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91,100 | It is positive definite in the sense that, for any s {\displaystyle s} , the element {\displaystyle } is in the closed positive cone of M {\displaystyle M} , and ≠ 0 {\displaystyle \neq 0} if s ≠ 0 {\displaystyle s\neq 0} . This bilinear map is unique up to isomorphism. The Lie superalgebra g = g 0 ⊕ g 1 = M ⊕ S {\di... | Super Minkowski space | 0.78067 |
91,101 | This supergroup has the following Lie superalgebra. Suppose that M {\displaystyle M} is Minkowski space (of dimension d {\displaystyle d} ), and S {\displaystyle S} is a finite sum of irreducible real spinor representations for d {\displaystyle d} -dimensional Minkowski space. Then there is an invariant, symmetric bili... | Super Minkowski space | 0.78067 |
91,102 | The underlying supermanifold of super Minkowski space is isomorphic to a super vector space given by the direct sum of ordinary Minkowski spacetime in d dimensions (often taken to be 4) and a number N {\displaystyle {\mathcal {N}}} of real spinor representations of the Lorentz algebra. (When d ≡ 2 mod 4 {\displaystyle ... | Super Minkowski space | 0.78067 |
91,103 | We define the spin representation S {\displaystyle S} to be the representation constructed using the exterior algebra of some vector space, as described here. The complex dimension of S {\displaystyle S} is 2 m {\displaystyle 2^{m}} . If the signature is even, then this splits into two irreducible half-spin representat... | Super Minkowski space | 0.78067 |
91,104 | For this section, the dimension of the Minkowski space under consideration is d = 4 {\displaystyle d=4} . Super Minkowski space can be concretely realized as the direct sum of Minkowski space, which has coordinates x μ {\displaystyle x^{\mu }} , with 'spin space'. The dimension of 'spin space' depends on the number N {... | Super Minkowski space | 0.78067 |
91,105 | Abstractly, super Minkowski space is the space of (right) cosets within the Super Poincaré group of Lorentz group, that is, Super Minkowski space ≅ Super Poincaré group Lorentz group {\displaystyle {\text{Super Minkowski space}}\cong {\frac {\text{Super Poincaré group}}{\text{Lorentz group}}}} .This is analogous to the... | Super Minkowski space | 0.78067 |
91,106 | Using earlier notation, if there are N 1 {\displaystyle {\mathcal {N}}_{1}} copies of the one representation and N 2 {\displaystyle {\mathcal {N}}_{2}} of the other, then defining N = N 1 + N 2 {\displaystyle {\mathcal {N}}={\mathcal {N}}_{1}+{\mathcal {N}}_{2}} , the earlier expression holds. In physics the letter P i... | Super Minkowski space | 0.78067 |
91,107 | The notation can be extended to include the signature of the underlying spacetime, often this is R 1 , d − 1 | n {\displaystyle \mathbb {R} ^{1,d-1|n}} if m = d {\displaystyle m=d} . The relation is as follows: the integer d {\displaystyle d} in the physics notation is the integer m {\displaystyle m} in the mathematics... | Super Minkowski space | 0.78067 |
91,108 | In the physics literature, a super Minkowski spacetime is often specified by giving the dimension d {\displaystyle d} of the even, bosonic part (dimension of the spacetime), and the number of times N {\displaystyle {\mathcal {N}}} that each irreducible spinor representation occurs in the odd, fermionic part. This N {\d... | Super Minkowski space | 0.78067 |
91,109 | In mathematics and physics, super Minkowski space or Minkowski superspace is a supersymmetric extension of Minkowski space, sometimes used as the base manifold (or rather, supermanifold) for superfields. It is acted on by the super Poincaré algebra. | Super Minkowski space | 0.78067 |
91,110 | The CI abundance is more properly linked to the abundances in the solar photosphere. Small differences exist between the solar interior, photosphere, and corona/solar wind. Heavy elements may settle to the interiors of stars (for the Sun, this effect appears low); the corona and thus the solar wind are affected by plas... | CI chondrite | 0.780669 |
91,111 | Goldschmidt noted the primitive (pre-differentiated) compositions of some meteorites, calling it the "cosmic" abundance- he assumed meteorites had arrived from free space, not our Solar System. In turn, the study of such abundances stimulated- then validated- work in nucleosynthesis and stellar physics. In a sense, Gol... | CI chondrite | 0.780669 |
