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86,500 | The dynamic events included an acceleration run, an autocross race and an endurance event. McGill University finished the fastest in autocross competition and also finished fastest in the endurance race. Yale University's car was the fastest in electric-only acceleration. Florida Institute of Technology's car was the f... | Formula Hybrid | 0.782496 |
86,501 | The total points possible were a 1000 (per team). For the static events, each team could score a maximum of 300 points and for the dynamic (racing) events, each team could score a maximum of 700 points. The official results of the 2011 competition are as follows:1st Place Overall –Texas A&M University 2nd Place Overall... | Formula Hybrid | 0.782496 |
86,502 | Technology and Culture is a quarterly academic journal founded in 1959. It is an official publication of the Society for the History of Technology (SHOT), whose members routinely refer to it as "T&C." Besides scholarly articles and critical essays, the journal publishes reviews of books and museum exhibitions. Occasion... | Technology and Culture | 0.782496 |
86,503 | There cannot be inferences about seed dispersal syndromes without robust phylogenies and evolutionary studies. There is also a gap in the understanding of genetic consequences of zoochory. Using genetics could help clarify if these syndromes were formed at random or if they correspond to evolution of seed dispersal. | Seed dispersal syndrome | 0.782496 |
86,504 | In organic chemistry, Carnelley's rule, established in 1882 by Thomas Carnelley, states that high molecular symmetry is associated with high melting point. Carnelley based his rule on examination of 15,000 chemical compounds. For example, for three structural isomers with molecular formula C5H12 the melting point incre... | Liquefaction point | 0.782495 |
86,505 | A shroud of suitable geometry can increase the flow velocity across the turbine by 3 to 4 times the open or free stream velocity. More power generated means greater returns on investment. The number of suitable sites is increased as sites formerly too slow for commercial development become viable. Where large cumbersom... | Shrouded tidal turbine | 0.782494 |
86,506 | Most shrouded turbines are directional, although one exception is the version off Southern Vancouver Island in British Columbia. One-direction fixed shrouds may not capture flow efficiently - in order for the shroud to produce maximum efficiency to use both flood and ebb tide they need to be yawed like a windmill on a ... | Shrouded tidal turbine | 0.782494 |
86,507 | Its water-solubility, together with its status as the only known photoactive protein containing a carotenoid, makes the OCP a valuable model for studying solution-state energetic and photophysical properties of carotenoids, which are a diverse class of molecules found across all domains of life. Moreover, carotenoids a... | Orange carotenoid protein | 0.782493 |
86,508 | The connection between spatial cognition, human activity, and survival has existed since ancient times. As learned from etymology, geometry originates in land surveying of the annual floods of the Nile river. Spatial cognition developed from the study of cognitive psychology which began to be considered as a separate f... | Cognitive geography | 0.782489 |
86,509 | The French Crystallographic Association (AFC) brings together physicists, chemists and biologists that use crystals and crystallography in their research or develop new crystallographic methods. Originally part of the French Society of Mineralogy, the AFC was founded in 1953 by Hubert Curien and André Guinier. Today, i... | French Crystallographic Association | 0.782488 |
86,510 | When a Sahlqvist formula is used as an axiom in a normal modal logic, the logic is guaranteed to be complete with respect to the elementary class of frames the axiom defines. This result comes from the Sahlqvist completeness theorem . But there is also a converse theorem, namely a theorem that states which first-order ... | Sahlqvist formula | 0.782487 |
86,511 | In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties. The Sahlqvist correspondence theorem states that every Sahlqvist formula is canonical, and corresponds to a first-order definable class of Kripke frames. Sahlqvist's definition characterizes a decidable set of modal formu... | Sahlqvist formula | 0.782487 |
