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8,000 | In radio astronomy, the unit of electromagnetic flux is the jansky (symbol Jy), equivalent to 10−26 watts per square metre per hertz (= 10−26 kg/s2 in base units, about 8.8×10−31 BTU/ft2). It is named after the pioneering radio astronomer Karl Jansky. The brightest natural radio sources have flux densities of the order... | List of unusual units of measurement | 0.821984 |
8,001 | In nuclear engineering and astrophysics contexts, the shake is sometimes used as a conveniently short period of time. 1 shake is defined as 10 nanoseconds. | List of unusual units of measurement | 0.821984 |
8,002 | RASP can be integrated as a framework or module that runs in conjunction with a program's codes, libraries and system calls. The technology can also be implemented as a virtualization. RASP is similar to interactive application security testing (IAST), the key difference is that IAST is focused on identifying vulnerabi... | Runtime application self-protection | 0.821971 |
8,003 | For example, consider the ordinary differential equation The Euler method for solving this equation uses the finite difference quotient to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get The ... | Finite Difference Method | 0.821966 |
8,004 | For a n-times differentiable function, by Taylor's theorem the Taylor series expansion is given as where n! denotes the factorial of n, and Rn(x) is a remainder term, denoting the difference between the Taylor polynomial of degree n and the original function. We will derive an approximation for the first derivative of ... | Finite Difference Method | 0.821966 |
8,005 | In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the sol... | Finite Difference Method | 0.821966 |
8,006 | It is conceptually distinct from the descriptions in explicit terms of Maxwellian electromagnetic fields or of photon distribution. It refers to material physics as distinct from psychophysics. For the concept of specific intensity, the line of propagation of radiation lies in a semi-transparent medium which varies con... | Specific radiative intensity | 0.821966 |
8,007 | In North America, kinesiologists may study to earn a Bachelor of Science, Master of Science, or Doctorate of Philosophy degree in Kinesiology or a Bachelor of Kinesiology degree, while in Australia or New Zealand, they are often conferred an Applied Science (Human Movement) degree (or higher). Many doctoral level facul... | Human kinetics | 0.821963 |
8,008 | Kinesiology studies the science of human movement, performance, and function by applying the fundamental sciences of Cell Biology, Molecular Biology, Chemistry, Biochemistry, Biophysics, Biomechanics, Biomathematics, Biostatistics, Anatomy, Physiology, Exercise Physiology, Pathophysiology, Neuroscience, and Nutritional... | Human kinetics | 0.821963 |
8,009 | Condensation is a probabilistic algorithm that attempts to solve this problem. The algorithm itself is described in detail by Isard and Blake in a publication in the International Journal of Computer Vision in 1998. One of the most interesting facets of the algorithm is that it does not compute on every pixel of the im... | Condensation algorithm | 0.821955 |
8,010 | The condensation algorithm (Conditional Density Propagation) is a computer vision algorithm. The principal application is to detect and track the contour of objects moving in a cluttered environment. Object tracking is one of the more basic and difficult aspects of computer vision and is generally a prerequisite to obj... | Condensation algorithm | 0.821955 |
8,011 | GeneralRing (mathematics) Commutative algebra, Commutative ring Ring theory, Noncommutative ring Algebra over a field Non-associative algebra Relatives to rings: Semiring, Nearring, Rig (algebra)StructureSubring, Subalgebra Center (algebra) Ring ideal Principal ideal Ideal quotient Maximal ideal, minimal ideal Primitiv... | List of abstract algebra topics | 0.821954 |
8,012 | GeneralModule (mathematics) Bimodule Annihilator (ring theory)StructureSubmodule Pure submodule Module homomorphism Essential submodule Superfluous submodule Singular submodule Socle of a module Radical of a moduleConstructionsFree module Quotient module Direct sum, Direct product of modules Direct limit, Inverse limit... | List of abstract algebra topics | 0.821954 |
8,013 | GeneralAssociative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup Nonassociative ring, Non-associative algebra Universal enveloping algebra Lie algebra (see also list of Lie group topics and list of representation theory topics) Jordan algebra Alternative algebra Power associativity ... | List of abstract algebra topics | 0.821954 |
