#jsDisabledContent { display:none; } My Account |  Register |  Help

Search Results (9 titles)

Searched over 7.2 Billion pages in 0.3 seconds

Equivalence relation (X) Algebra (X)

 1 Records: 1 - 9 of 9 - Pages:
 Book Id: WPLBN0002096589 Subjects: Non Fiction, Education, Algebra Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details... Preface 5 1. Preliminary notions 1.1 Binary Relation 7 1.2 Mappings 9 1.3 Semigroup and Smarandache Semigroup... ...marandache semigroups. In Chapter one, we introduce some basic notation, Binary relations, mappings and the concept of semigroup and Smarandache sem... ...appings and the concept of semigroup and Smarandache semigroup. 1.1 Binary Relation Let A be any non-empty set. We consider the Cartesian pr... ...s called the 8 diagonal of A × A. A subset S of A × A is said to define an equivalence relation on A if (a, a) ∈ S for all a ∈ A (a, b) ∈ S ... ... 8 diagonal of A × A. A subset S of A × A is said to define an equivalence relation on A if (a, a) ∈ S for all a ∈ A (a, b) ∈ S implies (b, ... ...ollowing definition. DEFINITION: The binary relation ~ on A is said to be an equivalence relation on A if for all a, b, c in A i. a ~ a ii. a... ...reflexivity, the second, symmetry and the third transitivity. The concept of an equivalence relation is an extremely important one and plays a centr... ... a central role in all mathematics. DEFINITION: If A is a set and if ~ is an equivalence relation on A, then the equivalence class of a ∈ A is th... ... ∈ A/ a ~ x}. We write this set as cl(a) or [a]. THEOREM 1.1.1: The distinct equivalence classes of an equivalence relation on A provide us with ...
 Book Id: WPLBN0002097100 ► Abstract Full Text Search Details... and applies it to the case of neutrosophic cognitive maps and neutrosophic relational maps. The last section of this chapter clearly illustrates ho... ...out this book by ‘I ’ we denote the indeterminacy of any notion / concept / relation. That is when we are not in a position to associate a relation ... ...f the neutrosophic vector space V over R. A study of these basis and its relations happens to be an interesting form of research. DEFINITION 1... ... Cognitive Maps and use rectangular neutrosophic matrices for Neutrosophic Relational Maps. 13 Chapter Two SOME BASIC RESULTS... ...ion of a graph in which people are represented by points and interpersonal relations by lines. Such relations include love, hate, communication and... ...is reachable from the other. It is easily verified that disconnection is an equivalence relation on the vertex set of D and if the equivalence class... ...onigsberg bridge problem has no solution. The following theorem which gives equivalence of three conditions is left for the reader as an exercise to...
 Book Id: WPLBN0002097644 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details... n . (D 2n is called the dihedral group of order 2n given by the following relation, D 2n = {a, b/ a 2 = b n = 1; bab = a}. 13. Give an examp... ...ces used in this book. DEFINITION 1.2.1: Let A and B be non-empty sets. A relation R from A to B is a subset of A × B. Relations from A to B are c... ...lation R from A to B is a subset of A × B. Relations from A to B are called relations on A, for short, if (a, b) ∈ R then we write aRb and say that ... ...ions on A, for short, if (a, b) ∈ R then we write aRb and say that 'a is in relation R to b’. Also if a is not in relation R to b, we write b R a / ... ...itive if for a, b, c in A; aRb and bRc imply aRc. A relation R on A is an equivalence relation if R is reflexive, symmetric and transitive. In the... ...ve, symmetric and transitive. In the case [a] = {b ∈ A| aRb}, is called the equivalence class of a for any a ∈ A. DEFINITION 1.2.2: A relation R o... ... DEFINITION (MONICO, CHRIS): A congruence relation on a semiring S is an equivalence relation ~ that also satisfies        + + + + ⇒ c x... ...ongruence relation) ~ if we have a S-subsemiring A of S such that '~' is an equivalence relation that also satisfies        + + + + ⇒ ... ...61, 66, 91, 95-96, 100 Distributive law, 19, 39 Division ring, 19 E Equivalence class, 12 Equivalence relation, 12, 51, 80 Extension field...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...× µ ) (x, y) = min {λ(x), µ (y)} for every (x, y) ∈ X × Y. A fuzzy binary relation R λ on a set X is defined as a fuzzy subset of X × X. The co... ...X is defined as a fuzzy subset of X × X. The composition of two fuzzy relations R λ and R µ is defined by (R λ o R µ )(x, y) = sup X t∈ {min R... ... y)}, for every x, y ∈ X. DEFINITION 1.1.12: Let R λ be a fuzzy binary relation on a set X. A fuzzy subset µ of the set X is said to be a pre cla... ... {µ (x), µ (y) } ≤ R λ (x, y) for every x, y ∈ X. 11 A fuzzy binary relation R λ on a set X is said to be a similarity relation on the set X i... ....2: A relation ρ on an R-module M is called a congruence on M if it is an equivalence relation on M such that (a, b) ∈ ρ and (c, d) ∈ ρ imply that (a... ...uzzy relation α on M [i.e. a mapping α : M × M → [0,1]] is called a fuzzy equivalence relation if i. z , y , x all for ) z , y ( ) x , x ( sup M ... ...