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33,200 | J. Differential Geom. 31 (1990), no. 2, 547–599.1996 Richard S. Hamilton for:The formation of singularities in the Ricci flow. Surveys in differential geometry, Vol. | Oswald Veblen Prize in Geometry | 0.803549 |
33,201 | Journal of Differential Geometry 17 (1982), no. 3, 357–453.1991 Andrew Casson for:his work on the topology of low dimensional manifolds and specifically for the discovery of an integer valued invariant of homology three spheres whose reduction mod(2) is the invariant of Rohlin.1991 Clifford Taubes for:Self-dual Yang-Mi... | Oswald Veblen Prize in Geometry | 0.803549 |
33,202 | of Math. (2) 112 (1980), no. 3, 441–484. (with William Meeks)1986 Michael Freedman for:The topology of four-dimensional manifolds. | Oswald Veblen Prize in Geometry | 0.803549 |
33,203 | 65 (1979), no. 1, 45–76. (with Richard Schoen) Topology of three-dimensional manifolds and the embedding problems in minimal surface theory. Ann. | Oswald Veblen Prize in Geometry | 0.803549 |
33,204 | Math. 30 (1977), no. 1, 41–68. (with Shiu-Yuen Cheng) Calabi's conjecture and some new results in algebraic geometry. | Oswald Veblen Prize in Geometry | 0.803549 |
33,205 | 1964 Christos Papakyriakopoulos 1964 Raoul Bott 1966 Stephen Smale 1966 Morton Brown and Barry Mazur 1971 Robion Kirby 1971 Dennis Sullivan 1976 William Thurston 1976 James Harris Simons 1981 Mikhail Gromov for:Manifolds of negative curvature. Journal of Differential Geometry 13 (1978), no. 2, 223–230. Almost flat mani... | Oswald Veblen Prize in Geometry | 0.803549 |
33,206 | The Oswald Veblen Prize in Geometry is an award granted by the American Mathematical Society for notable research in geometry or topology. It was funded in 1961 in memory of Oswald Veblen and first issued in 1964. The Veblen Prize is now worth US$5000, and is awarded every three years. | Oswald Veblen Prize in Geometry | 0.803549 |
33,207 | The first seven prize winners were awarded for works in topology. James Harris Simons and William Thurston were the first ones to receive it for works in geometry (for some distinctions, see geometry and topology). As of 2020, there have been thirty-four prize recipients. | Oswald Veblen Prize in Geometry | 0.803549 |
33,208 | Some examples of orders are: If A {\displaystyle A} is the matrix ring M n ( K ) {\displaystyle M_{n}(K)} over K {\displaystyle K} , then the matrix ring M n ( R ) {\displaystyle M_{n}(R)} over R {\displaystyle R} is an R {\displaystyle R} -order in A {\displaystyle A} If R {\displaystyle R} is an integral domain and L... | Order (ring theory) | 0.803544 |
33,209 | In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that A {\displaystyle A} is a finite-dimensional algebra over the field Q {\displaystyle \mathbb {Q} } of rational numbers O {\displaystyle {\mathcal {O}}} spans A {\displaystyle A} ov... | Order (ring theory) | 0.803544 |
33,210 | The Sommerfeld model predicted that the magnetic moment of an atom measured along an axis will only take on discrete values, a result which seems to contradict rotational invariance but which was confirmed by the Stern–Gerlach experiment. This was a significant step in the development of quantum mechanics. It also desc... | Bohr-Sommerfeld model | 0.803542 |
33,211 | For example, up to first-order perturbations, the Bohr model and quantum mechanics make the same predictions for the spectral line splitting in the Stark effect. At higher-order perturbations, however, the Bohr model and quantum mechanics differ, and measurements of the Stark effect under high field strengths helped co... | Bohr-Sommerfeld model | 0.803542 |
33,212 | {\displaystyle \;\rho '=\sum _{i}P_{i}\rho P_{i}.} If one assumes that the probabilities of measurement outcomes are linear functions of the projectors P i {\displaystyle P_{i}} , then they must be given by the trace of the projector with a density operator. Gleason's theorem shows that in Hilbert spaces of dimension 3... | Density Matrix | 0.803536 |
33,213 | Density matrices are a basic tool of quantum mechanics, and appear at least occasionally in almost any type of quantum-mechanical calculation. Some specific examples where density matrices are especially helpful and common are as follows: Statistical mechanics uses density matrices, most prominently to express the idea... | Density Matrix | 0.803536 |
33,214 | Most ICR software has a self-learning system referred to as a neural network, which automatically updates the recognition database for new handwriting patterns. It extends the usefulness of scanning devices for the purpose of document processing, from printed character recognition (a function of OCR) to hand-written ma... | Intelligent Character Recognition | 0.803531 |
33,215 | Beginning with the pilot episode "Encounter at Farpoint" of The Next Generation, Q became a recurring character, with pronounced comedic and dramatic chemistry with Jean-Luc Picard. He serves as a major antagonist throughout The Next Generation, playing a pivotal role in both the first and final episodes. Q is initiall... | Q Continuum | 0.80353 |
33,216 | Q is a fictional character, as well as the name of a race, in Star Trek appearing in the Next Generation, Deep Space Nine, Voyager, Lower Decks, and Picard series and in related media. The most familiar Q is portrayed by John de Lancie. He is an extra-dimensional being of unknown origin who possesses immeasurable power... | Q Continuum | 0.80353 |
33,217 | Research and education in chemistry has been conducted at the department since 1778, when the first Laboratorium Chymicum was established. Since then, the chemists have moved several times. In 1962, Universitetets Kemiske Laboratorium moved to its present location in the H.C. Ørsted Institute (HCØ), named after Hans Ch... | UCPH Department of Chemistry | 0.80353 |
33,218 | The Department of Chemistry (Danish: Kemisk Institut) is a department under the Faculty of Science, University of Copenhagen. It is the largest basic research institute in chemistry in Denmark, and is responsible for the teaching of chemistry at all levels at the University of Copenhagen's Faculty of Science: from unde... | UCPH Department of Chemistry | 0.80353 |
33,219 | In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms. | Congruence of squares | 0.803527 |
33,220 | A naive divide-and-conquer approach to computing the linearization of a class may invoke the algorithm recursively to find the linearizations of parent classes for the merge-subroutine. However, this will result in an infinitely looping recursion in the presence of a cyclic class hierarchy. To detect such a cycle and t... | C3 linearization | 0.803527 |
33,221 | In contemporary usage, the term radical refers to various free radicals, which are species that have an unpaired electron and need not be charged.A simple example of a polyatomic ion is the hydroxide ion, which consists of one oxygen atom and one hydrogen atom, jointly carrying a net charge of −1; its chemical formula ... | Polyatomic ion | 0.803525 |
33,222 | In the measure-theoretic formalization of probability theory, a random variable is defined as a measurable function X {\displaystyle X} from a probability space ( Ω , F , P ) {\displaystyle (\Omega ,{\mathcal {F}},\mathbb {P} )} to a measurable space ( X , A ) {\displaystyle ({\mathcal {X}},{\mathcal {A}})} . Given tha... | Continuous random variable | 0.803524 |
33,223 | The Birth and Death of the Sun is a popular science book by theoretical physicist and cosmologist George Gamow, first published in 1940, exploring atomic chemistry, stellar evolution, and cosmology. The book is illustrated by Gamow. It was revised in 1952. | The Birth and Death of the Sun | 0.803524 |
33,224 | Critical reception has been positive. In February 1941, Gerard F. W. Mulders gave a favorable review for The Birth and Death of the Sun, writing that "t gives authentic information in nontechnical language from which mathematical formulae have been completely eliminated. The entertaining presentation of the most modern... | The Birth and Death of the Sun | 0.803524 |
33,225 | With this condition, a stable matching will still exist, and can still be found by the Gale–Shapley algorithm. For this kind of stable matching problem, the rural hospitals theorem states that: The set of assigned doctors, and the number of filled positions in each hospital, are the same in all stable matchings. Any ho... | Stable marriage problem | 0.803524 |
33,226 | The rural hospitals theorem concerns a more general variant of the stable matching problem, like that applying in the problem of matching doctors to positions at hospitals, differing in the following ways from the basic n-to-n form of the stable marriage problem: Each participant may only be willing to be matched to a ... | Stable marriage problem | 0.803524 |
33,227 | In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the eleme... | Stable marriage problem | 0.803524 |
33,228 | In fact, Shannon's proof of the capacity theorem for q-ary symmetric channels can be viewed in light of the above claim for random codes. Under the mandate of list-decoding, for worst-case errors, the decoder is allowed to output a small list of codewords. With some context specific or side information, it may be possi... | List decoding | 0.803521 |
33,229 | Theorem (List-Decoding Capacity). Let q ⩾ 2 , 0 ⩽ p ⩽ 1 − 1 q {\displaystyle q\geqslant 2,0\leqslant p\leqslant 1-{\tfrac {1}{q}}} and ϵ ⩾ 0. {\displaystyle \epsilon \geqslant 0.} The following two statements hold for large enough block length n {\displaystyle n} . | List decoding | 0.803521 |
33,230 | Algorithms developed for list decoding of several interesting code families have found interesting applications in computational complexity and the field of cryptography. Following is a sample list of applications outside of coding theory: Construction of hard-core predicates from one-way permutations. Predicting witne... | List decoding | 0.803521 |
33,231 | This work has been invited to the Research Highlights section of the Communications of the ACM (which is “devoted to the most important research results published in Computer Science in recent years”) and was mentioned in an article titled “Coding and Computing Join Forces” in the Sep 21, 2007 issue of the Science maga... | List decoding | 0.803521 |
33,232 | Activities in education: Colloquium series Workshop NanoDay: a one-day workshop, which shows the broad spectrum of nanotechnology of the LNQE with talks and a poster session. This annual event takes place since 2005. Study course nanotechnology: bachelor course and master course at the Leibniz University Hannover. PhD-... | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,233 | The Laboratory of Nano and Quantum Engineering (LNQE) is an interdisciplinary research center of the Leibniz Universität Hannover in the field of nanotechnology. Substantive goals are both excellent basic research as well as application-oriented engineering at the nanoscale accompanied by appropriate cross-disciplinary... | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,234 | The Laboratory of Nano and Quantum Engineering (LNQE) is an interdisciplinary research center for nanotechnology of the Leibniz University Hannover in Germany. | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,235 | The LNQE comprises currently 34 research groups from physics, chemistry and engineering of the Leibniz University Hannover. It is led at least by an executive board of four members which nominate a speaker from their middle. The executive board is supported by the LNQE-Office. Location overview of the participating mem... | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,236 | To continue with the proof sketch, we conjure the union bound in probability theory which tells us that the probability of a bad event happening for a given ( y , m 0 , … , m L ) {\displaystyle (y,m_{0},\dots ,m_{L})} is upper bounded by the quantity q − n ( L + 1 ) ( 1 − H q ( p ) ) {\displaystyle q^{-n(L+1)(1-H_{q}(p... | List decoding | 0.803521 |
33,237 | Nanotechnology is the technology of small things with new features and functionalities. Nano engineering is the engineering on the nanoscale, i.e., the selective artificial fabrication of nanotechnology structures such as tiny transistors on computer chips. With nano engineering the closely related term quantum enginee... | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,238 | The collective term nanotechnology describes the study and manipulation of objects at smallest sizes. In general, the nanotechnology deals with structures ranging in size from 1-100 nanometers in at least one spatial direction. 100 nanometers are roughly one-thousandth of the diameter of a normal human hair. With these... | Laboratory of Nano and Quantum Engineering | 0.803521 |
33,239 | (From DDC 23) 000 – Computer science, information and general works 100 – Philosophy and psychology 200 – Religion 300 – Social sciences 400 – Language 500 – Pure science 600 – Technology 700 – Arts and recreation 800 – Literature 900 – History and geography | Dewey Decimal System | 0.803521 |
33,240 | Libraries not needing the full level of detail of the classification can trim right-most decimal digits from the class number to obtain more general classifications. For example: 500 Natural sciences and mathematics 510 Mathematics 516 Geometry 516.3 Analytic geometries 516.37 Metric differential geometries 516.375 Fin... | Dewey Decimal System | 0.803521 |
33,241 | The Lisp programming language has survived since 1958 as a primary language for Artificial Intelligence research. This text was published in 1992 as the Common Lisp standard was becoming widely adopted. Norvig introduces Lisp programming in the context of classic AI programs, including General Problem Solver (GPS) from... | Paradigms of AI Programming | 0.80352 |
33,242 | Paradigms of AI Programming: Case Studies in Common Lisp (ISBN 1-55860-191-0) is a well-known programming book by Peter Norvig about artificial intelligence programming using Common Lisp. | Paradigms of AI Programming | 0.80352 |
33,243 | This distortion acts to force a maximum number of electrons into the internuclear (bond axis) region, helping to efficiently bind the nuclei together. The presence of any additional nearby nuclei can partially relax the influence of correlation effects on the electronic geometry. Therefore, it is possible for two elect... | Linnett Double-Quartet Theory | 0.80352 |
33,244 | In chemical bonding, the presence of additional nuclei causes the electrons to seek to maximise their attractive electrostatic interactions with all nearby nuclei. This can result in the formation of coincident or ‘close-paired’ electron pairs, in accordance with Lewis’ bonding model. Thus, it has previously been argue... | Linnett Double-Quartet Theory | 0.80352 |
33,245 | Hence, unlike the Lewis model which predicts four lone pairs, all electrons in the fluoride ion are spatially separated. Therefore, the following statement by Luder is found to be true for all mononuclear species:“In an isolated atom, no valence electron is close-paired with another”. If a proton then approaches the fl... | Linnett Double-Quartet Theory | 0.80352 |
33,246 | Each quartet consists of electrons of one spin only, and these electrons can act and orient themselves independently. One can then obtain molecular structures by arranging the electrons in such a way as to maximise the separations between the electrons, hence minimising the mutual inter-electronic repulsions, while sim... | Linnett Double-Quartet Theory | 0.80352 |
33,247 | Most strikingly, the molecule changes its geometry upon excitation, going from a simple linear symmetry to a trans-bent structure. This is in excellent agreement with both the landmark results of Ingold and King, which were the first demonstration of an excited state having a qualitatively different geometry than the g... | Linnett Double-Quartet Theory | 0.80352 |
33,248 | This is in contrast with the Lewis structure which would place the fluorine lone pair electrons into discrete coincident pairs. Further, the lone pairs of electrons associated with the central chlorine atom reside in two kidney-shaped lobes which lie in the equatorial plane along with one of the fluorine atoms. This st... | Linnett Double-Quartet Theory | 0.80352 |
33,249 | However, the unavoidability part of the proof was verified in over 400 pages of microfiche, which had to be checked by hand with the assistance of Haken's daughter Dorothea Blostein (Appel & Haken 1989). Appel and Haken's announcement was widely reported by the news media around the world, and the math department at th... | Four Color Theorem | 0.803518 |
33,250 | Both the unavoidability and reducibility parts of this new proof must be executed by a computer and are impractical to check by hand. In 2001, the same authors announced an alternative proof, by proving the snark conjecture. This proof remains unpublished, however. In 2005, Benjamin Werner and Georges Gonthier formaliz... | Four Color Theorem | 0.803518 |
33,251 | Since the proving of the theorem, a new approach has led to both a shorter proof and a more efficient algorithm for 4-coloring maps. In 1996, Neil Robertson, Daniel P. Sanders, Paul Seymour, and Robin Thomas created a quadratic-time algorithm (requiring only O(n2) time, where n is the number of vertices), improving on ... | Four Color Theorem | 0.803518 |
33,252 | GDDR5X — new memory standard supporting 10Gbit/s data rates, updated memory controller. Simultaneous Multi-Projection - generating multiple projections of a single geometry stream, as it enters the SMP engine from upstream shader stages. | Pascal microarchitecture | 0.803518 |
33,253 | GP100: Nvidia Tesla P100 GPU accelerator is targeted at GPGPU applications such as FP64 double precision compute and deep learning training that uses FP16. It uses HBM2 memory. Quadro GP100 also uses the GP100 GPU. GP102: This GPU is used in the TITAN Xp, Titan X and the GeForce GTX 1080 Ti. | Pascal microarchitecture | 0.803518 |
33,254 | While all CU versions consist of 64 shader processors (i.e. 4 SIMD Vector Units (each 16-lane wide)= 64), Nvidia (regularly calling shader processors "CUDA cores") experimented with very different numbers: On Tesla 1 SM combines 8 single-precision (FP32) shader processors On Fermi 1 SM combines 32 single-precision (FP3... | Pascal microarchitecture | 0.803518 |
33,255 | Perhaps one effect underlying this common misconception is the fact that the color restriction is not transitive: a region only has to be colored differently from regions it touches directly, not regions touching regions that it touches. If this were the restriction, planar graphs would require arbitrarily large number... | Four Color Theorem | 0.803518 |
33,256 | Because the four color theorem is true, this is always possible; however, because the person drawing the map is focused on the one large region, they fail to notice that the remaining regions can in fact be colored with three colors. This trick can be generalized: there are many maps where if the colors of some regions... | Four Color Theorem | 0.803518 |
33,257 | The four color theorem has been notorious for attracting a large number of false proofs and disproofs in its long history. At first, The New York Times refused, as a matter of policy, to report on the Appel–Haken proof, fearing that the proof would be shown false like the ones before it. Some alleged proofs, like Kempe... | Four Color Theorem | 0.803518 |
33,258 | While other teams of mathematicians were racing to complete proofs, Kenneth Appel and Wolfgang Haken at the University of Illinois announced, on June 21, 1976, that they had proved the theorem. They were assisted in some algorithmic work by John A. Koch.If the four-color conjecture were false, there would be at least o... | Four Color Theorem | 0.803518 |
33,259 | During the 1960s and 1970s, German mathematician Heinrich Heesch developed methods of using computers to search for a proof. Notably he was the first to use discharging for proving the theorem, which turned out to be important in the unavoidability portion of the subsequent Appel–Haken proof. He also expanded on the co... | Four Color Theorem | 0.803518 |
33,260 | A set is declared to be Π α 0 {\displaystyle \mathbf {\Pi } _{\alpha }^{0}} if and only if its complement is Σ α 0 {\displaystyle \mathbf {\Sigma } _{\alpha }^{0}} . A set A is declared to be Σ δ 0 {\displaystyle \mathbf {\Sigma } _{\delta }^{0}} , δ > 1, if there is a sequence ⟨ Ai ⟩ of sets, each of which is Π λ ( i ... | Descriptive set theory | 0.803518 |
33,261 | The class of Borel sets of a topological space X consists of all sets in the smallest σ-algebra containing the open sets of X. This means that the Borel sets of X are the smallest collection of sets such that: Every open subset of X is a Borel set. If A is a Borel set, so is X ∖ A {\displaystyle X\setminus A} . That is... | Descriptive set theory | 0.803518 |
33,262 | In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces. As well as being one of the primary areas of research in set theory, it has applications to other areas of mathematics such as functional analysis, ergodic theory, the ... | Descriptive set theory | 0.803518 |
33,263 | The concept of a nanocar built out of molecular "tinkertoys" was first hypothesized by M.T. Michalewicz at the Fifth Foresight Conference on Molecular Nanotechnology (November 1997). Subsequently, an expanded version was published in Annals of Improbable Research. These papers were supposed to be a not-so-serious contr... | Molecular car | 0.803517 |
33,264 | Many multi-layer artificial neural networks are fully connected, receiving input from every neuron in the previous layer and signalling every neuron in the subsequent layer. Although these networks have achieved breakthroughs in many fields, they are biologically inaccurate and do not mimic the operation mechanism of n... | Spiking neural networks | 0.803516 |
33,265 | In chemistry, a phosphaalkyne (IUPAC name: alkylidynephosphane) is an organophosphorus compound containing a triple bond between phosphorus and carbon with the general formula R-C≡P. Phosphaalkynes are the heavier congeners of nitriles, though, due to the similar electronegativities of phosphorus and carbon, possess re... | Phosphaalkyne | 0.803516 |
33,266 | Dihalophospaalkenes of the general form R-P=CX2, where X is Cl, Br, or I undergo lithium-halogen exchange with organolithium reagents to yield intermediates of the form R-P=CXLi. These species then eject the corresponding lithium halide salt, LiX, to putatively give a phospha-isocyanide, which can rearrange, much in th... | Phosphaalkyne | 0.803516 |
33,267 | Phosphaalkynes with small substituents (H, F, Me, Ph, etc.) undergo decomposition at or below room temperature by way of polymerization/oligimerization to yield mixtures of products which are challenging to characterize. The same is largely true of kinetically stable phosphaalkynes, which undergo oligomerization reacti... | Phosphaalkyne | 0.803516 |
33,268 | One of the most developed areas of phosphaalkyne chemistry is that of cycloadditions. Like other multiply bonded molecular fragments, phosphaalkynes undergo myriad reactions such as cycloadditions, cycloadditions, and cycloadditions. This reactivity is summarized in graphical format below, which includes some exampl... | Phosphaalkyne | 0.803516 |
33,269 | Consider an ensemble of molecules absorbing radiation in the UV/vis. Initially, all molecules are in the ground electronic state Because of the molecular zero-point energy and temperature, the molecular geometry has a distribution around the equilibrium geometry. From a classical point of view, supposing that the photo... | Nuclear ensemble approach | 0.803513 |
33,270 | The spectrum simulation requires the calculation of transition probabilities for hundreds of different nuclear geometries, which may become prohibitive due to the high computational costs. Machine learning methods coupled to NEA have been proposed to reduce these costs. == References == | Nuclear ensemble approach | 0.803513 |