8,014 | Basic conceptsField (mathematics) Subfield (mathematics) Multiplicative group Primitive element (field theory) Field extension Algebraic extension Splitting field Algebraically closed field Algebraic element Algebraic closure Separable extension Separable polynomial Normal extension Galois extension Abelian extension T... | List of abstract algebra topics | 0.821954 |
8,015 | Algebraic structures are defined primarily as sets with operations. Algebraic structure Subobjects: subgroup, subring, subalgebra, submodule etc. Binary operation Closure of an operation Associative property Distributive property Commutative property Unary operator Additive inverse, multiplicative inverse, inverse elem... | List of abstract algebra topics | 0.821954 |
8,016 | Algebraic structure Universal algebra Variety (universal algebra) Congruence relation Free object Generating set (universal algebra) Clone (algebra) Kernel of a function Kernel (algebra) Isomorphism class Isomorphism theorem Fundamental theorem on homomorphisms Universal property Filtration (mathematics) Category theor... | List of abstract algebra topics | 0.821954 |
8,017 | Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rule... | List of abstract algebra topics | 0.821954 |
8,018 | StructureGroup (mathematics) Lagrange's theorem (group theory) Subgroup Coset Normal subgroup Characteristic subgroup Centralizer and normalizer subgroups Derived group Frattini subgroup Fitting subgroup Classification of finite simple groups Sylow theorems Local analysisConstructionsFree group Presentation of a group ... | List of abstract algebra topics | 0.821954 |
8,019 | Semigroup Subsemigroup Free semigroup Green's relations Inverse semigroup (or inversion semigroup, cf. ) Krohn–Rhodes theory Semigroup algebra Transformation semigroup Monoid Aperiodic monoid Free monoid Monoid (category theory) Monoid factorisation Syntactic monoid | List of abstract algebra topics | 0.821954 |
8,020 | Representation theory Algebra representation Group representation Lie algebra representation Maschke's theorem Schur's lemma Equivariant map Frobenius reciprocity Induced representation Restricted representation Affine representation Projective representation Modular representation theory Quiver (mathematics) Represent... | List of abstract algebra topics | 0.821954 |
8,021 | As a brief summary of the book's contents, reviewer Brian Hopkins quotes The Pirates of Penzance: "With many cheerful facts about the square of the hypotenuse. "The book is divided into 15 chapters (or 16, if one counts the added material as a separate chapter). The first three of these define the primitive Pythagorean... | Pythagorean Triangles | 0.821952 |
8,022 | The book is aimed at mathematics teachers, in order to inspire their interest in this subject, but (despite complaining that some of its proofs are overly complicated) reviewer Donald Vestal also suggests this as a "fun book for a mostly general audience".Reviewer Brian Hopkins suggests that some of the book's material... | Pythagorean Triangles | 0.821952 |
8,023 | Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled Trójkąty pitagorejskie), and published in Warsaw in 1954. Indian mathematician Ambikeshwar Sharma translated it into English, with some adde... | Pythagorean Triangles | 0.821952 |
8,024 | In this case the Mermin–Wagner Theorem states that the order parameter expectation value vanishes in d = 2 {\displaystyle d=2} at T > 0 {\displaystyle T>0} , and there thus is no phase transition of the usual type at d L = 2 {\displaystyle d_{L}=2} and below. For systems with quenched disorder a criterion given by Imry... | Critical dimension | 0.821942 |
8,025 | Determining the upper critical dimension of a field theory is a matter of linear algebra. It is worthwhile to formalize the procedure because it yields the lowest-order approximation for scaling and essential input for the renormalization group. It also reveals conditions to have a critical model in the first place. | Critical dimension | 0.821942 |
8,026 | In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory beco... | Critical dimension | 0.821942 |
8,027 | There exist a number of competitions and prizes to reward distinguished contributions and to encourage developments in biotechnology. | Competitions and prizes in biotechnology | 0.821939 |
8,028 | The Gotham Prize for Cancer Research was a US$1,000,000 prize awarded annually to "encourage new and innovative approaches to cancer research by fostering collaboration among top thinkers in the field--with the goal of leading to progress in the prevention, diagnosis, etiology and treatment of cancer." Gruber Prize in ... | Competitions and prizes in biotechnology | 0.821939 |
8,029 | gcc and clang offer the -mno-red-zone flag to disable red-zone optimizations. If the callee is a variadic function, then the number of floating point arguments passed to the function in vector registers must be provided by the caller in the AL register. : 55 Unlike the Microsoft calling convention, a shadow space is no... | X86 calling conventions | 0.821937 |
