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Equivalent
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 Economic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalent Weight
In chemistry, equivalent weight (also known as gram equivalent) is the mass of one equivalent, that is the mass of a given substance which will combine with or displace a fixed quantity of another substance. The equivalent weight of an element is the mass which combines with or displaces 1.008 gram of hydrogen or 8.0 grams of oxygen or 35.5 grams of chlorine. These values correspond to the atomic weight divided by the usual valence; for oxygen as example that is 16.0 g / 2 = 8.0 g. For acid–base reactions, the equivalent weight of an acid or base is the mass which supplies or reacts with one mole of hydrogen cations (). For redox reactions, the equivalent weight of each reactant supplies or reacts with one mole of electrons (e−) in a redox reaction. Equivalent weight has the units of mass, unlike atomic weight, which is now used as a synonym for relative atomic mass and is dimensionless. Equivalent weights were originally determined by experiment, but (insofar as t ... [...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] |
Album-equivalent Unit
The album-equivalent unit, or album equivalent, is a measurement unit in music industry to define the consumption of music that equals the purchase of one album copy. This consumption includes streaming and song downloads in addition to traditional album sales. The album-equivalent unit was introduced in the mid- 2010s as an answer to the drop of album sales in the 21st century. Album sales more than halved from 1999 to 2009, declining from a $14.6 to $6.3 billion industry. For instance, the only albums that went platinum in the United States in 2014 were the '' Frozen'' soundtrack and Taylor Swift's ''1989'', whereas several artists' works had in 2013. The usage of the album-equivalent units revolutionized the charts from the "best-selling albums" ranking into the "most popular albums" ranking. The International Federation of the Phonographic Industry (IFPI) have used album-equivalent unit to measure their Global Recording Artist of the Year since 2013. Terminology The ter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalent (chemistry)
An equivalent (symbol: officially equiv; unofficially but often Eq) is the amount of a substance that reacts with (or is ''equivalent'' to) an arbitrary amount (typically one mole) of another substance in a given chemical reaction. It is an archaic unit of measurement that was used in chemistry and the biological sciences (see '). The mass of an equivalent is called its equivalent weight. Formula : ''milligrams to = mg x V / MW'' :: Example for elemental compounds: (mg element / elemental compound mass fraction) x V / MV : '' to milligrams = mEq x MW / V'' Common examples mEq to milligram Milligram to mEq Formal definition In a more formal definition, the ''equivalent'' is the amount of a substance needed to do one of the following: * react with or supply one mole of hydrogen ions () in an acid–base reaction * react with or supply one mole of electrons in a redox reaction. The "hydrogen ion" and the "electron" in these examples are respectively called the "reaction ... [...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] |
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 (music)
In music theory, equivalence class is an equality ( =) or equivalence between properties of sets (unordered) or twelve-tone rows (ordered sets). A relation rather than an operation, it may be contrasted with derivation.Schuijer (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', p.85. . "It is not surprising that music theorists have different concepts of equivalence rom each other.." "Indeed, an informal notion of equivalence has always been part of music theory and analysis. Pitch class set theory, however, has adhered to formal definitions of equivalence." Traditionally, octave equivalency is assumed, while inversional, permutational, and transpositional equivalency may or may not be considered (sequences and modulations are techniques of the common practice period which are based on transpositional equivalency; similarity within difference; unity within variety/variety within unity). A definition of equivalence between two twelve-tone series tha ... [...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] |
Turing Equivalence (theory Of Computation)
In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine (devised by English mathematician and computer scientist Alan Turing). This means that this system is able to recognize or decide other data-manipulation rule sets. Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. A related concept is that of Turing equivalence two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. The Church–Turing thesis conjectures that any function whose values can be computed by an algorithm can be computed by a Turing machine, and therefore that if any real-world computer can simulate a Turing machine, it is Turing equivalent to a Turing machine. A universal Turin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Equivalence (recursion Theory)
In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set. Overview The concept of Turing degree is fundamental in computability theory, where sets of natural numbers are often regarded as decision problems. The Turing degree of a set is a measure of how difficult it is to solve the decision problem associated with the set, that is, to determine whether an arbitrary number is in the given set. Two sets are Turing equivalent if they have the same level of unsolvability; each Turing degree is a collection of Turing equivalent sets, so that two sets are in different Turing degrees exactly when they are not Turing equivalent. Furthermore, the Turing degrees are partially ordered, so that if the Turing degree of a set ''X'' is less than the Turing degree of a set ''Y'', then any (noncomputable) procedure that correctly decides whether numbers a ... [...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] |
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] |