33,271 | Spectrum simulation is one of the most fundamental tasks in quantum chemistry. It allows comparing the theoretical results to experimental measurements. There are many theoretical methods for simulating spectra. Some are simple approximations (like stick spectra); others are high-level, accurate approximations (like th... | Nuclear ensemble approach | 0.803513 |
33,272 | Phase Contrast imaging is commonly used in atomic physics to describe a range of techniques for dispersively imaging Ultracold atoms. Dispersion is the phenomena of the propagation of electromagnetic fields (light) in matter. In general, the Refractive index of a material, which alters the Phase velocity and Refraction... | Phase contrast | 0.803512 |
33,273 | The DOS-BIOS or System BIOS would then combine multiple physical sectors into logical sectors for the file system to work with. These changes were transparent to the file system implementation in the DOS kernel. The underlying DOS-BIOS translated these logical sectors into physical sectors according to partitioning inf... | FAT file system | 0.803511 |
33,274 | The Java memory model describes how threads in the Java programming language interact through memory. On modern platforms, code is frequently not executed in the order it was written. It is reordered by the compiler, the processor and the memory subsystem to achieve maximum performance. The Java programming language do... | Java concurrency | 0.80351 |
33,275 | Since the 1980s, molecular biology and bioinformatics have created the need for DNA annotation. DNA annotation or genome annotation is the process of identifying the locations of genes and all of the coding regions in a genome and determining what those genes do. An annotation (irrespective of the context) is a note ad... | Semantic annotation | 0.80351 |
33,276 | There are several semantic labelling types which utilises machine learning techniques. These techniques can be categorised following the work of Flach as follows: geometric (using lines and planes, such as Support-vector machine, Linear regression), probabilistic (e.g., Conditional random field), logical (e.g., Decisio... | Semantic annotation | 0.80351 |
33,277 | Vavilov's Journal of Genetics and Breeders Ateroskleroz The Siberian Scientific Medical Journal | Institute of Cytology and Genetics | 0.803509 |
33,278 | Institute of Cytology and Genetics of the Siberian Branch of the Russian Academy of Sciences (Russian: Институт цитологии и генетики СО РАН) is a research institute based in Novosibirsk, Russia. It was founded in 1957. | Institute of Cytology and Genetics | 0.803509 |
33,279 | This process, called query optimization, depended on the fact that queries were expressed in terms of mathematical logic. Codd's paper was picked up by two people at Berkeley, Eugene Wong and Michael Stonebraker. They started a project known as INGRES using funding that had already been allocated for a geographical dat... | Database programming | 0.803509 |
33,280 | As well as identifying rows/records using logical identifiers rather than disk addresses, Codd changed the way in which applications assembled data from multiple records. Rather than requiring applications to gather data one record at a time by navigating the links, they would use a declarative query language that expr... | Database programming | 0.803509 |
33,281 | But Codd was more interested in the difference in semantics: the use of explicit identifiers made it easier to define update operations with clean mathematical definitions, and it also enabled query operations to be defined in terms of the established discipline of first-order predicate calculus; because these operatio... | Database programming | 0.803509 |
33,282 | Each table would contain a fixed number of columns containing the attributes of the entity. One or more columns of each table were designated as a primary key by which the rows of the table could be uniquely identified; cross-references between tables always used these primary keys, rather than disk addresses, and quer... | Database programming | 0.803509 |
33,283 | A database management system provides three views of the database data: The external level defines how each group of end-users sees the organization of data in the database. A single database can have any number of views at the external level. The conceptual level (or logical level) unifies the various external views i... | Database programming | 0.803509 |
33,284 | A holomorphic elliptic function is constant.This is the original form of Liouville's theorem and can be derived from it. A holomorphic elliptic function is bounded since it takes on all of its values on the fundamental domain which is compact. So it is constant by Liouville's theorem. | Doubly periodic | 0.803509 |
33,285 | Every elliptic function has finitely many poles in C / Λ {\displaystyle \mathbb {C} /\Lambda } and the sum of its residues is zero.This theorem implies that there is no elliptic function not equal to zero with exactly one pole of order one or exactly one zero of order one in the fundamental domain. | Doubly periodic | 0.803509 |
