id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
83,900 | In geometry, the Reye configuration, introduced by Theodor Reye (1882), is a configuration of 12 points and 16 lines. Each point of the configuration belongs to four lines, and each line contains three points. Therefore, in the notation of configurations, the Reye configuration is written as 124163. | Reye configuration | 0.783578 |
83,901 | Aravind (2000) pointed out that the Reye configuration underlies some of the proofs of the Bell–Kochen–Specker theorem about the non-existence of hidden variables in quantum mechanics. | Reye configuration | 0.783578 |
83,902 | An 83122 configuration of eight points in the real projective plane and 12 lines connecting them, with the connection pattern of a cube, can be extended to form the Reye configuration if and only if the eight points are a perspective projection of a parallelepiped (Servatius & Servatius 2010) The 24 permutations of the... | Reye configuration | 0.783578 |
83,903 | Catalytic resonance theory is constructed on the Sabatier principle of catalysis developed by French chemistry Paul Sabatier. In the limit of maximum catalytic performance, the surface of a catalyst is neither too strong nor too weak. Strong binding results in an overall catalytic reaction rate limitation due to produc... | Catalytic resonance theory | 0.783578 |
83,904 | For any integer n > 0 {\displaystyle n>0} , we have 4 n 2 n ≤ ( 2 n n ) . {\displaystyle {\frac {4^{n}}{2n}}\leq {\binom {2n}{n}}.} Proof: Applying the binomial theorem, 4 n = ( 1 + 1 ) 2 n = ∑ k = 0 2 n ( 2 n k ) = 2 + ∑ k = 1 2 n − 1 ( 2 n k ) ≤ 2 n ( 2 n n ) , {\displaystyle 4^{n}=(1+1)^{2n}=\sum _{k=0}^{2n}{\binom ... | Proof of Bertrand's postulate | 0.783578 |
83,905 | In mathematics, Bertrand's postulate (actually now a theorem) states that for each n ≥ 2 {\displaystyle n\geq 2} there is a prime p {\displaystyle p} such that n < p < 2 n {\displaystyle n | Proof of Bertrand's postulate | 0.783578 |
83,906 | The full quantum-mechanical treatment of bremsstrahlung is very involved. The "vacuum case" of the interaction of one electron, one ion, and one photon, using the pure Coulomb potential, has an exact solution that was probably first published by A. Sommerfeld in 1931. This analytical solution involves complicated mathe... | Bremsstrahlung | 0.783577 |
83,907 | In particle physics, bremsstrahlung (German pronunciation: ; from German bremsen 'to brake', and Strahlung 'radiation') is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinet... | Bremsstrahlung | 0.783577 |
83,908 | If C is a cone in a TVS X then C is normal if U = C {\displaystyle {\mathcal {U}}=\left_{C}} , where U {\displaystyle {\mathcal {U}}} is the neighborhood filter at the origin, C = { : U ∈ U } {\displaystyle \left_{C}=\left\{\left:U\in {\mathcal {U}}\right\}} , and C := ( U + C ) ∩ ( U − C ) {\displaystyle _{C}:=\lef... | Ordered topological vector space | 0.783576 |
83,909 | Let X be an ordered vector space over the reals that is finite-dimensional. Then the order of X is Archimedean if and only if the positive cone of X is closed for the unique topology under which X is a Hausdorff TVS. Let X be an ordered vector space over the reals with positive cone C. Then the following are equivalent... | Ordered topological vector space | 0.783576 |
83,910 | The Workshop on Software Engineering for Adaptive and Self-Managing Systems (SEAMS) is an academic conference for exchanging research results and experiences in the areas of autonomic computing, self-managing, self-healing, self-optimizing, self-configuring, and self-adaptive systems theory. It was established in 2006 ... | Software Engineering for Adaptive and Self-Managing Systems | 0.783573 |
83,911 | In probability theory and statistics, the poly-Weibull distribution is a continuous probability distribution. The distribution is defined to be that of a random variable defined to be the smallest of a number of statistically independent random variables having non-identical Weibull distributions. | Poly-Weibull distribution | 0.783573 |
83,912 | Both clusters include proteins from Gram-negative and Gram-positive bacteria. The sulfate permease, CysP (TC# 2.A.20.4.1), is distantly related to the phosphate permeases. Members of the PiT family arose by a tandem internal gene duplication event. Surprisingly, TopPred predicts a 12 TMS topology for the yeast Pho89 pr... | Inorganic phosphate transporter family | 0.783571 |
