Refimprove date April 2009 Context date April 2009 Gotthard Gunther introduced the term proemial relation in his 1970 paper Cognition and Volition . Meaning to preface , it specifically refers to the intercoherence prerequisite relation of subject grammar subject and object grammar object . Subject and object arise together. In fact, subject is a mere abbreviation of Subject superject which is an actual entity in Alfred North Whitehead s technical phraseology. The abstractions related are Subjectivity and Profundity . In Gotthard Gunther s mathematics, Subjectivity is called polycontexturality . References Reflist DEFAULTSORT Proemial Relation Category Syntactic entities ... more details
Clairaut s relation , named after Alexis Claude de Clairaut , is a formula in classical differential geometry . The formula relates the distance r t from a point on a great circle of the unit sphere to the z axis, and the angle t between the tangent vector and the latitudinal circle math r t cos theta t text constant . , math The relation remains valid for a geodesic on an arbitrary surface of revolution . References M. do Carmo, Differential Geometry of Curves and Surfaces , page 257. See also Clairaut s theorem Category Differential geometry Category Differential geometry of surfaces Category Geodesy math stub de Satz von Clairaut Differentialgeometrie fr Relation de Clairaut ... more details
In mathematics , a dependence relation is a binary relation which generalizes the relation of linear dependence . Let math X math be a set mathematics set . A binary relation math triangleleft math between an element math a math of math X math and a subset math S math of math X math is called a dependence relation , written math a triangleleft S math , if it satisfies the following properties if math a in S math , then math a triangleleft S math if math a triangleleft S math , then there is a finite set finite subset math S 0 math of math S math , such that math a triangleleft S 0 math if math T math is a subset of math X math such that math b in S math implies math b triangleleft T math , then math a triangleleft S math implies math a triangleleft T math if math a triangleleft S math but math a not triangleleft S lbrace b rbrace math for some math b in S math , then math b triangleleft S lbrace b rbrace cup lbrace a rbrace math . Given a dependence relation math triangleleft math on math X math , a subset math S math of math X math is said to be independent if math a not triangleleft S lbrace a rbrace math for all math a in S. math If math S subseteq T math , then math S math is said to span math T math if math t triangleleft S math for every math t in T. math math S math is said to be a basis of math X math if math S math is independent and math S math spans math X. math Remark. If math X math is a non empty set with a dependence relation math triangleleft math , then math X math always has a basis with respect to math triangleleft. math Furthermore, any two bases of math ... field math F. math The relation math triangleleft math , defined by math upsilon triangleleft S math ... relation. This is logical equivalence equivalent to the definition of linear independence linear dependence ... triangleleft math is a dependence relation. This is equivalent to the definition of algebraic dependence . See also matroid PlanetMath attribution id 5792 title Dependence relation Category Linear ... more details
In mathematics , a binary relation R over a Set mathematics set X is total if for all a and b in X , a is related to b or b is related to a or both . In mathematical notation , this is math forall a, b in X, a R b or b R a. math Total relations are sometimes said to have comparability . Examples For example, is less than or equal to is a total relation over the set of real numbers, because for two numbers either the first is less than or equal to the second, or the second is less than or equal to the first. On the other hand, is less than is not a total relation, since one can pick two equal numbers, and then neither the first is less than the second, nor is the second less than the first. But note that is less than is a weak order which gives rise to a total order, namely is less than or equal to . The relationship between strict orders and weak orders is discussed at partially ordered set . The relation is a proper subset of is also not total. Properties and related notions Totality implies Reflexive relation reflexivity . If a transitive relation is also total, it is a strict weak ordering Total preorders total preorder . If a partially ordered set partial order is also total, it is a total order . A binary relation R over X is called connex if for all a and b in X such that a b , a is related to b or b is related to a or both ref citation title A concise introduction to mathematical logic last Rautenberg first Wolfgang edition 2nd publisher Birkh user year 2006 isbn 9780387302942 ref math forall a, b in X, a R b or b R a or a b. math Connexity does not imply reflexivity. A strict partial order is a strict total order if and only if it is connex. References references Category Mathematical relations ca Relaci total cs pln relace es Relaci n total eo Tuteca rilato it Relazione totale ja pl Relacja pe na pt Rela o total ... more details