86,512 | Pfeffer was a pioneer of modern plant physiology. His scientific interests included the thermonastic and photonastic movements of flowers, the nyctinastic movements of leaves, protoplastic physics and photosynthesis. In 1877, while researching plant metabolism, Pfeffer developed a semi-porous membrane to study the phen... | Pfeffer cell | 0.782487 |
86,513 | In applied mathematics, multimodal optimization deals with optimization tasks that involve finding all or most of the multiple (at least locally optimal) solutions of a problem, as opposed to a single best solution. Evolutionary multimodal optimization is a branch of evolutionary computation, which is closely related t... | Evolutionary multimodal optimization | 0.782487 |
86,514 | Knowledge of multiple solutions to an optimization task is especially helpful in engineering, when due to physical (and/or cost) constraints, the best results may not always be realizable. In such a scenario, if multiple solutions (locally and/or globally optimal) are known, the implementation can be quickly switched t... | Evolutionary multimodal optimization | 0.782487 |
86,515 | He studied chemistry and pharmacy at the University of Göttingen, where his instructors included Friedrich Wöhler (1800-1882), William Eduard Weber (1804-1891) and Wilhelm Rudolph Fittig (1835-1910). Afterwards, he furthered his education at the universities of Marburg and Berlin. At Berlin, he studied under Alexander ... | Pfeffer cell | 0.782487 |
86,516 | Recently, an evolutionary multiobjective optimization (EMO) approach was proposed, in which a suitable second objective is added to the originally single objective multimodal optimization problem, so that the multiple solutions form a weak pareto-optimal front. Hence, the multimodal optimization problem can be solved f... | Evolutionary multimodal optimization | 0.782487 |
86,517 | De Jong's crowding method, Goldberg's sharing function approach, Petrowski's clearing method, restricted mating, maintaining multiple subpopulations are some of the popular approaches that have been proposed by the community. The first two methods are especially well studied, however, they do not perform explicit separ... | Evolutionary multimodal optimization | 0.782487 |
86,518 | Finding and maintenance of multiple solutions is wherein lies the challenge of using EAs for multi-modal optimization. Niching is a generic term referred to as the technique of finding and preserving multiple stable niches, or favorable parts of the solution space possibly around multiple solutions, so as to prevent co... | Evolutionary multimodal optimization | 0.782487 |
86,519 | Classical techniques of optimization would need multiple restart points and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. Evolutionary algorithms (EAs) due to their population based approach, provide a natural advantage over classical optimization techniques... | Evolutionary multimodal optimization | 0.782487 |
86,520 | This is combined with linear recording density improvements enabling 36-53 sectors per track through partial-response maximum-likelihood and zone bit recording. The true capacity of these "SD120MB" drives is 120.375 MiB aka 126.22 MB (FAT16B with logical geometry 963/8/32 CHS × 512 bytes). The "SD240MB" drives have a c... | SuperDisk drive | 0.782486 |
86,521 | 1.44 MB HD floppies formatted to 32 MB as "FD32MB" (FAT16B with logical geometry 1024/2/32 CHS × 512 bytes) in the LS-240 show a dummy FAT12 file system (with logical geometries 160/2/9 or 80/2/18) when inserted into a normal floppy drive. SuperDisk drives have been sold in parallel port, USB, ATAPI and SCSI variants. | SuperDisk drive | 0.782486 |
86,522 | In the mathematical field of partial differential equations, Harnack's principle or Harnack's theorem is a corollary of Harnack's inequality which deals with the convergence of sequences of harmonic functions. Given a sequence of harmonic functions u1, u2, ... on an open connected subset G of the Euclidean space Rn, wh... | Harnack's theorem | 0.782486 |
86,523 | The Hasse derivative is a generalized derivation on k and extends to a generalized derivation on the function field k(X), satisfying an analogue of the product rule D ( r ) ( f g ) = ∑ i = 0 r D ( i ) ( f ) D ( r − i ) ( g ) {\displaystyle D^{(r)}(fg)=\sum _{i=0}^{r}D^{(i)}(f)D^{(r-i)}(g)} and an analogue of the chain ... | Hasse derivative | 0.782485 |
86,524 | In mathematics, the Hasse derivative is a generalisation of the derivative which allows the formulation of Taylor's theorem in coordinate rings of algebraic varieties. | Hasse derivative | 0.782485 |
86,525 | In mathematical analysis, Zorich's theorem was proved by Vladimir A. Zorich in 1967. The result was conjectured by M. A. Lavrentev in 1938. | Zorich's theorem | 0.782485 |
86,526 | The projection filter in direct metric, when implemented on a manifold S Θ {\displaystyle S_{\Theta }} of mixture families, leads to equivalence with a Galerkin method.The projection filter in Hellinger/Fisher metric when implemented on a manifold S Θ 1 / 2 {\displaystyle S_{\Theta }^{1/2}} of square roots of an expone... | Projection filters | 0.782482 |
86,527 | Indeed, the Stratonovich-based projection filters optimized the approximations of the SPDE separate coefficients on the chosen manifold but not the SPDE solution as a whole. This has been dealt with by introducing the optimal projection filters. The innovation here is to work directly with Ito calculus, instead of reso... | Projection filters | 0.782482 |
86,528 | Now rather than considering the exact filter SPDE in Stratonovich calculus form, one keeps it in Ito calculus form d p t = L t ∗ p t d t + p t T . {\displaystyle dp_{t}={\cal {L}}_{t}^{*}p_{t}\ dt+p_{t}^{T}.} In the Stratonovich projection filters above, the vector fields F {\displaystyle F} and G {\displaystyle G} w... | Projection filters | 0.782482 |
86,529 | To do this, the chosen finite dimensional family is equipped with a manifold structure as in information geometry. The projection filter was tested against the optimal filter for the cubic sensor problem. The projection filter could track effectively bimodal densities of the optimal filter that would have been difficul... | Projection filters | 0.782482 |
86,530 | If this distribution has a density, the density satisfies specific stochastic partial differential equations (SPDEs) called Kushner-Stratonovich equation, or Zakai equation. It is known that the nonlinear filter density evolves in an infinite dimensional function space.One can choose a finite dimensional family of prob... | Projection filters | 0.782482 |
86,531 | Projection filters are a set of algorithms based on stochastic analysis and information geometry, or the differential geometric approach to statistics, used to find approximate solutions for filtering problems for nonlinear state-space systems. The filtering problem consists of estimating the unobserved signal of a ran... | Projection filters | 0.782482 |
86,532 | Libgcrypt is a cryptography library developed as a separated module of GnuPG. It can also be used independently of GnuPG, but depends on its error-reporting library Libgpg-error.It provides functions for all fundamental cryptographic building blocks: Libgcrypt features its own multiple precision arithmetic implementati... | Libgcrypt | 0.782481 |
86,533 | Genes with different or multiple stop codons will be unaffected. SUP35, a nonsense suppressor identified by Wickner in 1994, is a prion protein. In synthetic biology, artificial suppressor elongator tRNAs are used to incorporate unnatural amino acids at nonsense codons placed in the coding sequence of a gene. | Nonsense suppressor | 0.78248 |
86,534 | A group of scientists tested whether or not the chemical composition of methylnitronitrosoguanidine would directly affect the growth of tumors and cancer cells in rats.In the experiment, the cancer cells from a Japanese cancer patient was injected into 8 rats. The biochemical tool and showed a decline of cancer cells i... | Methylnitronitrosoguanidine | 0.782479 |
86,535 | The algebraic structure of the problem is, as explained in later sections, SO(4)/Z2 ~ SO(3) × SO(3). The three components Li of the angular momentum vector L have the Poisson brackets where i=1,2,3 and εijs is the fully antisymmetric tensor, i.e., the Levi-Civita symbol; the summation index s is used here to avoid conf... | Runge–Lenz vector | 0.782477 |
