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79,900 | Hipparchus is considered to have been among the most important Greek astronomers, because he introduced the concept of exact prediction into astronomy. He was also the last innovative astronomer before Claudius Ptolemy, a mathematician who worked at Alexandria in Roman Egypt in the 2nd century. Ptolemy's works on astro... | Hellenistic astronomy | 0.785153 |
79,901 | Modern historians of astronomy have determined that Eudoxus' models could only have approximated retrogradation crudely for some planets, and not at all for others. In the 2nd century BCE, Hipparchus, aware of the extraordinary accuracy with which Babylonian astronomers could predict the planets' motions, insisted that... | Hellenistic astronomy | 0.785153 |
79,902 | The deferent-and-epicycle model can mimic the eccentric model, as shown by Apollonius' theorem. It can also explain retrogradation, which happens when planets appear to reverse their motion through the zodiac for a short time. | Hellenistic astronomy | 0.785153 |
79,903 | describes the elementary moves generating the equivalence relation on braids given by the equivalence of their closures. More precisely Markov's theorem can be stated as follows: given two braids represented by elements β n , β m ′ {\displaystyle \beta _{n},\beta _{m}'} in the braid groups B n , B m {\displaystyle B_{n... | Markov theorem | 0.785153 |
79,904 | In mathematics the Markov theorem gives necessary and sufficient conditions for two braids to have closures that are equivalent knots or links. The conditions are stated in terms of the group structures on braids. Braids are algebraic objects described by diagrams; the relation to topology is given by Alexander's theor... | Markov theorem | 0.785153 |
79,905 | In 2017, Antonio Paris, Assistant Professor of Astronomy and Astrophysics at St. Petersburg College, Florida, proposed that the hydrogen cloud surrounding two comets, 266P/Christensen and 335P/Gibbs, now known to have been in the same region of the sky, could have been the source of the Wow! signal. This hypothesis was... | Wow! signal | 0.785152 |
79,906 | signal's coordinates with a 12-meter radio telescope at the National Radio Astronomy Observatory in Green Bank, West Virginia, also achieving a null result. In 1995 and 1996, Gray again searched for the signal using the Very Large Array, which is significantly more sensitive than Big Ear. | Wow! signal | 0.785152 |
79,907 | The region of the sky in question lies northwest of the globular cluster M55, in the constellation Sagittarius, roughly 2.5 degrees south of the fifth-magnitude star group Chi Sagittarii, and about 3.5 degrees south of the plane of the ecliptic. The closest easily visible star is Tau Sagittarii.Initially, no nearby Sun... | Wow! signal | 0.785152 |
79,908 | There are several methods used to define the prior/posterior distribution over the objective function. The most common two methods use Gaussian processes in a method called kriging. Another less expensive method uses the Parzen-Tree Estimator to construct two distributions for 'high' and 'low' points, and then finds th... | Bayesian Optimization | 0.785149 |
79,909 | The approach has been applied to solve a wide range of problems, including learning to rank, computer graphics and visual design, robotics, sensor networks, automatic algorithm configuration, automatic machine learning toolboxes, reinforcement learning, planning, visual attention, architecture configuration in deep lea... | Bayesian Optimization | 0.785149 |
79,910 | The term is generally attributed to Jonas Mockus and is coined in his work from a series of publications on global optimization in the 1970s and 1980s. | Bayesian Optimization | 0.785149 |
79,911 | The maximum of the acquisition function is typically found by resorting to discretization or by means of an auxiliary optimizer. Acquisition functions are typically well-behaved and are maximized using a numerical optimization technique, such as Newton's Method or quasi-Newton methods like the Broyden–Fletcher–Goldfarb... | Bayesian Optimization | 0.785149 |
79,912 | Examples of acquisition functions include probability of improvement expected improvement Bayesian expected losses upper confidence bounds (UCB) or lower confidence bounds Thompson samplingand hybrids of these. They all trade-off exploration and exploitation so as to minimize the number of function queries. As such, Ba... | Bayesian Optimization | 0.785149 |
