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27,000 | By total antisymmetry of the quartic element, it can be considered to be a volume form. In fact, this observation extends to a discussion of Clifford algebras as a generalization of the exterior algebra: both arise as quotients of the tensor algebra, but the exterior algebra gives a more restrictive quotient, where the... | Dirac algebra | 0.806866 |
27,001 | Proponents of geometric algebra strive to work with real algebras wherever that is possible. They argue that it is generally possible (and usually enlightening) to identify the presence of an imaginary unit in a physical equation. Such units arise from one of the many quantities in a real Clifford algebra that square t... | Dirac algebra | 0.806866 |
27,002 | The Dirac algebra can be regarded as a complexification of the real spacetime algebra Cℓ1,3( R {\displaystyle \mathbb {R} } ): C ℓ 1 , 3 ( C ) = C ℓ 1 , 3 ( R ) ⊗ C . {\displaystyle \mathrm {C\ell } _{1,3}(\mathbb {C} )=\mathrm {C\ell } _{1,3}(\mathbb {R} )\otimes \mathbb {C} .} Cℓ1,3( R {\displaystyle \mathbb {R} } ) ... | Dirac algebra | 0.806866 |
27,003 | The exponential map for matrices is well defined. The S μ ν {\displaystyle S^{\mu \nu }} satisfy the Lorentz algebra, and turn out to exponentiate to a representation of the spin group Spin ( 1 , 3 ) {\displaystyle {\text{Spin}}(1,3)} of the Lorentz group SO ( 1 , 3 ) {\displaystyle {\text{SO}}(1,3)} (strictly, the fut... | Dirac algebra | 0.806866 |
27,004 | Insofar as the presentation of charge and parity can be a confusing topic in conventional quantum field theory textbooks, the more careful dissection of these topics in a general geometric setting can be elucidating. Standard expositions of the Clifford algebra construct the Weyl spinors from first principles; that the... | Dirac algebra | 0.806866 |
27,005 | Some of these proponents also question whether it is necessary or even useful to introduce an additional imaginary unit in the context of the Dirac equation. In the mathematics of Riemannian geometry, it is conventional to define the Clifford algebra Cℓp,q( R {\displaystyle \mathbb {R} } ) for arbitrary dimensions p,q;... | Dirac algebra | 0.806866 |
27,006 | There is another way to write this which holds even when μ = ν {\displaystyle \mu =\nu }: S μ ν = 1 2 ( γ μ γ ν − η μ ν ) . {\displaystyle S^{\mu \nu }={\frac {1}{2}}(\gamma ^{\mu }\gamma ^{\nu }-\eta ^{\mu \nu }).} This form can be used to show that the S μ ν {\displaystyle S^{\mu \nu }} form a representation of the L... | Dirac algebra | 0.806866 |
27,007 | For the theory in this section, there are many choices of conventions found in the literature, often corresponding to factors of ± i {\displaystyle \pm i} . For clarity, here we will choose conventions to minimise the number of numerical factors needed, but may lead to generators being anti-Hermitian rather than Hermit... | Dirac algebra | 0.806866 |
27,008 | The algebra can be generated by taking products of the γ μ {\displaystyle \gamma ^{\mu }} alone: the identity arises as I 4 = ( γ 0 ) 2 {\displaystyle I_{4}=(\gamma ^{0})^{2}} while the others are explicitly products of the γ μ {\displaystyle \gamma ^{\mu }} . These elements span the space generated by γ μ {\displaysty... | Dirac algebra | 0.806866 |
27,009 | The algebra has a basis I 4 , {\displaystyle I_{4},} γ μ , {\displaystyle \gamma ^{\mu },} γ μ γ ν , {\displaystyle \gamma ^{\mu }\gamma ^{\nu },} γ μ γ ν γ ρ , {\displaystyle \gamma ^{\mu }\gamma ^{\nu }\gamma ^{\rho },} γ μ γ ν γ ρ γ σ = γ 0 γ 1 γ 2 γ 3 {\displaystyle \gamma ^{\mu }\gamma ^{\nu }\gamma ^{\rho }\gamma... | Dirac algebra | 0.806866 |
27,010 | It is common convention in physics to include a factor of ± i {\displaystyle \pm i} , so that Hermitian conjugation (where transposing is done with respect to the spacetime greek indices) gives a 'Hermitian matrix' of sigma generators only 6 of which are non-zero due to antisymmetry of the bracket, span the six-dimensi... | Dirac algebra | 0.806866 |
27,011 | For this article we fix the signature to be mostly minus, that is, ( + , − , − , − ) {\displaystyle (+,-,-,-)} . The Dirac algebra is then the linear span of the identity, the gamma matrices γ μ {\displaystyle \gamma ^{\mu }} as well as any linearly independent products of the gamma matrices. This forms a finite-dimens... | Dirac algebra | 0.806866 |
