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29,600 | In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolution is directly connected to angular resolution, other instruments, like syn... | Spatial resolution | 0.80538 |
29,601 | In the celestial equatorial coordinate system Σ(α, δ) in astronomy, polar distance (PD) is an angular distance of a celestial object on its meridian measured from the celestial pole, similar to the way declination (dec, δ) is measured from the celestial equator. | Polar distance (astronomy) | 0.805375 |
29,602 | For infinite Boolean algebras, this is no longer true, but every infinite Boolean algebra can be represented as a subalgebra of a power set Boolean algebra (see Stone's representation theorem). The power set of a set S forms an abelian group when it is considered with the operation of symmetric difference (with the emp... | Power set | 0.805373 |
29,603 | The power set of the set of natural numbers can be put in a one-to-one correspondence with the set of real numbers (see Cardinality of the continuum). The power set of a set S, together with the operations of union, intersection and complement, can be viewed as the prototypical example of a Boolean algebra. In fact, on... | Power set | 0.805373 |
29,604 | Obviously |2S| = 2|S| holds. Generally speaking, XY is the set of all functions from Y to X and |XY| = |X||Y|.Cantor's diagonal argument shows that the power set of a set (whether infinite or not) always has strictly higher cardinality than the set itself (or informally, the power set must be larger than the original s... | Power set | 0.805373 |
29,605 | An algebra all of whose operations are unary is called a presheaf. Every class of presheaves contains a presheaf Ω that plays the role for subalgebras that 2 plays for subsets. Such a class is a special case of the more general notion of elementary topos as a category that is closed (and moreover cartesian closed) and ... | Power set | 0.805373 |
29,606 | Furthermore, the subgraphs of a multigraph G are in bijection with the graph homomorphisms from G to the multigraph Ω definable as the complete directed graph on two vertices (hence four edges, namely two self-loops and two more edges forming a cycle) augmented with a fifth edge, namely a second self-loop at one of the... | Power set | 0.805373 |
29,607 | Secondly, whereas the subsets of a set are in bijection with the functions from that set to the set {0,1} = 2, there is no guarantee that a class of algebras contains an algebra that can play the role of 2 in this way. Certain classes of algebras enjoy both of these properties. The first property is more common; the ca... | Power set | 0.805373 |
29,608 | So in that regard, subalgebras behave analogously to subsets. However, there are two important properties of subsets that do not carry over to subalgebras in general. First, although the subsets of a set form a set (as well as a lattice), in some classes it may not be possible to organize the subalgebras of an algebra ... | Power set | 0.805373 |
29,609 | A set can be regarded as an algebra having no nontrivial operations or defining equations. From this perspective, the idea of the power set of X as the set of subsets of X generalizes naturally to the subalgebras of an algebraic structure or algebra. The power set of a set, when ordered by inclusion, is always a comple... | Power set | 0.805373 |
29,610 | The binomial theorem is closely related to the power set. A k–elements combination from some set is another name for a k–elements subset, so the number of combinations, denoted as C(n, k) (also called binomial coefficient) is a number of subsets with k elements in a set with n elements; in other words it's the number o... | Power set | 0.805373 |
29,611 | In software engineering, these activities are known as software maintenance (cf. ISO/IEC 9126). Closely related concepts in the software engineering domain are evolvability, modifiability, technical debt, and code smells. The maintainability index is calculated with certain formulae from lines-of-code measures, McCabe ... | Maintainability | 0.805372 |
29,612 | In mathematics and computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root v to any other vertex u in T is the shortest path distance from v to u in G. In connected graphs where shortest paths are well-defined (i.e. ... | Shortest-path tree | 0.805372 |
