In mathematics , a partialequivalencerelation often abbreviated as PER math R math on a set math X math is a relation that is symmetric relation symmetric and transitive relation transitive . In other words, it holds for all math a, b, c in X math that if math a R b math , then math b R a math symmetry ... math is defined at math y math , and math f x f y math is a partialequivalencerelation but not an equivalencerelation. It possesses the symmetry and transitivity properties, but it is not reflexive .... MIT Press, 1996. See also Equivalencerelation Binary relation DEFAULTSORT PartialEquivalenceRelation ... reflexive relation reflexive , then math R math is an equivalencerelation . In a set theoretic context, there is a simple structure to the general PER math R math on math X math it is an equivalencerelation on the subset math Y x in X x ,R ,x subseteq X math . math Y math is the subset of math ... and therefore an equivalencerelation on math Y math . Notice that math R math is actually only true ... math and math y R y math by transitivity. Conversely, given a subset Y of X , any equivalencerelation ... of math A math for which math approx math is an equivalencerelation is precisely the subset on which math f math is defined. Functions respecting equivalence relations Let X and Y be sets equipped with equivalence relations or PERs math approx X, approx Y math . For math f,g X to Y math , define ... and constructive mathematics , particularly to define setoid s, sometimes called partial setoids ... in classical set theoretic mathematics. Examples A simple example of a PER that is not an equivalencerelation is the empty relation math R emptyset math unless math X emptyset math , in which case the empty relation is an equivalencerelation and is the only relation on math X math . Kernels of partial functions For another example of a PER, consider a set math A math and a partial function math f math that is defined on some elements of math A math but not all. Then the relation math approx ... more details
subgroup s. Equality mathematics Equality is both an equivalencerelation and a partial order. Equality is also the only relation on a set that is reflexive, symmetric and antisymmetric. A strict partial order is irreflexive, transitive, and asymmetric relation asymmetric . A partialequivalencerelation ... preorder Symmetric and transitive The relation R on N , defined as aRb ab 0. Or any partialequivalence ... . In mathematics , an equivalencerelation is a binary relationrelation that, loosely speaking, Partition ... to the equivalencerelation if and only if they are elements of the same cell. The intersection of any ... right thumb An equivalencerelation partition of a set partitions a set into several disjoint ... a and b of a set are equivalent with respect to an equivalencerelation R , the most common are a b ... R sub b , a sub R sub b , or aRb . Definition A given binary relation on a set A is said to be an equivalence ... of A be related if their difference is even. This is an equivalencerelation, which partitions ... not imply that 5 7. It is, however, a Partially ordered set partial order . The relation has a common ... equal to between real numbers, even if more precisely defined, is not an equivalencerelation, because ... at that point, then this defines an equivalencerelation. The relation is a sibling of used to connote ... to other relations A partial order is a relation that is reflexive relation reflexive , antisymmetric relation antisymmetric , and transitive relation transitive . A congruence relation is an equivalence ... under an equivalencerelation If is an equivalencerelation on X , and P x is a property of elements ... arguments under an equivalencerelation sub A sub to equivalent values under an equivalencerelation ... relation defined by math x sim y iff f x f y math . The equivalence kernel of an Injective function .... Since every equivalencerelation over X corresponds to a partition of X , and vice versa, the number ..., R. M., 2004. Abstract Algebra , 3rd ed. p. 3, Prop. 2. John Wiley & Sons. ref An equivalencerelation ... more details
In algebraic geometry , a branch of mathematics , an adequate equivalencerelation is an equivalencerelation on algebraic cycles of smooth projective varieties used to obtain a well working theory of such cycles ... the concept of an adequate equivalencerelation in 1958. ref citation last Samuel first C. title ... adequate equivalencerelation, one may define the category of motive algebraic geometry pure motives with respect to that relation. Possible and useful adequate equivalence relations include rational , algebraic , homological and numerical equivalence . They are called adequate because dividing out by the equivalencerelation is functorial, i.e. push forward with change of co dimension and pull back of cycles is well defined. Codimension one cycles modulo rational equivalence form the classical group of Divisor algebraic geometry divisor s. All cycles modulo rational equivalence form the Chow ... equivalencerelation is a family of equivalencerelation s, sub X sub on Z sup sup X , one for each smooth projective variety X , satisfying the following three conditions Linearity The equivalencerelation is compatible with addition of cycles. Moving lemma If math alpha, beta in Z X math ... , such that V X 0 Z and V X Z . the finest adequate equivalencerelation. denotes intersection in the cycle theoretic sense i.e. with multiplicities . see also Chow ring algebraic equivalence Z sub ... the coarsest equivalencerelation Notes references References Citation last1 Kleiman first1 Steven .... year 2000 pages 225 260 DEFAULTSORT Adequate EquivalenceRelation Category Algebraic geometry ... . The last axiom allows us to push forward cycles by a correspondence. Examples of equivalence relations The most common equivalence relations, listed from strongest to weakest, are gathered below in a table. class wikitable style text align center definition remarks rational equivalence Z sub ... points c and d on the curve. strictly stronger than homological equivalence, see also N ron Severi ... more details
