credit card terminal. In the late 1990s and early 2000s contactless payment systems were introduced and the payment terminals were updated to include the ability to read these cards using near field communication (NFC) technology.
|
Payment terminal
|
Typical features
|
Key entry (for customer not present mail and telephone order) Tips/gratuities Refunds and adjustments Settlement (including automatic) Pre-authorisation Payments using near field communication enabled devices Remote initialisation and software update Point of sale (POS) integration Multi-merchant capabilities Pen or PIN authorization by the customer Surcharge function Secure password operation Additional PIN pad attachmentsLike automated teller machines, many payment terminals are also equipped with raised tactile buttons and an earphone jack which allow the blind to audibly finish the payment process.
|
Payment terminal
|
Major manufacturers
|
There are three main global players who offer both a wide range of payment terminals, sell worldwide, and continue to develop to the latest international payment industry standards. In most countries terminals are provided to merchants via a multitude of distributors that support and pre-configure devices to operate with local payment networks or financial institutions.
Ingenico PAX Technology VeriFone
|
Payment terminal
|
Alternatives
|
A merchant can replace the functionality of dedicated credit card terminal hardware using a terminal application running on a PC or mobile device, such as a smartphone. The payment acceptance applications are also called tap-on-phone or software point of sale. They usually work with dedicated hardware readers that can transfer magnetic stripe data to the application, while there are also some that also work with smart cards (using technology such as EMV), although this is rarely seen on smartphone readers. In case the necessary hardware is unavailable, these applications usually support manual entry of the card number and other data. In addition, more and more devices are beginning to offer built-in RFID or NFC technology to accommodate contactless or mobile device payment methods, often without requiring additional external hardware.Some payment processors offer virtual terminals for processing payments without the card being present, for example when taking payments over the phone.Mobile payment systems such as those based on QR code payments bypass the need for payment terminals altogether, relying on smartphones and a printed QR code.
|
Acne with facial edema
|
Acne with facial edema
|
Acne with facial edema occurs uncommonly, and is associated with a peculiar inflammatory edema of the mid-third of the face.
|
DDX41
|
DDX41
|
Probable ATP-dependent RNA helicase DDX41 is an enzyme that in humans is encoded by the DDX41 gene.DEAD box proteins, characterized by the conserved motif Asp-Glu-Ala-Asp (DEAD), are putative RNA helicases. They are implicated in a number of cellular processes involving alteration of RNA secondary structure, such as translation initiation, nuclear and mitochondrial splicing, and ribosome and spliceosome assembly. Based on their distribution patterns, some members of the DEAD box protein family are believed to be involved in embryogenesis, spermatogenesis, and cellular growth and division. This gene encodes a member of this family. The function of this member has not been determined. Based on studies in Drosophila, the abstrakt gene is widely required during post-transcriptional gene expression. Germ line DDX41 mutations define a unique subtype of myeloid neoplasms.
|
DDX41
|
Function
|
DDX41 is believed to take part in several cell functions. It is mainly concentrated in the nucleus of the cell, but it can also be expressed in the citoplasm.
In the citoplasm it takes part in the Interferon I production pathway by recognizing foreign citoplasmic DNA and signaling STING. It has been observed that hypomorphic DDX41 mutations impair the immune system response to viral and bacterial infections.
In the nucleus, DDX41 is believed to regulate the transcriptional elongation process signaling Pol II to slow down the elongation while the splicing process is taking place. Underexpression and inhibition of DDX41have been shown to lead to the formation of an R-loop which results in transcriptional errors with no specific patterns.
DDX41 is also believed to take part in the ribosome biogenesis process, given its implications in the processing of snoRNA.
|
Dialogue in Silence
|
Dialogue in Silence
|
Dialogue in Silence is an exhibition about non-verbal communication, where participants discover a repertoire of expression possibilities with the help of deaf and hearing impaired guides and trainers. Participants enter an area of complete silence, wearing noise-cancelling headsets, and experience an environment that helps them discover openness, empathy and an enhanced power of concentration. Throughout the entire exhibition tour, a reversal of roles is created: hearing visitors lose their usual routines of articulating themselves and discover a new repertoire of non-verbal expression. They experience a different openness and empathy towards "the other".
