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 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details...nal products 164 Chapter Two SOME APPLICATIONS OF FRE 2.1 Use of FRE in Chemical Engineering 167 2.2 New FRE to estimate the peak hours o... ... motor-drive system 197 2.10 Application of genetic algorithm to problems in chemical industries 199 2.11 Semantics of implication operators ... ... has 10 sections: we elaborately give the applications of FRE in flow rates in chemical industry problems, preference and determination of peak hou... ...m X to Y, binary relations R(X, Y) may assign to each element of X two or more elements of Y. Some basic operations on functions such as the invers... ...n that each element of Y has to an element of X is equal to the degree of that elements membership in the range of R. In addition, the height of a ... ...responding to one set is distinguished from nodes representing the other set. Elements of X × Y with non-zero membership grades in R(X, Y) are rep... ... ik ] ° [q kj ] where r ij = k max min (p ik q kj ). Observe that the same elements of P and Q are used in the calculation of R as would be use... ... give several of the applications of fuzzy relational equations in studies like chemical engineering, transportation, medicine etc. The fuzzy relati... ... applied to special problem. [81, 85, 100-101,111, 114] 2.1 Use of FRE in chemical engineering The use of fuzzy relational equations (FRE) f...
 Book Id: WPLBN0002096589 Subjects: Non Fiction, Education, Algebra Collections: Math, Literature, Education, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details... of a set A with itself; A × A. Note that if the set A is a finite set having n elements, then the set A × A is also a finite set, but has n 2 elem... ...nts, then the set A × A is also a finite set, but has n 2 elements. The set of elements (a, a) in A × A is called the 8 diagonal of A × A. A s... ...bout subsets of A × A we can now speak about a binary relation (one between two elements of A) on A itself, by defining b to be related to a if (a, ... ...chapters of this book. The example deals with nothing but mapping of a set of n elements to itself. Example 1.2.1: Let (1, 2, 3) be the set S. Le... ...he set S. Let S(3) denote the set of all mappings of S to itself. The number of elements in S(3) is 27 = 3 3 . 10 Example 1.2.2: Let S = (1, 2... ...theory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, five Ph.D. sch...
 Book Id: WPLBN0002097100 ► Abstract Full Text Search Details....6: Let G(I) be a neutrosophic vector space over the field K. The number of elements in the neutrosophic basis is called the neutrosophic dimension ... ...g neutrosophic vector space over the neutrosophic field K(I). The number of elements in the strong neutrosophic basis is called the strong neutrosop... ...tinguished from the others), with point of degree at most 4 and finally the chemical problem of trees in which every point has degree 1 or 4. Jorda... ...e that Jordan did so without having any suspicion of its bearing on modern chemical doctrine. The most famous problem in graph theory and perhaps i... ...nite non empty set V = V (G) of p points. (vertex, node, junction O-simplex elements) together with a prescribed set X of q unordered pairs of disti... ...Each pair x = {u, v} of points in X is a line (edge, arc, branch, 1-simplex elements) of G and x is said to join u and v. We write x = uv and say t... ...graph is a complete graph. Thus in a tournament for every pair of distinct elements u and v either (u, v) or (v, u) but not both is an arc of D. To... ...ry, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars...
 Book Id: WPLBN0002097044 Collections: Math, Literature, Algebra, Authors Community, Mathematics ► Abstract Full Text Search Details...(B 1 + B 2 ). Thus two bimatrices are added by adding the corresponding elements only when compatibility of usual matrix addition exists. No... ...y square bimatrix then ( ) 2 mm mm II × × = . A bimatrix A B all of whose elements are zero is called a null or zero bimatrix and it is denoted by... ...This is a m th order square bimatrix. This will not have 2m 2 arbitrary elements since 11 ij ji aa = and 22 ij ji aa = (where A 1 = 1 ij (a ... ...nd A 2 = 2 ij (a )) both below and above the main diagonal. The number of elements above the main diagonal of A B = A 1 ∪ A 2 is (m 2 – m). Th... ... above the main diagonal of A B = A 1 ∪ A 2 is (m 2 – m). The diagonal elements are also arbitrary. Thus the total number of arbitrary elements... ...ry, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars...