In mathematics , a Borel equivalencerelation on a Polish space X is an equivalencerelation on X that is a Borel algebra Borel subset of X × X in the product topology . Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one says that E is Borel reducible to F , in symbols E sub B sub F , if and only if there is a Borel function X Y such that for all x , x X , one has xEx x F x . Conceptually, if E is Borel reducible to F , then E is not more complicated than F , and the quotient space X E has a lesser or equal Borel cardinality than Y F , where Borel cardinality is like cardinality except for a definability restriction on the witnessing mapping. Kuratowski s theorem A measure space X is called a standard Borel space if it is Borel isomorphic to a Borel subset of a Polish space. Kuratowski s theorem then states that two standard Borel spaces X and Y are Borel isomorphic iff X Y . References cite journal author Harrington, L. A., A. S. Kechris, A. Louveau journal Journal of the American Mathematical Society volume 3 issue 2 year Oct. 1990 pages 903 928 title A Glimm Effros Dichotomy for Borel equivalence relations doi 10.2307 1990906 publisher Journal of the American Mathematical Society, Vol. 3, No. 4 jstor 1990906 cite book author Kechris, Alexander S. authorlink Alexander S. Kechris title Classical Descriptive Set Theory publisher Springer Verlag year 1994 isbn 0 387 94374 9 cite journal author Silver, Jack H. journal Annals of Mathematical Logic volume 18 issue 1 year 1980 pages 1 28 title Counting the number of equivalence classes of Borel and coanalytic equivalence relations doi 10.1016 0003 4843 80 90002 9 Category Descriptive set theory mathlogic stub ... more details
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 EquivalencerelationEquivalence 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 equivalencerelation 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
wiktionary Relationrelation relations Relation or Relations may refer to tocright General use Kinship , relationship by genealogical origin Social relation s, in social science, social interaction between two or more individuals International relations , strategies chosen by a state to safeguard its national interests and achieve its foreign policy objectives Logic and philosophy Relation philosophy , links between properties of an object Relation logic , term in set theory and logic, for a property that assigns truth values to k tuples of individuals Relation of Ideas , in the Human sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations in contrast to a Matter of Fact Relational theory , framework to understand reality or a physical system in such a way that the positions and other properties of objects are only meaningful relative to other objects Computers and technology Relation database , in the relational model of databases ... Relationships Ontology components relation , a component of an ontology Binary relation , a synonym for dyadic relation and 2 place relation Mathematics Relational algebra , an offshoot of first order logic and of algebra of sets , deals with a set of finitary relations see also relation database which is closed under certain operators Relation mathematics , a generalization of arithmetic relations, such as and , that occur in statements, such as 5 6 and 2 2 4 Ternary relation ,finitary relation in which the number of places in the relation is three. Ternary relations may also be referred ... as being observer dependent, that is, the state is the relation between the observer and the system Relation journal Relation journal , the first newspaper Sexual relations, euphemistic term for human ... Relativity disambiguation disambig bs Relacija vor cs Relace de Relation Begriffskl rung es Relaci n eo Rilato fr Relation io Relato it Relazione ja pl Relacja pt Rela o ro Rela ie simple Relation ... more details
Wiktionary partialPartial may refer to partial derivative , in mathematics , the partial derivative symbol, often read as partialpartial function , in mathematics partial algorithm , in computer science Contract bridge glossary partial part score , in contract bridge Harmonic series music Partialpartial wave , in acoustics and music disambig Long comment to avoid being listed on short pages cs Parci ln fr Partiel ... more details
with respect to the equivalencerelation 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 equivalencerelation math is denoted as math X and called the quotient set of mvar X by math . Each equivalencerelation has a canonical ... by the equivalencerelation, hence both the name quotient , and the notation, which are both reminiscent ... points identified. Examples If mvar X is the set of all cars, and math is the equivalencerelation ... equivalencerelation 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 classes one class ... pairs of integers math a , b with mvar b not zero, and define an equivalencerelation math on mvar ... math a , b can be identified with the rational number math a b , and this equivalencerelation ... to the same set of the partition. It follows from the properties of an equivalencerelation that math x y if and only if math 1 x y . In other words, if math is an equivalencerelation on a set math ... sim y math math x y math math x cap y ne emptyset math . Invariants If math is an equivalencerelation ... function mathematics function math f X Y itself defines an equivalencerelation on mvar X according ... math x is the inverse image of math f x . This equivalencerelation is known as the kernel of a function ... relation math sub X sub on mvar X to equivalent values under an equivalencerelation math sub ... see equivalence class music . In mathematics , given a Set mathematics set mvar X and an equivalencerelation 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 a . Notation and formal definition An equivalencerelation is a binary relation math satisfying three properties For every element mvar a in mvar X , math a a Reflexive relation reflexivity , For every two elements mvar a and mvar b in mvar X , if math ... more details
In category theory , an abstract branch of mathematics , an equivalence of categories is a relation between ... therefore view an adjointness relation between two functors as a very weak form of equivalence . Assuming ... 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 with terminology from homotopy theory . There is also a close relation to the concept of adjoint ... functors form an equivalence of categories, in this example one still can choose between ... is Birkhoff s representation theorem stating a duality between finite partial orders and finite distributive ... 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 ... 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 mathematics , math mathcal K math equivalence , or contact equivalence , is an equivalencerelation 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 equivalencerelation 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 equivalencerelation 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