29,613 | A Slower Speed of Light was developed in hopes of being used as an educational tool to explain special relativity in an easy-to-understand fashion. The game is meant to be used as an interactive learning tool for those interested in physics. | A Slower Speed of Light | 0.805372 |
29,614 | Similar work that predated Kripke's revolutionary semantic breakthroughs: Rudolf Carnap seems to have been the first to have the idea that one can give a possible world semantics for the modalities of necessity and possibility by means of giving the valuation function a parameter that ranges over Leibnizian possible wo... | Kripke semantics | 0.805371 |
29,615 | In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at least one edge out of every cycle in the graph. Removing these edges from the graph breaks all of the cycles, producing a directed acyclic graph, an acyclic subgraph o... | Minimum feedback arc set | 0.805368 |
29,616 | Additionally, cutting a circuit on a feedback arc a set reduces the remaining circuit to combinational logic, simplifying its analysis, and the size of the feedback arc set controls how much additional analysis is needed to understand the behavior of the circuit across the cut. Similarly, in process flowsheeting in che... | Minimum feedback arc set | 0.805368 |
29,617 | Alternatively, if these comparisons result in independent probabilities for each pairwise ordering, then the maximum likelihood estimation of the overall ranking can be obtained by converting these probabilities into log-likelihoods and finding a minimum-weight feedback arc set in the resulting tournament. The same max... | Minimum feedback arc set | 0.805368 |
29,618 | In planar directed graphs, the feedback arc set problem obeys a min-max theorem: the minimum size of a feedback arc set equals the maximum number of edge-disjoint directed cycles that can be found in the graph. This is not true for some other graphs; for instance the first illustration shows a directed version of the n... | Minimum feedback arc set | 0.805368 |
29,619 | Feedback arc sets have applications in circuit analysis, chemical engineering, deadlock resolution, ranked voting, ranking competitors in sporting events, mathematical psychology, ethology, and graph drawing. Finding minimum feedback arc sets and maximum acyclic subgraphs is NP-hard; it can be solved exactly in exponen... | Minimum feedback arc set | 0.805368 |
29,620 | Another form of Bayes' theorem for two competing statements or hypotheses is: P ( A | B ) = P ( B | A ) P ( A ) P ( B | A ) P ( A ) + P ( B | ¬ A ) P ( ¬ A ) . {\displaystyle P(A|B)={\frac {P(B|A)P(A)}{P(B|A)P(A)+P(B|\neg A)P(\neg A)}}.} For an epistemological interpretation: For proposition A and evidence or backgroun... | Bayes rule | 0.805367 |
29,621 | By Bayes' theorem, P ( X C | Y ) = P ( Y | X C ) P ( X C ) P ( Y ) = 0.01 ⋅ 0.50 0.024 = 5 24 {\displaystyle P(X_{C}|Y)={\frac {P(Y|X_{C})P(X_{C})}{P(Y)}}={\frac {0.01\cdot 0.50}{0.024}}={\frac {5}{24}}} Given that the item is defective, the probability that it was made by machine C is 5/24. Although machine C produces... | Bayes rule | 0.805367 |
29,622 | For example, if the factory produces 1,000 items, 200 will be produced by Machine A, 300 by Machine B, and 500 by Machine C. Machine A will produce 5% × 200 = 10 defective items, Machine B 3% × 300 = 9, and Machine C 1% × 500 = 5, for a total of 24. Thus, the likelihood that a randomly selected defective item was produ... | Bayes rule | 0.805367 |
29,623 | In statistics, the Tukey–Duckworth test is a two-sample location test – a statistical test of whether one of two samples was significantly greater than the other. It was introduced by John Tukey, who aimed to answer a request by W. E. Duckworth for a test simple enough to be remembered and applied in the field without ... | Tukey–Duckworth test | 0.805362 |
29,624 | Formulae in predicate logic translate easily into the Prolog artificial intelligence language. The modality is expressed by two different types of Prolog rules. Rules taken from the language creation stage of model building process are treated as incorrigible. While rules from the knowledge elicitation stage are marked... | Logico-linguistic modeling | 0.80536 |
