Wiktionarypar equivalenceEquivalence or equivalent may refer to In chemistry Equivalent chemistry Equivalence point Equivalent weight In computing Turing equivalence theory of computation In ethics Moral equivalence In history The Equivalent , a sum paid from England to Scotland at their Union in 1707. In logic Logical equivalence Logical biconditional In mathematics Equivalence relation Equivalence of categories Improper rotation equivalence Rotation al equivalence Probabilistic equivalence In patent law Doctrine of equivalents In music Equivalence class music In relativity Equivalence principle In translation Dynamic and formal equivalence In Medical Device Manufacturing Equivalency Document In international trade Equivalence trade , a requirement imposed on WTO Member countries regarding acceptable sanitary protection measures. In art Equivalent VIII , a minimalist sculpture by Carl Andre consisting of a collection of bricks. disambig cs Ekvivalence de quivalenz fr quivalence ia Equivalentia disambiguation hu Ekvivalencia egy rtelm s t lap nl Equivalent no Ekvivalens nn Ekvivalens pl Ekwiwalent ru sk Ekvivalencia fi Ekvivalenssi ... more details
In mathematics , math mathcal A math equivalence , sometimes called right left equivalence , is an equivalence relation between germ mathematics map germs . Let math M math and math N math be two manifold s, and let math f, g M,x to N,y math be two smooth germ mathematics map germs . We say that math f math and math g math are math mathcal A math equivalent if there exist diffeomorphism germs math phi M,x to M,x math and math psi N,y to N,y math such that math psi circ f g circ phi. math In other words, two germ mathematics map germs are math mathcal A math equivalent if one can be taken onto the other by a diffeomorphism diffeomorphic change of co ordinates in the source i.e. math M math and the target i.e. math N math . Let math Omega M x,N y math denote the space of smooth germ mathematics map germs math M,x to N,y . math Let math mbox diff M x math be the Group mathematics group of diffeomorphism germs math M,x to M,x math and math mbox diff N y math be the group of diffeomorphism germs math N,y to N,y . math The group math G mbox diff M x times mbox diff N y math acts on math Omega M x,N y math in the natural way math phi, psi cdot f psi 1 circ f circ phi. math Under this action we see that the germ mathematics map germs math f, g M,x to N,y math are math mathcal A math equivalent if, and only if, math g math lies in the orbit group theory orbit of math f math , i.e. math g in mbox orb G f math or vice versa . A map germ is called stable if its orbit group theory orbit under the Group action action of math G mbox diff M x times mbox diff N y math is open set open relative to the Whitney topology . Since math Omega M x,N y math is an infinite dimensional space metric topology is no longer trivial. Whitney topology compares the differences in successive derivatives and gives ... k in mathbb N math , math E 6, math math E 7, math and math E 8. math See also K equivalence contact equivalence References M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities . Graduate ... more details
In mathematics, weak equivalence may refer to Equivalence of categories Weak equivalence in category theory Weak equivalence homotopy theory Weak equivalence in homotopy theory Weak equivalence formal languages Weak equivalence in formal languages disambiguation ... more details
For unitary equivalence of bounded operator s in Hilbert space , see self adjoint operator . For unitary equivalence of unitary representation s see that page. mathdab ... more details
Turing equivalence may refer to Turing completeness , having computational power equivalent to a universal Turing machine Turing degree equivalence of sets , having the same level of unsolvability See Turing machine equivalents . disambig ... more details
. File Set partition.svg right thumb An equivalence relation partition of a set partitions a set into several disjoint set disjoint subsets, called equivalence class es. All the elements in a given equivalence class are equivalent among themselves, and no element is equivalent with any element from ... of the Bell number 52 equivalence relations on a 5 element set Colored fields, including those in light gray, stand for ones white fields for zeros. In mathematics , an equivalence relation is a binary ... are considered equivalent with respect to the equivalence relation if and only if they are elements ... to denote that two elements a and b of a set are equivalent with respect to an equivalence ... relation on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric ... with the relation is called a setoid . The equivalence class of a under , denoted a , is defined ... of integers, and let two elements of A be related if their difference is even. This is an equivalence relation, which partitions the integers into two equivalence classes, the even and odd integers. Examples Equivalence relations The following are all equivalence relations Is equal to on the set ..., is not an equivalence relation, because although reflexive and symmetric, it is not transitive ... some point if the limit of f g is 0 at that point, then this defines an equivalence relation. The relation ... of all human beings is not an equivalence relation. Although siblinghood is symmetric if A is a sibling ... be a sibling of A . The small modification, is a sibling of, or is the same person as , is an equivalence ... relation is an equivalence relation whose domain X is also the underlying set for an algebraic ... correspond to the normal subgroup s. Equality mathematics Equality is both an equivalence relation ... . A partial equivalence relation is transitive and symmetric. Transitive and symmetric imply reflexive ... and transitive. Well definedness under an equivalence relation If is an equivalence relation ... more details
see equivalence class music . In mathematics , given a Set mathematics set mvar X and an equivalence relation math on mvar X , the equivalence class of an element mvar x in mvar X is the subset of all elements in mvar X which are equivalent to mvar x . Equivalence classes among elements of a structure ... definition An equivalence relation is a binary relation math satisfying three properties For every ... relation transitivity . The equivalence class of an element mvar a is denoted math a and may be defined ... . The alternative notation math a sub R sub can be used to denote the equivalence class of the element mvar a specifically with respect to the equivalence relation mvar R . This is said to be the mvar R equivalence class of mvar a . The set of all equivalence classes in mvar X given an equivalence relation math is denoted as math X and called the quotient set of mvar X by math . Each equivalence ... of dividing the input set by the equivalence relation, hence both the name quotient , and the notation ... is that if mvar X is finite and the equivalence classes are all equinumerous , then the number of equivalence ... of elements in each equivalence class. The quotient set math X may be thought of as the set mvar ... is the equivalence relation has the same color as , then one particular equivalence class consists of all ... arithmetic modulo 2 equivalence relation on the set math Z of integer s math x y if and only if their difference math x &minus y is an even number . This relation gives rise to exactly two equivalence ... mvar X be the set of ordered pairs of integers math a , b with mvar b not zero, and define an equivalence relation math on mvar X according to which math a , b c , d if and only if math 1 ad bc . Then the equivalence class of the pair math a , b can be identified with the rational number math a b , and this equivalence relation and its equivalence classes can be used to give a formal definition of the set ... integral domain . Properties Every element mvar x of mvar X is a member of the equivalence class ... more details
In metadata , property equivalence is the statement that two properties have the same property extension or values. This usually but not always implies that the two properties have the same semantic s or meaning. Technically it only implies that the data elements have the same values. Property equivalence is one of the three ways that a metadata registry can store equivalence mappings to other metadata registries. Note that property equivalence is not the same as property equality. Equivalent properties have the same values i.e., the same property extension , but may have different Intension intensional meaning i.e., denote different concepts . Property equality should be expressed with the owl sameAs construct. As this requires that properties are treated as individuals, such axioms are only allowed in OWL Full. See also metadata registry Web ontology language Class equivalence Synonym Ring External links http www.w3.org TR owl ref equivalentProperty def OWL equivalent property definition http www.w3.org TR owl ref sameAs def OWL same as definition Category Metadata comp sci stub ... more details
In mathematics and theoretical physics , two geometries are conformally equivalent if there exists a conformal transformation an angle preserving transformation that maps one geometry to the other one. More generally, two Riemannian metric s on a manifold math M math are conformally equivalent if one is obtained from the other by multiplication by a positive function on math M math . See also conformal geometry biholomorphy biholomorphic equivalence equivalence relation AdS CFT correspondence geometry stub Category Conformal geometry nl Hoekgetrouwe equivalentie ... more details
In linear algebra , two rectangular m by n matrix mathematics matrices A and B are called equivalent if math B Q 1 A P math for some invertible matrix invertible n by n matrix P and some invertible m by m matrix Q . Equivalent matrices represent the same linear map linear transformation V W under two different choices of a pair of Basis linear algebra 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 Similar matrix 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 matrices. For two rectangular matrices of the same size, their equivalence can also be characterized by the following conditions The matrices can be transformed into one another by a combination of elementary row operation elementary row and column operations . The matrices have the same rank of a matrix rank . See also Similar matrix Row equivalence Matrix congruence Category Matrices de quivalenz Matrix nl Equivalente matrices sl Ekvivalentna matrika fi Matriisiekvivalenssi zh ... more details