79,913 | Bayesian optimization is typically used on problems of the form max x ∈ A f ( x ) {\textstyle \max _{x\in A}f(x)} , where A {\textstyle A} is a set of points, x {\textstyle x} , which rely upon less than 20 dimensions ( R d , d ≤ 20 {\textstyle \mathbb {R} ^{d},d\leq 20} ), and whose membership can easily be evaluated.... | Bayesian Optimization | 0.785149 |
79,914 | Bayesian optimization is a sequential design strategy for global optimization of black-box functions that does not assume any functional forms. It is usually employed to optimize expensive-to-evaluate functions. | Bayesian Optimization | 0.785149 |
79,915 | Optical and Quantum Electronics is a peer-reviewed scientific journal published monthly by Springer Science+Business Media. It covers original research and tutorials in optical physics, optoelectronics, photonics, and quantum electronics. Its editors-in-chief are Daoxin Dai, Trevor M. Benson, and Marian Marciniak. | Optical and Quantum Electronics | 0.785149 |
79,916 | Phagocytes are cells that protect the body by ingesting harmful foreign particles, bacteria, and dead or dying cells. Their name comes from the Greek phagein, "to eat" or "devour", and "-cyte", the suffix in biology denoting "cell", from the Greek kutos, "hollow vessel". They are essential for fighting infections and f... | Phagocytic cells | 0.785149 |
79,917 | The Aero-X hoverbike is an aircraft created by Aerofex, an aerospace engineering corporation based in Los Angeles, designed to carry up to two people. It is not known when it will be released for sale. | Aero-X | 0.785146 |
79,918 | Various techniques for feeding and bedding are tested on these farms. Demonstration farms run by universities are not only used for research, but are also used for teaching purposes. The Ontario Agricultural College operates a demonstration farm in which students take active participation in their classes. There has al... | Experimental farm | 0.785142 |
79,919 | His two most celebrated schools, the Scientific Educational Institution for the Higher Social Classes (1806) and the Poor School (1810) garnered attention and visitors from all over Europe and the United States.Through the establishment of an institution dedicated to the discipline of agricultural experimentation, impr... | Experimental farm | 0.785142 |
79,920 | The idea for Quantum Cloud came from Hiley's thoughts on pre-space as a mathematical structure underlying space-time and matter, and his comment that “algebra is the relationship of relationships.” The comment was made during a conversation between Gormley, Hiley and writer David Peat at a 1999 London gathering of arti... | Quantum Cloud | 0.785142 |
79,921 | In mathematics, the Laplace–Carson transform, named after Pierre Simon Laplace and John Renshaw Carson, is an integral transform with significant applications in the field of physics and engineering, particularly in the field of railway engineering. | Laplace–Carson transform | 0.785142 |
79,922 | {\displaystyle z_{1},z_{2}\in U.} A generalization of this theorem was proved by Shing-Tung Yau in 1973. == References == | Schwarz–Ahlfors–Pick theorem | 0.785141 |
79,923 | In mathematics, the Schwarz–Ahlfors–Pick theorem is an extension of the Schwarz lemma for hyperbolic geometry, such as the Poincaré half-plane model. The Schwarz–Pick lemma states that every holomorphic function from the unit disk U to itself, or from the upper half-plane H to itself, will not increase the Poincaré dis... | Schwarz–Ahlfors–Pick theorem | 0.785141 |
79,924 | Every other free group has infinitely many ends. Every finitely generated infinite group has either 1, 2, or infinitely many ends, and the Stallings theorem about ends of groups provides a decomposition of groups with more than one end. In particular: A finitely generated infinite group has 2 ends if and only if it has... | End (graph theory) | 0.785141 |
79,925 | A thick end of a graph G {\displaystyle G} is an end that contains infinitely many pairwise-disjoint rays. Halin's grid theorem characterizes the graphs that contain thick ends: they are exactly the graphs that have a subdivision of the hexagonal tiling as a subgraph. | End (graph theory) | 0.785141 |
79,926 | In the mathematics of infinite graphs, an end of a graph represents, intuitively, a direction in which the graph extends to infinity. Ends may be formalized mathematically as equivalence classes of infinite paths, as havens describing strategies for pursuit–evasion games on the graph, or (in the case of locally finite ... | End (graph theory) | 0.785141 |