8,030 | The crossing pattern of chords in a chord diagram may be described by a circle graph, the intersection graph of the chords: it has a vertex for each chord and an edge for each two chords that cross.In knot theory, a chord diagram can be used to describe the sequence of crossings along the planar projection of a knot, w... | Chord diagram (mathematics) | 0.821936 |
8,031 | Since many educators and policy makers are not experienced in evaluating scientific studies and studies have found that "teachers' beliefs are often guided by subjective experience rather than by empirical data", several non-profit organizations have been created to critically evaluate research studies and provide thei... | Evidence-based education | 0.821928 |
8,032 | The fundamental theorem of computability theory is that these three models of computation define the same set of computable functions, and that all the other models of computation that have ever been proposed define the same set of computable functions or a smaller one. The Church–Turing thesis is the claim that every ... | Function (mathematics) | 0.821926 |
8,033 | Except for computer-language terminology, "function" has the usual mathematical meaning in computer science. In this area, a property of major interest is the computability of a function. For giving a precise meaning to this concept, and to the related concept of algorithm, several models of computation have been intro... | Function (mathematics) | 0.821926 |
8,034 | For example, if_then_else is a function that takes three functions as arguments, and, depending on the result of the first function (true or false), returns the result of either the second or the third function. An important advantage of functional programming is that it makes easier program proofs, as being based on a... | Function (mathematics) | 0.821926 |
8,035 | The stable group 3 elements are thus often grouped with the 4f elements as the so-called rare earths.Typical transition-metal properties are mostly absent from this group, as they are for the heavier elements of groups 4 and 5: there is only one typical oxidation state and the coordination chemistry is not very rich (t... | Group III elements | 0.821925 |
8,036 | The metals burn easily to give the oxides, which are white high-melting solids. They are usually oxidized to the +3 oxidation state, in which they form mostly ionic compounds and have a mostly cationic aqueous chemistry. In this way they are similar to the lanthanides, although they lack the involvement of f orbitals t... | Group III elements | 0.821925 |
8,037 | Like other groups, the members of this family show patterns in their electron configurations, especially the outermost shells, resulting in trends in chemical behavior. Due to relativistic effects that become important for high atomic numbers, lawrencium's configuration has an irregular 7p occupancy instead of the expe... | Group III elements | 0.821925 |
8,038 | There are other, specialized notations for functions in sub-disciplines of mathematics. For example, in linear algebra and functional analysis, linear forms and the vectors they act upon are denoted using a dual pair to show the underlying duality. This is similar to the use of bra–ket notation in quantum mechanics. In... | Function (mathematics) | 0.821925 |
8,039 | It consists of terms that are either variables, function definitions (𝜆-terms), or applications of functions to terms. Terms are manipulated through some rules, (the α-equivalence, the β-reduction, and the η-conversion), which are the axioms of the theory and may be interpreted as rules of computation. In its original... | Function (mathematics) | 0.821925 |
8,040 | A rational function is the same, with divisions also allowed, such as f ( x ) = x − 1 x + 1 , {\displaystyle f(x)={\frac {x-1}{x+1}},} and f ( x ) = 1 x + 1 + 3 x − 2 x − 1 . {\displaystyle f(x)={\frac {1}{x+1}}+{\frac {3}{x}}-{\frac {2}{x-1}}.} An algebraic function is the same, with nth roots and roots of polynomials... | Function (mathematics) | 0.821925 |
8,041 | In mathematical analysis, and more specifically in functional analysis, a function space is a set of scalar-valued or vector-valued functions, which share a specific property and form a topological vector space. For example, the real smooth functions with a compact support (that is, they are zero outside some compact s... | Function (mathematics) | 0.821925 |
8,042 | In 1971, the Berkeley group did a whole series of experiments aimed at measuring the nuclear decay properties of element 103 isotopes, in which all previous results from Berkeley and Dubna were confirmed, except that the initial 257103 isotope reported at Berkeley in 1961 turned out to have been 258103. In 1992, the IU... | Group III elements | 0.821925 |