from q . There is a close relationship between material equivalence and logical equivalence. Formulas ... DEFAULTSORT Logical Equivalence Category Logic cs Ekvivalence logika de Logische quivalenz ... more details
In mathematics , math mathcal K math equivalence , or contact equivalence , is an equivalence relation between germ mathematics map germs . It was introduced by John Mather mathematician John Mather in his seminal work in Singularity theory in the 1970s as a technical tool for studying stable maps. Since then it has proved important in its own right. Roughly speaking, two map germs &fnof , g are math scriptstyle mathcal K math equivalent if &fnof sup &minus 1 sup 0 and g sup &minus 1 sup 0 are diffeomorphic . Definition Two map germs math f,g X to Y,0 math are math scriptstyle mathcal K math equivalent if there is a diffeomorphism math Psi X times Y to X times Y math of the form &Psi x,y &phi x ,&psi x,y , satisfying, math Psi x,0 phi x , 0 math , and math Psi x,f x phi x , g phi x math . In other words, &Psi maps the graph of f to the graph of g , as well as the graph of the zero map to itself. In particular, the diffeomorphism &phi maps f sup &minus 1 sup 0 to g sup &minus 1 sup 0 . The name contact is explained by the fact that this equivalence is measuring the contact between the graph of f and the graph of the zero map. Contact equivalence is the appropriate equivalence relation for studying the sets of solution of equations, and finds many applications in dynamical systems and bifurcation theory , for example. It is easy to see that this equivalence relation is weaker than A equivalence , in that any pair of math scriptstyle mathcal A math equivalent map germs are necessarily math scriptstyle mathcal K math equivalent. K sub V sub equivalence This modification of math scriptstyle mathcal K math equivalence was introduced by James Damon in the 1980s. Here V is a subset or subvariety of Y , and the diffeomorphism &Psi above is required to preserve not math X times 0 math but math X times V math that is, math y in V Rightarrow psi x,y in V math . In particular, &Psi maps f sup &minus 1 sup V to g sup &minus 1 sup V . See also A equivalence References J. Martinet ... more details
In computer metadata , semantic equivalence is a declaration that two data element s from different vocabularies contain data that has similar meaning. There are three types of semantic equivalence statements Class computer science Class or concept equivalence. A statement that two high level concepts have similar or equivalent meaning. Property philosophy Property or Attribute computing attribute equivalence. A statement that two properties, descriptors or attributes of a classes have similar meaning. Object computer science Instance equivalence. A statement that two instances of data are the same or refer to the same instance. Example Assume that there are two organizations, each having a separate data dictionary. The first organization has a data element entry DataElement Name PersonFamilyName Name Definition The name of a person shared with other members of their family. Definition DataElement and a second organization has a data dictionary with a data element with the following entry DataElement Name IndividualLastName Name Definition The name of an individual person shared with other members of their family. Definition DataElement these two data elements can be considered to have the same meaning and can be marked as semantically equivalent. See also Logical equivalence Metadata Vocabulary based transformation Web Ontology Language OWL References http www.w3.org TR owl ref World Wide Web OWL Language Reference http www.udef.org Universal Data Element Framework Web Site Semantic Equivalency for Standards and Integrations External links http www.w3.org TR owl ref equivalentClass def OWL definition of Class Equivalency http www.w3.org TR owl ref equivalentProperty def OWL definition of Property Equivalency Category Metadata ... more details