86,536 | In February 1990, Electron User published Timothy Grantham's simple implementation of Logo for the Acorn Electron under the article "Talking Turtle". Comenius Logo is an implementation of Logo developed by Comenius University Faculty of Mathematics and Physics. It started development in December 1991, and is also known... | Logo (programming language) | 0.782477 |
86,537 | Some modern derivatives of Logo allow thousands of independently moving turtles. There are two popular implementations: Massachusetts Institute of Technology's StarLogo and Northwestern University Center for Connected Learning's (CCL) NetLogo. They allow exploring emergent phenomena and come with many experiments in so... | Logo (programming language) | 0.782477 |
86,538 | Logo was created in 1967 at Bolt, Beranek and Newman (BBN), a Cambridge, Massachusetts research firm, by Wally Feurzeig, Cynthia Solomon, and Seymour Papert. Its intellectual roots are in artificial intelligence, mathematical logic and developmental psychology. For the first four years of Logo research, development and... | Logo (programming language) | 0.782477 |
86,539 | Kuran and Sunstein recommend that availability cascades be recognized, and institutional safeguards be implemented in all branches of government. They recommend expanded product defamation laws, analogous to personal libel laws, to discourage availability entrepreneurs from knowingly spreading false and damaging report... | Availability cascade | 0.782477 |
86,540 | Characteristic classes were later found for foliations of manifolds; they have (in a modified sense, for foliations with some allowed singularities) a classifying space theory in homotopy theory. In later work after the rapprochement of mathematics and physics, new characteristic classes were found by Simon Donaldson a... | Characteristic number | 0.782476 |
86,541 | What is more, the Chern class itself was not so new, having been reflected in the Schubert calculus on Grassmannians, and the work of the Italian school of algebraic geometry. On the other hand there was now a framework which produced families of classes, whenever there was a vector bundle involved. The prime mechanism... | Characteristic number | 0.782476 |
86,542 | Characteristic classes are phenomena of cohomology theory in an essential way — they are contravariant constructions, in the way that a section is a kind of function on a space, and to lead to a contradiction from the existence of a section we do need that variance. In fact cohomology theory grew up after homology and ... | Characteristic number | 0.782476 |
86,543 | In mathematics, a characteristic class is a way of associating to each principal bundle of X a cohomology class of X. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure f... | Characteristic number | 0.782476 |
86,544 | Thus it is representable. By using different methods, Dobbertin got the following result.Theorem (Dobbertin 1986). Every distributive (∨,0)-semilattice in which every principal ideal is at most countable is representable. Problem 2 (Dobbertin 1983). Is every conical refinement monoid measurable? | Huhn's theorem | 0.782473 |
86,545 | Theorem (Wehrung 2003). Every direct limit of a countable sequence of distributive lattices with zero and (∨,0)-homomorphisms is representable. Other important representability results are related to the cardinality of the semilattice. | Huhn's theorem | 0.782473 |
86,546 | Theorem (Schmidt 1981). Every distributive lattice with zero satisfies Schmidt's Condition; thus it is representable. This result has been improved further as follows, via a very long and technical proof, using forcing and Boolean-valued models. | Huhn's theorem | 0.782473 |
86,547 | We say that a (∨,0)-semilattice satisfies Schmidt's Condition, if it is isomorphic to the quotient of a generalized Boolean semilattice B under some distributive join-congruence of B. One of the deepest results about representability of (∨,0)-semilattices is the following. Theorem (Schmidt 1968). Any (∨,0)-semilattice ... | Huhn's theorem | 0.782473 |
86,548 | He did not publish the result but it appears as an exercise credited to him in Birkhoff 1948. The first published proof is in Grätzer and Schmidt 1962.Theorem (Dilworth ≈1940, Grätzer and Schmidt 1962). Every finite distributive lattice is isomorphic to the congruence lattice of some finite lattice. | Huhn's theorem | 0.782473 |