 Book Id: WPLBN0000661273 Subjects: Fiction, Literature, Literature & drama ► Abstract Full Text Search Details...hat permits a family- oriented life. But the demands made by each of these elements are not easy to reconcile. It is easier for us to make a choice be... ...ows that any level of force will only be met with more hijacking, possibly chemical or bio- logical weapons, and other forms of ter- ror. And suppose ...
 Book Id: WPLBN0002097122 ► Abstract Excerpt Details...ndence in the real world. It is also clear that the solid body and the clock do not in the conceptual edifice of physics play the part of irreducible elements, but that of composite structures, which may not play any independent part in theoretical physics." / Einstein then went on to say that, in spite of the foregoing comment, we should temporarily support the use of the... Full Text Search Details...ck do not in the conceptual edifice of physics play the part of irreducible elements, but that of composite structures, which may not play any indep... ...like the “light cone” equation 0 2 2 2 = − σ τ d d c ( 0 ≠ σ d , 0 ≠ τ d ), elements of which are world-trajectories of light-like particles. But, i... ...rvable quantities. So teleporting photons move along trajectories which are elements of the world-cone (like the light cone) in that space- time area... ...onents of the circuit like a battery or energy supply. The passive circuit elements like the capacitors and inductors and resistors can be modeled ... ...ion in the function space can be represented as a long sum whose terms have elements from the spectral set as factors. For example, the set {sin(nx)... ...echnology, proceedings of the Third International Conference of The Electro-chemical Society, Inc. 30 East 42 Street, New York, NY 10017; Editor Ro...
 Book Id: WPLBN0002097045 ► Abstract Full Text Search Details...∪ (B 1 + B 2 ). Thus two bimatrices are added by adding the corresponding elements only when compatibility of usual matrix addition exists. ... ...dence maps that associates with each element of E i (G) an unordered pair of elements of V i (G) i = 1, 2. It is to be noted that E 1 (G 1 ) ... ...simple. A bigraph G = G 1 ∪ G 2 is bisimple if |G| = n that is number of elements in G 1 and G 2 without repetition i.e. o (G 1 ∪ G 2 ) = o(... ...ion between the health hazards the agricultural labourer suffers 94 due to chemical pollution. Let us taken the 11 attributes (P 1 , P 2 ,…, P 11... ... – Ulcer / skin ailments in legs and hands P 3 – Manuring the fields with chemical fertilizers P 4 – Vomiting P 5 – Mouth and stomach ... ...e at a fixed bipoint as the bihidden pattern. Thus manuring the field with of chemical fertilizers makes all the coordinates on except P 4 which im... ...ey may not suffer the symptom of vomiting because of manuring the field with chemical fertilizers. Now we study the effect of the attribute Head... ...ed by them due to spray of pesticides insecticides and manuring the plants by chemical fertilizers. At the first stage we take arbitrary attributes ... ...concepts. We further assume no intermediate relation exists within the domain elements or node and the range spaces elements. The number of elements...
 Book Id: WPLBN0002097649 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details... loop-rings and introduction to Smarandache loop-rings 20 2.3 Smarandache elements in loop rings 30 2.4 Smarandache substructures in loop rings 40 ... ... Groupoid rings and Smarandache Groupoid rings 61 3.3 Smarandache special elements in Groupoid rings 69 3.4 Smarandache substructures in Groupoid ri... ...pace consists of the following: 1. a field K of scalars. 2. a set V of elements called vectors. 3. a rule or operation called vector addition whi... ...ly it is a vector quantity, only to mention that it is different from the elements of the field which are termed as scalars. 8 DEFINITION 1.1.2... ...s finite dimensional if there exists a finite set of linearly independent elements (v 1 , v 2 , …, v n ) in V which generate V, otherwise it is infi... ..., fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, five Ph.D. scholars a...
 Book Id: WPLBN0002097647 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...ngs and its properties 2.1 Definition and examples 21 2.2 Special elements in rings 24 2.3 Substructures of a ring 26 2.4 Homomorph... .... and S. D.C.C. 67 3.8 Some special types of rings 68 3.9 Special elements in S-rings 71 3.10 Special properties about S-rings 78 ... ... 115 4.2 Smarandache rings of level II 119 4.3 Some new Smarandache elements and their properties 121 4.4 New Smarandache substructures and th... ... a -1 a = aa -1 = e. A group, which contains only a finite number of elements, is called a finite group, otherwise it is termed as an infinite ... ...s an infinite group. By the order of a finite group we mean the number of elements in the group. 8 It may happen that a group G consists enti... ..., fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, five Ph.D. scholars ...