8,043 | The team at the University of California suggested the name lawrencium (after Ernest O. Lawrence, the inventor of cyclotron particle accelerator) and the symbol "Lw", for the new element; IUPAC accepted their discovery, but changed the symbol to "Lr". In 1965, nuclear-physics researchers in Dubna, Soviet Union (now Rus... | Group III elements | 0.821925 |
8,044 | Mechanisms commonly labeled executive functions include: working memory, inhibition, set shifting, as well as higher-order mechanisms that involve combinations of the prior (planning, problem-solving, reasoning).Piagetian tasks – tasks that measure behaviors that relate to cognitive abilities associated with Piaget's d... | Domain-general learning | 0.821923 |
8,045 | Researchers have expanded the search for domain-general mechanisms that underlie cognitive development beyond working memory. The advancement in cognitive neuroscience technology is credited as making this expansion possible. Within the last decade, researchers have begun to focus on a group of cognitive mechanisms, co... | Domain-general learning | 0.821923 |
8,046 | : 168–169 The published mise en pratique is not the only way in which a base unit can be determined: the SI Brochure states that "any method consistent with the laws of physics could be used to realise any SI unit. ": 111 Various consultative committees of the CIPM decided in 2016 that more than one mise en pratique wo... | International System of Units | 0.821921 |
8,047 | Electric current with named unit 'ampere' was chosen as the base unit, and the other electrical quantities derived from it according to the laws of physics. This became the foundation of the MKS system of units. In the late 19th and early 20th centuries, a number of non-coherent units of measure based on the gram/kilog... | International System of Units | 0.821921 |
8,048 | The three-dimensional density of states is: After combination and simplification, these expressions lead to: Here m ∗ {\displaystyle m^{*}} is the effective mass of the electrons in that particular semiconductor, and the quantity E c − E f {\displaystyle E_{c}-E_{f}} is the difference in energy between the conduction b... | Carrier density | 0.821912 |
8,049 | (Legendre–Cauchy) Two convex n-gons with equal corresponding side length have either zero or at least 4 sign changes in the cyclic sequence of the corresponding angle differences. (A.D. Alexandrov) Two convex n-gons with parallel corresponding sides and equal area have either zero or at least 4 sign changes in the cycl... | Four-vertex theorem | 0.821912 |
8,050 | There are several discrete versions of the four-vertex theorem, both for convex and non-convex polygons. Here are some of them: (Bilinski) The sequence of angles of a convex equilateral polygon with at least four vertices has at least four extrema. The sequence of side lengths of a convex equiangular polygon with at le... | Four-vertex theorem | 0.821912 |
8,051 | So for space curves a vertex is defined as a point of vanishing torsion. Every simple closed space curve which lies on the boundary of a convex body has four vertices. This theorem can be generalized to all curves which bound a locally convex disk. | Four-vertex theorem | 0.821912 |
8,052 | The four-vertex theorem was first proved for convex curves (i.e. curves with strictly positive curvature) in 1909 by Syamadas Mukhopadhyaya. His proof utilizes the fact that a point on the curve is an extremum of the curvature function if and only if the osculating circle at that point has fourth-order contact with the... | Four-vertex theorem | 0.821912 |
8,053 | The four-vertex theorem of geometry states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives from the convention of calling an extreme point of the curvature function a ve... | Four-vertex theorem | 0.821912 |
8,054 | For many years the proof of the four-vertex theorem remained difficult, but a simple and conceptual proof was given by Osserman (1985), based on the idea of the minimum enclosing circle. This is a circle that contains the given curve and has the smallest possible radius. If the curve includes an arc of the circle, it h... | Four-vertex theorem | 0.821912 |
8,055 | The converse to the four-vertex theorem states that any continuous, real-valued function of the circle that has at least two local maxima and two local minima is the curvature function of a simple, closed plane curve. The converse was proved for strictly positive functions in 1971 by Herman Gluck as a special case of a... | Four-vertex theorem | 0.821912 |
8,056 | If the curvature is constant over an arc of the curve, all points of that arc are considered to be vertices. The four-vertex theorem states that a smooth closed curve always has at least four vertices. An ellipse has exactly four vertices: two local maxima of curvature where it is crossed by the major axis of the ellip... | Four-vertex theorem | 0.821912 |