29,625 | Logico-linguistic modeling is a six-stage method developed primarily for building knowledge-based systems (KBS), but it also has application in manual decision support systems and information source analysis. Logico-linguistic models have a superficial similarity to John F. Sowa's conceptual graphs; both use bubble sty... | Logico-linguistic modeling | 0.80536 |
29,626 | The U of T supercomputer which can perform 300 trillion calculations per second will be used for highly calculation-intensive tasks such as problems involving quantum mechanical physics, weather forecasting, climate research, climate change models, molecular modeling (computing the structures and properties of chemical... | SciNet Consortium | 0.805358 |
29,627 | The SciNet offices are based on the St. George street campus, however, to accommodate the large floor space and power needs, the datacentre facility is housed in a warehouse about 30 km north of campus in Vaughan. At the core of SciNet research are six key areas of study: Astronomy and Astrophysics, Aerospace and Biome... | SciNet Consortium | 0.805358 |
29,628 | By measuring the isotopomer distribution of the differently labeled metabolites, the flux through each reaction can be determined.MFA combines the data harvested from isotope labeling with the stoichiometry of each reaction, constraints, and an optimization procedure resolve a flux map. The irreversible reactions provi... | Isotope affinity tags | 0.805358 |
29,629 | Comte found enumerative induction reliable as a consequence of its grounding in available experience. He asserted the use of science, rather than metaphysical truth, as the correct method for the improvement of human society. According to Comte, scientific method frames predictions, confirms them, and states laws—posit... | Inductive argument | 0.805358 |
29,630 | Positivism, developed by Henri de Saint-Simon and promulgated in the 1830s by his former student Auguste Comte, was the first late modern philosophy of science. In the aftermath of the French Revolution, fearing society's ruin, Comte opposed metaphysics. Human knowledge had evolved from religion to metaphysics to scien... | Inductive argument | 0.805358 |
29,631 | The SOLiD Sequencing System uses probes with dual base encoding. The underlying chemistry is summarized in the following steps:- Step 1, Preparing a Library: This step begins with shearing the genomic DNA into small fragments. Then, two different adapters are added (for example A1 and A2). The resulting library contain... | 2 Base Encoding | 0.805357 |
29,632 | Network analysis (electrical circuits) Mathematical methods in electronics Superposition theorem Topology (electronics) Mesh analysis Prototype filter | Resistive circuit | 0.805352 |
29,633 | The Fenske equation in continuous fractional distillation is an equation used for calculating the minimum number of theoretical plates required for the separation of a binary feed stream by a fractionation column that is being operated at total reflux (i.e., which means that no overhead product distillate is being with... | Fenske equation | 0.805351 |
29,634 | Organoiodine chemistry is the study of the synthesis and properties of organoiodine compounds, or organoiodides, organic compounds that contain one or more carbon–iodine bonds. They occur widely in organic chemistry, but are relatively rare in nature. The thyroxine hormones are organoiodine compounds that are required ... | Organoiodine compound | 0.805351 |
29,635 | An early form of height function was proposed by Giambattista Benedetti (c. 1563), who argued that the consonance of a musical interval could be measured by the product of its numerator and denominator (in reduced form); see Giambattista Benedetti § Music.Heights in Diophantine geometry were initially developed by Andr... | Height of a polynomial | 0.80535 |
29,636 | The Arakelov height on a projective space over the field of algebraic numbers is a global height function with local contributions coming from Fubini–Study metrics on the Archimedean fields and the usual metric on the non-Archimedean fields. It is the usual Weil height equipped with a different metric. | Height of a polynomial | 0.80535 |