 Book Id: WPLBN0002097643 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...n P by declaring a ∗ b = c if σ (a, b) = c. DEFINITION: A non empty set of elements G is said to form a groupoid if in G is defined a binary oper... ...all a ∈ G. We call the order of the groupoid G to be the number of distinct elements in it denoted by o(G) or |G|. If the number of elements in G ... ...order of this groupoid is 5. Example 1.2.2: Let (S, ∗) be a groupoid with 3 elements given by the following table: ∗ x 1 x 2 x 3 x 1 x 1 x... ... commutative semigroup. DEFINITION: Let S be a semigroup, if the number of elements in a semigroup is finite we say the semigroup S is of finite ... ...= {0, 1}} is a semigroup under matrix multiplication. PROBLEM 9: How many elements are there in S 3×3 given in example 1.3.6.? PROBLEM 10: Ca... ...eory, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, five Ph.D. schola...
 Book Id: WPLBN0002097651 Subjects: Non-Fiction, Education, Smarandache Collections ► Abstract Full Text Search Details...3 2 1 Clearly µ is a fuzzy subgroup of a group G and o(µ ) = number of elements of the set {x ∈ G | µ (x) = µ (e)} = number of elements of the se... ... [0, min{µ 1 (e 1 ), µ 2 (e 2 )}] where e 1 and e 2 denote the identity elements of the groups G 1 and G 2 respectively. Then t 1 t 2 t 1 2 G G... ...R µ , the ring of fuzzy cosets of µ in R is free from non-zero nilpotent elements. THEOREM 1.4.23: Let µ be any fuzzy ideal of a ring R such that... ... that Im µ = {t, s} with t > s. If the ring R µ has no non-zero nilpotent elements, then the fuzzy ideal µ is fuzzy semiprime. THEOREM [99]: A ri... ... If P : R → L is a prime fuzzy ideal and P P (0) ≠ 0, then P (R) has two elements. P is properly fuzzy if and only if P(R) has three elements. We s... ...Rings and Ideals, Addison-Wesley, Reading, MA, 1970. 30. CHAUVIN, Remi, Chemical Algebra I: Fuzzy subgroups, J. Math. Chemistry, 16, 245-256 (1994... ..., fuzzy groups, and applications of fuzzy theory to the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars a...
 Book Id: WPLBN0002097060 Subjects: Non Fiction, Philosophy, Art ► Abstract Full Text Search Details...: "The goal is to enlargement of the artistic sphere through non-artistic elements. But especially the counter-time, counter-sense creation. Also, t... ...arious observers (that’s why T, I, F are subsets - not necessarily single-elements), uncertainty due to incomplete knowledge or acquisition errors o... ...nd, not on an empty field, and uses in its construction not only opposite elements to , but elements of as well, and even elements of and have elements in common. Examples: There is little distinction bet... ...s would be required, especially in philosophy (alike Mendeleev's Table of Chemical Elements). The mathematization is required because it is not poss... ...a high level of awareness; - postmodernist; - an algebraic, physical and chemical philosophy; - consistent with its inconsistence. Transcende... ...coexist in the human body, but they can't be traced out through physical, chemical, anatomical means. Kundalini Energy (of divine nature) is th... ...and obtain something in between: s% spiritual and m% material? [kind of chemical alloy]. Or, as Boethius, a founder of scholasticism, urged to "jo... ...played on the page... A poem is a philosophical system. A physics law, a chemical formula, a mathematical equation too. For example, a blank page ...
 Book Id: WPLBN0002097043 Subjects: Non Fiction, Algebra, Smarandache Collections ► Abstract Full Text Search Details...by default of notation just say V a vector space over the field F and call elements of V as vectors only as matter of convenience for the vectors in... ... dimensional vector space) of k if every S- basis has only finite number of elements in it. It is interesting to note that if L is a finite dimension... ...We say the order of the bigroup G = G 1 ∪ G 2 is finite if the number of elements in them is finite; otherwise we say the bigroup G to be of infin... ...ace V = V 1 ∪ V 2 to be of dimension m + n. Thus there exists only m + n elements which are linearly independent and has the capacity to generate... ...0) if v ∈ V 2 then v = (0, 0, …, 0, y 1 , y 2 , …, y n ). We never add elements of V 1 and V 2 . We keep them separately as no operation may be... ...y, fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars ...
