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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 E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalent Weight
In chemistry, equivalent weight ( more precisely, equivalent mass) 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. The corresponding unit of measurement is sometimes expressed as "gram equivalent". The equivalent weight of an element is the mass of a mole of the element divided by the element's valence. That is, in grams, the atomic weight of the element divided by the usual valence. For example, the equivalent weight of oxygen is 16.0/2 = 8.0 grams. 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 ... [...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 if the infringing device or process does not fall within the literal scope of a patent claim but is nevertheless equivalent to the claimed invention. In the United States, 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: #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 the meaning of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Album-equivalent Unit
The album-equivalent unit, or album equivalent, often shortened to just unit, is a sales metric in the music industry that defines the number of streaming media, songs streamed and music download, songs downloaded equal to one Record sales, traditional album sale. 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, partly due to cheap digitally downloaded Single (music), singles. For instance, the only albums that Music recording certification, went platinum in the United States in 2014 were the Frozen (soundtrack), ''Frozen'' soundtrack and Taylor Swift's ''1989 (album), 1989'', whereas several albums had gone platinum in 2013. The use of album-equivalent units transformed the Record chart, music charts from a ranking of best-selling albums into a ranking of most popular albums. The International Federation of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Equivalence
In linear algebra, two rectangular ''m''-by-''n'' matrices ''A'' and ''B'' are called equivalent if :B = Q^ A P for some invertible ''n''-by-''n'' matrix ''P'' and some invertible ''m''-by-''m'' matrix ''Q''. Equivalent matrices represent the same linear transformation ''V'' → ''W'' under two different choices of a pair of bases of ''V'' and ''W'', with ''P'' and ''Q'' being the change of basis matrices in ''V'' and ''W'' respectively. The notion of equivalence should not be confused with that of similarity, which is only defined for square matrices, and is much more restrictive (similar matrices are certainly equivalent, but equivalent square matrices need not be similar). That notion corresponds to matrices representing the same endomorphism ''V'' → ''V'' under two different choices of a ''single'' basis of ''V'', used both for initial vectors and their images. Properties Matrix equivalence is an equivalence relation on the space of rectangular m ... [...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 quantity that was used in chemistry and the biological sciences (see '). The mass of an equivalent is called its equivalent weight. Formula The formula from milligrams (mg) to milli-equivalent (mEq) and back is as follows: \begin \text \to \text &: \quad \text \times \frac \\ pt\text \to \text &: \quad \text \times \frac \end where is the valence and is the molecular weight. For elemental compounds: \text \to \text : \quad \frac \times \frac 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 o ... [...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 Category (mathematics), 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 dual (category theory), 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 betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Equivalence
In model theory, a branch of mathematical logic, two structures ''M'' and ''N'' of the same signature ''σ'' are called elementarily equivalent if they satisfy the same first-order ''σ''-sentences. If ''N'' is a substructure of ''M'', one often needs a stronger condition. In this case ''N'' is called an elementary substructure of ''M'' if every first-order ''σ''-formula ''φ''(''a''1, …, ''a''''n'') with parameters ''a''1, …, ''a''''n'' from ''N'' is true in ''N'' if and only if it is true in ''M''. If ''N'' is an elementary substructure of ''M'', then ''M'' is called an elementary extension of ''N''. An embedding ''h'': ''N'' → ''M'' is called an elementary embedding of ''N'' into ''M'' if ''h''(''N'') is an elementary substructure of ''M''. A substructure ''N'' of ''M'' is elementary if and only if it passes the Tarski–Vaught test: every first-order formula ''φ''(''x'', ''b''1, …, ''b''''n'') with ... [...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. A simpler example is equality. Any number a is equal to itself (reflexive). If a = b, then b = a (symmetric). If a = b and b = c, then a = c (transitive). 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". Definitions A binary relation \,\si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Class (music)
In music theory, equivalence class is an Equality (mathematics), equality (Equals sign, =) or equivalence relation, equivalence between properties of set (music), sets (unordered) or twelve-tone rows (ordered sets). A relation rather than an operation, it may be contrasted with derivation (music), 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 [from 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 inversion (music), inversional, permutation (music), permutational, and Transposition (music)#Transpositional equivalency, transpositional equivalency may or may not be considered (sequence (music), sequences and modulation (music), modulations are techniqu ... [...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 model of computation, 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 decode 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 mac ... [...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 (possibly noncomputable) procedure that correctly decides wheth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or Expression (mathematics), expressions, stating that they have the same value, or represent the same mathematical object. Equality between and is written , and read " equals ". In this equality, and are distinguished by calling them ''sides of an equation, left-hand side'' (''LHS''), and ''right-hand side'' (''RHS''). Two objects that are not equal are said to be distinct. Equality is often considered a primitive notion, meaning it is not formally defined, but rather informally said to be "a relation each thing bears to itself and nothing else". This characterization is notably circular ("nothing else"), reflecting a general conceptual difficulty in fully characterizing the concept. Basic properties about equality like Reflexive relation, reflexivity, Symmetric relation, symmetry, and Transitive relation, transitivity have been understood intuitively since at least the ancient Greeks, but were not symboli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