29,637 | One of the conditions in the definition of an automorphic form on the general linear group of an adelic algebraic group is moderate growth, which is an asymptotic condition on the growth of a height function on the general linear group viewed as an affine variety. | Height of a polynomial | 0.80535 |
29,638 | This effect is compounded when overlapping generations are present (such as in social insect colonies and primate groups), which facilitates the horizontal transmission of pathogens from the older generation to the next. In the case of species that live in nests/burrows, stable, homeostatic temperatures and humidity ma... | Social immunity | 0.80535 |
29,639 | The terpenes in the conifer resin likely provide the antimicrobial activity, as they do in the antifungal secretions of soldier-caste Nasutitermes termites. The corpses of group members killed by an infectious disease present a serious hazard to colony health (as in natural environments death from disease is much more ... | Social immunity | 0.80535 |
29,640 | Already a model system in evolutionary ecology due to their extensive parental care, burying beetles like N. vespilloides hunt for small vertebrate carcasses which they then bury before intricately preparing it as a resource for its larvae to breed on-these carcasses are scarce and ephemeral yet are necessary for buryi... | Social immunity | 0.80535 |
29,641 | Sylvia Cremer defined social immunity in her seminal 2007 Current Biology paper 'Social Immunity' as the "collective action or altruistic behaviours of infected individuals that benefit the colony". She laid out a conceptual framework for the topic using examples from primates and eusocial insects. Cremer's definition ... | Social immunity | 0.80535 |
29,642 | The origin of polyandry in nature and its adaptive value is a subject of ongoing controversy in evolutionary biology, partly due to the seemingly numerous costs it places on females - additional energetic and temporal allocation to reproduction, increased risk of predation, increased risk of sexually transmitted diseas... | Social immunity | 0.80535 |
29,643 | In acoustics and fluid dynamics, an acoustic metric (also known as a sonic metric) is a metric that describes the signal-carrying properties of a given particulate medium. (Generally, in mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signal... | Acoustic metric | 0.805346 |
29,644 | For simplicity, we will assume that the underlying background geometry is Euclidean, and that this space is filled with an isotropic inviscid fluid at zero temperature (e.g. a superfluid). This fluid is described by a density field ρ and a velocity field v → {\displaystyle {\vec {v}}} . The speed of sound at any given ... | Acoustic metric | 0.805346 |
29,645 | Since acoustic metrics share some statistical behaviours with the way that we expect a future theory of quantum gravity to behave (such as Hawking radiation), these metrics have sometimes been studied in the hope that they might shed light on the statistical mechanics of actual black holes. Some people have suggested t... | Acoustic metric | 0.805346 |
29,646 | Thue's original proof that the equation named in his honour has finitely many solutions is through the proof of what is now known as Thue's theorem: it asserts that for any algebraic number α {\displaystyle \alpha } having degree d ≥ 3 {\displaystyle d\geq 3} and for any ε > 0 {\displaystyle \varepsilon >0} there exist... | Thue equation | 0.805341 |
29,647 | Finding all solutions to a Thue equation can be achieved by a practical algorithm, which has been implemented in the following computer algebra systems: in PARI/GP as functions thueinit() and thue(). in Magma computer algebra system as functions ThueObject() and ThueSolve(). in Mathematica through Reduce | Thue equation | 0.805341 |
29,648 | In mathematics, a Thue equation is a Diophantine equation of the form ƒ(x,y) = r,where ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue, who in 1909 proved that a Thue equation can have only finitely many solutions in inte... | Thue equation | 0.805341 |
29,649 | While there are several effective methods to solve Thue equations (including using Baker's method and Skolem's p {\displaystyle p} -adic method), these are not able to give the best theoretical bounds on the number of solutions. One may qualify an effective bound C ( f , r ) {\displaystyle C(f,r)} of the Thue equation ... | Thue equation | 0.805341 |