File Frontispiece Mourt s Relation 1622.jpg thumb right 200px Book frontispiece Frontispiece , Mourt s Relation , published in London , 1622 The book Mourt s Relation full title A Relation or Journal of the Beginning and Proceedings of the English Plantation Settled at Plimoth in New England was written primarily by Edward Winslow , although William Bradford 1590 1657 William Bradford appears to have written most of the first section. Written between November 1620 and November 1621, it describes in detail what happened from the landing of the Mayflower Pilgrims inside the fishhook tip of Cape Cod became Provincetown Harbor , through their exploring and eventual settling of Plymouth Colony the book describes their relations with the surrounding Indigenous peoples of the Americas native Indians , up to the First Thanksgiving and the arrival of the ship Fortune in November 1621. Mourt s Relation was first published in London in 1622, presumably by George Morton pilgrim father George Morton , sometimes called George Mourt ref Cite Appletons Morton, George year 1900 ref hence the title Mourt s Relation . The purpose of Mourt s Relation was clear to paint the new settlement in the brightest possible hues. Citation needed date December 2011 An English Puritan Separatist who had moved to Leiden, Holland, Morton stayed behind when the first settlers left for Plymouth, Massachusetts , ref ... helping write Mourt s Relation. ref http query.nytimes.com mem archive free pdf? r 1&res 9B0DEFDF1438E433A25753C2A96E9C94699ED7CF ..., according to MLA capitalization standards is br A Relation or Journall of the Beginning and Proceedings ... of, and Comfortable Planting Themselves in the Now Well Defended Towne of New Plimoth. As Also a Relation ... Parts. Notes reflist References cite book author William Bradford, Edward Winslow title Mourt s Relation ... links http www.histarch.uiuc.edu plymouth mourt1.html Mourt s Relation as transcribed by Caleb Johnson http www.mayflowerhistory.com PrimarySources MourtsRelation.pdf Mourt s Relation as transcribed ... more details
Distinguish2 relational algebra , a framework for finitary relation s and relational database s In mathematics and abstract algebra , a relation algebra is a residuated Boolean algebra reduct expanded ... of a relation algebra is the algebra 2 sup X sup of all binary relation s on a set X , that is, subsets ... composition of binary relations R and S , and with the converse of R interpreted as the inverse relation . Relation algebra emerged in the 19th century work of Augustus De Morgan and Charles Sanders ... form of relation algebra treated here was developed by Alfred Tarski and his students, starting in the 1940s. Tarski and Givant 1987 applied relation algebra to a variable free treatment of axiomatic ... without variables. Definition A relation algebra L , , , sup &minus sup , 0, 1, , I , sup math breve ... an axiomatization of relation algebra. A relation algebra is to a system of binary relations on a set ... math breve math sup . Hence a relation algebra can equally well be defined as an algebraic structure ... one that a relation algebra can then be defined in full simply as a residuated Boolean algebra ... with finitely many identities, so are relation algebras. Hence the latter form a Variety universal algebra variety , the variety RA of relation algebras. Expanding the above definition as equations ... Abstract Representation Problems for Relation Algebras, Bulletin of the AMS 54 80. ref L is a Boolean ... inverse relation converse sup math breve math sup is an involution mathematics involution with respect ... many of the usual properties of binary relation s can be expressed as succinct RA equalities or inequalities ... if style border top 1px solid 999 Functional relation Functional R sup math breve math sup R I Total relation Total or Connected I R R sup math breve math sup R sup math breve math sup is surjective ... function Reflexive relation Reflexive I R Irreflexive relation Irreflexive R &and I 0 Transitive relation Transitive R R R Preorder R is reflexive and transitive. Antisymmetric relation Antisymmetric ... more details
refimprove date May 2008 A spatial relation specifies how some object is located in space in relation to some reference object. Since the reference object is usually much bigger than the object to locate, the latter is often represented by a point. The reference object is often represented by a bounding box oblique or axis parallel . It might be the case that a spatial relation is not fully applicable. Thus, the degree of applicability is defined which specifies from 0 till 100 how strongly a spatial relation holds. Often researchers concentrate on defining the applicability function for various spatial relations. Commonly used spatial relations are directional relations distance relations Directional relations Directional relations can again be differentiated into external directional relations and internal directional relations. An internal directional relation specifies where an object is located inside the reference object while an external relations specifies where the object is located outside of the reference objects. Examples for internal directional relations left on the back athwart Examples for external directional relations on the right of behind in front of Distance relations Distance relations specify how far is the object away from the reference object. Examples are at nearby in the vicinity far away See also Anatomical terms of location Water level task References reflist http www.newhorizons.org spneeds inclusion teaching stockdale.html Spatial Relations and Learning this article has been posted courtesy of the ARK Institute of Learning by Carol Stockdale and Carol Possin, Ph.D. at newhorizons.org Category Cognitive science de R umliche Relation ... more details