86,549 | Theorem (Funayama and Nakayama 1942). The congruence lattice of any lattice is distributive. This says that α ∧ (β ∨ γ) = (α ∧ β) ∨ (α ∧ γ), for any congruences α, β, and γ of a given lattice. | Huhn's theorem | 0.782473 |
86,550 | A congruence of an algebra A is finitely generated if and only if it is a compact element of Con A. As every congruence of an algebra is the join of the finitely generated congruences below it (e.g., every submodule of a module is the union of all its finitely generated submodules), we obtain the following result, firs... | Huhn's theorem | 0.782473 |
86,551 | We shall denote by ε the `parity function' on the natural numbers, that is, ε(n)=n mod 2, for any natural number n. We let L be an algebra possessing a structure of semilattice (L,∨) such that every congruence of L is also a congruence for the operation ∨ . We put U ∨ V = { u ∨ v ∣ ( u , v ) ∈ U × V } , for all U , V ⊆... | Huhn's theorem | 0.782473 |
86,552 | Hence, the counterexample to CLP had been known for nearly ten years, it is just that nobody knew why it worked! All the results prior to the theorem above made use of some form of permutability of congruences. The difficulty was to find enough structure in congruence lattices of non-congruence-permutable lattices. | Huhn's theorem | 0.782473 |
86,553 | The following recent theorem solves CLP. Theorem (Wehrung 2007). The semilattice G(Ω) is not isomorphic to Conc L for any lattice L, whenever the set Ω has at least ℵω+1 elements. | Huhn's theorem | 0.782473 |
86,554 | Many investigations around this problem involve diagrams of semilattices or of algebras. A most useful folklore result about these is the following. Theorem. The functor Conc, defined on all algebras of a given signature, to all (∨,0)-semilattices, preserves direct limits. | Huhn's theorem | 0.782473 |
86,555 | The congruence lattice Con A of an algebra A is an algebraic lattice. The (∨,0)-semilattice of compact elements of Con A is denoted by Conc A, and it is sometimes called the congruence semilattice of A. Then Con A is isomorphic to the ideal lattice of Conc A. By using the classical equivalence between the category of a... | Huhn's theorem | 0.782473 |
86,556 | The semilattice Conc FV(Ω) does not satisfy WURP, for any set Ω of cardinality at least ℵ2 and any non-distributive variety V of lattices. Consequently, Conc FV(Ω) does not satisfy Schmidt's Condition. It is proved by Tůma and Wehrung in 2001 that Conc FV(Ω) is not isomorphic to Conc L, for any lattice L with permutabl... | Huhn's theorem | 0.782473 |
86,557 | The following result, proved by Ploščica, Tůma, and Wehrung in 1998, is more striking, because it shows examples of representable semilattices that do not satisfy Schmidt's Condition. We denote by FV(Ω) the free lattice on Ω in V, for any variety V of lattices. Theorem (Ploščica, Tůma, and Wehrung 1998). | Huhn's theorem | 0.782473 |
86,558 | For a set Ω, we consider the partially ordered vector space E(Ω) defined by generators 1 and ai,x, for i<2 and x in Ω, and relations a0,x+a1,x=1, a0,x ≥ 0, and a1,x ≥ 0, for any x in Ω. By using a Skolemization of the theory of dimension groups, we can embed E(Ω) functorially into a dimension vector space F(Ω). The vec... | Huhn's theorem | 0.782473 |
86,559 | The semilattice part of the result above is achieved via an infinitary semilattice-theoretical statement URP (Uniform Refinement Property). If we want to disprove Schmidt's problem, the idea is (1) to prove that any generalized Boolean semilattice satisfies URP (which is easy), (2) that URP is preserved under homomorph... | Huhn's theorem | 0.782473 |
86,560 | As the ℵ2 bound suggests, infinite combinatorics are involved. The principle used is Kuratowski's free set theorem, first published in 1951. Only the case n=2 is used here. | Huhn's theorem | 0.782473 |
86,561 | The abovementioned Problem 1 (Schmidt), Problem 2 (Dobbertin), and Problem 3 (Goodearl) were solved simultaneously in the negative in 1998. Theorem (Wehrung 1998). There exists a dimension vector space G over the rationals with order-unit whose positive cone G+ is not isomorphic to V(R), for any von Neumann regular rin... | Huhn's theorem | 0.782473 |