|
Dialogue in Silence
|
Background and history
|
In 2005, the World Health Organization (WHO) estimated 278 million people worldwide having moderate to profound hearing loss in both ears or are born deaf. "The impact of hearing impairment on a child's speech, language, education and social integration depends on the level and type of hearing impairment, and the age of onset, especially if it begins before the age when speech normally develops." The prototype of Dialogue in Silence was called “Schattensprache”. Focusing on silent communication it was presented for the first time 1998 in Frankfurt. Orna Cohen and Andreas Heinecke then developed this model further into the large exhibition format of today. In 2003 they introduced the new concept with great success to the public in Paris at the “Cité des Sciences et l’Industrie”. In 2006 the exhibition was established as first permanent exhibition at the Children’s Museum in Holon, Israel. In 2008 and 2009 Mexico hosted the exhibition at the Children Museum in Papalote. In Germany, the Museum für Kommunikation in Frankfurt presented the exhibition in 2010 and 2011. So did the DASA Museum in Dortmund in 2009. In September 2014 Dialogue in Silence became the second permanent exhibition at the Dialoghaus in Hamburg, next to Dialogue in the Dark. In 2015, the exhibition Dialogue in Silence also became a permanent exhibition in Istanbul, Turkey. In August 2017, a 30-days-trial will run in Japan, preparing for a longer exhibition in 2020.
|
Dialogue in Silence
|
Background and history
|
Corporate learning workshops are offered as a spin off from the actual exhibition. All Dialogue in Silence exhibitions and corporate learning workshops are handled by Dialogue Social Enterprise GmbH, Hamburg.
|
Dialogue in Silence
|
The exhibition layout
|
»Dialogue in Silence« is an exhibition that invites visitors into a world of silence. Different forms of expression are used here and language must be visible in order to be understood. Hearing-impaired guides lead visitors through the exhibition, which is totally soundproof. It is the encounter which lies at the heart of the experience. At the same time, a reversal of roles is created: hearing people are torn out of social routine and familiar perception. They discover their repertoire of non-verbal expression in order to communicate creatively by gestures and body language. Hearing-impaired people, who by virtue of their experience and ability to sign are more competent, support the visitors and become ambassadors of a world without sound which is no way poorer – but different.
|
Dialogue in Silence
|
The exhibition layout
|
The exhibition consists of a series of circular rooms dedicated to different aspects of non-verbal communication. All walls are specially constructed with a fabric absorbing sound to the best of effects, while providing a monochromatic background. The visitor’s visual concentration is not distracted and full attention can be is given to the visual experience and communication means. Each room has a name, indicating the activity it hosts. In each room, the scenario is broken down into several short stages thus creating a sense of progression: Invitation to Silence - Entrance into the world of silence Dance of Hands - Focus on hands and their capacity to express Gallery of Faces - Work on facial expressions and how to decipher them Play of Signs - Introduction to sign language Forum of Figures - Learning about the body's capacity to express via postures and movement Dialogue Room - Dialogue between visitors and the facilitator with the support of an interpreterWhereas headphones are worn during the first 5 rooms, visitors are invited to go back to verbal language in the last room to get into an intensive dialogue with the tour guide and learn more about deaf culture and
|
Dialogue in Silence
|
Venues
|
Dialogue in Silence currently presented in the following venues around the world: Dialoghaus Hamburg, Germany: Dialog im Stillen Children's Museum Holon, Israel: Invitation to Silence Diyalog Müzesi Istanbul, Turkey: Sessizlikte Dyjalog
|
Transient modelling
|
Transient modelling
|
Transient modelling is a way of looking at a process with the primary criterion of time, observing the pattern of changes in the subject being studied over time. Its obverse is Steady state, where you might know only the starting and ending figures but do not understand the process by which they were derived.
|
Transient modelling
|
Transient modelling
|
Transient models will reveal the pattern of a process, which might be sinusoidal or another shape that will help to design a better system to manage that process. Transient models can be done on a spreadsheet with an ability to generate charts, or by any software that can handle data of inputs and outputs and generate some sort of a display. Transient modelling does not need a computer. It is a methodology that has worked for centuries, by observers noting patterns of change against time, analysing the result and proposing improved design solutions.