27,012 | In mathematical physics, the Dirac algebra is the Clifford algebra Cl 1 , 3 ( C ) {\displaystyle {\text{Cl}}_{1,3}(\mathbb {C} )} . This was introduced by the mathematical physicist P. A. M. Dirac in 1928 in developing the Dirac equation for spin-½ particles with a matrix representation of the gamma matrices, which rep... | Dirac algebra | 0.806866 |
27,013 | Finally, active learning presumes the oracle is either free or charges uniform cost in label elicitation. Such an assumption is naive since cost is likely to be regulated by difficulty (amount of work required to formulate an answer) or other factors. "Proactive learning relaxes all four of these assumptions, relying o... | Proactive learning | 0.806865 |
27,014 | It is independent of the surface material and is weakly dependent upon the heated surface geometry described by the constant C. For large horizontal cylinders, spheres and large finite heated surfaces, the value of the Zuber constant C = π 24 ≈ 0.131 {\displaystyle C={\frac {\pi }{24}}\approx 0.131} . For large horizon... | Critical heat flux | 0.80686 |
27,015 | So, all sets in this metric space are clopen. As a less trivial example, consider the space Q {\displaystyle \mathbb {Q} } of all rational numbers with their ordinary topology, and the set A {\displaystyle A} of all positive rational numbers whose square is bigger than 2. Using the fact that 2 {\displaystyle {\sqrt {2}... | Clopen sets | 0.806856 |
27,016 | In any topological space X , {\displaystyle X,} the empty set and the whole space X {\displaystyle X} are both clopen.Now consider the space X {\displaystyle X} which consists of the union of the two open intervals ( 0 , 1 ) {\displaystyle (0,1)} and ( 2 , 3 ) {\displaystyle (2,3)} of R . {\displaystyle \mathbb {R} .} ... | Clopen sets | 0.806856 |
27,017 | A topological space X {\displaystyle X} is discrete if and only if all of its subsets are clopen. Using the union and intersection as operations, the clopen subsets of a given topological space X {\displaystyle X} form a Boolean algebra. Every Boolean algebra can be obtained in this way from a suitable topological spac... | Clopen sets | 0.806856 |
27,018 | In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible may seem counter-intuitive, as the common meanings of open and closed are antonyms, but their mathematical definitions are not mutually exclusive. A set is closed if its comp... | Clopen sets | 0.806856 |
27,019 | It has been formalized further by R.-J. Back and others in the refinement calculus. Some tools like B-Method now provide automated reasoning in order to promote this methodology. In the meta-theory of Hoare logic, weakest-preconditions appear as a key notion in the proof of relative completeness. | Predicate transformer semantics | 0.806854 |
27,020 | Computations of weakest-preconditions are largely used to statically check assertions in programs using a theorem-prover (like SMT-solvers or proof assistants): see Frama-C or ESC/Java2. Unlike many other semantic formalisms, predicate transformer semantics was not designed as an investigation into foundations of compu... | Predicate transformer semantics | 0.806854 |
27,021 | Sodium amide is mainly used as a strong base in organic chemistry, often in liquid ammonia solution. It is the reagent of choice for the drying of ammonia (liquid or gaseous). One of the main advantages to the use of sodium amide is its relatively low nucleophilicity. In the industrial production of indigo, sodium amid... | Sodium amide | 0.806854 |
27,022 | 2 Na + 2 NH3 → 2 NaNH2 + H2NaNH2 is a salt-like material and as such, crystallizes as an infinite polymer. The geometry about sodium is tetrahedral. In ammonia, NaNH2 forms conductive solutions, consistent with the presence of + and NH−2 ions. | Sodium amide | 0.806854 |
27,023 | Refinement calculus extends GCL with the notion of specification statement. Syntactically, we prefer to write a specification statement as x: l {\displaystyle x:l} which specifies a computation that starts in a state satisfying pre and is guaranteed to end in a state satisfying post by changing only x. We call l {\dis... | Predicate transformer semantics | 0.806854 |
27,024 | At first glance one might think of them as differing simply in the size of objects that they describe, classical objects being considered far larger as to mass and geometrical size than quantal objects, for example a football versus a fine particle of dust. More refined consideration distinguishes classical and quantum... | Macroscopic scale | 0.806853 |