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 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
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
theories with a scalar field and the relation to the equivalence principle and Mach s principle. C ... 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 the equivalence principle with special relativity to predict that clocks run at different ... field, even before he developed the concept of curved spacetime. So the original equivalence principle .... This form of the equivalence principle can be stated as follows. An observer in a windowless ... are absent from an accelerating spaceship in deep space. Although the equivalence principle guided the development ... equivalence principle and the strong equivalence principle, each of which assumes the weak equivalence .... 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 ... work properly. Cleanup section date January 2010 The weak equivalence principle , also known as the universality of free fall or the Galilean equivalence principle can be stated in many ways. The trajectory .... The falling equivalence principle embraces Galileo s, Newton s, and Einstein s conceptualization. Relativistic ... 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. References reflist Category Formal methods terminology Category Logic in computer science Comp sci theory stub ... 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
, both of these systems imply every equation of the form math ax by bz 0. , math Equivalence ... publisher Pearson Prentice Hall edition 7th External links Wikibooks Linear Algebra Row Equivalence Row Equivalence Category Linear algebra Category Matrices fi Riviekvivalenssi sr ... more details
False Equivalence is a logical fallacy which describes a situation where there is a logical and apparant 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 neccesarrily 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 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 are some examples to illustrate False Equivalence 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 External links http furrybrowndog.wordpress.com 2009 07 22 the fallacy of false equivalence Furry Brown Dog blog on False Equivalence http www.shortpacked.com 2011 comic book 13 05 the death of snkrs falseequivalence Shortpacked on False Equivalence in comic book culture. Categories Category Articles created via the Article Wizard Category Logical fallacies Category Critical thinking ... 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
dablink For weak equivalence in category theory, see Equivalence of categories . Split date April 2011 Mathematics refimprove date August 2009 In mathematics , a weak equivalence is a notion from homotopy theory which in some sense identifies objects that have the same basic shape . This notion is formalized in the axiom atic definition of a closed model category . A closed model category by definition contains a class of morphism s called weak equivalences , and these morphisms become isomorphism s upon passing to the associated homotopy category . In particular, if the weak equivalences of two model categories containing the same objects and morphisms are defined in the same way, the resulting homotopy categories will be the same, regardless of the definitions of fibration s and cofibration s in the respective categories. Different model categories define weak equivalences differently. For example ... equivalence s i.e. those morphisms X &rarr Y that induce isomorphisms in homotopy group s math pi n ... which is also a weak equivalence is also known as a trivial or acyclic fibration . A cofibration which is also a weak equivalence is also known as a trivial or acyclic cofibration . Formal Languages In formal language theory, weak equivalence of two formal grammars grammar s means they generate ... the notion is distinguished from strong equivalence strong or structural equivalence which additionally ... Vijay Shanker, K. and Weir, David J. 1994. The Equivalence of Four Extensions of Context Free ... languages are Strong equivalence strongly equivalent . Chomsky 1963 ref name chomsky1963 Chomsky ... of strong equivalence, and argues that only strong equivalence is relevant when comparing grammar ... equivalence that allows for isomorphic relationships between the syntactic analyses given by different ..., J. 2002. A formal proof of strong equivalence for a grammar conversion from LTAG to HPSG style .... References Reflist DEFAULTSORT Weak Equivalence Category Homotopy theory ... 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
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 when a titrant .... In some cases there are multiple equivalence points which are multiples of the first equivalent ... 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, 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 ... on a redox reaction the potential of the working electrode will suddenly change as the equivalence ... electrode . This allows the pH of the solution to be measured throughout the titration. At the equivalence ... or consumed by the reaction to determine the equivalence point. This is important in biochemistry ... in the sample solution. Instead, the equivalence point is determined by the rate of temperature ..., 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 be located precisely ... to 10 sup 5 sup K. Sharp equivalence points have been obtained in titrations where the temperature ... the equivalence point. Alternatively, the presence of free titrant indicating that the reaction .... The equivalence point can then be detected as a change in the current. This method is most useful when ... docente gutz Curtipot .html Equivalence points of virtual and real acid base titrations ... 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
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