α α ∈ ≥ for all x, y in M (fuzzy transitive). DEFINITION 1.8.5: A fuzzy equivalence relation α on an R-module M is called a fuzzy congruence if α ... ... [] [] ) y , z ( ), z , x ( Min sup M z µ µ ∈ α α . Thus α µ is a fuzzy equivalence relation on M. Now α µ (x + u, y + ν) = µ (x + u – ν – y... ... generates the half groupoid P. Now we introduce the notions of fuzzy equivalence relation as given by [144] and proceed on to recall the defini...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...dular lattices. DEFINITION 1.3.1: Let A and B be two non-empty sets. A relation R from A to B is a subset of A × B. Relations from A to A are ca... ...ion R from A to B is a subset of A × B. Relations from A to A are called relation on A, for short. If (a, b) ∈ R then we write aRb and say that a i... ...ion on A, for short. If (a, b) ∈ R then we write aRb and say that a is in relation R to b. Also if a is not in relation R to b we write a R / b. A r... ... a = b. R is transitive if for all a,b,c in A aRb and bRc imply aRc. A relation R on A is an equivalence relation, if R is reflexive, symmetric a... ...tive if for all a,b,c in A aRb and bRc imply aRc. A relation R on A is an equivalence relation, if R is reflexive, symmetric and transitive. In t... ...metric and transitive. In this case, [a] = {b ∈ A / aRb} is called the equivalence class of a for any a ∈ A. DEFINITION 1.3.2: A relation R on... ...exists e ∈ M such se = es = s. The reader is advised to develop Morita equivalence on semigroups with systems of local units. A ring (or semi... ...Can we ever find a ring R in which subring link relation happens to be an equivalence relation? 182. Can reals or ring of integers have pairs whi... ...es, Math. Issled, No. 66, 113-127, (1982). 58. Neklyudova V.V. Morita, Equivalence of semigroups with systems of local units, Fundam. Prikl. Math...
 Book Id: WPLBN0002097643 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...R + and Z ⊂ Q ⊂ R, where ' ⊂ ' denotes the containment that is ' contained ' relation. Z n = {0, 1, 2, ... , n-1} be the set of integers under mu... ... homomorphic image of a sub-semigroup of S 2 . In symbols G 1 | G 2 . The relation divides is denoted by '|'. DEFINITION: Let 1 K = (Z 1 ,... ...(z 1 , z 2 , z 3 )}, {a 1 , a 2 }, {0, 1}, δ, λ} Define the equivalence classes on Z as ~ 1 and ~ 2 . Find Z/~ 1 and Z/~ 2 . ...
 Date: 2013, Volume 3, October 2010 Book Id: WPLBN0002828350 ► Abstract Description Details... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati... Excerpt Details... how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb index, Zagreb index, graph operators. ... Table of Contents Details...SI Hypergraph Partitioning Using Taguchi Methods BY P.SUBBARAJ, S.SARAVANASANKAR and S.ANAND . . . . . . . . . . . . . . . . 69 Negation Switching Equivalence in Signed Graphs BY P.SIVA KOTA REDDY, K.SHIVASHANKARA and K.V.MADHUSUDHAN. . . . . . 85 Weak and Strong Reinforcement Number For a Graph BY PINAR DUNDAR, TUFAN TURACI and DERYA DOGAN. . . . . . . . . . . . . ....
 Date: 2013, Volume 4, December 2010 Book Id: WPLBN0002828354 ► Abstract Description Details... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati... Table of Contents Details.... . . . . . . . 70 Entire Semitotal-Point Domination in Graphs BY B.BASAVANAGOUD, S.M.HOSAMANI and S.H.MALGHAN. . . . . . . . . . . . . . .79 On k-Equivalence Domination in Graphs BY S.ARUMUGAM and M.SUNDARAKANNAN. . . . . . . . . . . . . . . . . . . . . . . 86 On Near Mean Graphs BY A.NAGARAJAN, A.NELLAI MURUGAN and S.NAVANEETHA KRISHNAN. . . . . . 94 On Pathos Lic...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details...el each of which assumes some economic parameter which describe the inter relations between the industries in the economy 32 under considerations... ...he collection of all polynomials of degree less than or equal to 4. So no relation among elements of V 1 and V 2 is possible. Thus we also show t... ...gebra and the linear bialgebra. Clearly the strong linear bialgebra has no relation with the linear bialgebra or a linear bialgebra has no relation ... ...d where as the strong linear bialgebra is defined over a bifield, hence no relation can ever be derived. In the similar means one cannot derive any... ...n can ever be derived. In the similar means one cannot derive any form of relation between the weak linear bialgebra and linear bialgebra. All th... ...d to define the notion of Jordan biform. The notion of Jordan form in each equivalence class of matrices under similarity and so it has been proved ...
 1 Records: 1 - 9 of 9 - Pages: