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...ions Deregulation and Monetary Control Act of 1980 forced S&L's to achieve interest parity with commercial banks, thus eliminating the interest ceil... ...LE - p16} 7. VARIANCE and STANDARD DEVIATION as measures of the difference between mathematics and reality. They are the measures of the frustrat...

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...ting a book, one encounters and overcomes many obstacles. Not the least of which is the occasional case of writer’s block. This is especially true in mathematics where sometimes the answer is currently and may for all time be unknown. There is nothing worse than writing yourself into a corner where your only exit is to build a door by solving unsolved problems. In any case...

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...ctually reached. That statement also holds for some of these problems. In mathematics, one often does not know what the consequences of a statement ... ...nt are. Cnlike a novel however, there are no complete plot resolutions in mathematics as there are no villains to rub out. As the French emphatically... ... divides n'. and associated consequences has spawned many new branches of mathematics. A previous volume in this series[2] introduced the function a... ...For any number of digits k, the number of elements of SEDS depends on the parity ofk. a) Ifk = 2j, then the number of elements of SEDS having m digi... ...ime to stop once again There are still unexplored regions in that area of mathematics loosely defined as the Smarandache notions, but they will be le...

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...he. In addition, I have edited two others that also deal with the areas of mathematics under the Smarandache Notions umbrella. All of this is a credit... ...nd the second is an even plus an even. Since all powers of B are even, the parity of the numbers will be based on the parity of the last term, which i... ...ng the previous term by a power of B, which is always even. Therefore, the parity of the next term will be based on the parity of the term number, whi... ...s, we have (12 . . . (r-1)) * 3 s + r*3 t + (r-1) . . . 21 which has odd parity. The next element of the sequence is formed by including an addition... ... r*3 w is also odd. Therefore, we have three segments whose sum is of odd parity and we added an additional odd term. This changes the parity to even... ...lement (12 . . . r)*3 s by additional powers of three will not change the parity of the term. Therefore, we have two terms whose combined parity is e... ...arandache is truly a Renaissance man, having produced quality work in art, mathematics and literature. This is my fifth book where I expand on some o...

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...zzy Algebra. Originally, the revolutionary theory of Smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Florentine Smarandache, is alike to that of Fuzzy Theory: both the fields imperatively questioned the dogmas of classical mathematics....

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...HE FUZZY ALGEBRA W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras Chennai – 600 036, Indi... ...tarted because of my perception at that time, that the world of classical mathematics – was a little too much of a black and white world, that the p... ...born as a paradoxist movement that challenged the status quo of existing mathematics. The genesis of Smarandache Notions, a field founded by Floren... ...y Theory: both the fields imperatively questioned the dogmas of classical mathematics. Despite the fact that Fuzzy Algebra has been studied for ov... ...1) (0: 0) Figure 7.1.4 404 This automaton is known as the parity check automaton. Now it is important and interesting to note th... ...Normalized fuzzy extension, 150 O Open fuzzy extension, 146 P Parity check automaton, 404 Penultimate, 224 P-fuzzy correspondence, 164 ... ...UTHOR Dr. W. B. Vasantha is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai, where she liv...

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...AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036... ...ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail:... ...cademia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, I... ... Even more general, of course, is to consider Θ as an operator (of some finite parity) which maps fuzzy sets and relations onto fuzzy sets or fuzzy... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph... ... Darwin (biology), Maxwell (electromagnetism), Einstein (mechanics) and Godel (mathematics). Although paradigm shifts vary from one another in thei...

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... A 2 B 1 B 2 4 0 1 2 3 1 W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology Madras, Chennai – 600036, ... ...e Smarandache Semigroup, International Conference on Combinatorial Methods in Mathematics, II Meeting of the project 'Algebra, Geometria e Combinato... ...i ) z 0 z 1 (0,0) (1;1) (1;1) (0,0) This automaton is know as the parity check automaton. Now it is important and interesting to not... ...7 Next state function, 93, 97 Output alphabet, 94 Output function, 94 Parity Check Automaton, 96 Semi automaton, 93-94, 96, 102 Semigroup... ...he Author Dr. W. B. Vasantha is an Associate Professor in the Department of Mathematics, Indian Institute of Technology Madras, Chennai, where she...