8,057 | One corollary of the theorem is that a homogeneous, planar disk rolling on a horizontal surface under gravity has at least 4 balance points. A discrete version of this is that there cannot be a monostatic polygon. However, in three dimensions there do exist monostatic polyhedra, and there also exists a convex, homogene... | Four-vertex theorem | 0.821912 |
8,058 | In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers, or text strings. The ability to perform integer ar... | Integer sorting | 0.821912 |
8,059 | The classical integer sorting algorithms of pigeonhole sort, counting sort, and radix sort are widely used and practical. Much of the subsequent research on integer sorting algorithms has focused less on practicality and more on theoretical improvements in their worst case analysis, and the algorithms that come from th... | Integer sorting | 0.821912 |
8,060 | In the Euclidean plane, let point p {\displaystyle p} have Cartesian coordinates ( p 1 , p 2 ) {\displaystyle (p_{1},p_{2})} and let point q {\displaystyle q} have coordinates ( q 1 , q 2 ) {\displaystyle (q_{1},q_{2})} . Then the distance between p {\displaystyle p} and q {\displaystyle q} is given by: This can be see... | Euclidean metric | 0.821908 |
8,061 | However, Ptolemy's inequality applies more generally to points in Euclidean spaces of any dimension, no matter how they are arranged. For points in metric spaces that are not Euclidean spaces, this inequality may not be true. Euclidean distance geometry studies properties of Euclidean distance such as Ptolemy's inequal... | Euclidean metric | 0.821908 |
8,062 | For polynomial rings of more than one variable, the products X⋅Y and Y⋅X are simply defined to be equal. A more general notion of polynomial ring is obtained when the distinction between these two formal products is maintained. Formally, the polynomial ring in n noncommuting variables with coefficients in the ring R is... | Polynomial algebra | 0.821905 |
8,063 | Various algorithms have been designed for computing such approximations, see Root finding of polynomials. There is an example of a field K such that there exist exact algorithms for the arithmetic operations of K, but there cannot exist any algorithm for deciding whether a polynomial of the form X p − a {\displaystyle ... | Polynomial algebra | 0.821905 |
8,064 | The existence of a factorization algorithm depends also on the ground field. In the case of the real or complex numbers, Abel–Ruffini theorem shows that the roots of some polynomials, and thus the irreducible factors, cannot be computed exactly. Therefore, a factorization algorithm can compute only approximations of th... | Polynomial algebra | 0.821905 |
8,065 | Polynomial rings in several variables over a field are fundamental in invariant theory and algebraic geometry. Some of their properties, such as those described above can be reduced to the case of a single indeterminate, but this is not always the case. In particular, because of the geometric applications, many interes... | Polynomial algebra | 0.821905 |
8,066 | One slight generalization of polynomial rings is to allow for infinitely many indeterminates. Each monomial still involves only a finite number of indeterminates (so that its degree remains finite), and each polynomial is a still a (finite) linear combination of monomials. Thus, any individual polynomial involves only ... | Polynomial algebra | 0.821905 |
8,067 | The two originally equatorial ligands then open out until they are 180 degrees apart, becoming axial groups perpendicular to where the axial groups were before the pseudorotation. This requires about 3.6 kcal/mol in PF5. This rapid exchange of axial and equatorial ligands renders complexes with this geometry unresolvab... | Berry mechanism | 0.821902 |
8,068 | The Berry mechanism in square pyramidal molecules (such as IF5) is somewhat like the inverse of the mechanism in bipyramidal molecules. Starting at the "transition phase" of bipyramidal pseudorotation, one pair of fluorines scissors back and forth with a third fluorine, causing the molecule to vibrate. Unlike with pseu... | Berry mechanism | 0.821902 |
8,069 | In physics (specifically in electromagnetism), the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force (in SI units) o... | Lorentz equation | 0.821898 |
8,070 | The above-mentioned formulae use the conventions for the definition of the electric and magnetic field used with SI units. These are the most common. However, other conventions with the same physics (i.e. forces on e.g. an electron) are possible and used. | Lorentz equation | 0.821898 |
8,071 | On the other hand, if we want to know if there is a solution for x less than some given limit c, this problem is NP-complete; however, this is a fixed-parameter tractable problem, where c is the parameter. In general, to determine if a is a quadratic residue modulo composite n, one can use the following theorem:Let n >... | Modular square root | 0.821898 |