86,562 | The following result was prepared for publication by Dobbertin after Huhn's passing away in 1985. The two corresponding papers were published in 1989.Theorem (Huhn 1985). Every distributive (∨,0)-semilattice of cardinality at most ℵ1 satisfies Schmidt's Condition. | Huhn's theorem | 0.782473 |
86,563 | Let V be an infinite-dimensional vector space over an uncountable field F. Then Con A isomorphic to Sub V implies that A has at least card F operations, for any algebra A. As V is infinite-dimensional, the largest element (unit) of Sub V is not compact. However innocuous it sounds, the compact unit assumption is essent... | Huhn's theorem | 0.782473 |
86,564 | As the next result shows, these algebraic lattices are difficult to represent. Theorem (Freese, Lampe, and Taylor 1979). | Huhn's theorem | 0.782473 |
86,565 | Theorem (Grätzer and Schmidt 1963). Every algebraic lattice is isomorphic to the congruence lattice of some algebra. The lattice Sub V of all subspaces of a vector space V is certainly an algebraic lattice. | Huhn's theorem | 0.782473 |
86,566 | The congruence lattice problem (CLP): Is every distributive algebraic lattice isomorphic to the congruence lattice of some lattice? The problem CLP has been one of the most intriguing and longest-standing open problems of lattice theory. Some related results of universal algebra are the following. | Huhn's theorem | 0.782473 |
86,567 | We denote by Con A the congruence lattice of an algebra A, that is, the lattice of all congruences of A under inclusion. The following is a universal-algebraic triviality. It says that for a congruence, being finitely generated is a lattice-theoretical property. Lemma. | Huhn's theorem | 0.782473 |
86,568 | In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most famous and long-standing open problems in lattice theory; it had a deep i... | Huhn's theorem | 0.782473 |
86,569 | This timeline lists significant discoveries in physics and the laws of nature, including experimental discoveries, theoretical proposals that were confirmed experimentally, and theories that have significantly influenced current thinking in modern physics. Such discoveries are often a multi-step, multi-person process. ... | Timeline of fundamental physics discoveries | 0.782472 |
86,570 | 585 BCE - Thales of Miletus: First prediction of a Solar eclipse as a phenomenon explained by a natural cause instead of supernatural 460–370 BCE - Democritus: Atomism via thought experiment 384–322 BCE - Aristotle: Aristotelian physics, the first empirically grounded effective theory of physics, in its appropriate dom... | Timeline of fundamental physics discoveries | 0.782472 |
86,571 | Copy protection engineers quickly figured out what Locksmith was doing and began to use the same technique to defeat it. Locksmith countered by introducing the ability to reproduce track alignment and prevented itself from being copied by embedding a special sequence of nibbles, that if found, would stop the copy proce... | Bit nibbler | 0.78247 |
86,572 | The "elementary solutions", as we referred to them above, are the so-called "stationary states" of the particle, and Fourier's algorithm, as described above, can still be used to solve the boundary value problem of the future evolution of ψ given its values for t = 0. Neither of these approaches is of much practical us... | Fourier transformation | 0.782469 |
86,573 | The other use of the Fourier transform in both quantum mechanics and quantum field theory is to solve the applicable wave equation. In non-relativistic quantum mechanics, Schrödinger's equation for a time-varying wave function in one-dimension, not subject to external forces, is − ∂ 2 ∂ x 2 ψ ( x , t ) = i h 2 π ∂ ∂ t ... | Fourier transformation | 0.782469 |
86,574 | The Fourier transform is useful in quantum mechanics in at least two different ways. To begin with, the basic conceptual structure of quantum mechanics postulates the existence of pairs of complementary variables, connected by the Heisenberg uncertainty principle. For example, in one dimension, the spatial variable q o... | Fourier transformation | 0.782469 |
86,575 | The space of such functions of a complex variable is called the Paley—Wiener space. This theorem has been generalised to semisimple Lie groups.If f is supported on the half-line t ≥ 0, then f is said to be "causal" because the impulse response function of a physically realisable filter must have this property, as no ef... | Fourier transformation | 0.782469 |