79,927 | In point-set topology, there is a concept of an end that is similar to, but not quite the same as, the concept of an end in graph theory, dating back much earlier to Freudenthal (1931). If a topological space can be covered by a nested sequence of compact sets κ 0 ⊂ κ 1 ⊂ κ 2 … {\displaystyle \kappa _{0}\subset \kappa ... | End (graph theory) | 0.785141 |
79,928 | In geometry, a k-skeleton of n-polytope P (functionally represented as skelk(P)) consists of all i-polytope elements of dimension up to k.For example: skel0(cube) = 8 vertices skel1(cube) = 8 vertices, 12 edges skel2(cube) = 8 vertices, 12 edges, 6 square faces | Skeleton (topology) | 0.785139 |
79,929 | In mathematics, particularly in algebraic topology, the n-skeleton of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions m ≤ n. In other words, given an inductive definition of a complex, the n-ske... | Skeleton (topology) | 0.785139 |
79,930 | Peacock, vicar of Sedbergh, 1796 to 1840. He wrote: The University should be more on its guard ... against the introduction of merely algebraic or analytical speculations into its public examinations.Nevertheless, the reforms were encouraged by younger members of Cambridge University. George Peacock successfully encour... | Analytical Society | 0.785137 |
79,931 | One was by George Peacock on differential and integral calculus; the other was by Herschel on the calculus of finite differences. They were joined in this by Whewell, who in 1819 published a book, An Elementary Treatise on Mechanics, which used the new notation and which became a standard textbook on the subject.John A... | Analytical Society | 0.785137 |
79,932 | The slow uptake of the continental methods in calculus led to the formation of the Analytical Society by Charles Babbage, John Herschel and George Peacock.Though the Society was disbanded by 1814 when most of the original members had graduated, its influence continued to be felt. The evidence of Analytical Society work... | Analytical Society | 0.785137 |
79,933 | The Analytical Society was a group of individuals in early-19th-century Britain whose aim was to promote the use of Leibnizian notation for differentiation in calculus as opposed to the Newton notation for differentiation. The latter system came into being in the 18th century as a convention of Sir Isaac Newton, and wa... | Analytical Society | 0.785137 |
79,934 | If the ring spectrum has an E 2 {\displaystyle E_{2}} -structure, the category of modules has a monoidal smash product; if it is at least E 4 {\displaystyle E_{4}} , then it has a symmetric monoidal (smash) product. One can form group ring spectra. One can define the algebraic K-theory, topological Hochschild homology,... | E-infinity ring spectrum | 0.785137 |
79,935 | Lurie, J. "Higher Algebra" (PDF). Archived from the original (PDF) on 2015-02-06. Mandell, M.A. | E-infinity ring spectrum | 0.785137 |
79,936 | Central limit theorem Continuous mapping theorem Glivenko–Cantelli theorem Law of large numbers Law of the iterated logarithm Slutsky's theorem Delta method | Asymptotic statistics | 0.785137 |
79,937 | In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞. In practice,... | Asymptotic statistics | 0.785137 |
79,938 | Phenol-Explorer (phenol-explorer.eu), a database dedicated to phenolics found in food by Augustin Scalbert, INRA Clermont-Ferrand, Unité de Nutrition Humaine (Human food unit) Phenols at ChEBI (Chemical Entities of Biological Interest) ChEMBLdb, a database of bioactive drug-like small molecules by the European Bioinfor... | Naturally occurring phenols | 0.785136 |
79,939 | Natural phenols can be involved in allelopathic interactions, for example in soil or in water. Juglone is an example of such a molecule inhibiting the growth of other plant species around walnut trees. The aquatic vascular plant Myriophyllum spicatum produces ellagic, gallic and pyrogallic acids and (+)-catechin, allel... | Naturally occurring phenols | 0.785136 |
79,940 | Nuclear Physics and Atomic Energy is a quarterly peer-reviewed open-access scientific journal published by Institute for Nuclear Research of the National Academy of Sciences of Ukraine. It was established in 2000 and covers all aspects of nuclear physics, particle physics, atomic energy, radiation physics, plasma physi... | Nuclear Physics and Atomic Energy (journal) | 0.785135 |
79,941 | PIT puts people at the center of policy making and improving community-driven problem-solving through the use of design, data and delivery skills and draws from technical fields like computer science, data science, and engineering, along with law, public policy, movement-building, philosophy, the social sciences, the a... | Public interest technology | 0.785135 |