8,072 | This phenomenon can best be described using the vocabulary of abstract algebra. The congruence classes relatively prime to the modulus are a group under multiplication, called the group of units of the ring Z/nZ, and the squares are a subgroup of it. Different nonresidues may belong to different cosets, and there is no... | Modular square root | 0.821898 |
8,073 | Previously, Augustus De Morgan wrote in A Budget of Paradoxes about cranks in multiple subjects, and Dudley wrote a book about angle trisection. However, this is the first book to focus on mathematical crankery as a whole.The book consists of 57 essays, loosely organized by the most common topics in mathematics for cra... | Mathematical Cranks | 0.821892 |
8,074 | A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.Optimal control is an extension of the calculus of variations, and is a mathematical optimization method for deriving control policies. The method is largely due to the work of Lev Pontryagin a... | Optimal Control | 0.821888 |
8,075 | Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecra... | Optimal Control | 0.821888 |
8,076 | Minimize the continuous-time cost functional subject to the first-order dynamic constraints (the state equation) the algebraic path constraints and the endpoint conditions where x ( t ) {\displaystyle {\textbf {x}}(t)} is the state, u ( t ) {\displaystyle {\textbf {u}}(t)} is the control, t {\displaystyle t} is the ind... | Optimal Control | 0.821888 |
8,077 | Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. A control problem includes a cost functional that is a function of state and control variables. An optimal control is a set of differential equations describing the paths of the contr... | Optimal Control | 0.821888 |
8,078 | Photomath is a mobile computer algebra system with an augmented optical character recognition system designed for use with a smartphone's camera to scan and recognize mathematical equations; the app then displays step-by-step explanations onscreen.The app is based on a text recognition engine developed by Microblink, a... | Photomath | 0.821886 |
8,079 | The semantics of an algebraic specifications is defined by axioms in the form of conditional equations.With respect to the signature of integer stacks, we have the following axioms: For any z ∈ Z {\displaystyle z\in \mathbb {Z} } and s ∈ S t a c k {\displaystyle s\in Stack} , A 1: p o p ( p u s h ( z , s ) ) = s A 2: d... | Algebraic semantics (computer science) | 0.821883 |
8,080 | The syntax of an algebraic specification is formulated in two steps: (1) defining a formal signature of data types and operation symbols, and (2) interpreting the signature through sets and functions. | Algebraic semantics (computer science) | 0.821883 |
8,081 | The signature of an algebraic specification defines its formal syntax. The word "signature" is used like the concept of "key signature" in musical notation. A signature consists of a set S {\displaystyle S} of data types, known as sorts, together with a family Σ {\displaystyle \Sigma } of sets, each set containing oper... | Algebraic semantics (computer science) | 0.821883 |
8,082 | The operational semantics of a specification means how to interpret it as a sequence of computational steps. We define a ground term as an algebraic expression without variables. The operational semantics of an algebraic specification refers to how ground terms can be transformed using the given equational axioms as le... | Algebraic semantics (computer science) | 0.821883 |
8,083 | The mathematical semantics (also known as denotational semantics) of a specification refers to its mathematical meaning. The mathematical semantics of an algebraic specification is the class of all algebras that satisfy the specification. In particular, the classic approach by Goguen et al. takes the initial algebra (u... | Algebraic semantics (computer science) | 0.821883 |
8,084 | In computer science, algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program specifications in a formal manner. | Algebraic semantics (computer science) | 0.821883 |
8,085 | Given any canonical algebraic specification, the mathematical semantics agrees with the operational semantics.As a result, canonical algebraic specifications have been widely applied to address program correctness issues. For example, numerous researchers have applied such specifications to the testing of observational... | Algebraic semantics (computer science) | 0.821883 |
8,086 | An algebraic specification is said to be confluent (also known as Church-Rosser) if the rewriting of any ground term leads to the same normal form. It is said to be terminating if the rewriting of any ground term will lead to a normal form after a finite number of steps. The algebraic specification is said to be canoni... | Algebraic semantics (computer science) | 0.821883 |