33,286 | In physics, the strong confinement limit, or "festina lente" limit, is a mode of an atom laser in which the frequency of emission of the Bose–Einstein condensate is less than the confinement frequency of the trap. == References == | Strong confinement limit | 0.803507 |
33,287 | Some definitions or results about relative consistency hold only in special cases. When the domains are composed of integers, bound consistency can be defined. This form of consistency is based on the consistency of the extreme values of the domains, that is, the minimum and maximum values a variable can take. When con... | Local consistency | 0.803507 |
33,288 | It was not until the 18th century, over 2000 years after Euclid, that Leonhard Euler proved that the formula 2p−1(2p − 1) will yield all the even perfect numbers. Thus, there is a one-to-one relationship between even perfect numbers and Mersenne primes; each Mersenne prime generates one even perfect number, and vice ve... | Euclid-Euler theorem | 0.803506 |
33,289 | Euclid proved that 2p−1(2p − 1) is an even perfect number whenever 2p − 1 is prime. This is the final result on number theory in Euclid's Elements; the later books in the Elements instead concern irrational numbers, solid geometry, and the golden ratio. Euclid expresses the result by stating that if a finite geometric ... | Euclid-Euler theorem | 0.803506 |
33,290 | For a number of this form to be prime, p itself must also be prime, but not all primes give rise to Mersenne primes in this way. For instance, 23 − 1 = 7 is a Mersenne prime, but 211 − 1 = 2047 = 23 × 89 is not. The Euclid–Euler theorem states that an even natural number is perfect if and only if it has the form 2p−1Mp... | Euclid-Euler theorem | 0.803506 |
33,291 | It has been conjectured that there are infinitely many Mersenne primes. Although the truth of this conjecture remains unknown, it is equivalent, by the Euclid–Euler theorem, to the conjecture that there are infinitely many even perfect numbers. However, it is also unknown whether there exists even a single odd perfect ... | Euclid-Euler theorem | 0.803506 |
33,292 | The Euclid–Euler theorem is a theorem in number theory that relates perfect numbers to Mersenne primes. It states that an even number is perfect if and only if it has the form 2p−1(2p − 1), where 2p − 1 is a prime number. The theorem is named after mathematicians Euclid and Leonhard Euler, who respectively proved the "... | Euclid-Euler theorem | 0.803506 |
33,293 | One direction of the theorem (the part already proved by Euclid) immediately follows from the multiplicative property: every Mersenne prime gives rise to an even perfect number. When 2p − 1 is prime, σ ( 2 p − 1 ( 2 p − 1 ) ) = σ ( 2 p − 1 ) σ ( 2 p − 1 ) . {\displaystyle \sigma (2^{p-1}(2^{p}-1))=\sigma (2^{p-1})\sigm... | Euclid-Euler theorem | 0.803506 |
33,294 | Its main purpose is to clarify the properties of matter in aggregate, in terms of physical laws governing atomic motion.Statistical mechanics arose out of the development of classical thermodynamics, a field for which it was successful in explaining macroscopic physical properties—such as temperature, pressure, and hea... | Fundamental assumption of statistical mechanics | 0.803504 |
33,295 | In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Sometimes called stati... | Fundamental assumption of statistical mechanics | 0.803504 |
33,296 | Phosphorus is an essential plant nutrient (the most often limiting nutrient, after nitrogen), and the bulk of all phosphorus production is in concentrated phosphoric acids for agriculture fertilisers, containing as much as 70% to 75% P2O5. That led to large increase in phosphate (PO43−) production in the second half of... | Phosphorus | 0.803503 |
33,297 | In geology, the term sedimentation is broadly applied to the entire range of processes that result in the formation of sedimentary rock, from initial formation of sediments by erosion of particles from rock outcrops, through sediment transport and settling, to the lithification of the sediments. However, the term is mo... | Sedimentation | 0.803502 |
33,298 | In geology, sedimentation is the deposition of sediments which results in the formation of sedimentary rock. The term is broadly applied to the entire range of processes that result in the formation of sedimentary rock, from initial erosion through sediment transport and settling to the lithification of the sediments. | Sedimentation | 0.803502 |
33,299 | In chemistry, sedimentation has been used to measure the size of large molecules (macromolecule), where the force of gravity is augmented with centrifugal force in an ultracentrifuge. | Sedimentation | 0.803502 |
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