27,025 | An example of a physical theory that takes a deliberately macroscopic viewpoint is thermodynamics. An example of a topic that extends from macroscopic to microscopic viewpoints is histology. Not quite by the distinction between macroscopic and microscopic, classical and quantum mechanics are theories that are distingui... | Macroscopic scale | 0.806853 |
27,026 | When applied to physical phenomena and bodies, the macroscopic scale describes things as a person can directly perceive them, without the aid of magnifying devices. This is in contrast to observations (microscopy) or theories (microphysics, statistical physics) of objects of geometric lengths smaller than perhaps some ... | Macroscopic scale | 0.806853 |
27,027 | In many ways, classical mechanics can be considered a mainly macroscopic theory. On the much smaller scale of atoms and molecules, classical mechanics may fail, and the interactions of particles are then described by quantum mechanics. Near the absolute minimum of temperature, the Bose–Einstein condensate exhibits effe... | Macroscopic scale | 0.806853 |
27,028 | The proton has a mass–energy of ~ 9.4×108 eV; some other massive quantum particles, both elementary and hadronic, have yet higher mass–energies. Quantum particles with lower mass–energies are also part of high energy physics; they also have a mass–energy that is far higher than that at the macroscopic scale (such as el... | Macroscopic scale | 0.806853 |
27,029 | Even photons with far higher energy, gamma rays of the kind produced in radioactive decay, have photon energy that is almost always between 105 eV and 107 eV – still two orders of magnitude lower than the mass–energy of a single proton. Radioactive decay gamma rays are considered as part of nuclear physics, rather than... | Macroscopic scale | 0.806853 |
27,030 | While macroscopic systems indeed have a larger total energy content than any of their constituent quantum particles, there can be no experiment or other observation of this total energy without extracting the respective amount of energy from each of the quantum particles – which is exactly the domain of high energy phy... | Macroscopic scale | 0.806853 |
27,031 | Even an entire beam of protons circulated in the Large Hadron Collider, a high energy physics experiment, contains ~ 3.23×1014 protons, each with 6.5×1012 eV of energy, for a total beam energy of ~ 2.1×1027 eV or ~ 336.4 MJ, which is still ~ 2.7×105 times lower than the mass–energy of a single gram of hydrogen. Yet, th... | Macroscopic scale | 0.806853 |
27,032 | Particle physics, dealing with the smallest physical systems, is also known as high energy physics. Physics of larger length scales, including the macroscopic scale, is also known as low energy physics. Intuitively, it might seem incorrect to associate "high energy" with the physics of very small, low mass–energy syste... | Macroscopic scale | 0.806853 |
27,033 | Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest. If they are bound together, they will both trace out ellipses; if they are moving apart, they will ... | Conic Sections | 0.806853 |
27,034 | The conic sections have been studied for thousands of years and have provided a rich source of interesting and beautiful results in Euclidean geometry. | Conic Sections | 0.806853 |
27,035 | Metrical concepts of Euclidean geometry (concepts concerned with measuring lengths and angles) can not be immediately extended to the real projective plane. They must be redefined (and generalized) in this new geometry. This can be done for arbitrary projective planes, but to obtain the real projective plane as the ext... | Conic Sections | 0.806853 |
27,036 | This follows from a fundamental property of pure functional languages, termed referential transparency: the value of a computed result does not depend on the order or time of evaluation, due to the absence of side effects. This simplifies reasoning about, and maintaining, pure functional programs. As many functional la... | Curry (programming language) | 0.806852 |
27,037 | In molecular biology, the calcium-binding EGF domain is an EGF-like domain of about forty amino-acid residues found in epidermal growth factor (EGF). This domain is present in a large number of membrane-bound and extracellular, mostly animal, proteins. Many of these proteins require calcium for their biological functio... | Calcium-binding EGF domain | 0.80685 |
27,038 | SortSite is a web crawler that scans entire websites for quality issues including accessibility, browser compatibility, broken links, legal compliance, search optimization, usability and web standards compliance. | SortSite | 0.806848 |
27,039 | Biomineralogy is a cross-over field between mineralogy, paleontology and biology. It is the study of how plants and animals stabilize minerals under biological control, and the sequencing of mineral replacement of those minerals after deposition. It uses techniques from chemical mineralogy, especially isotopic studies,... | Mineral ecology | 0.806844 |
27,040 | : 4: 15 X-ray diffraction was demonstrated by Max von Laue in 1912, and developed into a tool for analyzing the crystal structure of minerals by the father/son team of William Henry Bragg and William Lawrence Bragg. : 4 More recently, driven by advances in experimental technique (such as neutron diffraction) and availa... | Mineral ecology | 0.806844 |
27,041 | : 54–55 X-rays have wavelengths that are the same order of magnitude as the distances between atoms. Diffraction, the constructive and destructive interference between waves scattered at different atoms, leads to distinctive patterns of high and low intensity that depend on the geometry of the crystal. In a sample that... | Mineral ecology | 0.806844 |
27,042 | In addition, there are operations that displace all the points: translation, screw axis, and glide plane. In combination with the point symmetries, they form 230 possible space groups. : 125–126 Most geology departments have X-ray powder diffraction equipment to analyze the crystal structures of minerals. | Mineral ecology | 0.806844 |
27,043 | In 2011, several researchers began to develop a Mineral Evolution Database. This database integrates the crowd-sourced site Mindat.org, which has over 690,000 mineral-locality pairs, with the official IMA list of approved minerals and age data from geological publications.This database makes it possible to apply statis... | Mineral ecology | 0.806844 |
27,044 | The modern study of mineralogy was founded on the principles of crystallography (the origins of geometric crystallography, itself, can be traced back to the mineralogy practiced in the eighteenth and nineteenth centuries) and to the microscopic study of rock sections with the invention of the microscope in the 17th cen... | Mineral ecology | 0.806844 |
27,045 | One of these, atomic absorption spectroscopy, is similar to wet chemistry in that the sample must still be dissolved, but it is much faster and cheaper. The solution is vaporized and its absorption spectrum is measured in the visible and ultraviolet range. : 225–226 Other techniques are X-ray fluorescence, electron mic... | Mineral ecology | 0.806844 |
27,046 | A few minerals are chemical elements, including sulfur, copper, silver, and gold, but the vast majority are compounds. The classical method for identifying composition is wet chemical analysis, which involves dissolving a mineral in an acid such as hydrochloric acid (HCl). The elements in solution are then identified u... | Mineral ecology | 0.806844 |
27,047 | Mineralogy is a subject of geology specializing in the scientific study of the chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts. Specific studies within mineralogy include the processes of mineral origin and formation, classification of minerals, their geog... | Mineral ecology | 0.806844 |
27,048 | Mineral collecting is also a recreational study and collection hobby, with clubs and societies representing the field. Museums, such as the Smithsonian National Museum of Natural History Hall of Geology, Gems, and Minerals, the Natural History Museum of Los Angeles County, the Carnegie Museum of Natural History, the Na... | Mineral ecology | 0.806844 |
27,049 | Simply put, hydrocarbon cracking is the process of breaking a long chain of hydrocarbons into short ones. This process requires high temperatures.More loosely, outside the field of petroleum chemistry, the term "cracking" is used to describe any type of splitting of molecules under the influence of heat, catalysts and ... | Cracking (chemistry) | 0.806841 |