91,112 | In nutrition, biology, and chemistry, fat usually means any ester of fatty acids, or a mixture of such compounds, most commonly those that occur in living beings or in food.The term often refers specifically to triglycerides (triple esters of glycerol), that are the main components of vegetable oils and of fatty tissue... | Dietary fat | 0.780669 |
91,113 | The exact biochemical process by which trans fats produce specific health problems are a topic of continuing research. Intake of dietary trans fat perturbs the body's ability to metabolize essential fatty acids (EFAs, including omega-3) leading to changes in the phospholipid fatty acid composition of the arterial walls... | Dietary fat | 0.780669 |
91,114 | There are plenty of examples of stratifolds. The first example to consider is the open cone over a manifold M. We define a continuous function from S to the reals to be in C if and only if it is smooth on M × ( 0 , 1 ) {\displaystyle M\times (0,1)} and it is locally constant around the cone point. The last condition is... | Stratifold | 0.780668 |
91,115 | In differential topology, a branch of mathematics, a stratifold is a generalization of a differentiable manifold where certain kinds of singularities are allowed. More specifically a stratifold is stratified into differentiable manifolds of (possibly) different dimensions. Stratifolds can be used to construct new homol... | Stratifold | 0.780668 |
91,116 | {\displaystyle \}.} For an n-dimensional manifold M we have that M n = M {\displaystyle M_{n}=M} and all other strata are empty. We are now ready for the definition of a stratifold, where more than one stratum may be non-empty: A k-dimensional stratifold is a differential space ( S , C ) , {\displaystyle (S,C),} where ... | Stratifold | 0.780668 |
91,117 | Before we come to stratifolds, we define a preliminary notion, which captures the minimal notion for a smooth structure on a space: A differential space (in the sense of Sikorski) is a pair ( X , C ) , {\displaystyle (X,C),} where X is a topological space and C is a subalgebra of the continuous functions X → R {\displa... | Stratifold | 0.780668 |
91,118 | {\displaystyle f:S\to M.} Then make ƒ transversal to N. The intersection of S and N defines a new stratifold S' with a map to N, which represents a class in H k + dim ( N ) − dim ( M ) ( N ) . {\displaystyle H_{k+\dim(N)-\dim(M)}(N).} It is possible to repeat this construction in the context of an embedding of Hilb... | Stratifold | 0.780668 |
91,119 | One can develop enough differential topology of stratifolds to show that these define a homology theory. Clearly, S H k ( point ) = 0 {\displaystyle SH_{k}({\text{point}})=0} for k > 0 {\displaystyle k>0} since every oriented stratifold S is the boundary of its cone, which is oriented if dim ( S ) > 0. {\displaystyle... | Stratifold | 0.780668 |
91,120 | This is equivalent to the condition that Var ( β ~ ) − Var ( β ^ ) {\displaystyle \operatorname {Var} \left({\widetilde {\beta }}\right)-\operatorname {Var} \left({\widehat {\beta }}\right)} is a positive semi-definite matrix for every other linear unbiased estimator β ~ {\displaystyle {\widetilde {\beta }}} . The ... | Gauss–Markov theorem | 0.780668 |
91,121 | Suppose we have, in matrix notation, the linear relationship y = X β + ε , ( y , ε ∈ R n , β ∈ R K and X ∈ R n × K ) {\displaystyle y=X\beta +\varepsilon ,\quad (y,\varepsilon \in \mathbb {R} ^{n},\beta \in \mathbb {R} ^{K}{\text{ and }}X\in \mathbb {R} ^{n\times K})} expanding to, y i = ∑ j = 1 K β j X i j + ε i ∀ i =... | Gauss–Markov theorem | 0.780668 |
91,122 | One can show that S H 0 ( point ) ≅ Z . {\displaystyle SH_{0}({\text{point}})\cong \mathbb {Z} .} Hence, by the Eilenberg–Steenrod uniqueness theorem, S H k ( X ) ≅ H k ( X ) {\displaystyle SH_{k}(X)\cong H_{k}(X)} for every space X homotopy-equivalent to a CW-complex, where H denotes singular homology. | Stratifold | 0.780668 |
91,123 | In physics, lattice field theory is the study of lattice models of quantum field theory, that is, of field theory on a space or spacetime that has been discretised onto a lattice. | Lattice field theory | 0.780668 |
91,124 | It can be seen as a permisisonless distributed network of agents (miners, blockchain developers, clients and other service providers that rely on the main network) that provides a global and very secure token exchange service. Some argue that this service amounts to a store of value, others consider it as a currency. B... | Peer production | 0.780668 |