79,942 | Complex dynamics, hydrodynamics, including vortex induced vibrations (VIVs) and physics of pipe interactions with the seabed are involved. Those are tough on materials used to build the SCR pipe. Dr. Langner had carried out years of analytical and design work before an application for his US patent was filed. | Steel catenary riser | 0.785135 |
79,943 | Path analysis was developed around 1918 by geneticist Sewall Wright, who wrote about it more extensively in the 1920s. It has since been applied to a vast array of complex modeling areas, including biology, psychology, sociology, and econometrics. | Path analysis (statistics) | 0.785133 |
79,944 | In statistics, path analysis is used to describe the directed dependencies among a set of variables. This includes models equivalent to any form of multiple regression analysis, factor analysis, canonical correlation analysis, discriminant analysis, as well as more general families of models in the multivariate analysi... | Path analysis (statistics) | 0.785133 |
79,945 | This is the smallest genome among Klosneuviruses as mentioned above. GC content is 26.6 % Classification of metagenome, made by analyzing 18S rRNA indicate that their hosts are relate to the simple Cercozoa.Phylogenetic tree topology of Mimiviridae is still under discussion. Some authors (CNS 2018) like to put Klosneuv... | Indivirus | 0.785133 |
79,946 | The hyperbolic functions represent an expansion of trigonometry beyond the circular functions. Both types depend on an argument, either circular angle or hyperbolic angle. Since the area of a circular sector with radius r and angle u (in radians) is r2u/2, it will be equal to u when r = √2. In the diagram, such a circl... | Hyperbolic cotangent | 0.78513 |
79,947 | The following inequality is useful in statistics: cosh ( t ) ≤ e t 2 / 2 {\displaystyle \operatorname {cosh} (t)\leq e^{t^{2}/2}} It can be proved by comparing term by term the Taylor series of the two functions. | Hyperbolic cotangent | 0.78513 |
79,948 | By Lindemann–Weierstrass theorem, the hyperbolic functions have a transcendental value for every non-zero algebraic value of the argument.Hyperbolic functions were introduced in the 1760s independently by Vincenzo Riccati and Johann Heinrich Lambert. Riccati used Sc. | Hyperbolic cotangent | 0.78513 |
79,949 | They also occur in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates. Laplace's equations are important in many areas of physics, including electromagnetic theory, heat transfer, fluid dynamics, and special re... | Hyperbolic cotangent | 0.78513 |
79,950 | In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola. Also, similarly to how the deriva... | Hyperbolic cotangent | 0.78513 |
79,951 | In computer science, particularly the study of approximation algorithms, an L-reduction ("linear reduction") is a transformation of optimization problems which linearly preserves approximability features; it is one type of approximation-preserving reduction. L-reductions in studies of approximability of optimization pr... | L-reduction | 0.78513 |
79,952 | Let A and B be optimization problems and cA and cB their respective cost functions. A pair of functions f and g is an L-reduction if all of the following conditions are met: functions f and g are computable in polynomial time, if x is an instance of problem A, then f(x) is an instance of problem B, if y' is a solution ... | L-reduction | 0.785129 |
79,953 | Social constructivists might argue that scientific realism is unable to account for the rapid change that occurs in scientific knowledge during periods of scientific revolution. Constructivists may also argue that the success of theories is only a part of the construction. However, these arguments ignore the fact that ... | Scientific realism | 0.785129 |
79,954 | AMD's portfolio of dedicated graphics processors as of 2017 Radeon – brand for consumer line of graphics cards; the brand name originated with ATI. Mobility Radeon offers power-optimized versions of Radeon graphics chips for use in laptops. Radeon Pro – Workstation graphics card brand. Successor to the FirePro brand. R... | AMD | 0.785127 |
79,955 | Most notable public AMD software is on the GPU side. AMD has opened both its graphic and compute stacks: GPUOpen is AMD's graphics stack, which includes for example FidelityFX Super Resolution. ROCm (Radeon Open Compute platform) is AMD's compute stack for machine learning and high-performance computing, based on the L... | AMD | 0.785127 |