In dentistry, centric relation is the human mandible mandibular jaw position in which the mandibular condyle head of the condyle is situated as far Commonly used terms of relationship and comparison in dentistry anterior and superior as it possibly can within the mandibular fossa glenoid fossa . This position is used when restoring edentulous patients with dentures removable or either dental implant implant supported hybrid or fixed prosthodontics fixed prostheses. Because the dentist want to be able to reproducibly relate the patient s maxilla and mandible, but the patient does not have teeth with which to establish his or her own vertical dimension of occlusion , another method has been devised to achieve this goal. The condyle can only be in the same place as it was the last time it was positioned by the dentist if it is consistently moved to the most superior and anterior position within the fossa. Centric relation is an old concept in dentistry based on an old mechanical viewpoint of dentistry. There are over 26 different definitions of Centric Relation since the term was first developed as a starting point for making dentures. It is not a physiologic position but rather a border position that is used for reproducibility. The Temporomandibular Joint, does not normally function in a Centric Relation position. Long centric is a term that describes a functional position that patients restored in Centric Relation frequently migrate to. Centric Relation is a border position that is inherently unstable. Mandibular fossa is put anterior and superior as possible. First aid for the NERB I br Centric Relation believers state that the relationship of the mandible to the maxilla when the properly aligned condyle disc assemblies are in the most superior position against the eminentiae ..., the condyle disc assemblies are braced medially, thus centric relation is also the midmost position. A properly aligned condyle disc assembly in centric relation can resist maximum loading by the elevator ... more details
an extra cell. The Hasse diagram depicting the covering relation of a Tamari lattice is the n skeleton skeleton of an associahedron . The covering relation of any distributive lattice forms a median ... another. Properties If a partially ordered set is finite, its covering relation is the transitive reduction of the partial order relation. Such partially ordered sets are therefore completely described ... more details
orphan date May 2011 In mathematics , a separation relation is a formal way to arrange a set of objects in an unoriented circle. It is defined as a quaternary relation S a , b , c , d satisfying certain axioms, which is interpreted as asserting that a and c separate b from d . ref Citation last Huntington first Edward V. date July 1935 title Inter Relations Among the Four Principal Types of Order journal Transactions of the American Mathematical Society volume 38 issue 1 pages 1 9 doi 10.1090 S0002 9947 1935 1501800 1 url http www.ams.org journals tran 1935 038 01 S0002 9947 1935 1501800 1 S0002 9947 1935 1501800 1.pdf accessdate 8 May 2011 ref Whereas a linear order endows a set with a positive end and a negative end, a separation relation forgets not only which end is which, but also where the ends are. In this way it is a final, further weakening of the concepts of a betweenness relation and a cyclic order . There is generally nothing else that can be forgotten up to the relevant sense of interdefinability, these three relations are the only nontrivial reduct s of the ordered set of rational number s. ref Citation last Macpherson first H. Dugald year 2011 title A survey of homogeneous structures journal Discrete Mathematics doi 10.1016 j.disc.2011.01.024 url http www.amsta.leeds.ac.uk pure staff macpherson homog final2.pdf accessdate 28 April 2011 ref References Reflist Category Order theory math stub ... more details
Unreferenced stub auto yes date December 2009 A Relation of Ideas , in the David Hume Humean 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 . In a Immanuel Kant Kantian philosophy, it is equivalent to the Analytic synthetic distinction analytic A priori and a posteriori philosophy a priori . It is also closely coincident with the so called Truths of Reason of Leibniz , which are defined as those statements whose denials are Contradiction self contradictory . Examples br Mathematics 8 x 10 80. br Logic Definitions All islands are surrounded by water by definition . How We Know br We can demonstrate these truths. br Denying these will lead to a logical contradiction. DEFAULTSORT Relation Of Ideas Philo stub Category David Hume ... more details