83,913 | Metal carbonyls are coordination complexes of transition metals with carbon monoxide ligands. Metal carbonyls are useful in organic synthesis and as catalysts or catalyst precursors in homogeneous catalysis, such as hydroformylation and Reppe chemistry. In the Mond process, nickel tetracarbonyl is used to produce pure ... | Metal carbonyl complex | 0.783571 |
83,914 | A pervasive space is characterised by the physical and informational interaction between the occupants and the built environment e.g. the act of controlling the building is a physical interaction, while the space responding to this action/user instruction is an informational interaction. Intelligent pervasive spaces ar... | Pervasive informatics | 0.78357 |
83,915 | Mumford proved that if g > 1, there exists a coarse moduli scheme of smooth curves of genus g, which is quasi-projective. According to a recent survey by János Kollár, it "has a rich and intriguing intrinsic geometry which is related to major questions in many branches of mathematics and theoretical physics." Braungard... | Fine moduli scheme | 0.783569 |
83,916 | In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extension of the 'geometric object' concept (algebrai... | Fine moduli scheme | 0.783569 |
83,917 | Phasor notation (also known as angle notation) is a mathematical notation used in electronics engineering and electrical engineering. 1 ∠ θ {\displaystyle 1\angle \theta } can represent either the vector ( cos θ , sin θ ) {\displaystyle (\cos \theta ,\,\sin \theta )} or the complex number cos θ + i sin θ = e i ... | Complex amplitudes | 0.783568 |
83,918 | The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann surface theory, in connection with surfaces with maximal symmetry, namely the Hurwitz surfaces. The Hurwitz quaternion order was studied in 1967 by Goro Shimura, but fi... | Hurwitz quaternion order | 0.783568 |
83,919 | Let K {\displaystyle K} be the maximal real subfield of Q {\displaystyle \mathbb {Q} } ( ρ ) {\displaystyle (\rho )} where ρ {\displaystyle \rho } is a 7th-primitive root of unity. The ring of integers of K {\displaystyle K} is Z {\displaystyle \mathbb {Z} } , where the element η = ρ + ρ ¯ {\displaystyle \eta =\rho +{... | Hurwitz quaternion order | 0.783568 |
83,920 | We can also define the complex power S = P + jQ and the apparent power which is the magnitude of S. The power law for an AC circuit expressed in phasors is then S = VI* (where I* is the complex conjugate of I, and the magnitudes of the voltage and current phasors V and of I are the RMS values of the voltage and current... | Complex amplitudes | 0.783568 |
83,921 | In analysis of three phase AC power systems, usually a set of phasors is defined as the three complex cube roots of unity, graphically represented as unit magnitudes at angles of 0, 120 and 240 degrees. By treating polyphase AC circuit quantities as phasors, balanced circuits can be simplified and unbalanced circuits c... | Complex amplitudes | 0.783568 |
83,922 | In 1958, two Swiss alpinists, Juesi and Marti teamed together, creating the first commercially available rope ascender known as the Jumar. In 1968 Bruno Dressler asked Petzl, who worked as a metals machinist, to build a rope-ascending tool, today known as the Petzl Croll, that he had developed by adapting the Jumar for... | Single rope technique | 0.783567 |
83,923 | Between samples no measurement of the signal is made; the sampling theorem guarantees non-ambiguous representation and recovery of the signal only if it has no energy at frequency fs/2 or higher (one half the sampling frequency, known as the Nyquist frequency); higher frequencies will not be correctly represented or re... | Linear pulse-code modulation | 0.783567 |
83,924 | The Nyquist–Shannon sampling theorem shows PCM devices can operate without introducing distortions within their designed frequency bands if they provide a sampling frequency at least twice that of the highest frequency contained in the input signal. For example, in telephony, the usable voice frequency band ranges from... | Linear pulse-code modulation | 0.783567 |
83,925 | According to Shoshichi Kobayashi (1975), the geometry of complex Finsler structures was first studied in the paper (Rizza 1964): however, Rizza announced his results nearly two years before, in the short communications (Rizza 1962a) and (Rizza 1962b), proving them in the article (Rizza 1963), nearly one year earlier th... | Rizza manifold | 0.783566 |
83,926 | In differential geometry a Rizza manifold, named after Giovanni Battista Rizza, is an almost complex manifold also supporting a Finsler structure: this kind of manifold is also referred as almost Hermitian Finsler manifold. | Rizza manifold | 0.783566 |
83,927 | XALOC aims to provide the present and future Structural Biology groups with a flexible and reliable tool to help in finding solutions for structures of macromolecules and complexes. The beamline allows a broad variety of crystal sizes and unit cell parameters, with both wavelength-dependent and -independent experiments... | ALBA (synchrotron) | 0.783563 |
83,928 | The Materials science and powder diffraction beamline is for high-resolution powder diffraction and high pressure powder diffraction using diamond anvil cells. The beamline works between 8 and 50 keV. This energy range adequately covers the desirable range for almost any powder diffraction experiment, and at the same t... | ALBA (synchrotron) | 0.783563 |
83,929 | Small-angle X-ray scattering (SAXS) experiments provide structural and dynamic information of large molecular assemblies like polymers, colloids, proteins and fibres. A wide range of fields (medicine, biology, chemistry, physics, archaeological, environmental and conservation sciences and materials) can be covered by t... | ALBA (synchrotron) | 0.783563 |
83,930 | Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., and Brian L. Joiner in conjunction with Triola Statistics Company in 1972. It began as a light version of OMNITAB, a statistical analysis program by National Institute of Standards and Tec... | Minitab | 0.783562 |
83,931 | Minitab is a statistics package developed at the Pennsylvania State University by researchers Barbara F. Ryan, Thomas A. Ryan, Jr., Brian L. Joiner in 1972. The project received funding from the Triola Statistics Company. It began as a light version of OMNITAB, a statistical analysis program by NIST, which was conceive... | Minitab | 0.783562 |
83,932 | Organomagnesium compounds are widespread in organic chemistry. They are commonly found as Grignard reagents. Magnesium can react with haloalkanes to give Grignard reagents. Examples of Grignard reagents are phenylmagnesium bromide and ethylmagnesium bromide. | Magnesium ribbon | 0.78356 |
83,933 | The isotope 28Mg is radioactive and in the 1950s to 1970s was produced by several nuclear power plants for use in scientific experiments. This isotope has a relatively short half-life (21 hours) and its use was limited by shipping times. The nuclide 26Mg has found application in isotopic geology, similar to that of alu... | Magnesium ribbon | 0.78356 |
83,934 | Magnesium forms a variety of compounds important to industry and biology, including magnesium carbonate, magnesium chloride, magnesium citrate, magnesium hydroxide (milk of magnesia), magnesium oxide, magnesium sulfate, and magnesium sulfate heptahydrate (Epsom salts). | Magnesium ribbon | 0.78356 |
83,935 | The important interaction between phosphate and magnesium ions makes magnesium essential to the basic nucleic acid chemistry of all cells of all known living organisms. More than 300 enzymes require magnesium ions for their catalytic action, including all enzymes using or synthesizing ATP and those that use other nucle... | Magnesium ribbon | 0.78356 |
83,936 | The related butadiene-magnesium adduct serves as a source for the butadiene dianion. Magnesium in organic chemistry also appears as low valent magnesium compounds, primarily with the magnesium forming diatomic ions in the +1 oxidation state but more recently also with zero oxidation state or a mixture of +1 and zero st... | Magnesium ribbon | 0.78356 |
83,937 | Thus we may be faced with the possibility that the origin of life (like the origin of the universe) becomes an impenetrable barrier to science, and a residue to all attempts to reduce biology to chemistry and physics. He explained that the difficulty of testing had led some people to describe natural selection as a tau... | Karl Popper | 0.78356 |
83,938 | For Popper, it is in the interplay between the tentative theories (conjectures) and error elimination (refutation) that scientific knowledge advances toward greater and greater problems; in a process very much akin to the interplay between genetic variation and natural selection. Popper also wrote extensively against t... | Karl Popper | 0.78356 |
83,939 | They also represented extensive critiques of the philosophical presuppositions underpinning all forms of totalitarianism.Popper believed that there was a contrast between the theories of Sigmund Freud and Alfred Adler, which he considered non-scientific, and Albert Einstein's theory of relativity which set off the revo... | Karl Popper | 0.78356 |
83,940 | He found that Bohr's interpretation introduced subjectivity into physics, claiming later in his life that: Bohr was "a marvelous physicist, one of the greatest of all time, but he was a miserable philosopher, and one couldn't talk to him. He was talking all the time, allowing practically only one or two words to you an... | Karl Popper | 0.78356 |
83,941 | Popper commented that this "was perhaps a cowardly but in a way a right decision".In 1928, Popper earned a doctorate in psychology, under the supervision of Karl Bühler—with Moritz Schlick being the second chair of the thesis committee. His dissertation was titled Zur Methodenfrage der Denkpsychologie (On Questions of ... | Karl Popper | 0.78356 |
83,942 | His father was a bibliophile who had 12,000–14,000 volumes in his personal library and took an interest in philosophy, the classics, and social and political issues. Popper inherited both the library and the disposition from him. Later, he would describe the atmosphere of his upbringing as having been "decidedly bookis... | Karl Popper | 0.78356 |
83,943 | CSIRO had a pioneering role in the scientific discovery of the universe through radio "eyes". A team led by Paul Wild built and operated (from 1948) the world's first solar radiospectrograph, and from 1967 the 3-kilometre-diameter (1.9 mi) radioheliograph at Culgoora in New South Wales. For three decades, the Division ... | CSIRO | 0.783559 |
83,944 | After the Great Depression, research was extended into manufacturing and other secondary industries.In 1949 the Act was changed again, and the entity name amended to the Commonwealth Scientific and Industrial Research Organisation. The amendment enlarged and reconstituted the organisation and its administrative structu... | CSIRO | 0.783559 |
83,945 | Notable inventions and breakthroughs by CSIRO include: A4 DSP chip Aerogard, insect repellent Atomic absorption spectroscopy Biological control of Salvinia Development of Linola (a flax variety with low alpha-linolenic acid content) with a longer life used as a stockfeed Distance measuring equipment (DME) used for avia... | CSIRO | 0.783559 |
83,946 | In the early 1990s, CSIRO radio astronomy scientists John O'Sullivan, Graham Daniels, Terence Percival, Diethelm Ostry and John Deane undertook research directed to finding a way to make wireless networks work as fast as wired networks within confined spaces such as office buildings. The technique they developed, invol... | CSIRO | 0.783559 |
83,947 | One currently active field of research is the use of linear optics versus the use of nonlinear optics in quantum computing. For example, one model of linear optical quantum computing, the KLM model, is universal for quantum computing, and another model, the boson sampling-based model, is believed to be non-universal (f... | Linear optics | 0.783559 |
83,948 | As an example, and using the Dirac bracket notations (see bra-ket notations), the transformation | k ⟩ → e i k θ | k ⟩ {\displaystyle |k\rangle \rightarrow e^{ik\theta }|k\rangle } is linear, while the transformation α 0 | 0 ⟩ + α 1 | 1 ⟩ + α 2 | 2 ⟩ → α 0 | 0 ⟩ + α 1 | 1 ⟩ − α 2 | 2 ⟩ {\displaystyle \alpha _{0}|0\rang... | Linear optics | 0.783559 |
83,949 | Besides the fundamental interest in the mechanism of this behavior, such block copolymers have been proposed for application in smart emulsification, drug delivery, and rheology control. Schizophrenic diblock copolymer have also been applied as thin films for potential use as sensors, smart coatings or nanoswitches, an... | Temperature-responsive polymers | 0.783558 |
83,950 | In mathematical physics, Kundt spacetimes are Lorentzian manifolds admitting a geodesic null congruence with vanishing optical scalars (expansion, twist and shear). A well known member of Kundt class is pp-wave. Ricci-flat Kundt spacetimes in arbitrary dimension are algebraically special. | Kundt spacetime | 0.783558 |
83,951 | Let D, E, and F be given on the lines BC, AC, and AB so that the equation holds. Let F′ be the point where DE crosses AB. Then by the theorem, the equation also holds for D, E, and F′. | Menelaus' theorem | 0.783558 |
83,952 | Al-Biruni's work, The Keys of Astronomy, lists a number of those works, which can be classified into studies as part of commentaries on Ptolemy's Almagest as in the works of al-Nayrizi and al-Khazin where each demonstrated particular cases of Menelaus's theorem that led to the sine rule, or works composed as independen... | Menelaus' theorem | 0.783558 |
83,953 | It is uncertain who actually discovered the theorem; however, the oldest extant exposition appears in Spherics by Menelaus. In this book, the plane version of the theorem is used as a lemma to prove a spherical version of the theorem.In Almagest, Ptolemy applies the theorem on a number of problems in spherical astronom... | Menelaus' theorem | 0.783558 |
83,954 | In the case where the domain Ω is a unit ball in Rn, the formula for d coincides with the expression for the distance between points in the Cayley–Klein model of hyperbolic geometry, up to a multiplicative constant. If the cone K is the positive orthant in Rn then the induced metric on the projectivization of K is ofte... | Hilbert metric | 0.783557 |
83,955 | In mathematics, the Hilbert metric, also known as the Hilbert projective metric, is an explicitly defined distance function on a bounded convex subset of the n-dimensional Euclidean space Rn. It was introduced by David Hilbert (1895) as a generalization of Cayley's formula for the distance in the Cayley–Klein model of ... | Hilbert metric | 0.783557 |
83,956 | Hilbert introduced his metric in order to construct an axiomatic metric geometry in which there exist triangles ABC whose vertices A, B, C are not collinear, yet one of the sides is equal to the sum of the other two — it follows that the shortest path connecting two points is not unique in this geometry. In particular,... | Hilbert metric | 0.783557 |
83,957 | Recently, these color centers in silicon carbide have shown promise in becoming one of the best single-photon emitters for non-classical light sources. Traditionally, attenuated lasers have been the substitute for single-photon sources. This works for quantum cryptography, but they are a partial substitute, and in the ... | Silicon Carbide Color Centers | 0.783555 |
83,958 | When studied at the single defect level, single emitters could be isolated. As a result of this, silicon carbide color centers can be used for applications in quantum cryptography protocols. One example of this was a study on nitrogen-vacancy centers in diamonds in 2014, which are similar to color centers in silicon ca... | Silicon Carbide Color Centers | 0.783555 |
83,959 | Pentamethylcyclopentadienyl iridium dichloride dimer is an organometallic compound with the formula 2, commonly abbreviated 2 This bright orange air-stable diamagnetic solid is a reagent in organometallic chemistry. | Pentamethylcyclopentadienyl iridium dichloride dimer | 0.783553 |
83,960 | Workplace robotics safety is an aspect of occupational safety and health when robots are used in the workplace. This includes traditional industrial robots as well as emerging technologies such as drone aircraft and wearable robotic exoskeletons. Types of accidents include collisions, crushing, and injuries from mechan... | Workplace robotics safety | 0.783553 |
83,961 | Safety standards are being developed by the Robotic Industries Association (RIA) in conjunction with the American National Standards Institute (ANSI). On October 5, 2017, OSHA, NIOSH and RIA signed an alliance to work together to enhance technical expertise, identify and help address potential workplace hazards associa... | Workplace robotics safety | 0.783553 |
83,962 | Using data from the Bureau of Labor Statistics, NIOSH and its state partners have investigated 4 robot-related fatalities under the Fatality Assessment and Control Evaluation Program. In addition the Occupational Safety and Health Administration (OSHA) has investigated robot-related deaths and injuries, which can be re... | Workplace robotics safety | 0.783553 |