79,956 | Another more general version (also called the projective plane theorem, and due to David B. A. Epstein) is: Let M {\displaystyle M} be any 3-manifold and N {\displaystyle N} a π 1 ( M ) {\displaystyle \pi _{1}(M)} -invariant subgroup of π 2 ( M ) {\displaystyle \pi _{2}(M)} . If f: S 2 → M {\displaystyle f\colon S^{2}\... | Sphere theorem (3-manifolds) | 0.785127 |
79,957 | In mathematics, in the topology of 3-manifolds, the sphere theorem of Christos Papakyriakopoulos (1957) gives conditions for elements of the second homotopy group of a 3-manifold to be represented by embedded spheres. One example is the following: Let M {\displaystyle M} be an orientable 3-manifold such that π 2 ( M ) ... | Sphere theorem (3-manifolds) | 0.785127 |
79,958 | Graduated pipettes are a type of macropipette consisting of a long tube with a series of graduations, as on a graduated cylinder or burette, to indicate different calibrated volumes. They also require a source of vacuum; in the early days of chemistry and biology, the mouth was used. The safety regulations included the... | Combustion pipette | 0.785126 |
79,959 | A pipette (sometimes spelled as pipet) is a laboratory tool commonly used in chemistry, biology and medicine to transport a measured volume of liquid, often as a media dispenser. Pipettes come in several designs for various purposes with differing levels of accuracy and precision, from single piece glass pipettes to mo... | Combustion pipette | 0.785126 |
79,960 | The first simple pipettes were made in glass, such as Pasteur pipettes. Large pipettes continue to be made in glass; others are made in squeezable plastic for situations where an exact volume is not required. The first micropipette was patented in 1957 by Dr Heinrich Schnitger (Marburg, Germany). The founder of the com... | Combustion pipette | 0.785126 |
79,961 | The "-P Convention" or "P Question" refers to the act of making a statement into a question by appending "P." When spoken aloud, the "P" is literally pronounced as a separate syllable "Pee." This practice originated among users of the Lisp programming language, in which there is the convention of appending the letter "... | P convention | 0.785122 |
79,962 | In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons (bits), nats or hartleys) obtained about one random variable by obser... | Average mutual information | 0.785122 |
79,963 | Suppose we want to transmit information about a source to the user with a distortion not exceeding D. Rate–distortion theory tells us that at least R ( D ) {\displaystyle R(D)} bits/symbol of information from the source must reach the user. We also know from Shannon's channel coding theorem that if the source entropy i... | Rate distortion function | 0.785122 |
79,964 | The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit: learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion. ... | Average mutual information | 0.785122 |
79,965 | He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies t... | Average mutual information | 0.785122 |
79,966 | Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized. Detection of phase synchronization in time series analysis. In the in... | Average mutual information | 0.785122 |
79,967 | Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection. Mutual information is used in determining the similarity of two differen... | Average mutual information | 0.785122 |
79,968 | In 2014, OASPA's investigation concluded that MDPI continued to meet its membership criteria.In April 2017, an update of all available Australian added sugars consumption data titled "Declining consumption of added sugars and sugar-sweetened beverages in Australia: a challenge for obesity prevention" was published in t... | Australian paradox | 0.785121 |
79,969 | Tom McNeill argued that Rikkers et al.'s paper was significantly flawed, writing: "Rikkers et al.'s biggest source of error is the inclusion of incorrect products in the category of "moderate to high sugar content", in violation of their study inclusion criteria. Fruit juices and fruit drinks have been added to the ana... | Australian paradox | 0.785121 |
79,970 | Some people have criticized Brand-Miller's 2011 study, such as economist Rory Robertson, who argued that " regular claim – "In Australia sugar consumption has dropped 23 per cent since 1980" – is woefully misleading, based as it is on a series that was abandoned by the Australian Bureau of Statistics (ABS) as unreliabl... | Australian paradox | 0.785121 |
79,971 | 251). The work of (Grün 1936) studied aspects of the transfer and fusion as well, resulting in Grün's first theorem: P ∩ Ap(G) is generated by P ∩ and P ∩ where N = NG(P) and Q ranges over the set of Sylow p-subgroups Q = Pg of G (Gorenstein 1980, Theorem 7.4.2, p. 252). | Lower p-series | 0.78512 |