Orphan date January 2012 In materials science and fatigue material fatigue , the Goodman relation , named after ????? Goodman , is an equation used to quantify the interaction of mean and alternating stress physics stresses on the Fatigue material fatigue life of a material. Mathematical description Image GoodmanRelation.jpg thumb 200px The area below the curve indicates that the material should not fail given the stresses. The area above the curve represents likely failure of the material. The Goodman relation can be represented mathematically as math sigma text a sigma text fat times left 1 frac sigma text m sigma text ts right . math Where math sigma text a math is the alternating stress, math sigma text m math is the mean stress, math sigma text fat math is the fatigue limit for completely reversed loading, and math sigma text ts math is the ultimate tensile stress of the material. The general trend given by the Goodman relation is one of decreasing fatigue life with increasing mean stress for a given level of applied stress. The relation can be plotted to determine the safe cyclic loading of a part if the coordinate given by the mean stress and the applied stress lies under the curve given by the relation, then the part will survive. If the coordinate is above the curve, then the part will fail for the given stress parameters. ref Hertzberg, p. 530 31. ref References Notes Reflist Bibliography Goodman, J., Mechanics Applied to Engineering , Longman, Green & Company, London, 1899 Hertzberg, Richard W., Deformation and Fracture Mechanics and Engineering Materials . John Wiley and Sons, Hoboken, NJ 1996. Category Materials science Category Fracture mechanics classicalmechanics stub ... more details
Multiple issues primarysources January 2011 refimprove January 2011 COI January 2011 Infobox film name The Taste of Relation image caption director Mukesh Asopa producer Asopa Films Incorporation br Twinkle Productions, writer Mukesh Asopa br Twinkle Asopa starring Mukesh Asopa br Kamal Nandi br Aruna Bhatnagar br Swetalina Tripathy br Tree Ryde released Film date 2009 12 21 runtime 87 minutes language Hindi country Film Canada The Taste of Relations 2009 is the second film from Canadian based Asopa Films Incorporation, Twinkle Productions and Asopa Films International. The first was Aisha and Rahul . Plot Empty section date February 2011 Cast Mukesh Asopa as Raj Mittal Kamal Nandi as Ramswaroop Mittal Aruna Bhatnagar as Yashoda Maa Swetalina Tripathy as Kiran Tree Ryde as Jennifer Soundtrack The Taste of Relation Happy Version Sung, Composed and Lyrics by Farita, Music by Studio Pros and Selasi Senate Music Tumhare Bina Aapke Bina Sung, Composed and Lyrics by Farita, Music by Studio Pros and Selasi Senate Music Without You Sung, Composed and Lyrics by Righteous Allah, Music by Marvin Hall and DJ Konn The Taste of Relation Sad Version Sung, Composed and Lyrics by Farita, Music by Studio Pros and Selasi Senate Music Awards Vista India Award at the Global Cinema Festival 2009 in India Golden Palm Award at the Mexico International Film Festival 2010 Rising Star Award at the Canada International Film Festival 2010 Official Finalist Award at the Las Vegas International Film Festival 2010 Official selection and nominee for a Golden Aphrodite at the Cyprus International Film Festival Special Jury Prize at the http www.CalFilmAwards.com CALIFORNIA FILM AWARDS 2011 Winner of Platinum Award at the http www.nevadafilmfestival.com Festival 2007 10platinum.aspx Nevada Film Festival 2010 External links http www.imdb.com title tt1502960 The Taste of Relation at the http www.imdb.com Internet Movie Database http www.asopafilms.com Official Site DEFAULTSORT Taste Of Relation ... more details
pp move vandalism small yes Context date October 2009 semiotics A sign relation is the basic construct ... In his picturesque illustration of a sign relation, along with his tracing of a corresponding .... Peirce s definition of a sign defines it in relation to its object and its interpretant sign ... places. In this definition, signhood is a role in a triadic relation , a role that a thing bears ... to the whole triadic sign relation itself. In particular, his use of this term should not be taken ... of an individual triadic relation three place relation called the sign relation of that interpreter. Understood in terms of its set theory set theoretic extension semantics extension , a sign relation ... domain , the sign domain , and the interpretant domain , respectively, of the sign relation L unicode O S I . Broadly speaking, the three domains of a sign relation ... of the domains O , S , I for a given sign relation L , one may refer to this set as the world of L and write ... 0 style background lightcyan font weight bold text align center width 60 Sign Relation of Interpreter ... 0 style background lightcyan font weight bold text align center width 60 Sign Relation of Interpreter ... relation , that is, one element of the relation s set theoretic extension. Already in this elementary ... the needed distinctions. Dyadic aspects of sign relations For an arbitrary triadic relation L unicode O S I , whether it is a sign relation or not, there are six binary relation dyadic relations that can ... S I . The six dyadic projections of a triadic relation L are defined and notated ... notation, here is what the first definition says in ordinary language. The dyadic relation that results ... i in L for some interpretant i in the interpretant domain I . In the case where L is a sign relation, which it becomes by satisfying one of the definitions of a sign relation, some of the dyadic ... references fall within the projection of the sign relation on the plane that is spanned by its ... more details