91,125 | The categorical center is particularly useful in the context of higher categories. This is illustrated by the following example: the center of the (abelian) category M o d R {\displaystyle \mathrm {Mod} _{R}} of R-modules, for a commutative ring R, is M o d R {\displaystyle \mathrm {Mod} _{R}} again. The center of a mo... | Center (category theory) | 0.780668 |
91,126 | A refined scheme for stellar classification was published in 1943 by William Wilson Morgan and Philip Childs Keenan. The existence of our galaxy, the Milky Way, as a separate group of stars was only proven in the 20th century, along with the existence of "external" galaxies, and soon after, the expansion of the univers... | History of astronomy | 0.780667 |
91,127 | The spectra of stars were further understood through advances in quantum physics. This allowed the chemical composition of the stellar atmosphere to be determined. As evolutionary models of stars were developed during the 1930s, Bengt Strömgren introduced the term Hertzsprung–Russell diagram to denote a luminosity-spec... | History of astronomy | 0.780667 |
91,128 | Mars is also mentioned in preserved astronomical codices and early mythology.Although the Maya calendar was not tied to the Sun, John Teeple has proposed that the Maya calculated the solar year to somewhat greater accuracy than the Gregorian calendar. Both astronomy and an intricate numerological scheme for the measure... | History of astronomy | 0.780667 |
91,129 | The Sun was found to be part of a galaxy made up of more than 1010 stars (10 billion stars). The existence of other galaxies, one of the matters of the great debate, was settled by Edwin Hubble, who identified the Andromeda nebula as a different galaxy, and many others at large distances and receding, moving away from ... | History of astronomy | 0.780666 |
91,130 | With the accumulation of large sets of astronomical data, teams like the Harvard Computers rose in prominence which lead to many female astronomers, previously relegated as assistants to male astronomers, gaining recognition in the field. The United States Naval Observatory (USNO) and other astronomy research instituti... | History of astronomy | 0.780666 |
91,131 | Astronomy played a considerable part in religious matters for fixing the dates of festivals and determining the hours of the night. The titles of several temple books are preserved recording the movements and phases of the Sun, Moon and stars. The rising of Sirius (Egyptian: Sopdet, Greek: Sothis) at the beginning of t... | History of astronomy | 0.780666 |
91,132 | In the 3rd century BC, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous phenomena for each planet. About the same time, or shortly afterwards, astronomers created mathematical models that allowed ... | History of astronomy | 0.780666 |
91,133 | The systematic records of ominous phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year cycle of lunar eclipses, for example. The Greek astronomer Ptolemy later used Nabonassar's reign to fix the beginning of an era, since he felt that the earliest usable ... | History of astronomy | 0.780666 |
91,134 | The origins of Western astronomy can be found in Mesopotamia, the "land between the rivers" Tigris and Euphrates, where the ancient kingdoms of Sumer, Assyria, and Babylonia were located. A form of writing known as cuneiform emerged among the Sumerians around 3500–3000 BC. Our knowledge of Sumerian astronomy is indirec... | History of astronomy | 0.780666 |
91,135 | Early cultures identified celestial objects with gods and spirits. They related these objects (and their movements) to phenomena such as rain, drought, seasons, and tides. It is generally believed that the first astronomers were priests, and that they understood celestial objects and events to be manifestations of the ... | History of astronomy | 0.780666 |
91,136 | In an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F = ma. (It is assumed here that the mass m is constant) When one body exerts a force on a second body, the second body simultaneously exerts a force equal in... | History of astronomy | 0.780666 |