29,650 | Stages of in silico, in vitro and in vivo research are conducted to determine safe exposure doses in model organisms. If necessary, the next phase of research involves human toxicology testing during a first-in-man study. Toxicology testing may be conducted by the pharmaceutical industry, biotechnology companies, contr... | Toxicology testing | 0.805338 |
29,651 | A contract research organization (CRO) is an organization that provides support to the pharmaceutical, biotechnology, chemical, and medical device industries in the form of research services outsourced on a contract basis. A CRO may provide toxicity testing services, along with others such as assay development, preclin... | Toxicology testing | 0.805338 |
29,652 | Albert Einstein published his theory of general relativity in 1915. It, like his earlier theory of special relativity, described space and time as a unified spacetime subject to what are now known as the Einstein field equations. These form a set of coupled nonlinear partial differential equations (PDEs). After more th... | Numerical relativity | 0.805336 |
29,653 | All of these methods begin with a snapshot of the gravitational fields on some hypersurface, the initial data, and evolve these data to neighboring hypersurfaces.Like all problems in numerical analysis, careful attention is paid to the stability and convergence of the numerical solutions. In this line, much attention i... | Numerical relativity | 0.805336 |
29,654 | Numerical relativity is applied to many areas, such as cosmological models, critical phenomena, perturbed black holes and neutron stars, and the coalescence of black holes and neutron stars, for example. In any of these cases, Einstein's equations can be formulated in several ways that allow us to evolve the dynamics. ... | Numerical relativity | 0.805336 |
29,655 | In the excision technique, which was first proposed in the late 1990s, a portion of a spacetime inside of the event horizon surrounding the singularity of a black hole is simply not evolved. In theory this should not affect the solution to the equations outside of the event horizon because of the principle of causality... | Numerical relativity | 0.805336 |
29,656 | Whereas compact matrix pseudogroups are typically versions of Drinfeld-Jimbo quantum groups in a dual function algebra formulation, with additional structure, the bicrossproduct ones are a distinct second family of quantum groups of increasing importance as deformations of solvable rather than semisimple Lie groups. Th... | Quantum groups | 0.805336 |
29,657 | Strictly, the quantum group Uq(G) is not quasitriangular, but it can be thought of as being "nearly quasitriangular" in that there exists an infinite formal sum which plays the role of an R-matrix. This infinite formal sum is expressible in terms of generators ei and fi, and Cartan generators tλ, where kλ is formally i... | Quantum groups | 0.805336 |
29,658 | On the other hand, a finite-dimensional representation of G can be used to generate a *-subalgebra of C(G) which is also a Hopf *-algebra. Specifically, if g ↦ ( u i j ( g ) ) i , j {\displaystyle g\mapsto (u_{ij}(g))_{i,j}} is an n-dimensional representation of G, then for all i, j uij ∈ C(G) and Δ ( u i j ) = ∑ k u i... | Quantum groups | 0.805336 |
29,659 | By the Gelfand theorem, a commutative C*-algebra is isomorphic to the C*-algebra of continuous complex-valued functions on a compact Hausdorff topological space, and the topological space is uniquely determined by the C*-algebra up to homeomorphism. For a compact topological group, G, there exists a C*-algebra homomorp... | Quantum groups | 0.805336 |
29,660 | }}f_{i}^{n}f_{j}f_{i}^{1-a_{ij}-n}&=0\end{aligned}}} where the q-factorial, the q-analog of the ordinary factorial, is defined recursively using q-number: q i ! = 1 q i ! = ∏ m = 1 n q i , q i = q i m − q i − m q i − q i − 1 {\displaystyle {\begin{aligned}{}_{q_{i}}!&=1\\{}_{q_{i}}!&=\prod _{m=1}^{n}_{q_{i}},&&_{q_... | Quantum groups | 0.805336 |
29,661 | w {\displaystyle k_{\lambda }\cdot (v\otimes w)=k_{\lambda }\cdot v\otimes k_{\lambda }.w} , and in the case of coproduct Δ1, e i ⋅ ( v ⊗ w ) = k i ⋅ v ⊗ e i ⋅ w + e i ⋅ v ⊗ w {\displaystyle e_{i}\cdot (v\otimes w)=k_{i}\cdot v\otimes e_{i}\cdot w+e_{i}\cdot v\otimes w} and f i ⋅ ( v ⊗ w ) = v ⊗ f i ⋅ w + f i ⋅ v ⊗ k i... | Quantum groups | 0.805336 |