|
Transient modelling
|
Transient modelling
|
A simple example is a garden water tank. This is being topped up by rainfall from the roof, but when the tank is full, the remaining water goes to the drain. When the gardener draws water off, the level falls. If the garden is large and the summer is hot, a steady state will occur in summer where the tank is nearly always empty in summer. If the season is wet, the garden is getting water from the sky, and the tank is not being emptied sufficiently, so in steady state it will be observed to be always full. If the gardener has a way of observing the level of water in the tank, and a record of daily rainfall and temperatures, and is precisely metering the amount of water being drawn off every day, the numbers and the dates can be recorded in spreadsheet at daily intervals. After enough samples are taken, a chart can be developed to model the rise and fall pattern over a year, or over 2 years. With a better understanding of the process, it might emerge that a 200litre water tank would run out 20–25 days a year, but a 400-litre water tank would never run out, and a 300-litre tank would run out only 1-2 day a year and therefore that would be an acceptable risk and it would be the most economical solution.
|
Transient modelling
|
Transient modelling
|
One of the best examples of transient modelling is transient climate simulation. The analysis of ice cores in glaciers to understand climate change. Ice cores have thousands of layers, each of which represents a winter season of snowfall, and trapped in these are bubbles of air, particle of space dust and pollen which reveal climatic data of the time. By mapping these to a time scale, scientists can analyse the fluctuations over time and make predictions for the future.
|
Transient modelling
|
Transient modelling
|
Transient modelling is the basis of weather forecasting, of managing ecosystems, rail timetabling, managing the electricity grid, setting the national budget, floating currency, understanding traffic flows on a freeway, solar gains on glass fronted buildings, or even of checking the day-to-day transactions of one's monthly bank statement.
With the transient modelling approach, you understand the whole process better when the inputs and outputs are graphed against time.
|
Fredholm theory
|
Fredholm theory
|
In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space. The theory is named in honour of Erik Ivar Fredholm.
|
Fredholm theory
|
Overview
|
The following sections provide a casual sketch of the place of Fredholm theory in the broader context of operator theory and functional analysis. The outline presented here is broad, whereas the difficulty of formalizing this sketch is, of course, in the details.
|
Fredholm theory
|
Fredholm equation of the first kind
|
Much of Fredholm theory concerns itself with the following integral equation for f when g and K are given: g(x)=∫abK(x,y)f(y)dy.
|
Fredholm theory
|
Fredholm equation of the first kind
|
This equation arises naturally in many problems in physics and mathematics, as the inverse of a differential equation. That is, one is asked to solve the differential equation Lg(x)=f(x) where the function f is given and g is unknown. Here, L stands for a linear differential operator. For example, one might take L to be an elliptic operator, such as L=d2dx2 in which case the equation to be solved becomes the Poisson equation. A general method of solving such equations is by means of Green's functions, namely, rather than a direct attack, one first finds the function K=K(x,y) such that for a given pair x,y, LK(x,y)=δ(x−y), where δ(x) is the Dirac delta function. The desired solution to the above differential equation is then written as an integral in the form of a Fredholm integral equation, g(x)=∫K(x,y)f(y)dy.
|
Fredholm theory
|
Fredholm equation of the first kind
|
The function K(x,y) is variously known as a Green's function, or the kernel of an integral. It is sometimes called the nucleus of the integral, whence the term nuclear operator arises.
In the general theory, x and y may be points on any manifold; the real number line or m-dimensional Euclidean space in the simplest cases. The general theory also often requires that the functions belong to some given function space: often, the space of square-integrable functions is studied, and Sobolev spaces appear often.
|
Fredholm theory
|
Fredholm equation of the first kind
|
The actual function space used is often determined by the solutions of the eigenvalue problem of the differential operator; that is, by the solutions to Lψn(x)=ωnψn(x) where the ωn are the eigenvalues, and the ψn(x) are the eigenvectors. The set of eigenvectors span a Banach space, and, when there is a natural inner product, then the eigenvectors span a Hilbert space, at which point the Riesz representation theorem is applied. Examples of such spaces are the orthogonal polynomials that occur as the solutions to a class of second-order ordinary differential equations.
|
Fredholm theory
|
Fredholm equation of the first kind
|
Given a Hilbert space as above, the kernel may be written in the form K(x,y)=∑nψn(x)ψn(y)ωn.