86,576 | The integral for the Fourier transform f ^ ( ξ ) = ∫ − ∞ ∞ e − i 2 π ξ t f ( t ) d t {\displaystyle {\hat {f}}(\xi )=\int _{-\infty }^{\infty }e^{-i2\pi \xi t}f(t)\,dt} can be studied for complex values of its argument ξ. Depending on the properties of f, this might not converge off the real axis at all, or it might co... | Fourier transformation | 0.782469 |
86,577 | This is, from the mathematical point of view, the same as the wave equation of classical physics solved above (but with a complex-valued wave, which makes no difference in the methods). This is of great use in quantum field theory: each separate Fourier component of a wave can be treated as a separate harmonic oscillat... | Fourier transformation | 0.782469 |
86,578 | In relativistic quantum mechanics, Schrödinger's equation becomes a wave equation as was usual in classical physics, except that complex-valued waves are considered. A simple example, in the absence of interactions with other particles or fields, is the free one-dimensional Klein–Gordon–Schrödinger–Fock equation, this ... | Fourier transformation | 0.782469 |
86,579 | Physically realisable states are L2, and so by the Plancherel theorem, their Fourier transforms are also L2. (Note that since q is in units of distance and p is in units of momentum, the presence of Planck's constant in the exponent makes the exponent dimensionless, as it should be.) Therefore, the Fourier transform ca... | Fourier transformation | 0.782469 |
86,580 | The variable p is called the conjugate variable to q. In classical mechanics, the physical state of a particle (existing in one dimension, for simplicity of exposition) would be given by assigning definite values to both p and q simultaneously. Thus, the set of all possible physical states is the two-dimensional real v... | Fourier transformation | 0.782469 |
86,581 | The Palmiet Pumped Storage Scheme consists of two 200 megawatts (270,000 hp) turbine units located 2 kilometres (1.2 mi) upstream of the Kogelberg Dam on the Palmiet River near Cape Town, South Africa. The pumped-storage hydroelectricity plant is capable of responding to a surge in peak power demand in minutes. At nigh... | Palmiet Pumped Storage Scheme | 0.782468 |
86,582 | Recent research in neuroscience has implicated mirror neurons as a neurophysiology basis for social learning, observational learning, motor cognition and social cognition. Mirror neurons have been heavily linked to social learning in humans. Mirror neurons were first discovered in primates in studies which involved tea... | Social learning theory | 0.782468 |
86,583 | Experimental results have demonstrated the effectiveness and efficiency of the social learning algorithm, which has in turn also verified through computer simulations the outcomes of the social learning behavior in human society.Another example is the social cognitive optimization, which is a population-based metaheuri... | Social learning theory | 0.782468 |
86,584 | In modern field of computational intelligence, the social learning theory is adopted to develop a new computer optimization algorithm, the social learning algorithm. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with... | Social learning theory | 0.782468 |
86,585 | In probability theory, the matrix analytic method is a technique to compute the stationary probability distribution of a Markov chain which has a repeating structure (after some point) and a state space which grows unboundedly in no more than one dimension. Such models are often described as M/G/1 type Markov chains be... | Matrix analytic method | 0.782466 |
86,586 | Suppose that g is a completely solvable Lie algebra, and f is an element of the dual g*. A polarization of g at f is a subspace h of maximal dimension subject to the condition that f vanishes on , that is also a subalgebra. The Dixmier map I is defined by letting I(f) be the kernel of the twisted induced representation... | Dixmier mapping | 0.782464 |
86,587 | In mathematics, the Dixmier mapping describes the space Prim(U(g)) of primitive ideals of the universal enveloping algebra U(g) of a finite-dimensional solvable Lie algebra g over an algebraically closed field of characteristic 0 in terms of coadjoint orbits. More precisely, it is a homeomorphism from the space of orbi... | Dixmier mapping | 0.782464 |