For the term as used in elementary geometry congruence geometry In abstract algebra , a congruence relation or simply congruence is an equivalence relation on an algebraic structure such as a group mathematics ... congruence relation has a corresponding quotient structure, whose elements are the equivalence class es or congruence classes for the relation. Basic example The prototypical example of a congruence relation is Modular arithmetic Congruence relation congruence modulo math n math on the set of integer ... of abstract algebra, congruence modulo math n math is a congruence relation on the ring mathematics .... The common theme is that a congruence is an equivalence relation on an algebraic object that is compatible ... G math is a group with operation &lowast , a congruence relation on G is an equivalence relation &equiv ..., a ring possesses both addition and multiplication, and a congruence relation on a ring must ... quotient ring . The general notion of a congruence relation can be given a formal definition ... . In this setting, a congruence relation is an equivalence relation &equiv on an algebraic ... i sub &equiv a sub i sub &prime for each i . Relation with homomorphisms If &fnof ... homomorphism of groups , or a linear map between vector space s , then the relation &equiv defined ... &fnof a sub 1 sub &fnof a sub 2 sub is a congruence relation. By the first isomorphism ... relation on G , then is a congruence whenever Given any element a of G , a a Reflexive relation reflexivity Given any elements a and b of G , material implication if a b , then b a Symmetric relation ... relation transitivity Given any elements a , a , b , and b of G , if a a and b b , then a b a b ... relation . A congruence is determined entirely by the set a G a e of those elements of G ... relation on an algebra A is a subset of the direct product A × A that is both an equivalence relation on A and a subalgebra of A × A . The kernel universal algebra kernel of a homomorphism ... more details
In a Plasma physics plasma , the Boltzmann relation describes the number density of an isothermal charged particle fluid when the thermal and the electrostatic forces acting on the fluid have reached equilibrium. Due to their small mass and larger mobility, in many situations the electron density of a plasma is assumed to behave according to the Boltzmann relation. If the local electrostatic potential is represented by sub 1 sub and sub 2 sub at two nearby locations, the Boltzmann relation for the electrons takes the form n sub e sub sub 2 sub n sub e sub sub 1 sub exp e &phi Boltzmann constant k sub B sub T sub e sub where n sub e sub and T sub e sub are the electron density and temperature respectively. A simple derivation of the Boltzmann relation for the electrons can be obtained using the momentum fluid equation of the two fluid model of plasma physics in absence of a magnetic field. When the electrons reach dynamic equilibrium, the inertial and the collisional terms of the momentum equations are zero, and the only terms left in the equation are the pressure and electric terms. For an isothermal fluid, the pressure force takes the form math k BT e nabla n e math , while the electric term is math e n e nabla phi math . Simple integration leads to the expression given above. In many problems of plasma physics, it is not useful to calculate the electric potential on the basis of the Poisson equation because the electron and ion densities are not known a priori , and if they were, because of Plasma physics Potentials quasineutrality the net charge density is the small difference of two large quantities, the electron and ion charge densities. If the ion density is known and the assumptions hold sufficiently well, the electric potential can be calculated simply from the Boltzmann relation. Discrepancies with the Boltzmann relation can occur, for example, when oscillations occur so fast that the electrons cannot find a new equilibrium see e.g. plasma oscillation ... more details
Image Similarity relation.png thumb right Similarity relation audio Similarity relation.mid Play . 047 followed by 047t and 0478, respectively. 