27,050 | In petrochemistry, petroleum geology and organic chemistry, cracking is the process whereby complex organic molecules such as kerogens or long-chain hydrocarbons are broken down into simpler molecules such as light hydrocarbons, by the breaking of carbon-carbon bonds in the precursors. The rate of cracking and the end ... | Cracking (chemistry) | 0.806841 |
27,051 | A common misconception is that countable choice has an inductive nature and is therefore provable as a theorem (in ZF, or similar, or even weaker systems) by induction. However, this is not the case; this misconception is the result of confusing countable choice with finite choice for a finite set of size n (for arbitr... | Axiom of countable choice | 0.806841 |
27,052 | There are many longstanding unsolved problems in mathematics for which a solution has still not yet been found. The notable unsolved problems in statistics are generally of a different flavor; according to John Tukey, "difficulties in identifying problems have delayed statistics far more than difficulties in solving pr... | List of unsolved problems in statistics | 0.806836 |
27,053 | Multiple comparisons: There are various ways to adjust p-values to compensate for the simultaneous or sequential testing of hypothesis. Of particular interest is how to simultaneously control the overall error rate, preserve statistical power, and incorporate the dependence between tests into the adjustment. These issu... | List of unsolved problems in statistics | 0.806836 |
27,054 | Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the difference of two means when the variances are unknown and possibly unequal. That is, there is no exact test (meaning that, if the means are in fact equal, one that rejects the null hypothesis with probability exact... | List of unsolved problems in statistics | 0.806836 |
27,055 | Sampling of species problem: How is a probability updated when there is unanticipated new data? Doomsday argument: How valid is the probabilistic argument that claims to predict the future lifetime of the human race given only an estimate of the total number of humans born so far? Exchange paradox: Issues arise within ... | List of unsolved problems in statistics | 0.806836 |
27,056 | The Developmental Studies Hybridoma Bank (DSHB) is a National Resource established by the National Institutes of Health (NIH) in 1986 to bank and distribute at cost hybridomas and the monoclonal antibodies (mAbs) they produce to the basic science community worldwide. It is housed in the Department of Biology at the Uni... | Developmental Studies Hybridoma Bank | 0.806836 |
27,057 | The DSHB is directed by David R. Soll at the University of Iowa. There are currently over 5000 hybridomas in the DSHB collection. The DSHB has obtained hybridomas from a variety of individuals and institutions, the latter including the Muscular Dystrophy Association, the National Cancer Institute, the NIH Common Fund, ... | Developmental Studies Hybridoma Bank | 0.806836 |
27,058 | In polymer chemistry and polymer physics, the Flory–Fox equation is a simple empirical formula that relates molecular weight to the glass transition temperature of a polymer system. The equation was first proposed in 1950 by Paul J. Flory and Thomas G. Fox while at Cornell University. Their work on the subject overturn... | Flory-Fox equation | 0.806834 |
27,059 | Theoretical understanding of condensed matter physics is closely related to the notion of emergence, wherein complex assemblies of particles behave in ways dramatically different from their individual constituents. For example, a range of phenomena related to high temperature superconductivity are understood poorly, al... | Condensed Matter Physics | 0.806834 |
27,060 | The theoretical physics of condensed matter shares important concepts and methods with that of particle physics and nuclear physics.A variety of topics in physics such as crystallography, metallurgy, elasticity, magnetism, etc., were treated as distinct areas until the 1940s, when they were grouped together as solid-st... | Condensed Matter Physics | 0.806834 |
27,061 | Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other physics theories to develop mathematical models. The diversity of systems and phen... | Condensed Matter Physics | 0.806834 |