91,137 | While he was able to avoid punishment for a little while he was eventually tried and pled guilty to heresy in 1633. Although this came at some expense, his book was banned, and he was put under house arrest until he died in 1642. Sir Isaac Newton developed further ties between physics and astronomy through his law of u... | History of astronomy | 0.780666 |
91,138 | During the renaissance period, astronomy began to undergo a revolution in thought known as the Copernican Revolution, which gets the name from the astronomer Nicolaus Copernicus, who proposed a heliocentric system, in which the planets revolved around the Sun and not the Earth. His De revolutionibus orbium coelestium w... | History of astronomy | 0.780666 |
91,139 | Depending on the historian's viewpoint, the acme or corruption of Classical physical astronomy is seen with Ptolemy, a Greco-Roman astronomer from Alexandria of Egypt, who wrote the classic comprehensive presentation of geocentric astronomy, the Megale Syntaxis (Great Synthesis), better known by its Arabic title Almage... | History of astronomy | 0.780666 |
91,140 | DIO: The International Journal of Scientific History Journal for the History of Astronomy Journal of Astronomical History and Heritage | History of astronomy | 0.780666 |
91,141 | This idea, together with a belief in intelligent extraterrestrial life, was among the charges brought against him by the Inquisition. The idea became mainstream in the later 17th century, especially following the publication of Conversations on the Plurality of Worlds by Bernard Le Bovier de Fontenelle (1686), and by t... | History of astronomy | 0.780666 |
91,142 | Astronomy is the oldest of the natural sciences, dating back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy... | History of astronomy | 0.780666 |
91,143 | The Buddhist University of Nalanda at the time offered formal courses in astronomical studies. Other important astronomers from India include Madhava of Sangamagrama, Nilakantha Somayaji and Jyeshtadeva, who were members of the Kerala school of astronomy and mathematics from the 14th century to the 16th century. Nilaka... | History of astronomy | 0.780666 |
91,144 | The Shunga period is known as the "Golden age of astronomy in India". It saw the development of calculations for the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses. Indian astronomers by the 6th century believed that comets were celestial bodies that re-ap... | History of astronomy | 0.780666 |
91,145 | He accurately calculated many astronomical constants, such as the periods of the planets, times of the solar and lunar eclipses, and the instantaneous motion of the Moon. Early followers of Aryabhata's model included Varāhamihira, Brahmagupta, and Bhāskara II. Astronomy was advanced during the Shunga Empire and many st... | History of astronomy | 0.780666 |
91,146 | According to the Vedanga Jyotisha, in a yuga or "era", there are 5 solar years, 67 lunar sidereal cycles, 1,830 days, 1,835 sidereal days and 62 synodic months. During the 6th century, astronomy was influenced by the Greek and Byzantine astronomical traditions.Aryabhata (476–550), in his magnum opus Aryabhatiya (499), ... | History of astronomy | 0.780666 |
91,147 | Astronomy in the Indian subcontinent dates back to the period of Indus Valley Civilisation during 3rd millennium BCE, when it was used to create calendars. As the Indus Valley civilization did not leave behind written documents, the oldest extant Indian astronomical text is the Vedanga Jyotisha, dating from the Vedic p... | History of astronomy | 0.780666 |
91,148 | The arrival of these new texts coincided with the rise of the universities in medieval Europe, in which they soon found a home. Reflecting the introduction of astronomy into the universities, John of Sacrobosco wrote a series of influential introductory astronomy textbooks: the Sphere, a Computus, a text on the Quadran... | History of astronomy | 0.780666 |
91,149 | The most influential writers to pass on this ancient tradition in Latin were Macrobius, Pliny, Martianus Capella, and Calcidius. In the 6th century Bishop Gregory of Tours noted that he had learned his astronomy from reading Martianus Capella, and went on to employ this rudimentary astronomy to describe a method by whi... | History of astronomy | 0.780666 |