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...re more interested to attract all types of reader we have not used very high mathematics. DEFINITION 1.1.1: An FCM is a directed graph with conc... ...sacred thread? Do all the non-Brahmins who 122 wear the sacred thread, have parity with the Brahmins? Now, in our country the Singurao, Chettiar, ... ...ics, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2001). 7. Bechtel, J.H... ...es, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, (2000). 22. Kananaikal, ... ...oblem, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (1999). 26. Ko... ...dents, Masters Dissertation, Guide: Dr.W.B.Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, (2001). 32. Ma...

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...erican Research Press Rehoboth 2002 József Sándor DEPARTMENT OF MATHEMATICS BABE Ş-BOLYAI UNIVERSITY 3400 CLUJ-NAPOCA, ROMANIA Geome... ...n its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics..." (K.F. Gauss, Disquisitiones arithmeticae, G ottingen, 1801... ...uable advice or support in the preparation of this material. These are the Mathematics Department of the Babe s-Bolyai University, the Domus Hun- gar... ...ntimate correlation between the Theory of numbers and other departments of Mathematics, not excluding geometry..." (Felix Klein, Evanston Colloquium L... ...b =d(v 2 u 2 ) c = 2duv (1) where (u;v) = 1, v > u and u;v have distinct parity; d is arbitrary (or b! c, c! b). The area of ABC is A = bc 2 =d 2 uv... ...be written as (m 2 + n 2 )j2 mn (m 2 n 2 ). Since (m;n) = 1, of di erent parity, it is immediate that ( m 2 + n 2 ; 2mn(m 2 n 2 )) = 1, giving (m ... ...m 2 +n 2 ) (18) where k 1 is arbitrary and (m;n) = 1, m>n are of di erent parity. In the same manner, by r a = p a = uq b u in case i) b u = (... ...v 2 ) 2uv; (5) where u>v, (u;v) = 1 are positive integers of the di erent parity, and t 1 is arbitrary positive integer, (and x!y, y!x, z!z). Proof.... ... 2 u 4 + 4dv 2 = 3T 2 and z = T du 2 2 . ThereforeT anddu 2 have the same parity. Now, by solving the equationd 2 u 4 4dv 2 +3T = 0 one obtains d =...

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...he software metaphor is correct, the brain must contain the following features: 1. Parity checks through back propagation of signals. The brain's e... ... back (to the origin) and forward, simultaneously, in order to establish a feedback parity loop. 2. The neuron cannot be a binary (two state) machi... ...measurement and by organizing the results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it... ...d measurement and organizes the results, often presenting them in the language of mathematics. In some quarters, these practices lends it an air o... ...measurement and by organizing its results and presenting them using the language of mathematics. This does not atone for its primordial sin: that it...

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...he software metaphor is correct, the brain must contain the following features: 1. Parity checks through back propagation of signals. The brain's e... ... back (to the origin) and forward, simultaneously, in order to establish a feedback parity loop. 2. The neuron cannot be a binary (two state) mach... ...be no preferred direction, no clustering of mass or of energy, no time, charge, or parity asymmetry in elementary particles. The notion of continuu... ...ractitioners sought to disguise its nature as a social science by applying complex mathematics where common sense and direct experimentation would ... ...ifferently to the same transformation? Arithmetic, formal logic, and, by extension, mathematics and physics deal with proving identities in equation... ...ecognized as an important contribution and applied to problems in geometry, logic, mathematics, computation and physics. One of the first questions... ...t infinite sets are organized in a hierarchy. Russel and Whitehead concluded that mathematics was a branch of the logic of sets and that it is ana... ...ations require an "intuition of mathematical order" without which no creativity in mathematics is possible. He described how some of his creative w...

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...ed, is the small- est State in the Union. I may perhaps best show its dis- parity to other States by saying that New York extends about two hundred an... ...n intended that it should be given. But there are axioms in politics as in mathematics, which recommend themselves to the mind at once, and require no...