27,062 | Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with condensed phases of matter: systems of many constituents wi... | Condensed Matter Physics | 0.806834 |
27,063 | : 27–29 However, despite the success of Drude's free electron model, it had one notable problem: it was unable to correctly explain the electronic contribution to the specific heat and magnetic properties of metals, and the temperature dependence of resistivity at low temperatures. : 366–368 In 1911, three years after ... | Condensed Matter Physics | 0.806834 |
27,064 | The Cauchy problem d u d t = A u + f u ( 0 ) = u 0 ∈ D ( A ) {\displaystyle {\frac {\mathrm {d} u}{\mathrm {d} t}}=Au+f\quad u(0)=u_{0}\in D(A)} with f: [ 0 , ∞ ) → X {\displaystyle f:[0,\infty )\to X} , is called nonhomogeneous when f ( t ) ≠ 0 {\displaystyle f(t)\neq 0} . The following theorem gives some sufficient c... | Abstract differential equation | 0.806831 |
27,065 | An exhaustive treatment of the homogeneous ( f = 0 {\displaystyle f=0} ) case with a constant operator is given by the theory of C0-semigroups. Very often, the study of other abstract differential equations amounts (by e.g. reduction to a set of equations of the first order) to the study of this equation. The theory of... | Abstract differential equation | 0.806831 |
27,066 | In mathematics, an abstract differential equation is a differential equation in which the unknown function and its derivatives take values in some generic abstract space (a Hilbert space, a Banach space, etc.). Equations of this kind arise e.g. in the study of partial differential equations: if to one of the variables ... | Abstract differential equation | 0.806831 |
27,067 | This direction is an immediate consequence of basic category theory, so the deeper and more interesting part of the equivalence is the other implication. The representing object C above can be shown to depend functorially on F: any natural transformation from F to another functor satisfying the conditions of the theore... | Brown's representability theorem | 0.80683 |
27,068 | The representability theorem for CW complexes, due to Edgar H. Brown, is the following. Suppose that: The functor F maps coproducts (i.e. wedge sums) in Hotc to products in Set: F ( ∨ α X α ) ≅ ∏ α F ( X α ) , {\displaystyle F(\vee _{\alpha }X_{\alpha })\cong \prod _{\alpha }F(X_{\alpha }),} The functor F maps homotopy... | Brown's representability theorem | 0.80683 |
27,069 | In mathematics, Brown's representability theorem in homotopy theory gives necessary and sufficient conditions for a contravariant functor F on the homotopy category Hotc of pointed connected CW complexes, to the category of sets Set, to be a representable functor. More specifically, we are given F: Hotcop → Set,and the... | Brown's representability theorem | 0.80683 |
27,070 | Within plasma physics, PIC simulation has been used successfully to study laser-plasma interactions, electron acceleration and ion heating in the auroral ionosphere, magnetohydrodynamics, magnetic reconnection, as well as ion-temperature-gradient and other microinstabilities in tokamaks, furthermore vacuum discharges, ... | Particle-in-cell | 0.806829 |
27,071 | The final solution is then obtained by optimization until the required accuracy is reached. Also spectral methods, such as the fast Fourier transform (FFT), transform the PDEs into an eigenvalue problem, but this time the basis functions are high order and defined globally over the whole domain. The domain itself is no... | Particle-in-cell | 0.806829 |
27,072 | The most commonly used methods for solving Maxwell's equations (or more generally, partial differential equations (PDE)) belong to one of the following three categories: Finite difference methods (FDM) Finite element methods (FEM) Spectral methodsWith the FDM, the continuous domain is replaced with a discrete grid of p... | Particle-in-cell | 0.806829 |
27,073 | The real systems studied are often extremely large in terms of the number of particles they contain. In order to make simulations efficient or at all possible, so-called super-particles are used. A super-particle (or macroparticle) is a computational particle that represents many real particles; it may be millions of e... | Particle-in-cell | 0.806829 |
27,074 | Since the early days, it has been recognized that the PIC method is susceptible to error from so-called discrete particle noise. This error is statistical in nature, and today it remains less-well understood than for traditional fixed-grid methods, such as Eulerian or semi-Lagrangian schemes. Modern geometric PIC algor... | Particle-in-cell | 0.806829 |