91,150 | After the significant contributions of Greek scholars to the development of astronomy, it entered a relatively static era in Western Europe from the Roman era through the 12th century. This lack of progress has led some astronomers to assert that nothing happened in Western European astronomy during the Middle Ages. Re... | History of astronomy | 0.780666 |
91,151 | Much of early Chinese astronomy was for the purpose of timekeeping. The Chinese used a lunisolar calendar, but because the cycles of the Sun and the Moon are different, astronomers often prepared new calendars and made observations for that purpose. Astrological divination was also an important part of astronomy. | History of astronomy | 0.780666 |
91,152 | Astronomy in China has a long history. Detailed records of astronomical observations were kept from about the 6th century BC, until the introduction of Western astronomy and the telescope in the 17th century. Chinese astronomers were able to precisely predict eclipses. | History of astronomy | 0.780666 |
91,153 | The astronomy of East Asia began in China. Solar term was completed in Warring States period. The knowledge of Chinese astronomy was introduced into East Asia. | History of astronomy | 0.780666 |
91,154 | He noted that measurements by earlier (Indian, then Greek) astronomers had found higher values for this angle, possible evidence that the axial tilt is not constant but was in fact decreasing. In 11th-century Persia, Omar Khayyám compiled many tables and performed a reformation of the calendar that was more accurate th... | History of astronomy | 0.780666 |
91,155 | The Arabic and the Persian world under Islam had become highly cultured, and many important works of knowledge from Greek astronomy and Indian astronomy and Persian astronomy were translated into Arabic, used and stored in libraries throughout the area. An important contribution by Islamic astronomers was their emphasi... | History of astronomy | 0.780666 |
91,156 | Eratosthenes estimated the circumference of the Earth with great accuracy (see also: history of geodesy).Greek geometrical astronomy developed away from the model of concentric spheres to employ more complex models in which an eccentric circle would carry around a smaller circle, called an epicycle which in turn carrie... | History of astronomy | 0.780666 |
91,157 | The Ancient Greeks developed astronomy, which they treated as a branch of mathematics, to a highly sophisticated level. The first geometrical, three-dimensional models to explain the apparent motion of the planets were developed in the 4th century BC by Eudoxus of Cnidus and Callippus of Cyzicus. Their models were base... | History of astronomy | 0.780666 |
91,158 | Since 1990 our understanding of prehistoric Europeans has been radically changed by discoveries of ancient astronomical artifacts throughout Europe. The artifacts demonstrate that Neolithic and Bronze Age Europeans had a sophisticated knowledge of mathematics and astronomy. Among the discoveries are: Paleolithic archae... | History of astronomy | 0.780666 |
91,159 | This had a major impact on astronomy, spawning the fields of infrared astronomy, radio astronomy, x-ray astronomy and finally gamma-ray astronomy. With the advent of spectroscopy it was proven that other stars were similar to the Sun, but with a range of temperatures, masses and sizes. | History of astronomy | 0.780666 |
91,160 | Sir William Herschel found the first new planet, Uranus, to be observed in modern times in 1781. The gap between the planets Mars and Jupiter disclosed by the Titius–Bode law was filled by the discovery of the asteroids Ceres and Pallas in 1801 and 1802 with many more following. At first, astronomical thought in Americ... | History of astronomy | 0.780666 |
91,161 | Even if L i e q F {\displaystyle \mathrm {Lie} _{q}\,{\mathcal {F}}} is different from T q M {\displaystyle \ T_{q}M} , the attainable set from q {\displaystyle \ q} has nonempty interior in the orbit topology, as it follows from Krener's theorem applied to the control system restricted to the orbit through q {\display... | Krener's theorem | 0.780666 |
91,162 | Let q ˙ = f ( q , u ) {\displaystyle {\ }{\dot {q}}=f(q,u)} be a smooth control system, where q {\displaystyle {\ q}} belongs to a finite-dimensional manifold M {\displaystyle \ M} and u {\displaystyle \ u} belongs to a control set U {\displaystyle \ U} . Consider the family of vector fields F = { f ( ⋅ , u ) ∣ u ∈ U }... | Krener's theorem | 0.780666 |