86,588 | Organizations that adopted and support the conservation drone project, as well as share information are National Geographic, World Wildlife Fund, Zoo Zurich, Dronemapper, HornbillSurveys, DIYDrones, Philly Zoo, Orangutan Conservancy, Techpod Hobby UAV, Chester Zoo, and 3DRobotics. | Conservation Drones | 0.782464 |
86,589 | y and x: y is a square. The integer right triangle with legs b {\displaystyle b} and y {\displaystyle {\sqrt {y}}} and hypotenuse a {\displaystyle a} would have two sides (b and a) each of which is a square or twice a square, with a smaller hypotenuse than the original triangle ( a {\displaystyle a} compared to z = a 2... | Infinite descent | 0.782464 |
86,590 | The non-solvability of r 2 + s 4 = t 4 {\displaystyle r^{2}+s^{4}=t^{4}} in integers is sufficient to show the non-solvability of q 4 + s 4 = t 4 {\displaystyle q^{4}+s^{4}=t^{4}} in integers, which is a special case of Fermat's Last Theorem, and the historical proofs of the latter proceeded by more broadly proving the... | Infinite descent | 0.782464 |
86,591 | To show that A(Q)/2A(Q) is finite, which is certainly a necessary condition for the finite generation of the group A(Q) of rational points of A, one must do calculations in what later was recognised as Galois cohomology. In this way, abstractly-defined cohomology groups in the theory become identified with descents in ... | Infinite descent | 0.782464 |
86,592 | In the number theory of the twentieth century, the infinite descent method was taken up again, and pushed to a point where it connected with the main thrust of algebraic number theory and the study of L-functions. The structural result of Mordell, that the rational points on an elliptic curve E form a finitely-generate... | Infinite descent | 0.782464 |
86,593 | The thirteenth loaf is called the vantage loaf because it is considered advantageous overall to get 13 loaves for the price of 12.In Arthurian legend, which was recorded in Medieval texts, King Arthur is resting in Avalon with the twelve greatest knights of the Round Table, totalling 13, and will return when his countr... | 13 (number) | 0.782461 |
86,594 | In mathematics, the notion of being compactly embedded expresses the idea that one set or space is "well contained" inside another. There are versions of this concept appropriate to general topology and functional analysis. | Compactly embedded | 0.782461 |
86,595 | Every probability distribution is trivially a maximum entropy probability distribution under the constraint that the distribution has its own entropy. To see this, rewrite the density as p ( x ) = exp ( ln p ( x ) ) {\displaystyle p(x)=\exp {(\ln {p(x)})}} and compare to the expression of the theorem above. By choo... | Maximum entropy probability distribution | 0.782458 |
86,596 | Note that not all classes of distributions contain a maximum entropy distribution. It is possible that a class contain distributions of arbitrarily large entropy (e.g. the class of all continuous distributions on R with mean 0 but arbitrary standard deviation), or that the entropies are bounded above but there is no di... | Maximum entropy probability distribution | 0.782458 |
86,597 | Many statistical distributions of applicable interest are those for which the moments or other measurable quantities are constrained to be constants. The following theorem by Ludwig Boltzmann gives the form of the probability density under these constraints. | Maximum entropy probability distribution | 0.782458 |
86,598 | In the case of equality constraints, this theorem is proved with the calculus of variations and Lagrange multipliers. The constraints can be written as ∫ − ∞ ∞ f j ( x ) p ( x ) d x = a j {\displaystyle \int _{-\infty }^{\infty }f_{j}(x)p(x)dx=a_{j}} We consider the functional J ( p ) = ∫ − ∞ ∞ p ( x ) ln p ( x ) d x... | Maximum entropy probability distribution | 0.782458 |
86,599 | In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions. According to the principle of maximum entropy, if nothing is known about a distribution except that it belongs to a certa... | Maximum entropy probability distribution | 0.782458 |
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