False Equivalence is a logical fallacy which describes a situation where there is a logical and apparent equivalence, but when in fact there is none. ref Eisner, p. 157 ref Description A common way for this fallacy to be perpetuated is one shared trait between two subjects is assumed to show equivalence, especially in order of magnitude, when equivalence is not necessarily the logical result. The pattern of the fallacy is often as such If A is the set of c and d, and B is the set of d and e, then since they both contain d, A and B are equal. It should be noted though that d existing in both sets is not required, only a passing similarity is required to cause this fallacy to to be able to be used. The following statements are examples of False Equivalence Political party A says the sky is red, Political party B says the sky is blue, therefore since they must both be equally wrong, and the truth must be somewhere in the middle, the sky must be purple. They re both soft, cuddly pets, there s no difference between a cat and a dog. We re all born naked, we re all no different from each other. It s just a little white lie. Implied False Equivalence The phrase is usually used in cases where the lie is large enough to cause concern, and is being claimed as equivalent to small lies that are generally not considered worth mentioning. References See Wikipedia Footnotes on how to create references using ref ref tags which will then appear here automatically Eisner, A practical introduction to PSL , Springer, 2006 Reflist Categories Category Articles created via the Article Wizard Category Logical fallacies Category Critical thinking ... more details
prose date September 2011 merge Titration curve discuss Talk Equivalence point date September 2011 The equivalence point , or stoichiometry stoichiometric point , of a chemical reaction is when a titrant .... In some cases there are multiple equivalence points which are multiples of the first ... an inflection point at the equivalence point where the graph is steepest. ref http khanexercises.appspot.com video?v 299o6c Fkz4 Strong acid titration and equivalence point ref A striking fact about equivalence is that in a reaction the equivalence of the reactants as well as products is conserved. The endpoint similar to, but not the same as the equivalence point refers to the point at which the indicator changes color in a colorimetric titration. Methods to determine the equivalence point Different methods to determine the equivalence point include pH indicator This is a substance that changes ... of the equivalence point. Potentiometer A potentiometer can also be used. This is an instrument ... based on a redox reaction the potential of the working electrode will suddenly change as the equivalence .... At the equivalence point there will be a sudden change in the measured pH. It can be more ... uses the heat produced or consumed by the reaction to determine the equivalence point. This is important ... the amount of analyte in the sample solution. Instead, the equivalence point is determined by the rate ... by reaction with the titrant, a change in the rate of temperature increase or decrease reveals the equivalence point and an inflection in the temperature curve can be observed. The equivalence point ... can resolve temperatures to 10 sup 5 sup K. Sharp equivalence points have been obtained in titrations ... be used to determine the equivalence point. Alternatively, the presence of free titrant indicating ... in solution. The equivalence point can then be detected as a change in the current. This method ... links http www2.iq.usp.br docente gutz Curtipot .html Equivalence points of virtual and real ... more details
According to the principle of nuclear equivalence , the nuclei of essentially all differentiated adult cells of an individual are genetically though not necessarily metabolically identical to one another and to the nucleus of the zygote from which they descended. This means that virtually all somatic cells in an adult have the same genes. However, different cells express different subsets of these genes. The evidence for nuclear equivalence comes from cases in which differentiated cells or their nuclei have been found to retain the potential of directing the development of the entire organism. Such cells or nuclei are said to exhibit totipotency . ref cite book last Solomon, Berg, Martin first Eldra, Linda, Diana W. title BIOLOGY, 9th edition year 2011 publisher Brooks Cole isbn 978 1 111 77437 0 pages 370 ref References reflist Uncategorized date April 2012 ... more details
Strong equivalence Two metrics math d 1 math and math d 2 math are strongly equivalent if and only ... for topological equivalence listed above, strong equivalence requires that there is a single ... constants associated with each point of math X math . Strong equivalence of two metrics implies topological equivalence, but not vice versa. An intuitive reason why topological equivalence does not imply strong equivalence is that Bounded set Metric space bounded sets under one metric are also ... under a strongly equivalent one. ref Ok, p. 175. ref Properties preserved by equivalence The continuous ... more details