29,662 | Conversely, if a highest weight module is integrable, then its highest weight vector v satisfies k λ ⋅ v = c λ q ( λ , ν ) v {\displaystyle k_{\lambda }\cdot v=c_{\lambda }q^{(\lambda ,\nu )}v} , where cλ · v = dλv are complex numbers such that c 0 = 1 , {\displaystyle c_{0}=1,} c λ c μ = c λ + μ , {\displaystyle c_{\l... | Quantum groups | 0.805336 |
29,663 | A representation of the compact matrix quantum group is given by a corepresentation of the Hopf *-algebra (a corepresentation of a counital coassociative coalgebra A is a square matrix v = ( v i j ) i , j = 1 , … , n {\displaystyle v=(v_{ij})_{i,j=1,\dots ,n}} with entries in A (so v belongs to M(n, A)) such that Δ ( v... | Quantum groups | 0.805336 |
29,664 | A crucial ingredient was I. Heckenberger's classification of finite Nichols algebras for abelian groups in terms of generalized Dynkin diagrams. When small primes are present, some exotic examples, such as a triangle, occur (see also the Figure of a rank 3 Dankin diagram).Meanwhile, Schneider and Heckenberger have gene... | Quantum groups | 0.805336 |
29,665 | There has been considerable progress in describing finite quotients of quantum groups such as the above Uq(g) for qn = 1; one usually considers the class of pointed Hopf algebras, meaning that all subcoideals are 1-dimensional and thus there sum form a group called coradical: In 2002 H.-J. Schneider and N. Andruskiewit... | Quantum groups | 0.805336 |
29,666 | S. L. Woronowicz introduced compact matrix quantum groups. Compact matrix quantum groups are abstract structures on which the "continuous functions" on the structure are given by elements of a C*-algebra. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry. The continuous compl... | Quantum groups | 0.805336 |
29,667 | A highest weight module is a module generated by a weight vector v, subject to kλ · v = dλv for all weights μ, and ei · v = 0 for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i.e. a module generated by a weight vector v, subject to kλ · v = dλv for all weights λ, a... | Quantum groups | 0.805336 |
29,668 | The Petri dish is one of the most common items in biology laboratories and has entered popular culture. The term is sometimes written in lower case, especially in non-technical literature.What was later called Petri dish was originally developed by German physician Robert Koch in his private laboratory in 1881, as a pr... | Petri dish | 0.805335 |
29,669 | In software engineering, a freeze is a point in time in the development process after which the rules for making changes to the source code or related resources become more strict, or the period during which those rules are applied. A freeze helps move the project forward towards a release or the end of an iteration by... | Feature freeze | 0.805334 |
29,670 | Particularly in large software systems, any change to the source code may have unintended consequences, potentially introducing new bugs; thus, a code freeze helps ensure that a portion of the program that is known to work correctly will continue to do so. Code freezes are often employed in the final stages of developm... | Feature freeze | 0.805334 |
29,671 | As of Autumn 2012, the magazine is laid out as follows: Editorial—often offering a view of point from editor in chief on an educational and/or biological topics. Explore— New research methods and results on biology and/or education. World— Reports and explores on biological education worldwide. In Brief—Summaries of re... | Roshd Biological Education | 0.805328 |
29,672 | News and Reports—Offering short news and reports events on biology education. In Brief—Short articles explaining interesting facts. Questions and Answers—Questions about biology concepts and their answers. Book and periodical Reviews—About new publication on biology and/or education. Reactions—Letter to the editors. | Roshd Biological Education | 0.805327 |
29,673 | Roshd Biological Education is a quarterly science educational magazine covering recent developments in biology and biology education for a biology teacher Persian -speaking audience. Founded in 1985, it is published by The Teaching Aids Publication Bureau, Organization for Educational Planning and Research, Ministry of... | Roshd Biological Education | 0.805327 |
29,674 | In quantum mechanics, the discrete spectrum of an observable corresponds to the eigenvalues of the operator used to model that observable. According to the mathematical theory of such operators, its eigenvalues are a discrete set of isolated points, which may be either finite or countable. Discrete spectra are usually ... | Continuous spectrum | 0.805325 |
29,675 | Given a quasimetric on X, one can define an R-ball around x to be the set { y ∈ X | d ( x , y ) ≤ R } {\displaystyle \{y\in X|d(x,y)\leq R\}} . As in the case of a metric, such balls form a basis for a topology on X, but this topology need not be metrizable. For example, the topology induced by the quasimetric on the r... | Bounded space | 0.805324 |
29,676 | The Sustained Spheromak Physics Experiment (SSPX) is a program at Lawrence Livermore National Laboratory in the United States established to investigate spheromak plasma.A spheromak device produces a plasma in magnetohydrodynamic equilibrium mainly through self-induced plasma currents, as opposed to a tokamak device wh... | Sustained Spheromak Physics Experiment | 0.805324 |
29,677 | Logic circuits cannot produce any randomness, and in that sense they form an incomplete logic set. Remedy to that is found in adding an ad-hoc random bit generator to logic networks, or computers, such as in Probabilistic Turing machine. A recent work has introduced a theoretical concept of an inherently random logic c... | Boolean circuit | 0.805321 |
29,678 | Logic circuits are physical representation of simple logic operations, AND, OR and NOT (and their combinations, such as non-sequential flip-flops or circuit networks), that form a mathematical structure known as Boolean algebra. They are complete in sense that they can perform any deterministic algorithm. However, it j... | Boolean circuit | 0.805321 |
29,679 | The format is Γ ⊢ ψ {\displaystyle \Gamma \vdash \psi } , in which Γ is a (possibly empty) set of formulas called premises, and ψ is a formula called conclusion. The transformation rule Γ ⊢ ψ {\displaystyle \Gamma \vdash \psi } means that if every proposition in Γ is a theorem (or has the same truth value as the axioms... | Sentential calculus | 0.805321 |
29,680 | The set of initial points is empty, that is, I = ∅ {\displaystyle \mathrm {I} =\varnothing } . The set of transformation rules, Z {\displaystyle \mathrm {Z} } , is described as follows:Our propositional calculus has eleven inference rules. These rules allow us to derive other true formulas given a set of formulas that ... | Sentential calculus | 0.805321 |
29,681 | {\displaystyle \Omega _{2}=\{\land ,\lor ,\to ,\leftrightarrow \}.} In the following example of a propositional calculus, the transformation rules are intended to be interpreted as the inference rules of a so-called natural deduction system. The particular system presented here has no initial points, which means that i... | Sentential calculus | 0.805321 |
29,682 | An interpretation of a truth-functional propositional calculus P {\displaystyle {\mathcal {P}}} is an assignment to each propositional symbol of P {\displaystyle {\mathcal {P}}} of one or the other (but not both) of the truth values truth (T) and falsity (F), and an assignment to the connective symbols of P {\displayst... | Sentential calculus | 0.805321 |
29,683 | A propositional calculus is a formal system L = L ( A , Ω , Z , I ) {\displaystyle {\mathcal {L}}={\mathcal {L}}\left(\mathrm {A} ,\ \Omega ,\ \mathrm {Z} ,\ \mathrm {I} \right)} , where: The language of L {\displaystyle {\mathcal {L}}} , also known as its set of formulas, well-formed formulas, is inductively defined b... | Sentential calculus | 0.805321 |
29,684 | Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. ... | Sentential calculus | 0.805321 |
29,685 | In the 1980s, the National Association of Secondary School Principals (NASSP) formed a task force to study learning styles. The task force defined three broad categories of style—cognitive, affective, and physiological—and 31 variables, including the perceptual strengths and preferences from the VAK model of Barbe and ... | Learning styles | 0.805318 |
