|
Equivalence
Equivalence or Equivalent may refer to: Arts and entertainment *Album-equivalent unit, a measurement unit in the music industry *Equivalence class (music) *''Equivalent VIII'', or ''The Bricks'', a minimalist sculpture by Carl Andre *'' Equivalents'', a series of photographs of clouds by Alfred Stieglitz Language *Dynamic and formal equivalence in translation *Equivalence (formal languages) Law *The doctrine of equivalents in patent law *The equivalence principle as if impacts on the direct effect of European Union law Logic *Logical equivalence, where two statements are logically equivalent if they have the same logical content *Material equivalence, a relationship where the truth of either one of the connected statements requires the truth of the other Science and technology Chemistry *Equivalent (chemistry) *Equivalence point *Equivalent weight Computing *Turing equivalence (theory of computation), or Turing completeness *Semantic equivalence in computer metadata Economi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class. Notation Various notations are used in the literature to denote that two elements a and b of a set are equivalent with respect to an equivalence relation R; the most common are "a \sim b" and "", which are used when R is implicit, and variations of "a \sim_R b", "", or "" to specify R explicitly. Non-equivalence may be written "" or "a \not\equiv b". Definition A binary relation \,\sim\, on a set X is said to be an equivalence relation, if and only if it is reflexive, symmetric and transitive. That is, for all a, b, and c in X: * a \sim a ( ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Principle
In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is the same as the ''pseudo-force'' experienced by an observer in a non-inertial (accelerated) frame of reference. Einstein's statement of the equality of inertial and gravitational mass Development of gravitational theory Something like the equivalence principle emerged in the early 17th century, when Galileo expressed experimentally that the acceleration of a test mass due to gravitation is independent of the amount of mass being accelerated. Johannes Kepler, using Galileo's discoveries, showed knowledge of the equivalence principle by accurately describing what would occur if the Moon were stopped in its orbit and dropped towards Earth. This can be deduced without knowing if or in what manner gravity decreases ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Class
In mathematics, when the elements of some set S have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S into equivalence classes. These equivalence classes are constructed so that elements a and b belong to the same equivalence class if, and only if, they are equivalent. Formally, given a set S and an equivalence relation \,\sim\, on S, the of an element a in S, denoted by is the set \ of elements which are equivalent to a. It may be proven, from the defining properties of equivalence relations, that the equivalence classes form a partition of S. This partition—the set of equivalence classes—is sometimes called the quotient set or the quotient space of S by \,\sim\,, and is denoted by S / \sim. When the set S has some structure (such as a group operation or a topology) and the equivalence relation \,\sim\, is compatible with this structure, the quotient set often inherits a similar structure from its parent set. Examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricardian Equivalence
The Ricardian equivalence proposition (also known as the Ricardo–de Viti–Barro equivalence theorem) is an economic hypothesis holding that consumers are forward-looking and so internalize the government's budget constraint when making their consumption decisions. This leads to the result that, for a given pattern of government spending, the method of financing such spending does not affect agents' consumption decisions, and thus, it does not change aggregate demand. Introduction Governments can finance their expenditures by creating new money, by levying taxes, or by issuing bonds. Since bonds are loans, they must eventually be repaid—presumably by raising taxes in the future. The choice is therefore "tax now or tax later." Suppose that the government finances some extra spending through deficits; i.e. it chooses to tax later. According to the hypothesis, taxpayers will anticipate that they will have to pay higher taxes in future. As a result, they will save, rather than spe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moral Equivalence
Moral equivalence is a term used in political debate, usually to deny that a moral comparison can be made of two sides in a conflict, or in the actions or tactics of two sides. The term had some currency in polemic debates about the Cold War, and currently the Arab–Israeli conflict. "Moral equivalence" began to be used as a polemic ''term-of-retort'' to "moral relativism", which had been gaining use as an indictment against political foreign policy that appeared to use only a situation-based application of widely held ethical standards. International conflicts are sometimes viewed similarly, and interested parties periodically urge both sides to conduct a ceasefire and negotiate their differences. However these negotiations may prove difficult in that both parties in a conflict believe that they are morally superior to the other, and are unwilling to negotiate on basis of moral equivalence. Cold War In the Cold War context, the term was and is most commonly used by anticommun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Of Categories