In this form, the object K(x,y) is often called the Fredholm operator or the Fredholm kernel. That this is the same kernel as before follows from the completeness of the basis of the Hilbert space, namely, that one has δ(x−y)=∑nψn(x)ψn(y).
Since the ωn are generally increasing, the resulting eigenvalues of the operator K(x,y) are thus seen to be decreasing towards zero.
|
Fredholm theory
|
Inhomogeneous equations
|
The inhomogeneous Fredholm integral equation f(x)=−ωφ(x)+∫K(x,y)φ(y)dy may be written formally as f=(K−ω)φ which has the formal solution φ=1K−ωf.
A solution of this form is referred to as the resolvent formalism, where the resolvent is defined as the operator R(ω)=1K−ωI.
Given the collection of eigenvectors and eigenvalues of K, the resolvent may be given a concrete form as R(ω;x,y)=∑nψn(y)ψn(x)ωn−ω with the solution being φ(x)=∫R(ω;x,y)f(y)dy.
A necessary and sufficient condition for such a solution to exist is one of Fredholm's theorems. The resolvent is commonly expanded in powers of λ=1/ω , in which case it is known as the Liouville-Neumann series. In this case, the integral equation is written as g(x)=φ(x)−λ∫K(x,y)φ(y)dy and the resolvent is written in the alternate form as R(λ)=1I−λK.
|
Fredholm theory
|
Fredholm determinant
|
The Fredholm determinant is commonly defined as det exp Tr Kn] where Tr K=∫K(x,x)dx and Tr K2=∬K(x,y)K(y,x)dxdy and so on. The corresponding zeta function is det (I−sK).
The zeta function can be thought of as the determinant of the resolvent.
The zeta function plays an important role in studying dynamical systems. Note that this is the same general type of zeta function as the Riemann zeta function; however, in this case, the corresponding kernel is not known. The existence of such a kernel is known as the Hilbert–Pólya conjecture.
|
Fredholm theory
|
Main results
|
The classical results of the theory are Fredholm's theorems, one of which is the Fredholm alternative.
One of the important results from the general theory is that the kernel is a compact operator when the space of functions are equicontinuous.
A related celebrated result is the Atiyah–Singer index theorem, pertaining to index (dim ker – dim coker) of elliptic operators on compact manifolds.
|
Fredholm theory
|
History
|
Fredholm's 1903 paper in Acta Mathematica is considered to be one of the major landmarks in the establishment of operator theory. David Hilbert developed the abstraction of Hilbert space in association with research on integral equations prompted by Fredholm's (amongst other things).
|
Fantastická fakta
|
Fantastická fakta
|
Fantastická fakta (Fantastic facts) is a Czech monthly paranormal magazine. It deals with unexplained phenomena, UFOs, and urban legends.
|
Fantastická fakta
|
History and profile
|
Fantastická fakta was first published in August 1997. The headquarters is in Prague. The magazine is published on a monthly basis. The launching editor-in-chief was Vladimír Mátl. Ivan Mackerle was the chief editor from 1998 to 2002.
|
Derlin-1
|
Derlin-1
|
Derlin-1 also known as degradation in endoplasmic reticulum protein 1 is a membrane protein that in humans is encoded by the DERL1 gene. Derlin-1 is located in the membrane of the endoplasmic reticulum (ER) and is involved in retrotranslocation of specific misfolded proteins and in ER stress. Derlin-1 is widely expressed in thyroid, fat, bone marrow and many other tissues. The protein belongs to the Derlin-family proteins (also called derlins) consisting of derlin-1, derlin-2 and derlin-3 that are components in the endoplasmic reticulum-associated protein degradation (ERAD) pathway. The derlins mediate degradation of misfolded lumenal proteins within ER, and are named ‘der’ for their ‘Degradation in the ER’. Derlin-1 is a mammalian homologue of the yeast DER1 protein, a protein involved in the yeast ERAD pathway. Moreover, derlin-1 is a member of the rhomboid-like clan of polytopic membrane proteins.Overexpression of derlin-1 are associated with many cancers, including colon cancer, breast cancer, bladder cancer and non-small cell lung cancer.