Missing information non food uses of the phrase Substantial equivalence date March 2008 Over quotation date March 2008 Cleanup date August 2007 Substantial equivalence is a concept, developed by OECD in 1991 ... as the conventional food. Substantial equivalence is important from a regulatory point of view ... equivalence concept was proposed by the Food and Agriculture Organization FAO and World ..., substantial equivalence can allow products to get to market within months of their development. Reasoning about substantial equivalence is widely used by national and international agencies ... whybiotech.com http www.whybiotech.com index.asp?id 1244 Substantial Equivalence in Food Safety Assessment ... the doctrine of substantial equivalence the GMO industry has avoided safety testing, and that forthcoming ... of Substantial Equivalence , M C Journal of Media & Culture, 11 2 , 2008. ref Some other new biochemical concepts that are important for understanding the substantial equivalence of a novel ... the term substantial equivalence has been interpreted differently by the various participants in the debate ... biotech info.net http www.biotech info.net antinutrients.html Substantial equivalence of antinutrients .... The concept of substantial equivalence has been developed as part of a safety evaluation framework ... product, which are then subject to further toxicological investigation. Substantial equivalence ..., 2001 blockquote The utility of the substantial equivalence concept is illustrated by the way ... obtained are different. As a notion substantial equivalence was first articulated by the OECD ... UC London and Sue Mayer GeneWatch UK ref name ReferenceA Beyond substantial equivalence . Nature ... equivalence recognises the fact that existing foods often contain toxic components usually called ... Concepts&lang Agbios commentary on substantial equivalence ref It also recognised the well supported ... re affirmed in numerous scientific deliberations, ref name Henry I. Miller 1999 Substantial equivalence ... more details
Refimprove date August 2008 portal Software Testing Equivalence partitioning also called Equivalence Class Partitioning or ECP ref Citation title Practical Software Testing first1 Ilene last1 Burnstein publisher Springer Verlag year 2003 isbn 0 387 95131 8 page 623 ref is a software testing technique that divides the input data of a software unit into partitions of data from which test cases can be derived. In principle, test cases are designed to cover each partition at least once. This technique tries to define test cases that uncover classes of errors, thereby reducing the total number of test cases that must be developed. Equivalence partitioning is typically applied to the inputs of a tested component, but may be applied to the outputs in rare cases. The equivalence partitions are usually derived from the requirements specification for input attributes that influence the processing of the test object. An input has certain ranges which are valid and other ranges which are invalid. Invalid data here does not mean that the data is incorrect, it means that this data lies outside of specific partition. This may be best explained by the example of a function which takes a parameter month . The valid range for the month is 1 to 12, representing January to December. This valid range is called a partition. In this example there are two further partitions of invalid ranges. The first invalid partition would be 0 and the second invalid partition would be 13. ... 2 1 0 1 .............. 12 ... to equivalence partitioning says that only one test case of each partition is needed to evaluate ... is to relate equivalence partitioning to so called black box testing which is strictly checking a software ... that both paths are examined. To achieve this it is necessary to introduce additional equivalence ... valid partition P2 and 15 from invalid partition 2. Equivalence partitioning is not a stand alone method ... tool that is combining test path generation from UML state machines with equivalence class generation ... more details
An equivalence group is a biology term used to describe a set of unspecified cells that have the same ... suggests that equivalence groups are limited to cells of the same ancestry, also known as sibling ... of an equivalence group adopt different fates from one another. ref name greenwald cite journal author ... 1365402 doi 10.1016 0092 8674 92 90470 W last2 Rubin first2 GM ref Equivalence groups assume various ... when a signal originating from outside of the equivalence group specifies a subset of the na ve cells. ref name greenwald Another mode, known as lateral inhibition , arises when a signal within an equivalence ... ref In many examples of equivalence groups, both induction and lateral inhibition are used to define patterns of distinct cell types. Cells of an equivalence group that do not receive a signal adopt ... equivalence group journal Development volume 122 issue 6 pages 1839 47 year 1996 pmid 8674423 last2 Weisblat first2 DA ref At a certain point the fates of cells within an equivalence group become irreversibly determined, thus they loose their multipotent potential. The following provides examples of equivalence groups studied in nematodes and ascidians . Vulva Precursor Cell Equivalence Group Image VPCs.png thumb 400px alt Vulva Precursor Cell Equivalence Group Model for the determination of the VPCs ... example of an equivalence group is the vulva precursor cells VPCs of nematodes. In Caenorhabditis ... of cell of an equivalence group consisting of six VPCs, P3.p P8.p, which lie ventrally along the anterior ... pmid 3753901 doi 10.1016 0092 8674 86 90842 1 last2 Horvitz first2 HR ref The six VPCs form an equivalence ... equivalence group. Ascidian Pigment Precursor Equivalence Group Image Otolith Ocellus.png thumb 400px alt Otolith and Ocellus Two bilateral pigment precursor cells form an equivalence group that eventually ... for Studying Equivalence in Halocynthia roretzi To elucidate whether the fates of the otolith ... precursor equivalence group is specified. Cytochalasin treatment of early tailbud stage embryos ... more details