In category theory, a branch of abstract mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are "essentially the same". There are numerous examples of categorical equivalences from many areas of mathematics. Establishing an equivalence involves demonstrating strong similarities between the mathematical structures concerned. In some cases, these structures may appear to be unrelated at a superficial or intuitive level, making the notion fairly powerful: it creates the opportunity to "translate" theorems between different kinds of mathematical structures, knowing that the essential meaning of those theorems is preserved under the translation. If a category is equivalent to the opposite (or dual) of another category then one speaks of a duality of categories, and says that the two categories are dually equivalent. An equivalence of categories consists of a functor between the involved categories, which is required t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. Logical equivalences In logic, many common logical equivalences exist and are often listed as laws or properties. The following tables illustrate some of these. General logical equivalences Logical equivalences involving conditional statements :#p \implies q \equiv \neg p \vee q :#p \implies q \equiv \neg q \implies \neg p :#p \vee q \equiv \neg p \implies q :#p \wedge q \equiv \neg (p \implies \neg q) :#\neg (p \implies q) \equiv p \wedge \neg q :#(p \implies q) \wedge (p \implie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between and is written , and pronounced equals . The symbol "" is called an "equals sign". Two objects that are not equal are said to be distinct. For example: * x=y means that and denote the same object. * The identity (x+1)^2=x^2+2x+1 means that if is any number, then the two expressions have the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function. * \ = \ if and only if P(x) \Leftrightarrow Q(x). This assertion, which uses set-builder notation, means that if the elements satisfying the property P(x) are the same as the elements satisfying Q(x), then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalents
''Equivalents'' is a series of photographs of clouds taken by Alfred Stieglitz from 1925 to 1934. They are generally recognized as the first photographs intended to free the subject matter from literal interpretation, and, as such, are some of the first completely abstract photographic works of art. Description Stieglitz took at least 220 photographs that he called ''Equivalent'' or ''Equivalents''; all feature clouds in the sky. The majority of them show only the sky without any horizon, buildings or other objects in the frame, but a small number do include hills or trees. One series from 1927 prominently features poplar trees in the foreground. Almost all of the photographs are printed very darkly so the sky often appears black or nearly black. The contrast between the sky and the much lighter clouds is striking in all but a few of the prints. Some images include the sun either as a distinct element in the photograph or as an illuminating force behind the clouds. Background ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence (formal Languages)
In formal language theory, weak equivalence of two grammars means they generate the same set of strings, i.e. that the formal language they generate is the same. In compiler theory the notion is distinguished from strong (or structural) equivalence, which additionally means that the two parse trees are reasonably similar in that the same semantic interpretation can be assigned to both. Vijay-Shanker and Weir (1994) demonstrates that Linear Indexed Grammars, Combinatory Categorial Grammars, Tree-adjoining Grammars, and Head Grammars are weakly equivalent formalisms, in that they all define the same string languages. On the other hand, if two grammars generate the same set of derivation trees (or more generally, the same set of abstract syntactic objects), then the two grammars are strongly equivalent. Chomsky (1963) introduces the notion of strong equivalence, and argues that only strong equivalence is relevant when comparing grammar formalisms. Kornai and Pullum (1990)Kornai, A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence (trade)
Equivalence is a term applied by the Uruguay Round Agreement on the Application of Sanitary and Phytosanitary Measures. World Trade Organization (WTO) Member countries shall accord acceptance to the Sanitary and Phytosanitary (SPS) measures of other countries (even if those measures differ from their own or from those used by other Member countries trading in the same product) if the exporting country demonstrates to the importing country that its measures achieve the importer’s appropriate level of sanitary and phytosanitary protection. History In June 2021 a trade dispute threatened to erupt between the UK and the von der Leyen Commission over the Northern Irish Protocol (NIP) which flowed from Brexit. The position of Lord Frost and the Johnson government was that trade equivalence with the European Union over SPS measures could be maintained with "a recognition of mutually high standards", whereas his opposite number Maros Sefcovic insisted that Northern Ireland join the Co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctrine Of Equivalents
The doctrine of equivalents is a legal rule in many (but not all) of the world's patent systems that allows a court to hold a party liable for patent infringement even though the infringing device or process does not fall within the literal scope of a patent claim, but nevertheless is equivalent to the claimed invention. U.S. Judge Learned Hand has described its purpose as being "to temper unsparing logic and prevent an infringer from stealing the benefit of the invention". Standards for determining equivalents Germany German courts typically apply a three-step test known as Schneidmesser's questions. These questions are: #Does the variant solve the problem underlying the invention with means that objectively have the same effect? #Would the person skilled in the art, using the common general knowledge, have realised at the priority date that the variant has the same effect? #Are the considerations which the skilled person takes into account for the variant in the light of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