83,963 | A 1987 study found that line workers are at the greatest risk, followed by maintenance workers, and programmers. Poor workplace design and human error caused most injuries. Despite the lack of occupational surveillance data on injuries associated specifically with robots, researchers from the US National Institute for ... | Workplace robotics safety | 0.783553 |
83,964 | Many workplace robots are industrial robots used in manufacturing. According to the International Federation of Robotics, 1.7 million new robots are expected to be used in factories between 2017 and 2020. Emerging robot technologies include collaborative robots, personal care robots, construction robots, exoskeletons, ... | Workplace robotics safety | 0.783553 |
83,965 | However, there are a number of paradoxes regarding violation of the second law of thermodynamics, one of them due to the Poincaré recurrence theorem. This arrow of time seems to be related to all other arrows of time and arguably underlies some of them, with the exception of the weak arrow of time.Harold Blum's 1951 bo... | Time arrow | 0.783552 |
83,966 | Certain subatomic interactions involving the weak nuclear force violate the conservation of both parity and charge conjugation, but only very rarely. An example is the kaon decay. According to the CPT theorem, this means they should also be time-irreversible, and so establish an arrow of time. Such processes should be ... | Time arrow | 0.783552 |
83,967 | Two decoherent systems can no longer interact via quantum superposition, unless they become coherent again, which is normally impossible, by the second law of thermodynamics. In the language of relational quantum mechanics, the observer becomes entangled with the measured state, where this entanglement increases entrop... | Time arrow | 0.783552 |
83,968 | Quantum evolution is governed by equations of motions that are time-symmetric (such as Schrödinger equation in the non-relativistic approximation), and by wave function collapse, which is a time-irreversible process, and is either real (by the Copenhagen interpretation of quantum mechanics) or apparent only (by the man... | Time arrow | 0.783552 |
83,969 | In the 1928 book The Nature of the Physical World, which helped to popularize the concept, Eddington stated: Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases t... | Time arrow | 0.783552 |
83,970 | The last step in the equality can be seen from the figure. Now applying the distributivity of the geometric version of the dot product gives which is precisely the algebraic definition of the dot product. So the geometric dot product equals the algebraic dot product. | Scalar product | 0.783551 |
83,971 | In such a presentation, the notions of length and angle are defined by means of the dot product. The length of a vector is defined as the square root of the dot product of the vector by itself, and the cosine of the (non oriented) angle between two vectors of length one is defined as their dot product. So the equivalen... | Scalar product | 0.783551 |
83,972 | The dot product may be defined algebraically or geometrically. The geometric definition is based on the notions of angle and distance (magnitude) of vectors. The equivalence of these two definitions relies on having a Cartesian coordinate system for Euclidean space. In modern presentations of Euclidean geometry, the po... | Scalar product | 0.783551 |
83,973 | For example, if the above process was completed on a cylinder one would find that it is not curved overall as the curvature around the cylinder cancels with the flatness along the cylinder, this is a consequence of Gaussian curvature and Gauss' Theorema Egregium. A familiar example of this is a floppy pizza slice which... | Riemann–Christoffel curvature tensor | 0.78355 |
83,974 | The Walsh–Lebesgue theorem is a famous result from harmonic analysis proved by the American mathematician Joseph L. Walsh in 1929, using results proved by Lebesgue in 1907. The theorem states the following: Let K be a compact subset of the Euclidean plane ℝ2 such the relative complement of K {\displaystyle K} with resp... | Walsh–Lebesgue theorem | 0.78355 |
83,975 | The Walsh–Lebesgue theorem has been generalized to Riemann surfaces and to ℝn. This Walsh-Lebesgue theorem has also served as a catalyst for entire chapters in the theory of function algebras such as the theory of Dirichlet algebras and logmodular algebras. In 1974 Anthony G. O'Farrell gave a generalization of the Wals... | Walsh–Lebesgue theorem | 0.78355 |