8,087 | An algebra A {\displaystyle A} interprets the sorts and operation symbols as sets and functions. Each sort s {\displaystyle s} is interpreted as a set A s {\displaystyle A_{s}} , which is called the carrier of A {\displaystyle A} of sort s {\displaystyle s} , and each symbol σ {\displaystyle \sigma } in Σ s 1 s 2 . . . | Algebraic semantics (computer science) | 0.821883 |
8,088 | Semantics refers to the meaning or behavior. An algebraic specification provides both the meaning and behavior of the object in question. | Algebraic semantics (computer science) | 0.821883 |
8,089 | In modern chemistry, a chemical formula is a way of expressing information about the proportions of atoms that constitute a particular chemical compound, using a single line of chemical element symbols, numbers, and sometimes other symbols, such as parentheses, brackets, and plus (+) and minus (−) signs. For example, H... | Mathematical formula | 0.821878 |
8,090 | The second has ~12" diameter full casing, metal rings. Eindhoven Technical University Amirkabir University of Technology and Atomic Energy Organization of Iran have investigated the effect of strong pulsed magnetic fields on the neutron production rate of IEC device. Their study showed that by 1-2 Tesla magnetic field ... | Inertial electrostatic confinement | 0.821877 |
8,091 | Despite demonstration in 2000 of 7200 hours of operation without degradation at high input power as a sealed reaction chamber with automated control the FusionStar project was canceled and the company NSD Ltd was founded. The spherical FusionStar technology was then further developed as a linear geometry system with im... | Inertial electrostatic confinement | 0.821877 |
8,092 | Simultaneously, a key plasma physics text was published by Lyman Spitzer at Princeton in 1963. Spitzer took the ideal gas laws and adapted them to an ionized plasma, developing many of the fundamental equations used to model a plasma. Meanwhile, magnetic mirror theory and direct energy conversion were developed by Rich... | Inertial electrostatic confinement | 0.821877 |
8,093 | Fusors are popular with amateurs, because they can easily be constructed, can regularly produce fusion and are a practical way to study nuclear physics. Fusors have also been used as a commercial neutron generator for industrial applications.No fusor has come close to producing a significant amount of fusion power. | Inertial electrostatic confinement | 0.821877 |
8,094 | Besides using store to load (RAW or true) memory dependence prediction for the out-of-order scheduling of loads and stores, other applications of memory dependence prediction have been proposed. See for example.Memory dependence prediction is an optimization on top of memory dependency speculation. Sequential execution... | Memory dependence prediction | 0.821872 |
8,095 | The cleaved amplified polymorphic sequence (CAPS) method is a technique in molecular biology for the analysis of genetic markers. It is an extension to the restriction fragment length polymorphism (RFLP) method, using polymerase chain reaction (PCR) to more quickly analyse the results. Like RFLP, CAPS works on the prin... | Cleaved Amplified Polymorphic Sequence | 0.821872 |
8,096 | A deeper problem, still an active area of development as of 2014, is that providing HLL debugging information from machine code is quite difficult, basically because of the overhead of debugging information, and more subtly because compilation (particularly optimization) makes determining the original source for a mach... | High-level language computer architecture | 0.821866 |
8,097 | Analogous performance problems have a long history with interpreted languages (dating to Lisp (1958)), only being resolved adequately for practical use by just-in-time compilation, pioneered in Self and commercialized in the HotSpot Java virtual machine (1999). The fundamental problem is that HLLCAs only simplify the c... | High-level language computer architecture | 0.821866 |
8,098 | A detailed critique is given in Ditzel & Patterson (1980). The simplest reason for the lack of success of HLLCAs is that from 1980 optimizing compilers resulted in much faster code and were easier to develop than implementing a language in microcode. Many compiler optimizations require complex analysis and rearrangemen... | High-level language computer architecture | 0.821866 |
8,099 | One can ask whether a minimizer point x ∗ {\displaystyle x^{*}} of the original, constrained optimization problem (assuming one exists) has to satisfy the above KKT conditions. This is similar to asking under what conditions the minimizer x ∗ {\displaystyle x^{*}} of a function f ( x ) {\displaystyle f(x)} in an uncons... | Constraint qualification | 0.821863 |
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