|
Derlin-1
|
Discovery
|
In 2004 the DERL1 gene was discovered independently by two research groups when they were exploring the machinery of retrotranslocation in the ER in the cell. One evidence for the existence of DERL1 was provided by Professor Tom A. Rapoport and his research group at Harvard Medical School, Boston, Massachusetts. Another evidence of the DERL1 gene was discovered by Professor Hidde L. Ploegh and his research group who is also at Harvard Medical School, Boston, Massachusetts. As the mammalian DERL1 gene was found to be a homologue of the yeast DER1 gene found in 1996, it was named after the yeast gene.
|
Derlin-1
|
Gene location
|
The human DERL1 gene is located on the long (q) arm of chromosome 8 at region 2 band 4, from base pair 123,013,164 to 123,042,423 (Build GRCh37/hg19) (map).
|
Derlin-1
|
Function and mechanism
|
Rerouting factor during ER stress ER stress is caused by an accumulation of unfolded or misfolded proteins in ER and is critical for cell function. The accumulation of unfolded and misfolded proteins activates an unfolded protein response (UPR) which regulate the homeostasis of the cell. One of the strategies cells possess to ER stress as a quality control system is the ERAD pathway, by which Derlin-1 is a component of. As a part of an ER membrane protein complex (that includes VIMP, SEL1, HRD1, and HERP) derlin-1 detects misfolded proteins in ER and mediate them for their degradation in the ERAD pathway.Under ER stress, the carboxyl-terminus region of derlin-1 captures specific misfolded proteins in the ER lumen. Derlin-1 also interacts with VIMP, an ER membrane protein that recruits the cytosolic ATPase p97 and its cofactor. The interaction of derlin-1 with p97 via VIMP is essential for export of misfolded proteins. p97 is required for the transport of the misfolded proteins through the ER membrane and back to the cytosolic side for their degradation. This process is referred to as retrotranslocation. Hence, one of the functions of derlin-1 is to reroute specific misfolded protein to the cytosol for their degradation. Prior to the cytosolic degradation, the retrotranslocated misfolded proteins interacts with HRDI E3 ubiquitin ligase. This ligase ubiquitinates the misfolded proteins promoting their degradation in the cytosol by the ubiquitin-protease system (UPS). Currently, the molecular mechanism by which derlin-1 reroutes the misfolded proteins from ER to their degradation are not fully understood.
|
Derlin-1
|
Function and mechanism
|
The structure of Derlin-1 The cryo-EM analysis revealed that human Derlin-1 forms a tetrameric channel across the ER membrane. Derlin-1 channel holds a short, large transmembrane funnel in the center of tetramer with a diameter about 11-13 angstrom, which might serve as a permeation pathway for misfolded protein substrates in ERAD. Each protomer in human Derlin-1 tetramer shares a high structural similarity with yeast DER1 protein or other rhomboid members. However, this channel architecture makes human derlin-1 different from other known rhomboid structures and implies its centraal role in mammalian ERAD retrotranslocation.
|
Derlin-1
|
Clinical significance
|
Derlin 1 (DERL1) is up-regulated in metastatic canine mammary tumors as part of the unfolded protein response.
|
Derlin-1
|
Interactions
|
Derlin-1 has been shown to interact with the following proteins: HRD1 VIMP US11
|
Xyloglucan 4-glucosyltransferase
|
Xyloglucan 4-glucosyltransferase
|
In enzymology, a xyloglucan 4-glucosyltransferase (EC 2.4.1.168) is an enzyme that catalyzes the chemical reaction in which a beta-D-glucosyl residue is transferred from UDP-glucose to another glucose residue in xyloglucan, linked by a beta-1,4-D-glucosyl-D-glucose bond.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:xyloglucan 1,4-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-xyloglucan 4beta-glucosyltransferase, xyloglucan 4beta-D-glucosyltransferase, and xyloglucan glucosyltransferase.
|
Fleischer's syndrome
|
Fleischer's syndrome
|
Fleischer's syndrome is an extremely rare congenital anomaly characterized by displacement of the nipples, occasional polymastia, and hypoplasia of both kidneys.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.