83,976 | NSA Suite A Cryptography is NSA cryptography which "contains classified algorithms that will not be released." "Suite A will be used for the protection of some categories of especially sensitive information (a small percentage of the overall national security-related information assurance market)." Incomplete list of S... | NSA Suite A Cryptography | 0.783549 |
83,977 | For example, these two "sticky" ends are compatible: 5'-ATCTGACT GATGCGTATGCT-3' 3'-TAGACTGACTACG CATACGA-5' Also, since different restriction endonucleases usually create different overhangs, it is possible to create a plasmid by excising a piece of DNA (using a different enzyme for each end) and then joining it to an... | Sticky end/blunt end | 0.783549 |
83,978 | For example, if L is a line bundle on a smooth proper geometrically connected curve X over a field k, then χ ( X , L ) = deg ( L ) − genus ( X ) + 1 , {\displaystyle \chi (X,L)={\text{deg}}(L)-{\text{genus}}(X)+1,} where deg(L) denotes the degree of L. When combined with a vanishing theorem, the Riemann–Roch theorem ca... | Coherent cohomology | 0.783546 |
83,979 | For a proper scheme X over a field k, the Euler characteristic of a coherent sheaf E on X is the integer χ ( X , E ) = ∑ j ( − 1 ) j dim k ( H j ( X , E ) ) . {\displaystyle \chi (X,E)=\sum _{j}(-1)^{j}\dim _{k}(H^{j}(X,E)).} The Euler characteristic of a coherent sheaf E can be computed from the Chern classes of E, ... | Coherent cohomology | 0.783546 |
83,980 | More generally, for a closed subvariety Y {\displaystyle Y} of X {\displaystyle X} with inclusion i: Y → X {\displaystyle i:Y\to X} , a vector bundle E {\displaystyle E} on Y {\displaystyle Y} determines a coherent sheaf on X {\displaystyle X} , the direct image sheaf i ∗ E {\displaystyle i_{*}E} , which is zero outsid... | Coherent cohomology | 0.783546 |
83,981 | Coherent sheaves can be seen as a generalization of vector bundles. There is a notion of a coherent analytic sheaf on a complex analytic space, and an analogous notion of a coherent algebraic sheaf on a scheme. In both cases, the given space X {\displaystyle X} comes with a sheaf of rings O X {\displaystyle {\mathcal {... | Coherent cohomology | 0.783546 |
83,982 | In particular, the k {\displaystyle k} -vector spaces H i ( X , E ) {\displaystyle H^{i}(X,E)} and H n − i ( X , K X ⊗ E ∗ ) {\displaystyle H^{n-i}(X,K_{X}\otimes E^{*})} have the same (finite) dimension. (Serre also proved Serre duality for holomorphic vector bundles on any compact complex manifold.) Grothendieck dual... | Coherent cohomology | 0.783546 |
83,983 | Serre duality is an analog of Poincaré duality for coherent sheaf cohomology. In this analogy, the canonical bundle K X {\displaystyle K_{X}} plays the role of the orientation sheaf. Namely, for a smooth proper scheme X {\displaystyle X} of dimension n {\displaystyle n} over a field k {\displaystyle k} , there is a nat... | Coherent cohomology | 0.783546 |
83,984 | The ESRF site forms part of the "Polygone Scientifique", lying at the confluence of the rivers Drac and Isère about 1.5 km from the centre of Grenoble. It is served by Grenoble tramway system and local bus lines of Semitag (C6, 22 and 54). It is served by Grenoble–Isère Airport and Lyon–Saint-Exupéry Airport. The ESRF ... | European Synchrotron Radiation Facility | 0.783546 |
83,985 | Roderick MacKinnon, Nobel Prize in Chemistry 2003, have carried out experiments on beamline ID13. Venki Ramakrishnan, Thomas A. Steitz, and Ada Yonath, Nobel Prize in Chemistry 2009, have used macromolecular crystallography beamlies (ID14-1, -2, -4; and ID29) at the ESRF. Brian Kobilka and Robert Lefkowitz, Nobel Prize... | European Synchrotron Radiation Facility | 0.783546 |
83,986 | But even before this it was not possible to cycle continuously all the way around, since some of the beamlines exit the hall. Research at the ESRF focuses, in large part, on the use of X-ray radiation in fields as diverse as protein crystallography, earth science, paleontology, materials science, chemistry and physics.... | European Synchrotron Radiation Facility | 0.783545 |
83,987 | In mathematical queueing theory, Little's result, theorem, lemma, law, or formula is a theorem by John Little which states that the long-term average number L of customers in a stationary system is equal to the long-term average effective arrival rate λ multiplied by the average time W that a customer spends in the sys... | Little's lemma | 0.783545 |