27,075 | In plasma physics, the particle-in-cell (PIC) method refers to a technique used to solve a certain class of partial differential equations. In this method, individual particles (or fluid elements) in a Lagrangian frame are tracked in continuous phase space, whereas moments of the distribution such as densities and curr... | Particle-in-cell | 0.806829 |
27,076 | Poisson limit theorem: As n approaches ∞ and p approaches 0 with the product np held fixed, the Binomial(n, p) distribution approaches the Poisson distribution with expected value λ = np. de Moivre–Laplace theorem: As n approaches ∞ while p remains fixed, the distribution of X − n p n p ( 1 − p ) {\displaystyle {\frac ... | Binomially distributed | 0.806829 |
27,077 | Algorithms said to employ a Ping-Pong scheme exist in different fields of software engineering. They are characterized by an alternation between two entities. In the examples described below, these entities are communication partners, network paths or file blocks. | Ping-pong scheme | 0.806827 |
27,078 | In most database management systems durable database transactions are supported through a log file. However, multiple writes to the same page of that file can produce a slim chance of data loss. Assuming for simplicity that the log file is organized in pages whose size matches the block size of its underlying medium, t... | Ping-pong scheme | 0.806827 |
27,079 | Examples of topics are "The Geometry of Origami", "The Patterns of Juggling", and "Mathematical Morsels from The Simpsons and Futurama". The lectures are meant to be accessible and engaging for high school students and adults. The first lecture occurred on March 3, 2011. Twenty unique lectures had been delivered as of ... | National Museum of Mathematics | 0.806825 |
27,080 | On August 2, 2018, MoMath announced the creation of a Distinguished Chair for the Public Dissemination of Mathematics. Princeton professor and Fields Medal winner Manjul Bhargava was named as the first recipient of this position.Dr. Bhargava was succeeded by Peter Winkler, Dartmouth College Professor of Mathematics and... | National Museum of Mathematics | 0.806825 |
27,081 | That is, the equality relation may now be interpreted by an arbitrary equivalence relation on the domain of discourse that is congruent with respect to the functions and relations of the interpretation. When this second convention is followed, the term normal model is used to refer to an interpretation where no distinc... | Predicate calculus | 0.806825 |
27,082 | Second-order logic with full semantics is more expressive than first-order logic. For example, it is possible to create axiom systems in second-order logic that uniquely characterize the natural numbers and the real line. The cost of this expressiveness is that second-order and higher-order logics have fewer attractive... | Predicate calculus | 0.806825 |
27,083 | In 1686, Gottfried Wilhelm Leibniz, in Discourse on Metaphysics, gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances. He points out that force is conserved but quantity of motion, construed as the pro... | Conservation of linear momentum | 0.806824 |
27,084 | In quantum mechanics, momentum is defined as a self-adjoint operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables. For a single... | Conservation of linear momentum | 0.806824 |
27,085 | This minimizes redundancy while still representing the complete data set as no additional information would be gained from coding the total g groups: for example, when coding gender (where g = 2: male and female), if we only code females everyone left over would necessarily be males. In general, the group that one does... | Categorical data | 0.806823 |
27,086 | In statistics, a categorical variable (also called qualitative variable) is a variable that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or nominal category on the basis of some qualitative property. In computer ... | Categorical data | 0.806823 |
27,087 | Instead partial lists have been enumerated as n+k mirrors for k as 2, 3, and 4. Hypercompact Coxeter groups in three dimensional space or higher differ from two dimensional groups in one essential respect. Two hyperbolic n-gons having the same angles in the same cyclic order may have different edge lengths and are not ... | Coxeter diagram | 0.806821 |