91,163 | In mathematics, Krener's theorem is a result attributed to Arthur J. Krener in geometric control theory about the topological properties of attainable sets of finite-dimensional control systems. It states that any attainable set of a bracket-generating system has nonempty interior or, equivalently, that any attainable ... | Krener's theorem | 0.780666 |
91,164 | In finite dimensions, if the phase space is symplectic (i.e., the center of the Poisson algebra consists only of constants), it must have even dimension 2 n , {\displaystyle 2n,} and the maximal number of independent Poisson commuting invariants (including the Hamiltonian itself) is n {\displaystyle n} . The leaves of ... | Integrable Systems | 0.780666 |
91,165 | In the special setting of Hamiltonian systems, we have the notion of integrability in the Liouville sense. (See the Liouville–Arnold theorem.) Liouville integrability means that there exists a regular foliation of the phase space by invariant manifolds such that the Hamiltonian vector fields associated with the invaria... | Integrable Systems | 0.780666 |
91,166 | Yelena Bonner (1940) – human rights activist (widow of Andrei Sakharov) Leonid Kharitonov – actor Alisa Freindlich (c. 1942 – 1953) – major Russian movie and theater actress Yuri Matiyasevich (1962–1963) – mathematician who solved Hilbert's tenth problem Andrei Tolubeyev (?–1963) – theatrical and cinema actor, People's... | Saint Petersburg Lyceum 239 | 0.780665 |
91,167 | In 1990, the Russian Ministry of Education granted school the status of physico-mathematical lyceum and experimental laboratory for standard of education in physics, mathematics and informatics in Saint Petersburg. In 1994, the school won the George Soros grant. The US Mathematical society voted the school as one of to... | Saint Petersburg Lyceum 239 | 0.780665 |
91,168 | The school was founded in 1918. Originally, it was located in the Lobanov-Rostovsky Palace, also known as "house with lions" at the corner of Saint Isaac's Square and Admiralteysky Prospect. It was one of only handful of schools to remain open during Siege of Leningrad. In 1961 the school was granted status of city's s... | Saint Petersburg Lyceum 239 | 0.780665 |
91,169 | Presidential Physics and Mathematics Lyceum No. 239 (Russian: Президентский физико-математический лицей №239), is a public high school in Saint Petersburg, Russia that specializes in mathematics and physics. The school opened in 1918 and it became a specialized city school in 1961. The school is noted for its strong ac... | Saint Petersburg Lyceum 239 | 0.780665 |
91,170 | In the following examples, the set X is the real interval , and Σ {\displaystyle \Sigma } is the Borel sigma-algebra on X. μ {\displaystyle \mu } is the length measure on X. ν {\displaystyle \nu } assigns to each subset Y of X, twice the length of Y. Then, d ν d μ = 2 {\textstyle {\frac {d\nu }{d\mu }}=2} . μ {\display... | Radon−Nikodym derivative | 0.780663 |
91,171 | Early experimenters in X-ray and gamma-ray astronomy found that their detectors, flown on balloons or sounding rockets, were corrupted by the large fluxes of high-energy photon and cosmic-ray charged-particle events. Gamma-rays, in particular, could be collimated by surrounding the detectors with heavy shielding materi... | Compton suppression | 0.780663 |
91,172 | Modern experiments in nuclear and high-energy particle physics almost invariably use fast anticoincidence circuits to veto unwanted events. The desired events are typically accompanied by unwanted background processes that must be suppressed by enormous factors, ranging from thousands to many billions, to permit the de... | Compton suppression | 0.780663 |
91,173 | The abiF RNA motif is a conserved RNA structure that was discovered by bioinformatics. == References == | AbiF RNA motif | 0.780663 |
91,174 | Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen. | Spectral series | 0.780662 |
91,175 | In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold. It was introduced by Émile Picard for complex surfaces in his book Picard & Simart (1897), and extended to higher dimensions by Solomon Lefschetz (1924). It is ... | Picard–Lefschetz theory | 0.780662 |