83,988 | SaTScan is a software tool that employs scan statistics for the spatial and temporal analysis of clusters of events. The software is trademarked by Martin Kulldorff, and was designed originally for public health and epidemiology to identify clusters of cases in both space (geographical location) and time and to perform... | SaTScan | 0.783544 |
83,989 | SaTScan employs scan statistics to identify clusters of space and time phenomena. Scan statistics use regular shapes (usually circles) of varying sizes to evaluate a study area. Within each circle, the software computes if the phenomena within the circle is significantly different than expected compared to the area out... | SaTScan | 0.783544 |
83,990 | Biogeography now incorporates many different fields including but not limited to physical geography, geology, botany and plant biology, zoology, general biology, and modelling. A biogeographer's main focus is on how the environment and humans affect the distribution of species as well as other manifestations of Life su... | Biogeography | 0.783543 |
83,991 | The application of island biogeography theory to habitat fragments spurred the development of the fields of conservation biology and landscape ecology.Classic biogeography has been expanded by the development of molecular systematics, creating a new discipline known as phylogeography. This development allowed scientist... | Biogeography | 0.783543 |
83,992 | Though Wegener did not know the mechanism of this concept of Continental Drift, this contribution to the study of biogeography was significant in the way that it shed light on the importance of environmental and geographic similarities or differences as a result of climate and other pressures on the planet. Importantly... | Biogeography | 0.783543 |
83,993 | Mycogeography is the branch that studies distribution of fungi, such as mushrooms. Knowledge of spatial variation in the numbers and types of organisms is as vital to us today as it was to our early human ancestors, as we adapt to heterogeneous but geographically predictable environments. Biogeography is an integrative... | Biogeography | 0.783543 |
83,994 | Biogeography is a synthetic science, related to geography, biology, soil science, geology, climatology, ecology and evolution. Some fundamental concepts in biogeography include: allopatric speciation – the splitting of a species by evolution of geographically isolated populations evolution – change in genetic compositi... | Biogeography | 0.783543 |
83,995 | PSENEN, formally PEN-2 (presenilin enhancer 2), is a protein that is a regulatory component of the gamma secretase complex, a protease complex responsible for proteolysis of transmembrane proteins such as the Notch protein and amyloid precursor protein (APP). The gamma secretase complex consists of PEN-2, APH-1, nicast... | PEN-2 | 0.78354 |
83,996 | A mind-controlled wheelchair is a mind-machine interfacing device that uses thought (neural impulses) to command the motorised wheelchair's motion. The first such device to reach production was designed by Diwakar Vaish, Head of Robotics and Research at A-SET Training & Research Institutes. The wheelchair is of great i... | Mind Controlled Wheelchair | 0.78354 |
83,997 | Ketenes may react with unsaturated compounds to afford four-membered or larger rings. The first example of this phenomenon was observed in 1908, and since then, cycloadditions of ketenes have expanded and gained synthetic utility. Examples exist of , , and cycloaddition, and conjugated ketenes may act as 4π partners i... | Ketene cycloaddition | 0.783539 |
83,998 | Ketene cycloadditions proceed by a concerted, cycloaddition mechanism. Ketenes, unlike most alkenes, can align antarafacially with respect to other alkenes. Thus, the suprafacial- antarafacial geometry required for concerted, thermal cycloaddition can be achieved in reactions of ketenes. This geometry has the interes... | Ketene cycloaddition | 0.783539 |
83,999 | If we have two representations of a group G {\displaystyle G} , Π 1: G → G L ( V 1 ) {\displaystyle \Pi _{1}:G\rightarrow GL(V_{1})} and Π 2: G → G L ( V 2 ) {\displaystyle \Pi _{2}:G\rightarrow GL(V_{2})} , then the direct sum would have V 1 ⊕ V 2 {\displaystyle V_{1}\oplus V_{2}} as the underlying vector space, with ... | Representation theory of Lie groups | 0.783539 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.