047t and 0478 are in the relation R sub p sub , as they are with ten other sets ref name Forte . In music , a similarity relation or pitch class similarity is a comparison between set music sets of the same cardinality two sets containing the same number of pitch classes , based upon shared pitch class and or interval class content. Allen Forte originally designated four types R sub p sub maximal similarity with respect to pitch class , R sub 0 sub minimal similarity , R sub 1 sub first order maximal similarity , and sub R2 sub second order maximal similarity . In R sub p sub one pitch class is different, in R sub 0 sub all are different, and in R sub 1 sub and R sub 2 sub four interval classes are the same. Rp is defined for sets S sub 1 sub and S sub 2 sub of cardinal number n and S sub 3 sub of cardinal number n 1 as ref name Forte Forte, Allen 1977 . The Structure of Atonal Music , p.47. ISBN 0300021208. ref R sub p sub S sub 1 sub ,S sub 2 sub If and only if iff S sub 3 sub Subset S sub 1 sub , S sub 3 sub S sub 2 sub Meaning that S sub 1 sub and S sub 2 sub each have all the pitch classes of S sub 3 sub transposed or inverted , plus one. quote T he pc similarity relation R sub p sub is not especially significant when taken alone, since by that measure a given set may be similar to many others. When R sub p sub is combined with the interval class similarity measures, however, a considerable reduction is effected. Allen Forte ref Forte 1973 , p.49. quoted in Schuijer, Michiel 2008 . Analyzing Atonal Music Pitch Class Set Theory and Its Contexts , p.148. ISBN 978 1 58046 270 9. ref Sources references Further reading Isaacson, Eric. 1990 . Similarity of Interval class Content Between Pitch class Sets The IcVSIM Relation , Journal ... Similarity relation , SolomonsMusic.net . Category Music theory ... more details
dependent dispersion relations, there are the overarching Kramers Kronig relation s that connect ... medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation ..., f , are related by the dispersion relation math v lambda lambda f lambda . , math Dispersion ... math k 2 pi lambda math . Rewriting the relation above in these variables gives math omega k v k k. , math The use of k to describe the dispersion relation is standard because both the phase ... dispersion relation. In this case, phase velocity and group velocity are the same math v frac omega ... energy, momentum, and mass of particles are connected through the relativistic relation math E 2 ... Accordingly, frequency and wavenumber are connected through a dispersion relation, which in the nonrelativistic ... relation . For particles, this translates to a knowledge of energy as a function of momentum. Waves and optics See Dispersion optics The name dispersion relation originally comes from optics . It is possible ... traverses the figure in the time it takes the green dot to traverse half. The dispersion relation for deep ..., phase red and group green velocities are equal. For an ideal string, the dispersion relation can be written ... order of vibration frequency. Solid state In the study of solids, the study of the dispersion relation ... in a solid what photons are to light They are the quanta that carry it. The dispersion relation of phonon ... of the dispersion relation. Had he done so, he would almost certainly have invented the achromatic ... ref The universality of the Kramers Kronig relation s 1926 27 became apparent with subsequent papers on the dispersion relation s connection to causality in the scattering theory of all types of waves ... Causality and the dispersion relation Logical foundations journal Phys. Rev. volume 104 pages 1760 1770 ... and Ute Kaiser DEFAULTSORT Dispersion Relation Category Fundamental physics concepts de Dispersionsrelation fr Relation de dispersion it Relazione di dispersione he ms Hubungan sebaran ja ... more details
a simple definition of knot polynomials. Informally, a skein relation gives a linear relation between ... or tangles appearing in a skein relation may be oriented or unoriented. Funny, I was right ... relation patches.png The labelling is actually independent of direction insofar as it remains the same .... More formally, a skein relation can be thought of as defining the Kernel algebra kernel of a quotient ... P rm unknot 1 math and a triple of skein relation diagrams math D , D 0, D math satisfies the equation .... In this example, we calculate the Alexander polynomial of the cinquefoil knot Image skein relation ... s crossings highlighted in yellow so P Image skein relation cinquefoil minus sm.png A × P Image skein relation cinquefoil zero sm.png P Image skein relation cinquefoil plus sm.png The first ... P Image skein relation link24 minus sm.png A × P Image skein relation link24 zero sm.png P Image skein relation link24 plus sm.png gives, again, a trefoil, and two unknots with two crossings the Hopf link http mathworld.wolfram.com HopfLink.html . Patching the trefoil P Image skein relation trefoil minus sm.png A × P Image skein relation trefoil zero sm.png P Image skein relation ... relation link22 minus sm.png A × P Image skein relation link22 zero sm.png P Image skein relation ... of sneakiness P Image skein relation link20 minus sm.png A × P Image skein relation link20 zero sm.png P Image skein relation link20 plus sm.png We now have enough relations to compute the polynomials ... 3 P diagram tr th skein equation th ? th P in full tr td unknot td Image skein relation link20 minus sm.png Image skein relation link20 plus sm.png Image skein relation link22 zero sm.png Image skein relation trefoil minus sm.png td defined as 1 td td x 1 tr td unlink td Image skein relation link20 zero sm.png Image skein relation link22 minus sm.png td 1 A? 1 td 0 td x 0 tr td Hopf link td Image skein relation link22 plus sm.png Image skein relation link24 minus sm.png Image skein relation ... more details
