Full Text Search Details
... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXI... ...OSOPHIC RELATIONAL MAPS HEXIS Church Rock 2004 1 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasan... ... i c a t i o n 6 P r e f a c e 7 Chapter One FUZZY RELATIONAL EQUATIONS: BASIC CONCEPTS AND PROPERTIES 1.1 Fuzzy Rel... ... Fuzzy Relational Equations and their properties 10 1.2 Properties of Fuzzy Relations 16 1.3 Fuzzy compatibility relations and composition o... ...In this section we just recollect the properties of fuzzy relations like, fuzzy equivalence relation, fuzzy compatibility relations, fuzzy ordering ... ...more about these concepts please refer [43]. Now we proceed on to define fuzzy equivalence relation. A crisp binary relation R(X, X) that is reflex... ...inary relation R(X, X) that is reflexive, symmetric and transitive is called an equivalence relation. For each element x in X, we can define a crisp... ...sp set A x , which contains all the elements of X that are related to x, by the equivalence relation. A x = {y ⏐(x, y) ∈ R (X, X)} A x is cl... ...ed to any element of X not included in A x . This set A x is referred to an as equivalence class 17 of R (X, X) with respect to x. The members...

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...

Full Text Search Details
...s-manifolds are a very restricted subclass of the 7 polyhedral surfaces. The relationship between polyhedral surfaces and Riemannian manifolds is... ... The non-Euclidean vertices introduce a sort of curvature, and this affects the relationships between s-lines. The topology of an s-manifold can all... ...lines being parallel or not parallel at different points along them, since this relationship between s-lines changes as 21 we move from point to ... ...y, to change from region to region, this does not necessarily carry over to the relationships between lines, or 26 geodesics. This is, in fact, o... ...e to S-deny all of Hilbert’s axioms, and our choice to have congruence to be an equivalence relation further reduces our ability to S-deny Hilbert’s... ...all of Hilbert’s axioms, and our choice to have congruence to be an equivalence relation further reduces our ability to S-deny Hilbert’s axioms. Mos... ...nsitive. In fact, our definition of s- congruence satisfies the properties of an equivalence relation, i.e., it is reflexive, symmetric, and transiti... ...lexive, symmetric, and transitive. Using a notion of congruence that was not an equivalence relation would complicate the study of all related issue...

Full Text Search Details
... manifolds with higher dimension are inspired by the Riemann surfaces. The relation of maps with Riemann surfaces has been known in 80s in the last ce... ...etries, maps and the semi-arc automorphism group of a graph. Preface ii A relation for maps and Smarandache manifolds (abbreviated s-manifolds) and a... ...oted maps are established in this chapter. The last section determines the relation of the number of embeddings and rooted maps of a graph on genus. A... ...me for enumerating maps underlying a graph.........................17 §4 A relation among the total embeddings and rooted maps of a graph on genus20 4... ...pty boundary and to be analytic functions. Whence, we have the following relation: {Riemann Sufaces}⊂{Klein surfaces}. The upper half planeH ={z∈C|I... ...re exists an isomorphism ζ between them induced by an element ξ. Call ζ an equivalence between M 1 ,M 2 . Certainly, on an orientable surface, an equi... ...t1 2 Γ such that P ζ 1 = P 2 or P ζ 1 = P −1 2 . Proof By the definition of equivalence between maps, if κ is an equivalence between M 1 and M 2 , then... ...ducedtheconformalmappingbetween maps. Then, how can we define the conformal equivalence for maps enabling us to get the uniformiza- tion theorem of map...

Full Text Search Details
...ith that energy being subject to the Doppler effect because of the Planck relationship E = h υ according to the factor (1- β)/√(1- β 2 ). [3] Putt... ...the electric current." A similar statement may apply to gravitons in their relation to mass. [3] A is sail area, p is light pressure, k = 2/c ... ...e traveler ages most!" The Galilean-Newtonian-Einsteinian principle of equivalence equates gravitation and acceleration fields, and the speed of ... ... field would be expected to stop completely. Finally by the principle of equivalence, the same thing would be expected to happen in an infinite acce...