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Internal combustion engine cooling	Air-cooling	During that period, European firms such as Magirus-Deutz built air-cooled diesel trucks, Porsche built air-cooled farm tractors, and Volkswagen became famous with air-cooled passenger cars. In the United States, Franklin built air-cooled engines. For many years air cooling was favored for military applications as liquid cooling systems are more vulnerable to damage by shrapnel.
Internal combustion engine cooling	Air-cooling	The Czech Republic–based company Tatra is known for their large displacement air-cooled V8 car engines; Tatra engineer Julius Mackerle published a book on it. Air-cooled engines are better adapted to extremely cold and hot environmental weather temperatures: you can see air-cooled engines starting and running in freezing conditions that seized water-cooled engines and continue working when water-cooled ones start producing steam jets. Air-cooled engines have may be an advantage from a thermodynamic point of view due to higher operating temperature. The worst problem met in air-cooled aircraft engines was the so-called "Shock cooling", when the airplane entered in a dive after climbing or level flight with throttle open, with the engine under no load while the airplane dives generating less heat, and the flow of air that cools the engine is increased, a catastrophic engine failure may result as different parts of engine have different temperatures, and thus different thermal expansions. In such conditions, the engine may seize, and any sudden change or imbalance in the relation between heat produced by the engine and heat dissipated by cooling may result in an increased wear of engine, as a consequence also of thermal expansion differences between parts of engine, liquid-cooled engines having more stable and uniform working temperatures.
Internal combustion engine cooling	Liquid cooling	Today, most automotive and larger IC engines are liquid-cooled. Liquid cooling is also employed in maritime vehicles (vessels, ...). For vessels, the seawater itself is mostly used for cooling. In some cases, chemical coolants are also employed (in closed systems) or they are mixed with seawater cooling.
Internal combustion engine cooling	Transition from air cooling	The change of air cooling to liquid cooling occurred at the start of World War II when the US military needed reliable vehicles. The subject of boiling engines was addressed, researched, and a solution found. Previous radiators and engine blocks were properly designed and survived durability tests, but used water pumps with a leaky graphite-lubricated "rope" seal (gland) on the pump shaft. The seal was inherited from steam engines, where water loss is accepted, since steam engines already expend large volumes of water. Because the pump seal leaked mainly when the pump was running and the engine was hot, the water loss evaporated inconspicuously, leaving at best a small rusty trace when the engine stopped and cooled, thereby not revealing significant water loss. Automobile radiators (or heat exchangers) have an outlet that feeds cooled water to the engine and the engine has an outlet that feeds heated water to the top of the radiator. Water circulation is aided by a rotary pump that has only a slight effect, having to work over such a wide range of speeds that its impeller has only a minimal effect as a pump. While running, the leaking pump seal drained cooling water to a level where the pump could no longer return water to the top of the radiator, so water circulation ceased and water in the engine boiled. However, since water loss led to overheat and further water loss from boil-over, the original water loss was hidden.
Internal combustion engine cooling	Transition from air cooling	After isolating the pump problem, cars and trucks built for the war effort (no civilian cars were built during that time) were equipped with carbon-seal water pumps that did not leak and caused no more geysers. Meanwhile, air cooling advanced in memory of boiling engines... even though boil-over was no longer a common problem. Air-cooled engines became popular throughout Europe. After the war, Volkswagen advertised in the USA as not boiling over, even though new water-cooled cars no longer boiled over, but these cars sold well. But as air quality awareness rose in the 1960s, and laws governing exhaust emissions were passed, unleaded gas replaced leaded gas and leaner fuel mixtures became the norm. Subaru chose liquid-cooling for their EA series (flat) engine when it was introduced in 1966.
Internal combustion engine cooling	Low heat rejection engines	A special class of experimental prototype internal combustion piston engines have been developed over several decades with the goal of improving efficiency by reducing heat loss. These engines are variously called adiabatic engines, due to better approximation of adiabatic expansion, low heat rejection engines, or high-temperature engines. They are generally diesel engines with combustion chamber parts lined with ceramic thermal barrier coatings. Some make use of titanium pistons and other titanium parts due to its low thermal conductivity and mass. Some designs are able to eliminate the use of a cooling system and associated parasitic losses altogether. Developing lubricants able to withstand the higher temperatures involved has been a major barrier to commercialization.
Internal combustion engine cooling	Sources	Biermann, Arnold E.; Ellerbrock, Herman H., Jr (1939). The design of fins for air-cooled cylinders (PDF). NACA. Report Nº. 726.{{cite book}}: CS1 maint: multiple names: authors list (link) P V Lamarque: "The Design of Cooling Fins for Motor-Cycle Engines". Report of the Automobile Research Committee, Institution of Automobile Engineers Magazine, March 1943 issue, and also in "The Institution of Automobile Engineers Proceedings, XXXVII, Session 1942-43, pp 99-134 and 309-312.
Internal combustion engine cooling	Sources	"Air-cooled Automotive Engines", Julius Mackerle, M. E.; Charles Griffin & Company Ltd., London, 1972. engineeringtoolbox.com for physical properties of air, oil and water https://automotivedroid.com/can-low-coolant-cause-rough-idle/ for Low coolant causing rough idle.
Molecular Materials Research Group	Molecular Materials Research Group	The Molecular Materials Research Group (MMRG) is a multidisciplinary research group composed of several Ph.D. members as well as the expertise of other researchers in the field of Computational, Organic and Analytical Chemistry.Located at Madeira University in Madeira, its main scientific activity is devoted to the preparation and characterization of potentially useful molecular materials with enhanced electronic and biomedical properties. The development of new materials based in dendrimers for gene delivery and for non-linear optical applications is one of their primary goals.
Hypoestrogenism	Hypoestrogenism	Hypoestrogenism, or estrogen deficiency, refers to a lower than normal level of estrogen. It is an umbrella term used to describe estrogen deficiency in various conditions. Estrogen deficiency is also associated with an increased risk of cardiovascular disease, and has been linked to diseases like urinary tract infections and osteoporosis.
Hypoestrogenism	Hypoestrogenism	In women, low levels of estrogen may cause symptoms such as hot flashes, sleeping disturbances, decreased bone health, and changes in the genitourinary system. Hypoestrogenism is most commonly found in women who are postmenopausal, have primary ovarian insufficiency (POI), or are presenting with amenorrhea (absence of menstrual periods). Hypoestrogenism includes primarily genitourinary effects, including thinning of the vaginal tissue layers and an increase in vaginal pH. With normal levels of estrogen, the environment of the vagina is protected against inflammation, infections, and sexually transmitted infections. Hypoestrogenism can also occur in men, for instance due to hypogonadism.
Hypoestrogenism	Hypoestrogenism	There are both hormonal and non-hormonal treatments to prevent the negative effects of low estrogen levels and improve quality of life.
Hypoestrogenism	Signs and symptoms	Vasomotor Presentations of low estrogen levels include hot flashes, which are sudden, intense feelings of heat predominantly in the upper body, causing the skin to redden as if blushing. They are believed to occur due to the narrowing of the thermonuclear zone in the hypothalamus, making the body more sensitive to body temperature changes. Night disturbances are also common symptoms associated with hypoestrogenism. People may experience difficulty falling asleep, waking up several times a night, and early awakening with different variability between races and ethnic groups.
Hypoestrogenism	Signs and symptoms	Genitourinary Other classic symptoms include both physical and chemical changes of the vulva, vagina, and lower urinary tract. Genitals go through atrophic changes such as losing elasticity, losing vaginal rugae, and increasing of vaginal pH, which can lead to changes in the vaginal flora and increase the risk of tissue fragility and fissure. Other genital signs include dryness or lack of lubrication, burning, irritation, discomfort or pain, as well as impaired function. Low levels of estrogen can lead to limited genital arousal and cause dyspareunia, or painful sexual intercourse because of changes in the four layers of the vaginal wall. People with low estrogen will also experience higher urgency to urinate and dysuria, or painful urination. Hypoestrogenism is also considered one of the major risk factors for developing uncomplicated urinary tract infection in postmenopausal women who do not take hormone replacement therapy.
Hypoestrogenism	Signs and symptoms	Bone health Estrogen contributes to bone health in several ways; low estrogen levels increase bone resorption via osteoclasts and osteocytes, cells that help with bone remodeling, making bones more likely to deteriorate and increase risk of fracture. The decline in estrogen levels can ultimately lead to more serious illnesses, such as scoliosis or type I osteoporosis, a disease that thins and weakens bones, resulting in low bone density and fractures. Estrogen deficiency plays an important role in osteoporosis development for both genders, and it is more pronounced for women and at younger (menopausal) ages by five to ten years compared with men. Females are also at higher risk for osteopenia and osteoporosis.
Hypoestrogenism	Causes	A variety of conditions can lead to hypoestrogenism: menopause is the most common. Primary ovarian insufficiency (premature menopause) due to varying causes, such as radiation therapy, chemotherapy, or a spontaneous manifestation, can also lead to low estrogen and infertility.Hypogonadism (a condition where the gonads – testes for men and ovaries for women – have diminished activity) can decrease estrogen. In primary hypogonadism, elevated serum gonadotropins are detected on at least two occasions several weeks apart, indicating gonadal failure. In secondary hypogonadism (where the cause is hypothalamic or pituitary dysfunction) serum levels of gonadotropins may be low.Other causes include certain medications, gonadotropin insensitivity, inborn errors of steroid metabolism (for example, aromatase deficiency, 17α-hydroxylase deficiency, 17,20-lyase deficiency, 3β-hydroxysteroid dehydrogenase deficiency, and cholesterol side-chain cleavage enzyme or steroidogenic acute regulatory protein deficiency) and functional amenorrhea.
Hypoestrogenism	Causes	Risks Low endogenous estrogen levels can elevate the risk of cardiovascular disease in women who reach early menopause. Estrogen is needed to relax arteries using endothelial-derived nitric oxide resulting in better heart health by decreasing adverse atherogenic effects. Women with POI may have an increased risk of cardiovascular disease due to low estrogen production.
Hypoestrogenism	Pathophysiology	Estrogen deficiency has both vaginal and urologic effects; the female genitalia and lower urinary tract share common estrogen receptor function due to their embryological development. Estrogen is a vasoactive hormone (one that affects blood pressure) which stimulates blood flow and increases vaginal secretions and lubrication. Activated estrogen receptors also stimulate tissue proliferation in the vaginal walls, which contribute to the formation of rugae. This rugae aids in sexual stimulation by becoming lubricated, distended, and expanded.Genitourinary effects of low estrogen include thinning of the vaginal epithelium, loss of vaginal barrier function, decrease of vaginal folding, decrease of the elasticity of the tissues, and decrease of the secretory activity of the Bartholin glands, which leads to traumatization of the vaginal mucosa and painful sensations. This thinning of the vaginal epithelium layers can increase the risk of developing inflammation and infection, such as urinary tract infection.The vagina is largely dominated by bacteria from the genus Lactobacillus, which typically comprise more than 70% of the vaginal bacteria in women. These lactobacilli process glycogen and its breakdown products, which result in a maintained low vaginal pH. Estrogen levels are closely linked to lactobacilli abundance and vaginal pH, as higher levels of estrogen promote thickening of the vaginal epithelium and intracellular production of glycogen. This large presence of lactobacilli and subsequent low pH levels are hypothesized to benefit women by protecting against sexually transmitted pathogens and opportunistic infections, and therefore reducing disease risk.
Hypoestrogenism	Diagnosis	Hypoestrogenism is typically found in menopause and aids in diagnosis of other conditions such as POI and functional amenorrhea. Estrogen levels can be tested through several laboratory tests: vaginal maturation index, progestogen challenge test, and vaginal swabs for small parabasal cells.
Hypoestrogenism	Diagnosis	Menopause Menopause is usually diagnosed through symptoms of vaginal atrophy, pelvic exams, and taking a comprehensive medical history consisting of last menstruation cycle. There is no definitive testing available for determining menopause as the symptom complex is the primary indicator and because the lower levels of estradiol are harder to accurately detect after menopause. However, there can be laboratory tests done to differentiate between menopause and other diagnoses.
Hypoestrogenism	Diagnosis	Functional hypothalamic amenorrhea Functional hypothalamic amenorrhea (FHA) is diagnosed based on findings of amenorrhea lasting three months or more, low serum hormone of gonadotropins and estradiol. Since common causes of FHA include exercising too much, eating too little, or being under too much stress, diagnosis of FHA includes assessing for any changes in exercise, weight, and stress. In addition, evaluation of amenorrhea includes a history and physical examination, biochemical testing, imaging, and measuring estrogen level. Examination of menstrual problems and clinical tests to measure hormones such as serum prolactin, thyroid-stimulating hormone, and follicle-stimulating hormone (FSH) can help rule out other potential causes of amenorrhea. These potential conditions include hyperprolactinemia, POI, and polycystic ovary syndrome.
Hypoestrogenism	Diagnosis	Primary ovarian insufficiency Primary ovarian insufficiency, also known as premature ovarian failure, can develop in women before the age of forty as a consequence of hypergonadotropic hypogonadism. POI can present as amenorrhea and has similar symptoms to menopause, but measuring FSH levels is used for diagnosis.
Hypoestrogenism	Treatment	Hormone replacement therapy (HRT) can be used to treat hypoestrogenism and menopause related symptoms, and low estrogen levels in both premenopausal and postmenopausal women. Low-dose estrogen medications are approved by the U.S. Food and Drug Administration for treatment of menopause-related symptoms. HRT can be used with or without a progestogen to improve symptoms such as hot flashes, sweating, trouble sleeping, vaginal dryness and discomfort. The FDA recommends HRT to be avoided in women with a history or risk of breast cancer, undiagnosed genital bleeding, untreated high blood pressure, unexplained blood clots, or liver disease.HRT for the vasomotor symptoms of hypoestrogenism include different forms of estrogen, such as conjugated equine estrogens, 17β-estradiol, transdermal estradiol, ethinyl estradiol, and the estradiol ring. In addition to HRT, there are common progestogens that are used to protect the inner layer of the uterus, the endometrium. These medications include medroxyprogesterone acetate, progesterone, norethisterone acetate, and drospirenone.Non-pharmacological treatment of hot flashes includes using portable fans to lower the room temperature, wearing layered clothing, and avoiding tobacco, spicy food, alcohol and caffeine. There is a lack of evidence to support other treatments such as acupuncture, yoga, and exercise to reduce symptoms.
Hypoestrogenism	In men	Estrogens are also important in male physiology. Hypoestrogenism can occur in men due to hypogonadism. Very rare causes include aromatase deficiency and estrogen insensitivity syndrome. Medications can also be a cause of hypoestrogenism in men. Hypoestrogenism in men can lead to osteoporosis, among other symptoms. Estrogens may also be positively involved in sexual desire in men.
Environment of Russia	Climate	The climate of Russia is formed under the European peninsula. The enormous size of the country and the remoteness of many areas from the sea result in the dominance of the continental climate, which is prevalent in European and Asian Russia except for the tundra and the best extreme southeast. Mountains in the south obstructing the flow of cold air masses from the Arctic Ocean and the plain of the south and north makes the country open to Pacific and Atlantic influences.
Environment of Russia	Waste management	141 019 100 tonnes of hazardous waste was generated in Russia in 2009
Environment of Russia	Environmental policy and law	Treaties and international agreements Russia is a signatory to a number of treaties and international agreements: Party to Air Pollution, Air Pollution-Nitrogen Oxides, Air Pollution-Sulphur 85, Antarctic-Environmental Protocol, Antarctic Treaty, Biodiversity, Climate Change, Endangered Species, Environmental Modification, Hazardous Wastes, Law of the Sea, Marine Dumping, Nuclear Test Ban, Ozone Layer Protection, Ship Pollution, Tropical Timber 83, Wetlands, Whaling, Climate Change-Kyoto Protocol Signed, but not ratified Air Pollution-Sulphur 94,
Environment of Russia	Environmental issues	Air pollution from heavy industry, emissions of coal-fired electric plants, and transportation in major cities; industrial, municipal, and agricultural pollution of inland waterways and sea coasts; deforestation; soil erosion; soil contamination from improper application of agricultural chemicals; scattered areas of sometimes intense radioactive contamination; ground water contamination from toxic waste; considerable biodiversity addressed by the country's Biodiversity Action Plan.
Environment of Russia	Environmental issues	While Russia possesses vast mineral and energy wealth, this does not come without some price both to Russia and to the greater globe. Particularly, oil and gas extraction exacts a heavy cost to the health of the land and people. Drilling waste water, mud, and sludges are accumulated, annual volumes have been estimated at 1.7 million tons of chemical reagents contaminating 25 million cubic meters of topsoil. Considerable geomechanical disturbances, contamination of soils and water, and multiple increases of contaminated waste water ejected into surface water streams, is a serious problem offsetting Russia's profits from the industry. It has been estimated that between 1991-1999 the volume of contaminated waste waters from the Russian oil industry amounted to 200 million cubic meters. Complete utilization of co-extracted gas in oil extraction does not exceed 80% in Russia, it has been variously estimated that annually 5-17 billion cubic meters of un-utilized gas extracted alongside oil is burnt in "gas torches," with 400,000 tons or more hazardous substances released into the atmosphere from this each year, creating the double impact of wasted resource and negative environmental effect. 560 million tons of methane is estimated to leak annually into the atmosphere from oil and gas extraction, not counting accidental outbursts and pipe breakage. Other valuable industries also have their costs, such as the coal industry's release of vast quantities of hazardous, toxic, and radioactive materials. Also the Russian gold industry, with Russia being the only nation for at least a century with high extraction of gold from placer deposits, and having 4000+ large deposits, inevitably creates problems for the river systems. The associated pollution from using mass explosions in mining also can be a problem. Overall, the extensive mineral wealth and riches, brings with it both great benefit to the Russian economy & people, and the greater globe and all people, yet also several difficult problems to be dealt with.
Helpmate	Helpmate	A helpmate is a type of chess problem in which both sides cooperate in order to achieve the goal of checkmating Black. In a helpmate in n moves, Black moves first, then White, each side moving n times, to culminate in White's nth move checkmating Black. (In a helpmate in 2 for example, sometimes abbreviated h#2, the solution consists of a Black move, a White move, a second Black move, then a second White move, giving checkmate.) Although the two sides cooperate, all moves must be legal according to the rules of chess.
Helpmate	Helpmate	The example problem illustrated is a helpmate in 8 (or h#8) by Z. Maslar, published in Die Schwalbe in 1981. The solution is (recall that in helpmate solutions, Black's move is given first): 1. Kf3 Kd3 2. Bb3 Kc3 3. Ke4+ Kd2 4. Kd4 Ke2 5. Kc3 Nb4 6. Kb2 Kd2 7. Ka1 Kc1 8. Ba2 Nc2#
Helpmate	History	The first helpmate problem was by the German chess master Max Lange, published in Deutsche Schachzeitung, December 1854. The problem had White to move and White could play in a number of different ways to achieve the same mate (duals), considered a serious flaw today.
Helpmate	History	In The Chess Monthly, November 1860, American puzzle inventor Sam Loyd published the first helpmate with Black to move as is now standard, one intended main line, and an attractive but false solution (a try) to mislead solvers. However, this problem too had a minor dual, and also had the major flaw (or cook) of having a second, completely separate solution, not noted by the author. Even so, it was a much better problem than Lange's and its presentation, incorporating a story written by D. W. Fiske, established the genre.The first completely sound helpmate was by A. Barbe of Leipzig, published in 105 Leipziger Ill. Familien-Journal, 1861.The term "help-mate" originated in The Problem Art by T. B. and F. F. Rowland (Kingstown, 1897). The helpmate problem task has since increased in popularity to be second only to the directmate and is no longer considered to be part of fairy chess.
Helpmate	Varieties of helpmate problems	Multiple solutions Because the nature of helpmates sees Black and White cooperating, the play in helpmates may seem to be a great deal simpler than in directmates (the most common type of problem, where White tries to checkmate Black, and Black tries to avoid being mated). In directmates, a great variety of play can be found in the solution because although White has only one move at each juncture which will solve the problem, Black can choose between several to try to thwart White's efforts. In helpmates, however, both White's and Black's moves are limited to just one at each juncture; this may seem simple, but a well-constructed helpmate also shows thematic play, and the cooperating moves should not always be easy to find. It has been noted by Jean Oudot that "helpmates are the purest form of all the chess arts" In order to introduce more lines of play into a problem, various devices can be employed. Most straightforwardly, a problem can have more than one solution. The solutions will usually complement each other in some thematic and aesthetically pleasing way. Each solution can be considered a different phase of play. If there is more than one solution, the composer will state this; if there is no such statement, the problem has only one solution. The example to the right is a helpmate in 2 (h#2) with two solutions. It was published in the June 1975 issue of Schach and is by the helpmate specialist Chris J. Feather.
Helpmate	Varieties of helpmate problems	The two solutions are 1. Bxb8 Bd5 2. Nc7 Bxg5# and 1. Rdxd8 Bc6 2. Nd7 Rxb3#. These lines are very closely linked, with both exhibiting the same basic pattern: first, Black takes the white piece that gives mate in the other solution (this is known as a Zilahi), at the same time opening the line on which mate is eventually given, then White moves a bishop to close a line so that Black's next move will not give check. Black's second move closes another line so that after White's last move, giving check, Black will not be able to interpose one of his pieces.
Helpmate	Varieties of helpmate problems	Twinning Another way of giving variety to the play of a helpmate is twinning. Here, more than one problem is wrought from a single diagram by making small changes to it, such as moving a piece from one square to another, adding or removing a piece, turning the board round or some other device. Twinning is occasionally found in other types of problems, but is particularly common in helpmates. The example shown is a helpmate in 2 by Henry Forsberg (published in 1935 in Revista Romana de Şah). The twins are created by substituting the black queen on a6 with a different piece. The solutions are: a) diagram position: 1. Qf6 Nc5 2. Qb2 Ra4# b) with black rook at a6: 1. Rb6 Rb1 2. Rb3 Ra1# c) with black bishop at a6: 1. Bc4 Ne1 2. Ba2 Nc2# d) with black knight at a6: 1. Nc5 Nc1 2. Na4 Rb3# e) with black pawn at a6: 1. a5 Rb3+ 2. Ka4 Nc5# Duplex A further variation is the duplex, another way of getting two problems for the price of one. The first problem is a normal helpmate; the second starts from the same position but has White moving first and helping Black to checkmate him. Again, duplex problems have been composed with other types of problems, but the vast majority are helpmates. To the right is an example by Milan Vukcevich (from CHM avec 6 pieces Bad Pyrmont, 1996).
Helpmate	Varieties of helpmate problems	The solution with Black moving first is 1. Ng6 f8=Q 2. Ne5 d8=N#. With White moving first, it is 1. f8=R Nf7 2. d8=B Nd6#. These two lines are closely linked, with two white pawn promotions covering the black king's flight squares in the first part and promoted pieces blocking White's flight squares in the second. This problem is an Allumwandlung, a problem in which pawns are promoted to each of knight, bishop, rook and queen.
Helpmate	Varieties of helpmate problems	Unorthodox helpmate problems Very popular today also are helpmates where White moves first; then the stipulation contains a "½", for example a helpmate in 2½ moves. Helpmates, like other problems, can be composed with fairy chess pieces or with fairy conditions (chess variant rules), such as Circe chess, Grid chess, or Patrol chess. All of these variations can be, and have been, combined. (So it is possible to have, for instance, a series-helpmate in 7, twinned with two solutions in each phase, using nightriders and Madrasi chess.) Problems related to helpmates can have other kinds of stipulations involving cooperation between White and Black, in particular seriesmover problems, like seriesmates, serieshelpmates, serieshelpstalemates, etc.
Convex Polyhedra (book)	Convex Polyhedra (book)	Convex Polyhedra is a book on the mathematics of convex polyhedra, written by Soviet mathematician Aleksandr Danilovich Aleksandrov, and originally published in Russian in 1950, under the title Выпуклые многогранники. It was translated into German by Wilhelm Süss as Konvexe Polyeder in 1958. An updated edition, translated into English by Nurlan S. Dairbekov, Semën Samsonovich Kutateladze and Alexei B. Sossinsky, with added material by Victor Zalgaller, L. A. Shor, and Yu. A. Volkov, was published as Convex Polyhedra by Springer-Verlag in 2005.
Convex Polyhedra (book)	Topics	The main focus of the book is on the specification of geometric data that will determine uniquely the shape of a three-dimensional convex polyhedron, up to some class of geometric transformations such as congruence or similarity. It considers both bounded polyhedra (convex hulls of finite sets of points) and unbounded polyhedra (intersections of finitely many half-spaces).The 1950 Russian edition of the book included 11 chapters. The first chapter covers the basic topological properties of polyhedra, including their topological equivalence to spheres (in the bounded case) and Euler's polyhedral formula. After a lemma of Augustin Cauchy on the impossibility of labeling the edges of a polyhedron by positive and negative signs so that each vertex has at least four sign changes, the remainder of chapter 2 outlines the content of the remaining book. Chapters 3 and 4 prove Alexandrov's uniqueness theorem, characterizing the surface geometry of polyhedra as being exactly the metric spaces that are topologically spherical locally like the Euclidean plane except at a finite set of points of positive angular defect, obeying Descartes' theorem on total angular defect that the total angular defect should be 4π . Chapter 5 considers the metric spaces defined in the same way that are topologically a disk rather than a sphere, and studies the flexible polyhedral surfaces that result.Chapters 6 through 8 of the book are related to a theorem of Hermann Minkowski that a convex polyhedron is uniquely determined by the areas and directions of its faces, with a new proof based on invariance of domain. A generalization of this theorem implies that the same is true for the perimeters and directions of the faces. Chapter 9 concerns the reconstruction of three-dimensional polyhedra from a two-dimensional perspective view, by constraining the vertices of the polyhedron to lie on rays through the point of view. The original Russian edition of the book concludes with two chapters, 10 and 11, related to Cauchy's theorem that polyhedra with flat faces form rigid structures, and describing the differences between the rigidity and infinitesimal rigidity of polyhedra, as developed analogously to Cauchy's rigidity theorem by Max Dehn.The 2005 English edition adds comments and bibliographic information regarding many problems that were posed as open in the 1950 edition but subsequently solved. It also includes in a chapter of supplementary material the translations of three related articles by Volkov and Shor, including a simplified proof of Pogorelov's theorems generalizing Alexandrov's uniqueness theorem to non-polyhedral convex surfaces.
Convex Polyhedra (book)	Audience and reception	Robert Connelly writes that, for a work describing significant developments in the theory of convex polyhedra that was however hard to access in the west, the English translation of Convex Polyhedra was long overdue. He calls the material on Alexandrov's uniqueness theorem "the star result in the book", and he writes that the book "had a great influence on countless Russian mathematicians". Nevertheless, he complains about the book's small number of exercises, and about an inconsistent level presentation that fails to distinguish important and basic results from specialized technicalities.Although intended for a broad mathematical audience, Convex Polyhedra assumes a significant level of background knowledge in material including topology, differential geometry, and linear algebra.
Convex Polyhedra (book)	Audience and reception	Reviewer Vasyl Gorkaviy recommends Convex Polyhedra to students and professional mathematicians as an introduction to the mathematics of convex polyhedra. He also writes that, over 50 years after its original publication, "it still remains of great interest for specialists", after being updated to include many new developments and to list new open problems in the area.
Planetary phase	Planetary phase	A planetary phase is a certain portion of a planet's area that [[diffuse reflecti ntage point, as well as the period of time during which it occurs.
Planetary phase	Inferior planets	The two inferior planets, Mercury and Venus, which have orbits that are smaller than the Earth's, exhibit the full range of phases as does the Moon, when seen through a telescope. Their phases are "full" when they are at superior conjunction, on the far side of the Sun as seen from the Earth. It is possible to see them at these times, since their orbits are not exactly in the plane of Earth's orbit, so they usually appear to pass slightly above or below the Sun in the sky. Seeing them from the Earth's surface is difficult, because of sunlight scattered in Earth's atmosphere, but observers in space can see them easily if direct sunlight is blocked from reaching the observer's eyes. The planets' phases are "new" when they are at inferior conjunction, passing more or less between the Sun and the Earth. Sometimes they appear to cross the solar disk, which is called a transit of the planet. At intermediate points on their orbits, these planets exhibit the full range of crescent and gibbous phases.
Planetary phase	Superior planets	The superior planets, orbiting outside the Earth's orbit, do not exhibit the full range of phases as they appear almost always as gibbous or full. However, Mars often appears significantly gibbous, when it is illuminated by the Sun at a very different angle than it is seen by an observer on Earth, so an observer on Mars would see the Sun and the Earth widely separated in the sky. This effect is not easily noticeable for the giant planets, from Jupiter outward, since they are so far away that the Sun and the Earth, as seen from these outer planets, would appear to be in almost the same direction.
Planetary phase	See here also	Earth phase Lunar phase Phases of Venus
Method of support	Method of support	In statistics, the method of support is a technique that is used to make inferences from datasets.
Method of support	Method of support	According to A. W. F. Edwards, the method of support aims to make inferences about unknown parameters in terms of the relative support, or log likelihood, induced by a set of data for a particular parameter value. The technique may be used whether or not prior information is available. The method of maximum likelihood is part of the method of support, but note that the method of support also provides confidence regions that are defined in terms of their support.
Method of support	Method of support	Notable proponents of the method of support include A. W. F. Edwards.
Staggered tuning	Staggered tuning	Staggered tuning is a technique used in the design of multi-stage tuned amplifiers whereby each stage is tuned to a slightly different frequency. In comparison to synchronous tuning (where each stage is tuned identically) it produces a wider bandwidth at the expense of reduced gain. It also produces a sharper transition from the passband to the stopband. Both staggered tuning and synchronous tuning circuits are easier to tune and manufacture than many other filter types.
Staggered tuning	Staggered tuning	The function of stagger-tuned circuits can be expressed as a rational function and hence they can be designed to any of the major filter responses such as Butterworth and Chebyshev. The poles of the circuit are easy to manipulate to achieve the desired response because of the amplifier buffering between stages. Applications include television IF amplifiers (mostly 20th century receivers) and wireless LAN.
Staggered tuning	Rationale	Staggered tuning improves the bandwidth of a multi-stage tuned amplifier at the expense of the overall gain. Staggered tuning also increases the steepness of passband skirts and hence improves selectivity.
Staggered tuning	Rationale	The value of staggered tuning is best explained by first looking at the shortcomings of tuning every stage identically. This method is called synchronous tuning. Each stage of the amplifier will reduce the bandwidth. In an amplifier with multiple identical stages, the 3 dB points of the response after the first stage will become the 6 dB points of the second stage. Each successive stage will add a further 3 dB to what was the band edge of the first stage. Thus the 3 dB bandwidth becomes progressively narrower with each additional stage.As an example, a four-stage amplifier will have its 3 dB points at the 0.75 dB points of an individual stage. The fractional bandwidth of an LC circuit is given by, B = m − 1 Q B={{\sqrt {m-1}} \over Q} where m is the power ratio of the power at resonance to that at the band edge frequency (equal to 2 for the 3 dB point and 1.19 for the 0.75 dB point) and Q is the quality factor.The bandwidth is thus reduced by a factor of m − 1 {\sqrt {m-1}} . In terms of the number of stages m = 2 1 / n m=2^{1/n} . Thus, the four stage synchronously tuned amplifier will have a bandwidth of only 19% of a single stage. Even in a two-stage amplifier the bandwidth is reduced to 41% of the original. Staggered tuning allows the bandwidth to be widened at the expense of overall gain. The overall gain is reduced because when any one stage is at resonance (and thus maximum gain) the others are not, unlike synchronous tuning where all stages are at maximum gain at the same frequency. A two-stage stagger-tuned amplifier will have a gain 3 dB less than a synchronously tuned amplifier.Even in a design that is intended to be synchronously tuned, some staggered tuning effect is inevitable because of the practical impossibility of keeping all tuned circuits perfectly in step and because of feedback effects. This can be a problem in very narrow band applications where essentially only one spot frequency is of interest, such as a local oscillator feed or a wave trap. The overall gain of a synchronously tuned amplifier will always be less than the theoretical maximum because of this.Both synchronously tuned and stagger-tuned schemes have a number of advantages over schemes that place all the tuning components in a single aggregated filter circuit separate from the amplifier such as ladder networks or coupled resonators. One advantage is that they are easy to tune. Each resonator is buffered from the others by the amplifier stages so have little effect on each other. The resonators in aggregated circuits, on the other hand, will all interact with each other, particularly their nearest neighbours. Another advantage is that the components need not be close to ideal. Every LC resonator is directly working into a resistor which lowers the Q anyway so any losses in the L and C components can be absorbed into this resistor in the design. Aggregated designs usually require high Q resonators. Also, stagger-tuned circuits have resonator components with values that are quite close to each other and in synchronously tuned circuits they can be identical. The spread of component values is thus less in stagger-tuned circuits than in aggregated circuits.
Staggered tuning	Design	Tuned amplifiers such as the one illustrated at the beginning of this article can be more generically depicted as a chain of transconductance amplifiers each loaded with a tuned circuit. where for each stage (omitting the suffixes) gm is the amplifier transconductance C is the tuned circuit capacitance L is the tuned circuit inductance G is the sum of the amplifier output conductance and the input conductance of the next amplifier.
Staggered tuning	Design	Stage gain The gain A(s), of one stage of this amplifier is given by; A ( s ) = g m s L s 2 L C + s L G + 1 A(s)={\frac {g_{\mathrm {m} }sL}{s^{2}LC+sLG+1}} where s is the complex frequency operator.This can be written in a more generic form, that is, not assuming that the resonators are the LC type, with the following substitutions, ω 0 = 1 L C \omega _{0}={1 \over {\sqrt {LC}}} (the resonant frequency) A 0 := A ( ω 0 ) = g m G A_{0}:=A(\omega _{0})={\frac {g_{\mathrm {m} }}{G}} (the gain at resonance) Q = 1 ω 0 L G Q={1 \over \omega _{0}LG} (the stage quality factor)Resulting in, A ( s ) = A 0 s ω 0 s 2 Q + s ω 0 + ω 0 2 Q A(s)=A_{0}{\frac {s\omega _{0}}{s^{2}Q+s\omega _{0}+\omega _{0}^{2}Q}} Stage bandwidth The gain expression can be given as a function of (angular) frequency by making the substitution s = iω where i is the imaginary unit and ω is the angular frequency A ( ω ) = A 0 i ω ω 0 i ω ω 0 + ω 0 2 Q − ω 2 Q A(\omega )=A_{0}{\frac {i\omega \omega _{0}}{i\omega \omega _{0}+\omega _{0}^{2}Q-\omega ^{2}Q}} The frequency at the band edges, ωc, can be found from this expression by equating the value of the gain at the band edge to the magnitude of the expression, \| A ( ω c ) \| = A 0 m \|A(\omega _{c})\|={\frac {A_{0}}{\sqrt {m}}} where m is defined as above and equal to two if the 3 dB points are desired.Solving this for ωc and taking the difference between the two positive solutions finds the bandwidth Δω, Δ ω c = ω c 1 − ω c 2 = ω 0 ( m − 1 ) Q \Delta \omega _{\mathrm {c} }=\omega _{{\mathrm {c} }1}-\omega _{{\mathrm {c} }2}={\frac {\omega _{0}{\sqrt {(m-1)}}}{Q}} and the fractional bandwidth B, B := Δ ω c ω 0 = m − 1 Q B:={\frac {\Delta \omega _{\mathrm {c} }}{\omega _{0}}}={\frac {\sqrt {m-1}}{Q}} Overall response The overall response of the amplifier is given by the product of the individual stages, A T = A 1 A 2 A 3 ⋯ A_{\mathrm {T} }=A_{1}A_{2}A_{3}\cdots It is desirable to be able to design the filter from a standard low-pass prototype filter of the required specification. Frequently, a smooth Butterworth response will be chosen but other polynomial functions can be used that allow ripple in the response. A popular choice for a polynomial with ripple is the Chebyshev response for its steep skirt. For the purpose of transformation, the stage gain expression can be rewritten in the more suggestive form, A ( s ) = A 0 1 + Q ( s ω 0 + ω 0 s ) A(s)={\frac {A_{0}}{1+Q\left({\frac {s}{\omega _{0}}}+{\frac {\omega _{0}}{s}}\right)}} This can be transformed into a low-pass prototype filter with the transform Q ( s ω 0 + ω 0 s ) → s ω c ′ Q\left({\frac {s}{\omega _{0}}}+{\frac {\omega _{0}}{s}}\right)\to {\frac {s}{\omega _{c}'}} where ω'c is the cutoff frequency of the low-pass prototype.This can be done straightforwardly for the complete filter in the case of synchronously tuned amplifiers where every stage has the same ω0 but for a stagger-tuned amplifier there is no simple analytical solution to the transform. Stagger-tuned designs can be approached instead by calculating the poles of a low-pass prototype of the desired form (e.g. Butterworth) and then transforming those poles to a band-pass response. The poles so calculated can then be used to define the tuned circuits of the individual stages.
Staggered tuning	Design	Poles The stage gain can be rewritten in terms of the poles by factorising the denominator; A ( s ) = A 0 Q s ω 0 ( s − p ) ( s − p ∗ ) A(s)={\frac {A_{0}}{Q}}{\frac {s\omega _{0}}{(s-p)(s-p^{})}} where p, p are a complex conjugate pair of polesand the overall response is, A T = s a 1 ( s − p 1 ) ( s − p 1 ∗ ) ⋅ s a 2 ( s − p 2 ) ( s − p 2 ∗ ) ⋅ s a 3 ( s − p 3 ) ( s − p 3 ∗ ) ⋅ ⋯ A_{\mathrm {T} }={\frac {sa_{1}}{(s-p_{1})(s-p_{1}^{})}}\cdot {\frac {sa_{2}}{(s-p_{2})(s-p_{2}^{})}}\cdot {\frac {sa_{3}}{(s-p_{3})(s-p_{3}^{})}}\cdot \cdots where the ak = A0kω0k/Q0kFrom the band-pass to low-pass transform given above, an expression can be found for the poles in terms of the poles of the low-pass prototype, qk, p k , p k ∗ = 1 2 ( q k ω 0 B ω c ′ Q e f f ± ( q k ω 0 B ω c ′ Q e f f ) 2 − 4 ω 0 B 2 ) p_{k},p_{k}^{}={1 \over 2}\left({\frac {q_{k}\omega _{0{\mathrm {B} }}}{\omega '_{\mathrm {c} }Q_{\mathrm {eff} }}}\pm {\sqrt {\left({\frac {q_{k}\omega _{0{\mathrm {B} }}}{\omega '_{\mathrm {c} }Q_{\mathrm {eff} }}}\right)^{2}-4{\omega _{0{\mathrm {B} }}}^{2}}}\right) where ω0B is the desired band-pass centre frequency and Qeff is the effective Q of the overall circuit.Each pole in the prototype transforms to a complex conjugate pair of poles in the band-pass and corresponds to one stage of the amplifier. This expression is greatly simplified if the cutoff frequency of the prototype, ω'c, is set to the final filter bandwidth ω0B/Qeff.
Staggered tuning	Design	p k , p k ∗ = 1 2 ( q k ± q k 2 − 4 ω 0 B 2 ) p_{k},p_{k}^{}={1 \over 2}\left(q_{k}\pm {\sqrt {q_{k}^{2}-4{\omega _{0{\mathrm {B} }}}^{2}}}\right) In the case of a narrowband design ω0≫q which can be used to make a further simplification with the approximation, p k , p k ∗ ≈ q k 2 ± i ω 0 B p_{k},p_{k}^{}\approx {q_{k} \over 2}\pm i\omega _{0{\mathrm {B} }} These poles can be inserted into the stage gain expression in terms of poles. By comparing with the stage gain expression in terms of component values, those component values can then be calculated.
Staggered tuning	Applications	Staggered tuning is of most benefit in wideband applications. It was formerly commonly used in television receiver IF amplifiers. However, SAW filters are more likely to be used in that role nowadays. Staggered tuning has advantages in VLSI for radio applications such as wireless LAN. The low spread of component values make it much easier to implement in integrated circuits than traditional ladder networks.
The Appropriate Technology Library	The Appropriate Technology Library	The Appropriate Technology Library consists of 1050 books on 29 subject areas of small scale, do-it-yourself technology. Originally developed by Volunteers in Asia (VIA) it was transferred to Village Earth: The Consortium for Sustainable Village-Based Development in 1993. The Library was developed to be a low-cost and portable source of appropriate technology information for aid and relief workers around the world. Since its inception, it has been used in dozens of countries around the world.
Shot noise	Shot noise	Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where shot noise is associated with the particle nature of light.
Shot noise	Origin	In a statistical experiment such as tossing a fair coin and counting the occurrences of heads and tails, the numbers of heads and tails after many throws will differ by only a tiny percentage, while after only a few throws outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot. From the law of large numbers, one can show that the relative fluctuations reduce as the reciprocal square root of the number of throws, a result valid for all statistical fluctuations, including shot noise.
Shot noise	Origin	Shot noise exists because phenomena such as light and electric current consist of the movement of discrete (also called "quantized") 'packets'. Consider light—a stream of discrete photons—coming out of a laser pointer and hitting a wall to create a visible spot. The fundamental physical processes that govern light emission are such that these photons are emitted from the laser at random times; but the many billions of photons needed to create a spot are so many that the brightness, the number of photons per unit of time, varies only infinitesimally with time. However, if the laser brightness is reduced until only a handful of photons hit the wall every second, the relative fluctuations in number of photons, i.e., brightness, will be significant, just as when tossing a coin a few times. These fluctuations are shot noise.
Shot noise	Origin	The concept of shot noise was first introduced in 1918 by Walter Schottky who studied fluctuations of current in vacuum tubes.Shot noise may be dominant when the finite number of particles that carry energy (such as electrons in an electronic circuit or photons in an optical device) is sufficiently small so that uncertainties due to the Poisson distribution, which describes the occurrence of independent random events, are significant. It is important in electronics, telecommunications, optical detection, and fundamental physics.
Shot noise	Origin	The term can also be used to describe any noise source, even if solely mathematical, of similar origin. For instance, particle simulations may produce a certain amount of "noise", where because of the small number of particles simulated, the simulation exhibits undue statistical fluctuations which don't reflect the real-world system. The magnitude of shot noise increases according to the square root of the expected number of events, such as the electric current or intensity of light. But since the strength of the signal itself increases more rapidly, the relative proportion of shot noise decreases and the signal-to-noise ratio (considering only shot noise) increases anyway. Thus shot noise is most frequently observed with small currents or low light intensities that have been amplified.
Shot noise	Origin	For large numbers, the Poisson distribution approaches a normal distribution about its mean, and the elementary events (photons, electrons, etc.) are no longer individually observed, typically making shot noise in actual observations indistinguishable from true Gaussian noise. Since the standard deviation of shot noise is equal to the square root of the average number of events N, the signal-to-noise ratio (SNR) is given by: SNR=NN=N.
Shot noise	Origin	Thus when N is very large, the signal-to-noise ratio is very large as well, and any relative fluctuations in N due to other sources are more likely to dominate over shot noise. However, when the other noise source is at a fixed level, such as thermal noise, or grows slower than N , increasing N (the DC current or light level, etc.) can lead to dominance of shot noise.
Shot noise	Properties	Electronic devices Shot noise in electronic circuits consists of random fluctuations of DC current, which is due to electric current being the flow of discrete charges (electrons). Because the electron has such a tiny charge, however, shot noise is of relative insignificance in many (but not all) cases of electrical conduction. For instance 1 ampere of current consists of about 6.24×1018 electrons per second; even though this number will randomly vary by several billion in any given second, such a fluctuation is minuscule compared to the current itself. In addition, shot noise is often less significant as compared with two other noise sources in electronic circuits, flicker noise and Johnson–Nyquist noise. However, shot noise is temperature and frequency independent, in contrast to Johnson–Nyquist noise, which is proportional to temperature, and flicker noise, with the spectral density decreasing with increasing frequency. Therefore, at high frequencies and low temperatures shot noise may become the dominant source of noise.
Shot noise	Properties	With very small currents and considering shorter time scales (thus wider bandwidths) shot noise can be significant. For instance, a microwave circuit operates on time scales of less than a nanosecond and if we were to have a current of 16 nanoamperes that would amount to only 100 electrons passing every nanosecond. According to Poisson statistics the actual number of electrons in any nanosecond would vary by 10 electrons rms, so that one sixth of the time less than 90 electrons would pass a point and one sixth of the time more than 110 electrons would be counted in a nanosecond. Now with this small current viewed on this time scale, the shot noise amounts to 1/10 of the DC current itself.
Shot noise	Properties	The result by Schottky, based on the assumption that the statistics of electrons passage is Poissonian, reads for the spectral noise density at the frequency f ,S(f)=2e\|I\|, where e is the electron charge, and I is the average current of the electron stream. The noise spectral power is frequency independent, which means the noise is white. This can be combined with the Landauer formula, which relates the average current with the transmission eigenvalues Tn of the contact through which the current is measured ( n labels transport channels). In the simplest case, these transmission eigenvalues can be taken to be energy independent and so the Landauer formula is I=e2πℏV∑nTn, where V is the applied voltage. This provides for S=2e3πℏ\|V\|∑nTn, commonly referred to as the Poisson value of shot noise, SP . This is a classical result in the sense that it does not take into account that electrons obey Fermi–Dirac statistics. The correct result takes into account the quantum statistics of electrons and reads (at zero temperature) S=2e3πℏ\|V\|∑nTn(1−Tn).
Shot noise	Properties	It was obtained in the 1990s by Khlus, Lesovik (independently the single-channel case), and Büttiker (multi-channel case). This noise is white and is always suppressed with respect to the Poisson value. The degree of suppression, F=S/SP , is known as the Fano factor. Noises produced by different transport channels are independent. Fully open ( Tn=1 ) and fully closed ( Tn=0 ) channels produce no noise, since there are no irregularities in the electron stream.
Shot noise	Properties	At finite temperature, a closed expression for noise can be written as well. It interpolates between shot noise (zero temperature) and Nyquist-Johnson noise (high temperature). Examples Tunnel junction is characterized by low transmission in all transport channels, therefore the electron flow is Poissonian, and the Fano factor equals one. Quantum point contact is characterized by an ideal transmission in all open channels, therefore it does not produce any noise, and the Fano factor equals zero. The exception is the step between plateaus, when one of the channels is partially open and produces noise. A metallic diffusive wire has a Fano factor of 1/3 regardless of the geometry and the details of the material. In 2DEG exhibiting fractional quantum Hall effect electric current is carried by quasiparticles moving at the sample edge whose charge is a rational fraction of the electron charge. The first direct measurement of their charge was through the shot noise in the current.
Shot noise	Properties	Effects of interactions While this is the result when the electrons contributing to the current occur completely randomly, unaffected by each other, there are important cases in which these natural fluctuations are largely suppressed due to a charge build up. Take the previous example in which an average of 100 electrons go from point A to point B every nanosecond. During the first half of a nanosecond we would expect 50 electrons to arrive at point B on the average, but in a particular half nanosecond there might well be 60 electrons which arrive there. This will create a more negative electric charge at point B than average, and that extra charge will tend to repel the further flow of electrons from leaving point A during the remaining half nanosecond. Thus the net current integrated over a nanosecond will tend more to stay near its average value of 100 electrons rather than exhibiting the expected fluctuations (10 electrons rms) we calculated. This is the case in ordinary metallic wires and in metal film resistors, where shot noise is almost completely cancelled due to this anti-correlation between the motion of individual electrons, acting on each other through the coulomb force.
Shot noise	Properties	However this reduction in shot noise does not apply when the current results from random events at a potential barrier which all the electrons must overcome due to a random excitation, such as by thermal activation. This is the situation in p-n junctions, for instance. A semiconductor diode is thus commonly used as a noise source by passing a particular DC current through it.
Shot noise	Properties	In other situations interactions can lead to an enhancement of shot noise, which is the result of a super-poissonian statistics. For example, in a resonant tunneling diode the interplay of electrostatic interaction and of the density of states in the quantum well leads to a strong enhancement of shot noise when the device is biased in the negative differential resistance region of the current-voltage characteristics.Shot noise is distinct from voltage and current fluctuations expected in thermal equilibrium; this occurs without any applied DC voltage or current flowing. These fluctuations are known as Johnson–Nyquist noise or thermal noise and increase in proportion to the Kelvin temperature of any resistive component. However both are instances of white noise and thus cannot be distinguished simply by observing them even though their origins are quite dissimilar.
Shot noise	Properties	Since shot noise is a Poisson process due to the finite charge of an electron, one can compute the root mean square current fluctuations as being of a magnitude σi=2qIΔf where q is the elementary charge of an electron, Δf is the single-sided bandwidth in hertz over which the noise is considered, and I is the DC current flowing. For a current of 100 mA, measuring the current noise over a bandwidth of 1 Hz, we obtain 0.18 nA. If this noise current is fed through a resistor a noise voltage of σv=σiR would be generated. Coupling this noise through a capacitor, one could supply a noise power of P=12qIΔfR. to a matched load.
Shot noise	Properties	Detectors The flux signal that is incident on a detector is calculated as follows, in units of photons: where c is the speed of light, and h is the Planck constant. Following Poisson statistics, the photon noise is calculated as the square root of the signal: The SNR for a CCD camera can be calculated from the following equation: where: I = photon flux (photons/pixel/second), QE = quantum efficiency, t = integration time (seconds), Nd = dark current (electrons/pixel/sec), Nr = read noise (electrons).
Shot noise	Properties	Optics In optics, shot noise describes the fluctuations of the number of photons detected (or simply counted in the abstract) due to their occurrence independent of each other. This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons. In the case of photon detection, the relevant process is the random conversion of photons into photo-electrons for instance, thus leading to a larger effective shot noise level when using a detector with a quantum efficiency below unity. Only in an exotic squeezed coherent state can the number of photons measured per unit time have fluctuations smaller than the square root of the expected number of photons counted in that period of time. Of course there are other mechanisms of noise in optical signals which often dwarf the contribution of shot noise. When these are absent, however, optical detection is said to be "photon noise limited" as only the shot noise (also known as "quantum noise" or "photon noise" in this context) remains.
Shot noise	Properties	Shot noise is easily observable in the case of photomultipliers and avalanche photodiodes used in the Geiger mode, where individual photon detections are observed. However the same noise source is present with higher light intensities measured by any photo detector, and is directly measurable when it dominates the noise of the subsequent electronic amplifier. Just as with other forms of shot noise, the fluctuations in a photo-current due to shot noise scale as the square-root of the average intensity: (ΔI)2=def⟨(I−⟨I⟩)2⟩∝I.
Shot noise	Properties	The shot noise of a coherent optical beam (having no other noise sources) is a fundamental physical phenomenon, reflecting quantum fluctuations in the electromagnetic field. In optical homodyne detection, the shot noise in the photodetector can be attributed to either the zero point fluctuations of the quantised electromagnetic field, or to the discrete nature of the photon absorption process. However, shot noise itself is not a distinctive feature of quantised field and can also be explained through semiclassical theory. What the semiclassical theory does not predict, however, is the squeezing of shot noise. Shot noise also sets a lower bound on the noise introduced by quantum amplifiers which preserve the phase of an optical signal.
Piece goods	Piece goods	Piece goods were the textile materials sold in cut pieces as per the buyer's specification. The piece goods were either cut from a fabric roll or produced with a certain length, also called yard goods. Various textiles such as cotton, wool, silk, etc., were traded in terms of piece goods. The prices were determined as per the fabric quality.John Forbes Watson classified Indian textiles into two types: piece goods and loom goods. Piece goods are materials that must be cut and sewn before they can be used, whereas loom goods, such as scarves and Saris, are ready to use after leaving the loom.
Piece goods	Production	Many Indian clothes were ready to wear after leaving the loom. These were simple pieces of cloth of dimensions suited to the purposes. Lungi, Dhoti, and Sari are few specific examples of drape clothes. Other cloths produced according to specified dimensions are: Longcloth made at Coromandel Coast was of the length of 37 yards or 37 to 40 yards. Qutni at Damascus was weaved as per market specified dimensions; for example, Length 6.13 meters width 0.7 meters was for Syria, Baghdad and Constantinople, Smyrna, and Persia. But for Egypt, the length was slightly more, i.e., 6.83 with the same width. Chautar an old muslin has been recorded with specific dimensions, i.e., length 12.44 meters and width 77.75 centimeters. Chautar was compared with sansuo, which was a three shuttle cloth, type of fine cotton variety produced at Songjiang. Tasar, a silk and cotton cloth used for lining in quilts from Bengal was produced with 14 yards of length and 1.5 yards width. Alachas were 5 yards long. A type of Gulbadan (silk cloth), Sohren Gulbadan was with 36 feet long and 1 foot and 4 inches wide. Salampore was 16X1 yards. Sussi (cloth) a striped fabric was 10 to 20 yards long and one yard in wide. Khasas were having dimensions of 20 x 1 or 1.5 yards. The number of threads was in warp direction were 1400–2800 with the weight of 595 grams /pc (with 2800 threads). Mulboos khas special muslins, reserved for royal aristocracy were measured 10 yards X 1-yard when produced of half-length. They were having 1800-1900 threads in warp. Man-cheti was a “ginger yellow” cotton cloth made in India in the 14th century. Made in lengths of fifty feet and a width of four feet. Punjum, a kind of longcloth from the Northern Circars was produced in a variety of thread counts. As per John Forbes Watson, a common piece of Punjum weighs 14 pounds and is 18 yards long (36 Cubits). Its width ranges from 38 to 44 inches. Ghalta had a standard length of 9 yards and a width of 26 inches.: 91, 92 Kente cloth from Ghana, which dates back to the ninth century, consists of narrowly woven strips that are sewn together.
Piece goods	Trading practices	Textile piece goods have been sold globally in many varieties, including grey, bleached, or dyed and prints. And the practice is still being followed by many buyers. The knitted fabric is traded by weight also. History Historically drapers and cloth merchants were trading in piece goods. India was famous for its handloom cotton piece goods. Many fabrics of coarse to fine cotton qualities such as Baftas, calicos, and muslins were used to be exported during the Mughal era.
Piece goods	Trading practices	There are records stating that in 1664 the East India Company imported 273,746 pieces of cotton cloth from India (approximately 4.2 million sq. meters). This increasing trend finally peaked in 1684 at 1,760,315 pieces (or 26.9 million sq. meters). Woolen and silk piece goods were also traded. Woollen piece goods for example shawls were exported from Kashmir.The exports were continued until the British cloths emerged in the 19th century. Substantial quantities of various piece goods were exported from Madras in 18th and 19th century. Punjum cloths accounted for a sizable portion of Madras' exports in the 18th century. Punjum, Salampores, Palampores, Chintz, Book muslin and Longcloth, varieties of Ghingahm were among the piece goods which were exported to America from Madras.: 22, 429 During the 1920s, the Philippines was the largest market for cotton piece goods exported by the United States of America.
Piece goods	Trading practices	Currently Several textile piece goods are still traded with different HS codes to differentiate the weave, structure, and composition. For example, HS code 51123030 stands for hundred percent wool, and 58109100 is for woven dyed cotton with embroidery piece goods. The Harmonized System, or ‘HS,’ is an identification code developed by the World Customs Organization (WCO).
Steinmetz solid	Steinmetz solid	In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves of the intersection of two cylinders is an ellipse. The intersection of two cylinders is called a bicylinder. Topologically, it is equivalent to a square hosohedron. The intersection of three cylinders is called a tricylinder. A bisected bicylinder is called a vault, and a cloister vault in architecture has this shape. Steinmetz solids are named after mathematician Charles Proteus Steinmetz, who solved the problem of determining the volume of the intersection. However, the same problem had been solved earlier, by Archimedes in the ancient Greek world, Zu Chongzhi in ancient China, and Piero della Francesca in the early Italian Renaissance.
Steinmetz solid	Bicylinder	A bicylinder generated by two cylinders with radius r has the volume 16 3r3 and the surface area 16 r2 .The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume and surface area of a domical vault as a rational multiple of the volume and surface area of its enclosing prism hold more generally. In China, the bicylinder is known as Mou he fang gai, literally "two square umbrella"; it was described by the third-century mathematician Liu Hui.
Steinmetz solid	Bicylinder	Proof of the volume formula For deriving the volume formula it is convenient to use the common idea for calculating the volume of a sphere: collecting thin cylindric slices. In this case the thin slices are square cuboids (see diagram). This leads to 16 3r3 .It is well known that the relations of the volumes of a right circular cone, one half of a sphere and a right circular cylinder with same radii and heights are 1 : 2 : 3. For one half of a bicylinder a similar statement is true: The relations of the volumes of the inscribed square pyramid ( a=2r,h=r,V=43r3 ), the half bicylinder ( V=83r3 ) and the surrounding squared cuboid ( a=2r,h=r,V=4r3 ) are 1 : 2 : 3.
Steinmetz solid	Bicylinder	Using Multivariable Calculus Consider the equations of the cylinders: x2+z2=r2 x2+y2=r2 The volume will be given by: V=∭Vdzdydx With the limits of integration: −r2−x2⩽z⩽r2−x2 −r2−x2⩽y⩽r2−x2 −r⩽x⩽r Substituting, we have: 16 r33 Proof of the area formula The surface area consists of two red and two blue cylindrical biangles. One red biangle is cut into halves by the y-z-plane and developed into the plane such that half circle (intersection with the y-z-plane) is developed onto the positive ξ -axis and the development of the biangle is bounded upwards by the sine arc sin ⁡(ξr),0≤ξ≤πr . Hence the area of this development is sin ⁡(ξr)dξ=2r2 and the total surface area is: 16 r2 Alternate proof of the volume formula Deriving the volume of a bicylinder (white) can be done by packing it in a cube (red). A plane (parallel with the cylinders' axes) intersecting the bicylinder forms a square and its intersection with the cube is a larger square. The difference between the areas of the two squares is the same as 4 small squares (blue). As the plane moves through the solids, these blue squares describe square pyramids with isosceles faces in the corners of the cube; the pyramids have their apexes at the midpoints of the four cube edges. Moving the plane through the whole bicylinder describes a total of 8 pyramids.
Steinmetz solid	Bicylinder	The volume of the cube (red) minus the volume of the eight pyramids (blue) is the volume of the bicylinder (white). The volume of the 8 pyramids is: 8×13r2×r=83r3 , and then we can calculate that the bicylinder volume is 16 3r3
Steinmetz solid	Tricylinder	The intersection of three cylinders with perpendicularly intersecting axes generates a surface of a solid with vertices where 3 edges meet and vertices where 4 edges meet. The set of vertices can be considered as the edges of a rhombic dodecahedron. The key for the determination of volume and surface area is the observation that the tricylinder can be resampled by the cube with the vertices where 3 edges meet (s. diagram) and 6 curved pyramids (the triangles are parts of cylinder surfaces). The volume and the surface area of the curved triangles can be determined by similar considerations as it is done for the bicylinder above.The volume of a tricylinder is V=8(2−2)r3 and the surface area is 24 (2−2)r2.
Steinmetz solid	More cylinders	With four cylinders, with axes connecting the vertices of a tetrahedron to the corresponding points on the other side of the solid, the volume is 12 (22−6)r3 With six cylinders, with axes parallel to the diagonals of the faces of a cube, the volume is: 16 3(3+23−42)r3
Drug of last resort	Drug of last resort	A drug of last resort (DoLR), also known as a heroic dose, is a pharmaceutical drug which is tried after all other drug options have failed to produce an adequate response in the patient. Drug resistance, such as antimicrobial resistance or antineoplastic resistance, may make the first-line drug ineffective, especially in case of multidrug-resistant pathogens and tumors. Such an alternative may be outside of extant regulatory requirements or medical best practices, in which case it may be viewed as salvage therapy.
Drug of last resort	Purposes	The use of a drug of last resort may be based on agreement among members of a patient's care network, including physicians and healthcare professionals across multiple specialties, or on a patient's desire to pursue a particular course of treatment and a practitioner's willingness to administer that course. Certain situations such as severe bacterial related sepsis or septic shock can more commonly lead to last resorts.
Drug of last resort	Purposes	Therapies considered to be drugs of last resort may at times be used earlier in the event that an agent would likely show the most immediate dose-response related efficacy in time-critical situations such as high mortality circumstances. Many of the drugs considered last resorts fall into one or more of the categories of antibiotics, antivirals, and chemotherapy agents. These agents often exhibit what are considered to be among the most efficient dose-response related effects, or are drugs for which few or no resistant strains are known.
Drug of last resort	Purposes	With regard to antibiotics, antivirals, and other agents indicated for treatment of infectious pathological disease, drugs of last resort are commonly withheld from administration until after the trial and failure of more commonly used treatment options to prevent the development of drug resistance. One of the most commonly known examples of both antimicrobial resistance and the relationship to the classification of a drug of last resort is the emergence of Staphylococcus aureus (MRSA) (sometimes also referred to as multiple-drug resistant S. aureus due to resistance to non-penicillin antibiotics that some strains of S. aureus have shown to exhibit). In cases presenting with suspected S. aureus, it is suggested by many public health institutions (including the World Health Organization (WHO) and the Centers for Disease Control and Prevention (CDC) in the United States) to treat first with empirical therapies for S. aureus, with an emphasis on evaluating the response to initial treatment and laboratory diagnostic techniques to isolate cases of drug resistance.
Drug of last resort	Purposes	Due to the possibility of potential severe or fatal consequences of resistant strains, initial treatment often includes concomitant administration of multiple antimicrobial agents that are not known to show cross-resistance, so as to reduce the possibility of a resistant strain remaining inadequately treated by a single agent during the evaluation of drug response. Once a specific resistance profile has been isolated via clinical laboratory findings, treatment is often modified as indicated.
Drug of last resort	Purposes	Vancomycin has long been considered a drug of last resort, due to its efficiency in treating multiple drug-resistant infectious agents and the requirement for intravenous administration. Recently, resistance to even vancomycin has been shown in some strains of S. aureus (sometimes referred to as vancomycin resistant S. aureus (VRSA) or vancomycin intermediate-resistance S. aureus (VISA)) often coinciding with methicillin/penicillin resistance, prompting the inclusion of newer antibiotics (such as linezolid) that have shown efficacy in highly drug-resistant strains. There are also strains of enterococci that have developed resistance to vancomycin referred to as vancomycin resistant enterococcus (VRE).
Drug of last resort	Purposes	Agents classified as fourth-line (or greater) treatments or experimental therapies could be considered by default to be drugs of last resort due to their low placement in the treatment hierarchy. Such placement may result from a multitude of considerations, including greater efficacy of other agents, socioeconomic considerations, availability issues, unpleasant side effects or similar issues relating to patient tolerance. Some experimental therapies might also be called drugs of last resort when administered following the failure of all other currently accepted treatments.
Drug of last resort	Purposes	Although most of the notable drugs of last resort are antibiotics or antivirals, other drugs are sometimes considered drugs of last resort, such as cisapride.
Drug of last resort	Examples	Antimicrobials Aminoglycosides — their use is extremely restricted due to risk of hearing loss and kidney damage; Amphotericin B — used for life-threatening fungal infections and primary amoebic meningoencephalitis; its side effects are often severe or potentially fatal; Carbapenems (such as imipenem/cilastatin) — used as a drug of last resort for a variety of different bacterial infections; Ceftobiprole and ceftaroline — fifth-generation cephalosporins active against methicillin-resistant Staphylococcus aureus (MRSA); use is limited to prevent development of drug resistance; Cefiderocol — a cephalosporin used to treat complicated urinary tract infections (cUTI) caused by multi-drug resistant Gram-negative bacteria in patients with limited or no alternative options; Chloramphenicol — formerly first-line therapy for Rocky Mountain spotted fever (until doxycycline became available). Also first-line therapy (used topically) for bacterial conjunctivitis, and systemically for meningitis when allergies to penicillin or cephalosporin exist. Unacceptably high risk of irreversible, fatal aplastic anemia and gray baby syndrome causes intravenous chloramphenicol to be a drug of last resort; Colistin — used against certain life-threatening infections, such as those caused by Pseudomonas; carries risk of kidney and nerve damage; Linezolid — use is limited due to high cost and risk of vision loss or myopathy (due to mitochondrial damage); Tigecycline — used to kill Acinetobacter and Legionella species; this drug is limited by high cost and risk of liver injury.

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