 Book Id: WPLBN0002097118 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Full Text Search Details...tensor feld, we obtain the d’Alembert equations of the feld. The non- zero elements are the d’Alembert equations containing the feld-inducing sources.... ...re the d’Alembert equations containing the feld-inducing sources. The zero elements are the equations without the sources. If there are no sources the... ...er” comes from [ME
 Book Id: WPLBN0002097104 ► Abstract Full Text Search Details...n by artificial brains. Neural networks consists of many simple computing elements generally simple non linear summing junctions connected together ... ... classes say C 1 , C 2 , …, C t where C i may have different number of elements in them, where even n can be a prime number then we call such str... ...int cognitive maps here only the blocks need not contain equal number of elements. We illustrate as well as exhibit these models in the study of ... ...he attributes A 1 , 176 A 2 …, A n in to m classes with a overlap of s elements ie A 1 , A 2 ,…, A n is divided into classes C 1 ,…, C m where ... ... 2 ,…, A n is divided into classes C 1 ,…, C m where we have number of elements in each C i is s where there are common elements between the C i... ..., fuzzy groups, and applications of fuzzy theory of the problems faced in chemical industries and cement industries. Currently, six Ph.D. scholars a...
 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details... g μμ ∈(M g ,g g ), not by foisting upon (M g ,g g ) the interpretation of elements of (M s ,g s ) in the misguided fashion of the orthodox relativist... ...was located inside a box isolated from air convection and light radiation. Chemical reactions of the opposite directions, processes of crystallization... ... ˉQ(Λ) ! , (3.19) where Q(Λ) and ˉQ(Λ) are three-dimensional matrices, the elements of which are complex conjugates, ε is the three- dimensional unit ... ...he 2nd degenerate kind by Petrov’s classifcation . In emptiness (κ=0) some elements of the matrices x and y take the numerical values +1 and −1 thereb... ...5.25) where the three-dimensional matricesx,y,z are built on the following elements, respectively x ik =− 1 c 2 X ik , z ik = 1 c 2 ε imn ε kpq Z mn... ...itter hyperboloids to r=1, because this is the only choice for r where all elements in the bounded domains are also coset representatives, and therefo...
 Book Id: WPLBN0003466796 Subjects: Non Fiction, Science, Chemistry ► Abstract Description Details.... The most significant discoveries in chemistry and physics are presented chronologically to illustrate their contributions to the creation of the chemical sciences during the last 21 centuries.... Excerpt Details... to express the full extent of my emotions and reasons for writing this book on the STORY OF THE ATOM AND THE SCIENCES, with special reference to the CHEMICAL SCIENCES. In one sentence, I can distill the essence of the purpose for this study by simply stating that it has been a labor of love that transcended the written word because sentiments and ideas belong in the rea... Table of Contents Details...CT ON THE ATOM AND ITS ENERGY 11 THE CLASSIC GREEK AND ROMAN PHILOSOPHERS 17 EMPEDOCLES (492-432 BC) Greek Philosopher 20 Proposed the four basic elements: earth, water, air and fire. DEMOCRITUS (470-380 BC) Greek Philosopher 22 The founder of the atomic theory of antiquity. CLAUDIUS PTOLEMY (100-170) Greek Astronomer 24 Proponent of the geocentric theory of our ...
 Book Id: WPLBN0000661761 ► Abstract Full Text Search Details...entirely unnoticed, was first corrected in the third edition of Mr. Mill’s Elements of Political Economy. It can hardly, however, be said that Mr. Mil... ...he receivers may choose to expend it. NO NO NO NO NOTES TES TES TES TES 1 Elements of Political Economy, by James Mill, Esq., 3rd edit., pp. 120-1. 2... ... of 180 quarters. When we analyse the price of the seed and tools into its elements, we find that they must have been the pro- duce of the labour of 4... ...n of the wages of one labourer for a year, is the result of two concurrent elements or factors,—viz., 1st, the quantity of commodities which the state... ...te of interest; and to shew that although the rate of profit is one of the elements which combine to deter- mine the rate of interest, the latter is a... ...rinciples of the science of mechanics, it is necessary to bear in mind the chemical properties of the material, such as its liability to oxydize; its ...
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