79,972 | Various mathematicians have presented methods to calculate the focal subgroup from smaller groups. For instance, the influential work (Alperin 1967) develops the idea of a local control of fusion, and as an example application shows that: P ∩ Ap(G) is generated by the commutator subgroups where Q varies over a family ... | Lower p-series | 0.78512 |
79,973 | 246) shows that the focal subgroup of P in G is the intersection P∩ of the Sylow p-subgroup P of the finite group G with the derived subgroup of G. The focal subgroup is important as it is a Sylow p-subgroup of the derived subgroup. One also gets the following result: There exists a normal subgroup K of G with G/K an ... | Lower p-series | 0.78512 |
79,974 | One can define, as in (Isaacs 2008, p. 165) the focal subgroup of H with respect to G as: FocG(H) = ⟨ x−1 y | x,y in H and x is G-conjugate to y ⟩.This focal subgroup measures the extent to which elements of H fuse in G, while the previous definition measured certain abelian p-group homomorphic images of the group G. T... | Lower p-series | 0.78512 |
79,975 | The boron was identified by the rover's laser-shooting Chemistry and Camera (ChemCam) instrument, which was developed at Los Alamos National Laboratory. Hematite, clay minerals and boron are found to be more abundant in layers farther uphill in Gale Crater, compared with lower, older layers.Scientists developed two hyp... | Boron on Mars | 0.785118 |
79,976 | Jump height in terms of flow Dividing by constant ρ {\displaystyle \rho } and introducing the result from continuity gives v 0 2 ( h 0 − h 0 2 h 1 ) + g 2 ( h 0 2 − h 1 2 ) = 0. {\displaystyle v_{0}^{2}\left(h_{0}-{h_{0}^{2} \over h_{1}}\right)+{g \over 2}(h_{0}^{2}-h_{1}^{2})=0.} which, after some algebra, simplifies ... | Hydraulic jump | 0.785116 |
79,977 | When this happens, the jump can be accompanied by violent turbulence, eddying, air entrainment, and surface undulations, or waves. There are two main manifestations of hydraulic jumps and historically different terminology has been used for each. However, the mechanisms behind them are similar because they are simply v... | Hydraulic jump | 0.785116 |
79,978 | VTDK consists of three faculties: the Civil Engineering Faculty, the Technical Faculty and the Design Faculty. The college offers 15 full-time study programs, partial studies through exchange programs, as well as informal study courses and training. VTDK maintains close cooperation with many Lithuanian and foreign part... | Vilnius College of Technologies and Design | 0.785115 |
79,979 | Engineering Systems of Buildings Geodesy and Cadastre Transport Logistics Civil Engineering | Vilnius College of Technologies and Design | 0.785115 |
79,980 | Technical Maintenance of Automobiles Electrical and Automation Engineering Mechanical Technologies Engineering Railway Transport Engineering Transport Information Systems Renewable Energy Car Electronics | Vilnius College of Technologies and Design | 0.785115 |
79,981 | The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison.The LMA is used in many software applications for solving generic curve-fi... | Levenberg–Marquardt nonlinear least squares fitting algorithm | 0.785115 |
79,982 | A Höhere Technische Lehranstalt (German for Higher Technical Education Institute, or more loosely translated Technical College), commonly known as HTL, is an engineering-focused secondary school/institution of further education in Austria. As an umbrella term it is used for either Höhere Technische Lehranstalt (HTL, HT... | Höhere Technische Lehranstalt | 0.785115 |
79,983 | In mathematics and computer science, Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that are capable of carrying out computations involving a countably infinite number of algorithmic steps. These machines are ruled out in... | Zeno machine | 0.785115 |
79,984 | {\displaystyle \theta =\sum _{k=1}^{n}x_{k}{\frac {\partial }{\partial x_{k}}}.} As in one variable, the eigenspaces of θ are the spaces of homogeneous functions. (Euler's homogeneous function theorem) | Theta operator | 0.785114 |
79,985 | In linear algebra, Schur’s theorem is referred to as either the triangularization of a square matrix with complex entries, or of a square matrix with real entries and real eigenvalues. | Schur's theorem | 0.785112 |
79,986 | In functional analysis and the study of Banach spaces, Schur's theorem, due to I. Schur, often refers to Schur's property, that for certain spaces, weak convergence implies convergence in the norm. | Schur's theorem | 0.785112 |