In mathematical logic , the ancestral relation often shortened to ancestral of an arbitrary binary relation R is defined below. The ancestral makes its first appearance in Frege s Begriffsschrift . Frege later employed it in his Grundgesetze as part of his definition of the natural number s actually the finite cardinal number cardinals . Hence the ancestral was a key part of his search for a logicism logicist foundation of arithmetic. Definition The numbered propositions below are taken from his Begriffsschrift and recast in contemporary notation. The property philosophy property F is R hereditary if, whenever x is F and xRy , y is also F math Fx and xRy to Fy. math Frege then defined b to be an R ancestor of a , written aR b , iff b has every R hereditary property that all objects x such that aRx have 76 math Vdash aR b leftrightarrow forall F forall x forall y aRx to Fx wedge Fx wedge xRy to Fy to Fb math . The ancestral is transitive relation transitive 98 math vdash aR b wedge bR c to aR c. math Let the notation I R denote that R is function mathematics functional Frege calls such relations many one 115 math Vdash I R leftrightarrow forall x forall y forall z xRy wedge xRz to y z , math If R is function mathematics functional , we say nowadays that the ancestral of R is connectedness connected 133 math vdash I R wedge aR b wedge aR c to bR c vee b c vee cR b . math Discussion Principia Mathematica made repeated use of the ancestral, as does W. V. Quine Quine s 1951 Mathematical Logic . However, it is worth noting that the ancestral relation cannot be defined in first order logic , and following the resolution of Russell s paradox both Frege and Quine largely considered the use of second order logic a questionable approach. In particular, Quine did not consider second order logic to be logic at all, despite his reliance upon it for his 1951 book which largely retells Principia in abbreviated form, for which second order logic is required to fit its theorems . See ... more details
In modal logic , an accessibility relation is a binary relation, written as small math R , math small ... small math R , math . small The accessibility relation is a relationship between two possible worlds. More precisely, the accessibility relation is the idea that modal statements, like it s possible that it rains ... relation in detail. Put another way, these modal axioms describe in detail the accessibility relation, small math R , math small between two worlds. That relation, math R , math symbolizes ... relation has important uses in both the formal theoretical aspects of modal ... relation uses the basics of propositional modal logic see modal logic for a detailed discussion ... for reading about the accessibility relation. A sufficient condition a condition that is good enough ... the accessibility relation. In other words, it s good enough to be literate in order to learn about the accessibility relation, however it may not be necessary because the relation could be learned in different ... in terms of quantification over possible worlds, subject to the relation of accessibility ... symmetry, transitive property, etc. in all possible worlds is the accessibility relation. The relation of accessibility can now be defined as an uninterpreted relation small math R w 1,w 2 , math small ... explicit. The four types of the accessibility relation in formal semantics Formal semantics studies ... takes the form of the necessity relation described below. So, the accessibility relation, small math R , math small can take on at least four forms, that is, the accessibility relation can be described ... is true. The Euclidean relation euclidean property guarantees the truth of this. If small math A , math ... relation Though useful in all kinds of philosophical applications, the key innovation is, as David ... whatever is actual is necessarily possible, we could simply try asking is the relation math R ... contradiction of a necessary possibility is in fact not a contradiction but actually a relation ... more details
Expert subject Physics date March 2009 The McCumber relation or McCumber theory refers to the effective cross sections of absorption and emission of light in the physics of solid state laser s ref name mc D.E.McCumber. Einstein relations connecting broadband emission and absorption spectra. w Physical Review B PRB 136 4A , 954&ndash 957 1964 ref ref name B P.C.Becker, N.A.Olson, J.R.Simpson. Erbium .... The McCumbner relation is 1 math frac sigma rm e omega sigma rm a omega exp left frac ... ref ref name chi cite journal author D.Kouznetsov title Broadband laser materials and the McCumber relation ... state Deduction of the McCumber relation Image McCumberRelationActiveCemters.png right 500px ... math N 1 math and math N 2 math . Therefore, we can deduce the relation, assuming the thermal ... , which leads to the relation between the spectral rate of spontaneous emission math a omega math ... math t,t rm d t math , assuming that at time math t math the atom is excited. The relation D2 ... of D1 and D2 gives the relation 8 math frac n 1 n 2 frac sigma rm a omega sigma rm e omega exp left frac hbar omega k rm B T right . rm n1n2 mc1 math This relation is equivalent of the McCumber relation mc , if we define the zero line frequency math omega Z math as solution of equation 9 math ... Then n1n2 becomes equivalent of the McCumber relation mc . No specific property of sublevels of active medium is required to keep the McCumber relation. It follows from the assumption about quick transfer of energy among excited laser levels and among lower laser levels. The McCumber relation mc ... relation The McCumber relation is confirmed for various media ref name validity2 cite journal ... doi 10.1364 JOSAB.23.001770 bibcode 2006JOSAB..23.1770M ref . In particular relation 1 makes it possible .....22.1605K ref . Violation of the McCumber relation and perpetual motion image McCumberViolation.png ... frac 2 pi c omega math In 2006 the strong violation of McCumber relation was observed for Yb Gd sub ... more details