29,686 | The three independent dimensionful constants: c, ħ, and G, in the fundamental equations of physics must then be seen as mere conversion factors to convert Mass, Time and Length into each other. Just as in the case of critical properties of lattice models, one can recover the results of dimensional analysis in the appro... | Dimension (physical quantity) | 0.805316 |
29,687 | Now, the correlation length is the relevant length scale related to critical phenomena, so one can, e.g., surmise on "dimensional grounds" that the non-analytical part of the free energy per lattice site should be ∼ 1 / ξ d {\displaystyle \sim 1/\xi ^{d}} where d {\displaystyle d} is the dimension of the lattice. It ha... | Dimension (physical quantity) | 0.805316 |
29,688 | In computational complexity theory, the complexity class PPP (polynomial pigeonhole principle) is a subclass of TFNP. It is the class of search problems that can be shown to be total by an application of the pigeonhole principle. Christos Papadimitriou introduced it in the same paper that introduced PPAD and PPA. PPP c... | PPP (complexity) | 0.805316 |
29,689 | The constrained-SIS (short integer solution) problem, which is a generalization of the SIS problem from lattice-based cryptography, has been shown to be complete for PPP. Prior to that work, the only problems known to be complete for PPP were variants of PIGEON. | PPP (complexity) | 0.805316 |
29,690 | This also accounts for the majority of the electron negativity residing around the more electronegative molecule. Applying the LCAO-MO method allows us to move away from a more static Lewis structure type approach and actually account for periodic trends that influence electron movement. Non-bonding orbitals refer to l... | MO diagram | 0.805316 |
29,691 | A diatomic molecular orbital diagram is used to understand the bonding of a diatomic molecule. MO diagrams can be used to deduce magnetic properties of a molecule and how they change with ionization. They also give insight to the bond order of the molecule, how many bonds are shared between the two atoms.The energies o... | MO diagram | 0.805316 |
29,692 | PES energies are different from ionisation energies which relates to the energy required to strip off the nth electron after the first n − 1 electrons have been removed. MO diagrams with energy values can be obtained mathematically using the Hartree–Fock method. The starting point for any MO diagram is a predefined mol... | MO diagram | 0.805316 |
29,693 | In electrical engineering, the Ferranti effect is the increase in voltage occurring at the receiving end of a very long (> 200 km) AC electric power transmission line, relative to the voltage at the sending end, when the load is very small, or no load is connected. It can be stated as a factor, or as a percent increase... | Performance and modelling of AC transmission | 0.805314 |
29,694 | In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance. The SI unit of admittance is the siemens (symbol S); the older, synonymous unit is mho, and its symbol is ℧ (an upside-down uppercase omega Ω). Oliver Heavisid... | Performance and modelling of AC transmission | 0.805314 |
29,695 | The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively and equiv... | Performance and modelling of AC transmission | 0.805314 |
29,696 | The Journal of Algebra and Its Applications covers both theoretical and applied algebra, with a focus on practical applications. It is published by World Scientific.According to the Journal Citation Reports, the journal has a 2020 impact factor of 0.736. | Journal of Algebra and Its Applications | 0.805313 |
29,697 | In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are... | Performance and modelling of AC transmission | 0.805313 |
29,698 | Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. The capacitance is a function only of the geometry of the design (e.g. area of the plates and the distance between them) and the permittivity of the dielectric material between the plates of t... | Performance and modelling of AC transmission | 0.805313 |
29,699 | In projective geometry, a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity. If the cone is a quadratic cone, the plane at infinity (which passes through the vertex) can intersect the cone at two real lines, a single real line (actually a coincident pair of lines), or only at the vertex. These... | Parabolic cylinder | 0.805313 |
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