79,987 | In differential geometry, Schur's theorem compares the distance between the endpoints of a space curve C ∗ {\displaystyle C^{*}} to the distance between the endpoints of a corresponding plane curve C {\displaystyle C} of less curvature. Suppose C ( s ) {\displaystyle C(s)} is a plane curve with curvature κ ( s ) {\disp... | Schur's theorem | 0.785112 |
79,988 | As a result, for every set of relatively prime numbers { a 1 , … , a n } {\displaystyle \{a_{1},\ldots ,a_{n}\}} there exists a value of x {\displaystyle x} such that every larger number is representable as a linear combination of { a 1 , … , a n } {\displaystyle \{a_{1},\ldots ,a_{n}\}} in at least one way. This conse... | Schur's theorem | 0.785112 |
79,989 | In combinatorics, Schur's theorem tells the number of ways for expressing a given number as a (non-negative, integer) linear combination of a fixed set of relatively prime numbers. In particular, if { a 1 , … , a n } {\displaystyle \{a_{1},\ldots ,a_{n}\}} is a set of integers such that gcd ( a 1 , … , a n ) = 1 {\disp... | Schur's theorem | 0.785112 |
79,990 | Schur's theorem ensures that S(c) is well-defined for every positive integer c. The numbers of the form S(c) are called Schur's number. Folkman's theorem generalizes Schur's theorem by stating that there exist arbitrarily large sets of integers, all of whose nonempty sums belong to the same part. Using this definition,... | Schur's theorem | 0.785112 |
79,991 | In Ramsey theory, Schur's theorem states that for any partition of the positive integers into a finite number of parts, one of the parts contains three integers x, y, z with x + y = z . {\displaystyle x+y=z.} For every positive integer c, S(c) denotes the smallest number S such that for every partition of the integers ... | Schur's theorem | 0.785112 |
79,992 | In number theory, Issai Schur showed in 1912 that for every nonconstant polynomial p(x) with integer coefficients, if S is the set of all nonzero values { p ( n ) ≠ 0: n ∈ N } {\displaystyle {\begin{Bmatrix}p(n)\neq 0:n\in \mathbb {N} \end{Bmatrix}}} , then the set of primes that divide some member of S is infinite. | Schur's theorem | 0.785112 |
79,993 | In discrete mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem of Axel Schur. In functional analysis, Schur's theorem is often called Schur's property, also due to Issai Schur. | Schur's theorem | 0.785112 |
79,994 | Many of these chemists had little or no training in chemistry, and their lack of expertise was a danger to the public. Shortly after the Adulteration of Food and Drink Act 1860 the Society was formed. It established adulteration and food standards, and educated analysts in legal work.It published The Analyst, Analytica... | Society for Analytical Chemistry | 0.785112 |
79,995 | The Society of Public Analysts was formed in the United Kingdom in 1874 and subsequently became the Society for Analytical Chemistry. It was incorporated in 1907. The chemical industry had grown rapidly in the 19th century, and developments in the alkali, explosive and agricultural chemical fields produced a growing ne... | Society for Analytical Chemistry | 0.785112 |
79,996 | The last statement means in particular that, in a neighborhood of the point corresponding to a compact leaf with finite holonomy, the space of leaves is Hausdorff. Under certain conditions the Reeb local stability theorem may replace the Poincaré–Bendixson theorem in higher dimensions. This is the case of codimension o... | Reeb stability theorem | 0.78511 |
79,997 | Theorem: Let F {\displaystyle F} be a C 1 {\displaystyle C^{1}} , codimension k {\displaystyle k} foliation of a manifold M {\displaystyle M} and L {\displaystyle L} a compact leaf with finite holonomy group. There exists a neighborhood U {\displaystyle U} of L {\displaystyle L} , saturated in F {\displaystyle F} (also... | Reeb stability theorem | 0.78511 |
79,998 | Reeb Global Stability Theorem is false for foliations of codimension greater than one. However, for some special kinds of foliations one has the following global stability results: In the presence of a certain transverse geometric structure:Theorem: Let F {\displaystyle F} be a complete conformal foliation of codimensi... | Reeb stability theorem | 0.78511 |
79,999 | If F {\displaystyle F} is transversely orientable, then every leaf of F {\displaystyle F} is diffeomorphic to L {\displaystyle L} ; M {\displaystyle M} is the total space of a fibration f: M → S 1 {\displaystyle f:M\to S^{1}} over S 1 {\displaystyle S^{1}} , with fibre L {\displaystyle L} , and F {\displaystyle F} is t... | Reeb stability theorem | 0.78511 |
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