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 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: WPLBN0002097650 Subjects: Non-Fiction, Education, Smarandache Collections Collections: Technology, Literature, Education, Logic, Authors Community, Mathematics ► Abstract Full Text Search Details...belian or a commutative group. If the group G has only a finite number of elements we call G a group of finite order otherwise G is said to be of in... ...G is said to be of infinite order. If a b ≠ b a, for atleast a pair of elements a, b ∈ G, then we call G a non-commutative group. Notation: Let... ...up of G then o(H) is a divisor of o(G). Note: o(G) means the number of elements in G it will also be denoted by |G|. CAUCHY THEOREM (FOR ABELIA... ...ontain any non-trivial normal subloop. DEFINITION 1.1.4: If x and y are elements of a loop L, the commutator (x, y) is defined by xy = (yx) (x, y)... ... 〉 denotes the subloop generated by A. DEFINITION 1.1.5: If x, y, z are elements of a loop L an associator (x, y, z) is defined by (xy)z = (x(yz))... ..., 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: WPLBN0002097085 ► Abstract Full Text Search Details...omparative validity of conflicting statements in terms of their paradoxical elements. In fact, given the above broad definitions, it appears the sci... ... on a subjective value system, so that comparative methodology has inherent elements of uncertainty, i.e. characteristics of neutrosophy. [31] [36] ... ...ical characteristics in set {A} ∋ { a 1 , a 2 , a 3 ,…a n }, is composed of elements, {S} ∋ {s 1 + s 2 + s 3 +...+ s n }, having physical characte... ... variance with modern theory ―particularly in regard to the SQP paradoxical elements. Thus, the Smarandache quantum paradox set should provides an e... ...um distance ―the corners of the nuclear cube. 11. This indicates the noble elements, (Column 8A, Periodic Table), should possess perfect nuclear cu... ...charge field domains. For example, the exothermic or endothermic nature of chemical reactions indicates considerable energy stored in molecular bon... ...1994. [25] ibid., p. 169. [26] ibid., p. 74. [27] Masterton, Slowinski; CHEMICAL PRINCIPLES, Fourth Edition., Figure 6.14 Ionization energies of ...
 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: WPLBN0002097086 Subjects: Non Fiction, Education, Smarandache Collection ► Abstract Full Text Search Details...he space−time. 4.The fundamental law governing spatio-temporality and its elements is the permanent and stochastic motion. 5.The stochastic* (Brown... ...he brlliant anticipations of Martin Heidegger, religion has more and more elements characteristic of a scientific discipline; the real problem that ... ...eality, being able to communicate with ″living″ (materially split-in-two) elements, to the extent of their being affectively apt to this process. In ... ... although its material component already undergoes the natural process of chemical decomposition. The ghosts′ stay for a longer while within the mat... ...ing of the universal rationality) the supposed perfection. The disturbing elements are not the expression of the divine will, but the consequence of... ...ainment, upon the natural conclusion of the material life, the body being chemically decomposed and the soul being dissociated into the constituent ... ...as entertainment, beyond this level being in jeopardy to become dangerous elements of mystification and interested manipulation of reality. Assuming... ...ined by the appearance and disappearance of sensations. Genetic birth and chemical decomposition of the body are elements defining very clearly the ... ...ng the dissociation of the soul from the body, on the onset of the body′s chemical decomposition and on of the soul′s monadic dissociation. It means...
 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: WPLBN0002096913 Subjects: Non Fiction, Fine Arts, Art History ► Abstract Excerpt Details...ance. The aesthetic behaviour of the paradoxism characterized by the auto-suspension of the absurdity. In the table of distribution of the specific elements, it is collocated in the category of annihilators and perifractors of the convention (by the side of the comic, the ridicule, the grotesque, the absurd).... Full Text Search Details...suspension of the absurdity. In the table of distribution of the specific elements, it is collocated in the category of annihilators and perifractors... ...ician, a notional pulverization, including for this purpose heterogeneous elements, from scientific notions up to drawings, signs and the lack of th... ... of any word or literary sign whatever), any abstract sign (mathematical, chemical, physical) put on a page... The nonliterature, created in a par... ...the paradoxist essentiality should be? Here is the chart of the composing elements: a clear sweep of the former literature, the consideration of the... ...ity means impossibility. The poetical practice always results in other new elements, different of the obedient ones, like the continuation of a theor... ... “non-determined”, of the well thought “imperfection”. These are starting elements that combine a presentiment with regard to a “somewhere” reached o... ...tion in the relations domain at the king court”) and “Chinese, Bengalis, Chemical, Physical, Martian, Astrological, Metagalactical, ... prose” (the ...
 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 ...
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