27,088 | In organic chemistry, a hydrate is a compound formed by the hydration, i.e. "Addition of water or of the elements of water (i.e. H and OH) to a molecular entity". For example: ethanol, CH3−CH2−OH, is the product of the hydration reaction of ethene, CH2=CH2, formed by the addition of H to one C and OH to the other C, an... | Hydrate | 0.80682 |
27,089 | In addition, the sequence of secondary measures has applications in Quantum Mechanics. The sequence gives rise to the so-called sequence of residual spectral densities for specialized Pauli-Fierz Hamiltonians. This also provides a physical interpretation for the sequence of secondary measures. | Secondary measure | 0.806819 |
27,090 | The Hasse norm residue symbol ( ( α , L / K ) / p ) = ( α , L / K p ) {\displaystyle ((\alpha ,L/K)/p)=\left({\frac {\alpha ,L/K}{p}}\right)} is defined if p is a place of K and α an element of K. It is essentially the same as the local Artin symbol for the localization of K at p. The Hilbert symbol is a special case o... | Symbol (number theory) | 0.806818 |
27,091 | In number theory, a symbol is any of many different generalizations of the Legendre symbol. This article describes the relations between these various generalizations. The symbols below are arranged roughly in order of the date they were introduced, which is usually (but not always) in order of increasing generality. L... | Symbol (number theory) | 0.806818 |
27,092 | The fallacies are The network is reliable; Latency is zero; Bandwidth is infinite; The network is secure; Topology doesn't change; There is one administrator; Transport cost is zero; The network is homogeneous. | Fallacies of distributed computing | 0.806817 |
27,093 | Ignorance of bandwidth limits on the part of traffic senders can result in bottlenecks. Complacency regarding network security results in being blindsided by malicious users and programs that continually adapt to security measures. Changes in network topology can have effects on both bandwidth and latency issues, and t... | Fallacies of distributed computing | 0.806817 |
27,094 | Polbase is connected with various other databases. These include: The Protein Data Bank European Bioinformatics Institute ExPASy Bioinformatics Resource Portal UniProt BRENDA PubMed Various Scientific Journals | Polbase | 0.806817 |
27,095 | When the curvature of the Earth is taken into account, the concepts of vertical and horizontal take on yet another meaning. On the surface of a smoothly spherical, homogenous, non-rotating planet, the plumb bob picks out as vertical the radial direction. Strictly speaking, it is now no longer possible for vertical wall... | Vertical direction | 0.806815 |
27,096 | In graphical contexts, such as drawing and drafting and Co-ordinate geometry on rectangular paper, it is very common to associate one of the dimensions of the paper with a horizontal, even though the entire sheet of paper is standing on a flat horizontal (or slanted) table. In this case, the horizontal direction is typ... | Vertical direction | 0.806815 |
27,097 | Metal ions can be described as consisting of series of two concentric coordination spheres, the first and second. More distant from the second coordination sphere, the solvent molecules behave more like "bulk solvent." Simulation of the second coordination sphere is of interest in computational chemistry. The second co... | Coordination sphere | 0.806813 |
27,098 | All the computer programs and the readme files of this version could be sent electronically due to advances in computer technology. Around this time, the leadership of the MEGA project was taken over by Kumar (now at Temple University) and Tamura (now at Tokyo Metropolitan University). The monograph Molecular Evolution... | Molecular Evolutionary Genetics Analysis | 0.806805 |
27,099 | The molecular clock hypothesis suggests that all sequences have evolved at a constant rate over time. Therefore, the molecular clock test evaluates this statement in conjunction with the data provided by the user. In MEGA, this test is performed by applying a maximum likelihood test to a given tree topology and sequenc... | Molecular Evolutionary Genetics Analysis | 0.806805 |
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