A discourse relation or rhetorical relation is a description of how two segments of discourse are logic ally connected to one another. One method of modeling discourse involves a set of concepts that constitute segmented discourse representation theory SDRT . SDRT Asher and Lascarides categorize the discourse relations formalized in SDRT into five classes. Content level relations Empty section date January 2011 Text structuring relations Empty section date January 2011 Cognitive level discourse relations Empty section date January 2011 Divergent relations Empty section date January 2011 Metatalk relations Consequence , ref name AL03 333 Asher and Lascarides 2003 333 ref Explanation , ref name AL03 333 Explanation sub q sub , ref name AL03 333 Result , ref name AL03 333 See also Speech act Contrast linguistics Notes and references Reflist Bibliography Nicholas Asher Asher, Nicholas and Alex Lascarides 2003 . http books.google.com.au books?id VD 8yisFhBwC Logics of Conversation . Studies in Natural Language Processing. Cambridge University Press . ISBN 0521650585 http www.cis.upenn.edu epitler Pitler, Emily and others 2008 . http repository.upenn.edu cgi viewcontent.cgi?article 1929&context cis reports Easily Identifiable Discourse Relations . University of Pennsylvania Department of Computer and Information Science Technical Report No. MS CIS 08 24. http www.eecs.harvard.edu grosz Grosz, Barbara J . and Candice L. Sidner 1986 . Attention, Intentions, and the Structure of Discourse . Computational Linguistics journal Computational Linguistics 12 175 204. aka DSM Alistair Knott, http www.cs.otago.ac.nz staffpriv alik papers cirevision.pdf An Algorithmic Framework for Specifying the Semantics of Discourse Relations , Computational Intelligence journal Computational Intelligence 16 2000 . William C. Mann Mann, William C . and Sandra A .Thompson 1988 . http www.cis.upenn.edu ... Relation Category Discourse analysis Category Natural language processing Category Semantics ling ... more details
. Conflicting terminologies The term thematic relation is frequently confused with theta .... This is because theta roles are typically named by the most prominent thematic relation ... thematic relation. Almost every noun phrase bears at least one thematic relation the exception are Syntactic ... relation that refers to the semantic thematic relations. For example, take the sentence Reggie ... roles the verb takes. The theta role is named by the most prominent thematic relation associated ... more details
Merge Typed link discuss Talk Typed link Merge Typed link and Link relation ? date October 2011 HTML A link relation is a descriptive attribute attached to a hyperlink in order to define the type of the link, or the relationship between the source and destination resources. The attribute can be used by automated systems, or can be presented to a user in a different way. In HTML these are designated with the tt rel tt attribute on tt link tt , tt a tt or tt area tt elements. Example uses include the standard way of referencing Cascading Style Sheets CSS tt link rel stylesheet href example.css tt , which indicates that the external resource linked to with the tt href tt attribute is a stylesheet, so a web browser will generally fetch this file to render the page. Another example is tt rel favicon tt for the popular favicon icon. ref Cite web url http www.w3.org 2005 10 profile publisher World Wide Web Consortium accessdate 23 February 2011 title Web site meta data profile favicon, year 2005 month October first Karl last Dubost ref ref Cite web url http www.w3.org 2005 10 howto favicon title How to Add a Favicon to your Site last Dubost first Karl date 24 October 2005 publisher World Wide Web Consortium accessdate 25 February 2011 ref Link relations are used in some microformat s e.g. tt rel tag tt for Tag metadata tagging , in XHTML Friends Network XFN , and in the Atom standard Atom standard , in XLink , as well as in HTML. Standardized link relations are one of the foundations of HATEOAS as they allow the user agent to understand the meaning of the available state transitions in a Representational State Transfer REST system. The Internet Engineering Task Force IETF has a registry of standardized link relations, ref name link relations registry http www.iana.org assignments link relations link relations.xhtml IANA link relations registry ref and a procedure for extending it defined in RFC 5988. HTML 5 also defines valid link relations. ref name HTML 5 link relations http ... more details
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