91,176 | The All Sky Automated Survey (ASAS) is a Polish project implemented on 7 April 1997 to do photometric monitoring of approximately 20 million stars brighter than 14 magnitude all over the sky. The automatic telescopes discovered two new comets in 2004 and 2006. The ASAS-South, located in Chile and ASAS-North, located in... | All Sky Automated Survey | 0.780662 |
91,177 | In molecular biology, Small nucleolar RNA SNORA50 (also known as ACA50) is a non-coding RNA (ncRNA) molecule which functions in the biogenesis (modification) of other small nuclear RNAs (snRNAs). This type of modifying RNA is located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogenesis. It ... | Small nucleolar RNA SNORA50 | 0.780661 |
91,178 | The N-ray affair occurred shortly after a series of major breakthroughs in experimental physics. Victor Schumann discovered vacuum ultraviolet radiation in 1893, Wilhelm Röntgen discovered X-rays in 1895, Henri Becquerel discovered radioactivity in 1896, and, in 1897, J. J. Thomson discovered electrons, showing that th... | N ray | 0.780661 |
91,179 | The columns occupy the edges and the centre of the cell's projection on the bc plane. The potassium atoms are located between these columns; each K+ cation is surrounded by nine chlorine atoms. The mineral is optically biaxial (negative), with α = 1.653, β = 1.780, γ = 1.900', 2V= 85°. The mineral is named from the Lat... | Potassium trichloridocuprate | 0.780658 |
91,180 | The barrel cortex is a region of the somatosensory cortex that is identifiable in some species of rodents and species of at least two other orders and contains the barrel field. The 'barrels' of the barrel field are regions within cortical layer IV that are visibly darker when stained to reveal the presence of cytochro... | Barrel cortex | 0.780656 |
91,181 | Social informatics is also about teaching social issues of computing to computer science students. Depending on educational traditions, social informatics is scattered in the curriculum of different disciplines, as well as in computer science, information science, informatics (Europe) and web sociology. In some instanc... | Social informatics | 0.780653 |
91,182 | Although simple alkyllithium species are often represented as monomer RLi, they exist as aggregates (oligomers) or polymers. The degree of aggregation depends on the organic substituent and the presence of other ligands. These structures have been elucidated by a variety of methods, notably 6Li, 7Li, and 13C NMR spectr... | Organolithium reagent | 0.780651 |
91,183 | In organometallic chemistry, organolithium reagents are chemical compounds that contain carbon–lithium (C–Li) bonds. These reagents are important in organic synthesis, and are frequently used to transfer the organic group or the lithium atom to the substrates in synthetic steps, through nucleophilic addition or simple ... | Organolithium reagent | 0.780651 |
91,184 | Modern version of law of universal causation is connected with Newtonian physics, but is also criticized for instance by David Hume who presents skeptical reductionist view on causality. Since then his view on the concept of causality is often predominating (see Causality, After the Middle Ages). Kant answered to Hume ... | Universal causation | 0.78065 |
91,185 | Equivalently again, both sheets of the focal surface degenerate to conics. It follows that any Dupin cyclide is a channel surface (i.e., the envelope of a one-parameter family of spheres) in two different ways, and this gives another characterization. The definition in terms of spheres shows that the class of Dupin cyc... | Dupin cyclide | 0.78065 |
91,186 | 1802 by (and named after) Charles Dupin, while he was still a student at the École polytechnique following Gaspard Monge's lectures. The key property of a Dupin cyclide is that it is a channel surface (envelope of a one-parameter family of spheres) in two different ways. This property means that Dupin cyclides are natu... | Dupin cyclide | 0.78065 |
91,187 | Neglecting the carbon utilised for biomass formation (known to be a small fraction of the total carbon utilised) basic biochemistry balances can be performed based on the established metabolic pathways of these organisms. Using glucose as substrate the natural producing succinic acid producers are first considered. The... | Succinic acid fermentation | 0.780645 |