binding energy , etc. E tv s experiment s detect no composition or field equivalence principle violations ... In the physics of general relativity , the equivalence principle is any of several related concepts dealing with the equivalence of Gravitational mass gravitational and inertial mass , and to Albert .... Einstein s statement of the equivalence principle Quotation A little reflection will show that the law .... ref See momentum and velocity . Development of gravitation theory Something like the equivalence principle ... theory , in which the inertial and gravitational masses are identical. The equivalence principle proper ... g . Einstein stated it thus quote we ... assume the complete physical equivalence of a gravitational ... suggest the following corollary to the equivalence principle, which Einstein formulated precisely in 1911 ... equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference ... where Newton s mechanics holds sway, we are certain of the equivalence of the systems K and K ... Einstein combined postulate postulated the equivalence principle with special relativity to predict ... equivalence principle, as described by Einstein, concluded that free fall and inertial motion were physically equivalent. This form of the equivalence principle can be stated as follows. An observer ... field which are absent from an accelerating spaceship in deep space. Although the equivalence ... called Einstein equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence principle as a starting point. They only differ in whether or not they apply to gravitational experiments. Modern usage Three forms of the equivalence principle are in current use weak Galilean , Einsteinian, and strong. The weak equivalence principle Universality of free fall and weak equivalence principle redirect to this subsection. Please do not change its title without making sure the redirects work properly. Cleanup section date January 2010 The weak equivalence principle ... more details
In category theory , an abstract branch of mathematics , an equivalence of categories is a relation between ... examples of categorical equivalences from many areas of mathematics. Establishing an equivalence ... . An equivalence of categories consists of a functor between the involved categories, which is required ... is required, but this is of much less practical use than the equivalence concept. Definition Formally, given two categories C and D , an equivalence of categories consists of a functor F C D , a functor ... equivalent if there exists an equivalence respectively duality between them. Furthermore, we say that F is an equivalence of categories if an inverse functor G and natural isomorphisms as above exist ... F C D yields an equivalence of categories if and only if it is full functor full , i.e. for any ... functors. On the other hand, though the above properties guarantee the existence of a categorical equivalence ... with these properties is sometimes called a weak equivalence of categories unfortunately this conflicts ... therefore view an adjointness relation between two functors as a very weak form of equivalence . Assuming ... functors form an equivalence of categories, in this example one still can choose between ... skeleton . Properties As a rule of thumb, an equivalence of categories preserves all categorical concepts and properties. If F C D is an equivalence, then the following statements are all true the object ... s, we see that the equivalence F is an Regular category Exact sequences and regular functors exact ... into epimorphisms, kernels into cokernels, limits into colimits etc. If F C D is an equivalence ... are naturally isomorphic. If F C D is an equivalence of categories, and if C is a preadditive category ... hand, any equivalence between additive categories is necessarily additive. Note that the latter statement is not true for equivalences between preadditive categories. An auto equivalence of a category C is an equivalence F C C . The auto equivalences of C form a group mathematics group under composition ... more details