91,188 | The boustrophedon cell decomposition (BCD) is a method used in artificial intelligence and robotics for configuration space solutions. Like other cellular decomposition methods, this method transforms the configuration space into cell regions that can be used for path planning. A strength of the boustrophedon cell deco... | Boustrophedon cell decomposition | 0.780642 |
91,189 | An active area of organometallic chemistry encompasses the scission of C-F bonds by transition metal-based reagents. Both stoichiometric and catalytic reactions have been developed and are of interest from the perspectives of organic synthesis and remediation of xenochemicals. C-F bond activation has been classified as... | Organofluorine chemistry | 0.78064 |
91,190 | The development of organofluorine chemistry has contributed many reagents of value beyond organofluorine chemistry. Triflic acid (CF3SO3H) and trifluoroacetic acid (CF3CO2H) are useful throughout organic synthesis. Their strong acidity is attributed to the electronegativity of the trifluoromethyl group that stabilizes ... | Organofluorine chemistry | 0.78064 |
91,191 | In all of these cases, however, the mothers and children were not similarly affected, suggesting a variable clinical expression of the syndrome.In a study published by the American Journal of Human Genetics in 2012, exome sequencing was used to investigate a group of unrelated individuals with classic features of FHS a... | Floating–Harbor syndrome | 0.780638 |
91,192 | This algorithm is implemented by RivEX, an ESRI ArcGIS 10.7 tool. The input to their algorithm is a network of the centre lines of the bodies of water, represented as arcs (or edges) joined at nodes. Lake boundaries and river banks should not be used as arcs, as these will generally form a non-tree network with an inco... | Strahler number | 0.780637 |
91,193 | In molecular biology, MobiDB is a curated biological database designed to offer a centralized resource for annotations of intrinsic protein disorder. Protein disorder is a structural feature characterizing a large number of proteins with prominent members known as intrinsically unstructured (or disordered) proteins. Th... | MobiDB | 0.780635 |
91,194 | Tensor product of fields This is an operation on fields, that does not always produce a field.Tensor product of R-algebrasClifford module A representation of a Clifford algebra which gives a realisation of a Clifford algebra as a matrix algebra.Tor functors These are the derived functors of the tensor product, and feat... | Tensor notation | 0.780635 |
91,195 | An analogue to the Cauchy–Schwarz inequality holds for an inner-product A {\displaystyle A} -module E {\displaystyle E}: ⟨ x , y ⟩ A ⟨ y , x ⟩ A ≤ ‖ ⟨ y , y ⟩ A ‖ ⟨ x , x ⟩ A {\displaystyle \langle x,y\rangle _{A}\langle y,x\rangle _{A}\leq \Vert \langle y,y\rangle _{A}\Vert \langle x,x\rangle _{A}} for x {\displaystyl... | Hilbert C*-module | 0.780634 |
91,196 | Since the complex numbers C {\displaystyle \mathbb {C} } are a C*-algebra with an involution given by complex conjugation, a complex Hilbert space H {\displaystyle {\mathcal {H}}} is a Hilbert C {\displaystyle \mathbb {C} } -module under scalar multipliation by complex numbers and its inner product. | Hilbert C*-module | 0.780634 |
91,197 | One may also consider the following subspace of elements in the countable direct product of A {\displaystyle A} ℓ 2 ( A ) = H A = { ( a i ) | ∑ i = 1 ∞ a i ∗ a i converges in A } . {\displaystyle \ell _{2}(A)={\mathcal {H}}_{A}={\Big \{}(a_{i})|\sum _{i=1}^{\infty }a_{i}^{*}a_{i}{\text{ converges in }}A{\Big \}}.} Endo... | Hilbert C*-module | 0.780634 |
91,198 | Hilbert C*-modules are mathematical objects that generalise the notion of Hilbert spaces (which are themselves generalisations of Euclidean space), in that they endow a linear space with an "inner product" that takes values in a C*-algebra. Hilbert C*-modules were first introduced in the work of Irving Kaplansky in 195... | Hilbert C*-module | 0.780634 |
91,199 | Any C*-algebra A {\displaystyle A} is a Hilbert A {\displaystyle A} -module with the action given by right multiplication in A {\displaystyle A} and the inner product ⟨ a , b ⟩ = a ∗ b {\displaystyle \langle a,b\rangle =a^{*}b} . By the C*-identity, the Hilbert module norm coincides with C*-norm on A {\displaystyle A} ... | Hilbert C*-module | 0.780634 |
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