In abstract algebra , Morita equivalence is a relationship defined between ring mathematics rings that preserves many ring theoretic properties. It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958. Motivation ring mathematics Rings are commonly ... mathematics category of modules over that ring. Morita equivalence takes this viewpoint to a natural conclusion by defining rings to be equivalent if their module categories are Equivalence of categories ... if there is an Additive functor additive equivalence of the category of left modules over R , R Mod , and the category of left modules over S , S Mod . Under the equivalence functors, each R module .... This means that the notion of Morita equivalence does not depend on whether you are talking about ... S Mod math to math R Mod are additive covariant functors , then F and G are an equivalence if and only ... Cen S S math . Properties preserved by equivalence Many properties are preserved by the equivalence ... is a categorical property which will be preserved by the equivalence functor. For example, if F is the equivalence functor from R Mod to S Mod , then the R module M has any of the following properties ... equivalence, an equivalent ring S must also have all of its modules semisimple, and therefore be a semisimple ... modules are flat. Since flatness is preserved across Morita equivalence, it is now clear that von ... Artin Wedderburn theory . To see the equivalence, notice that if M is a left R module then M sup n sup ... n sub R module is obtained from V as described above. Criterion for equivalence For every right exact ... is given in terms of the hom functor rather than the tensor functor. Morita Equivalence can ... of C algebras, a stronger type equivalence, called strong Morita equivalence , is needed ... If two rings are Morita equivalent, there is an induced equivalence of the respective categories ... 18 19 ISBN 0 387 95183 0 Meyer, Ralf Morita Equivalence In Algebra And Geometry , http citeseer.ist.psu.edu ... more details
In theoretical computer science , stuttering equivalence , ref Jan Friso Groote and Frits W. Vaandrager, http citeseerx.ist.psu.edu viewdoc summary?doi 10.1.1.140.1834 An efficient algorithm for branching bisimulation and stuttering equivalence . In Proceedings of the 17th International Colloquium on Automata, Languages and Programming , Springer Verlag , Lecture Notes in Computer Science , Volume 443, pages 626 638, 1990. doi 10.1.1.140.1834 ref a relation written as math pi sim st pi math , can be seen as a partitioning of path math pi math and math pi math into blocks, so that states in the math k mathrm th math block of one path are labeled math L sdot math the same as states in the math k mathrm th math block of the other path. Corresponding blocks may have different lengths. Formally, this can be expressed as two infinite paths math pi s 0, s 1, ldots math and math pi r 0, r 1, ldots math which are stuttering equivalent math pi sim st pi math if there are two infinite sequences of integers math 0 i 0 i 1 i 2 ldots math and math 0 j 0 j 1 j 2 ldots math such that for every block math k geq 0 math holds math L s i k L s i k 1 ldots L s i k 1 1 L r j k L r j k 1 ldots L r j k 1 1 math . Stuttering equivalence is not the same as bisimulation , since bisimulation cannot capture the semantics of the eventually or finally operator found in Linear temporal logic linear temporal Computation tree logic computation tree logic branching time logic modal logic . So called branching bisimulation has to be used. CN date April 2012 References reflist Category Formal methods Category Logic in computer science Comp sci theory stub ... more details
Original research date September 2007 Moral equivalence is a term used in political debate, usually to criticize any denial that a moral moral hierarchy hierarchy can be assessed of two sides in a conflict, or in the actions or tactics of two sides. The term originates from a 1906 address by William James entitled wikisource The Moral Equivalent of War The Moral Equivalent of War , subsequently published ... Israeli conflict . Moral equivalence began to be used as a polemic term of retort to moral relativism ..., and are unwilling to negotiate on basis of moral equivalence. Cold War In the Cold War context, the term ... could be viewed as equally culpable in a struggle for supremacy, would be advocating moral equivalence ... called The Myth of Moral Equivalence in 1986, in which sharply criticized those who she alleged were ... of Moral Equivalence , Imprimis ref In fact, very few critics of United States policies in the Cold War era argued that there was a moral equivalence between the two sides. Communists , for instance ... that the United States itself created a moral equivalence when some of its actions, such as President ... of the moral equivalence device have continued to demand this in the form of NATO expansion , the overthrow ... conflict , the term is commonly used by defenders of Israel. They accuse of moral equivalence those ... Mowbray, Moral Equivalence in the Middle East, TownHall.com, Monday, June 16, 2003 http townhall.com columnists JoelMowbray 2003 06 16 moral equivalence in the middle east ref The Israeli writer Yaacov ... p.260 ref World War II atrocities Expand section date June 2008 As in the other cases, the moral equivalence ... happened thus make the possible worst case scenarios seem more likely. Suggesting a moral equivalence ... of Moral Equivalence , Imprimis , January 1986, Vol. 15, No. 1 References Reflist added under references heading by script assisted edit Refimprove date June 2006 DEFAULTSORT Moral Equivalence Category Morality Equivalence Category Political terms Category Concepts in ethics ... more details
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