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...d theoretical physicists, and a philosopher of science. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincar...

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...S....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..................

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...S....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen..................

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...presented at Second International Conference on Smarandache Type Notions In Mathematics and Quantum Physics, December 21 - 24, 2000 University of Cr... ...presented at Second International Conference on Smarandache Type Notions In Mathematics and Quantum Physics, December 21 - 24, 2000, University of C... ...andache, F. There Is No Speed Barrier In The Universe, "Bulletin of Pure and Applied Sciences", Delhi, India, Vol. 17D (Physics), No. 1, p. 61, Janua...

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...an interval neutrosophic inference system based on rst order interval neutrosophic predicate logic. The interval neutrosophic inference system can be applied to decision making. Chapter 3 gives one application of interval neutrosophic sets and logic in the eld of relational databases. Neutrosophic data model is the generalization of fuzzy data model and paraconsistent data...

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...@hotmail.com FLORENTIN SMARANDACHE University of New Mexico, Department of Mathematics, Gallup, NM 87301, USA. smarand@unm.edu http://www.gallup.unm....

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...ician of the World', by Charles T. Le", recenzie în <Journal of Recreational Mathematics>, USA, Vol. 28(2), 130, 1996-7. [2] Begay, Anthony, "The ... ...996-7. [2] Begay, Anthony, "The Smarandache Semantic Paradox", <Humanistic Mathematics Network Journal>, Harvey Mudd College, Claremont, CA, USA, ... ... Le, Charles T., "The Smarandache Class of Paradoxes", <Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 14 E (No. 2), 109-110, 1995. [5... ...st Mathematician of the World: Florentin Smarandache", <Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 15E (Maths & Statistics), No. 1, 8... ...rles T., "The Smarandache Class of Paradoxes", <Journal of Indian Academy of Mathematics>, Indore, Vol. 18, No. 1, 53-55, 1996. [7] Le, Charles T... ...N, USA, 94, 1996. [8] Mitroiescu, I., "The Smarandache Class of Paradoxes Applied in Computer Sciences", <Abstracts of Papers Presented to the Am... ...cies & Paradoxes", <The Eugene Strens Memorial on Intuitive and Recreational Mathematics and its History>, University of Calgary, Alberta, Canada, 27...

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...ral Tamil Nadu in India W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, ... ...n web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: s... ...ies (NAMs) that is an analogous model of Fuzzy Associative Memories. NAMs are applied to this problem and conclusions are based on this analysis. ... ... varies from women to women we are forced to analyze the problem using fuzzy mathematics. This chapter has two sections. In the first section we in... ...roduction of learning as encoding. We avoid all types of high and complicated mathematics. As our study is a psychological one, we give more import... ... a new neutrosophic model called the Neutrosophic Associative Memories and is applied to this problem. For in this model alone one can compare one ... ...f these blisters in several places. It looks pathetic for no medicine is even applied externally for her blisters. 39 On 10-02-2002 we met a ... ...rsey. 60. Kosko, B., (1987) “Adaptive Bidirectional Associative Memories,” Applied Optics, 26 4947-4960. 61. Kosko, B., (1988) “Bidirectional ... ...adu Human Development Report (1999) Employment. Department of Evaluation and Applied Research (DEAR), Government of Tamil Nadu. Tamil Nadu State AI...

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... Due to the body's high resistance, an alternating current of 2000-2400 volts is applied to electrocute the condemned. Only two electrodes, moist... ... word meaning "pirate, hijacker". In Spanish "filibustero" meant "freebooting" and applied to 16th century privateers. Irregular military adventure... ...n order to conserve the facial features. Facial hair is singed off and charcoal is applied to the eyes. The head is smoked, dried, and cured. It... ...ough his adaptation to life and to others can improve with treatment. Medication is applied to side-effects and behaviors (such as mood or affect d... ...NEP.htm l Newton, Isaac Isaac Newton (1642-1727), the father of modern physics and mathematics, was an avowed and dedicated alchemist, mystic, theo... ...intellectuals, the lingua franca, akin to English today. Nor was he acquainted with mathematics until he was 30. Leonardo was born out of wedloc...

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...memory in a kind of narrative or personal mythology. Can this conjecture be equally applied to unconscious mental states (e.g. subliminal perception... ...ished independently (as is often the case in science) the basics of a new branch in Mathematics (and logic): computability or recursive functions (l... ...possess the same sense organs that we do (eyes) and may not be acquainted with our mathematics and geometry. Reality can be successfully described ...

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...a person actually acquires knowledge. You might say that it involves a lot of mathematics and dry rules. It has nothing to do with psychology or oth... ... the Creator, whether it’s the Psalms, Agadot, Tanya, the literal Torah, even mathematics and physics, our daily life routine or even Buddhism. Ever... ...cognize our nature as bad, and we are repelled by its presence. Kabbalah is an applied, experimental science. Everything we now know about the spirit... ...re we can read about the spiritual world. Kabbalah, as we’ve said above, is an applied science. If we do not learn from our own experiences and do no... ...he law of gradual evolution is a law that works on the whole of nature and is applied in every particle of it. Take the earth, for example. First, i... ... it. This photograph has healing powers. One starts feeling better when it is applied to a hurting spot. Recently, I treated a severe wound on a dog... ...student. At first, the “mouth to ear” condition for relations and learning is applied, and afterwards, if the group merits it, “mouth to mouth” is a...

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...o each other not by terror or by money but by a new way of living art: art applied to life and not just to paintings and instruments. No longer a... ..., he started out from a hypothesis. He worked around this hypothesis using mathematics. Einstein could not offer experimental proof of his hypothesi...

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...I have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Jo...

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...eading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research P... ...tions at: the Arizona State University (Tempe, USA), Archives of American Mathematics (University of Texas at Austin, USA), University of Craiova Lib... ... fascinating and is halfway between the number theory and the recreational mathematics. Even though sometime this universe has a very simple structur... ...e numbers. Proof. A direct consequence of the fact that the function Zw applied to a squarefree number returns the squarefree itself and applied to... ...rhus Univ. Press, 1996 [3] E. Weisstein, CRC Concise Encyclopedia of Mathematics, CRC Press, 1999 [4] F. Smarandache, "Only Problems, not Soluti... ...bl. [5] J. Castillo, Smarandache continued fractions, Bulletin of pure and applied Sciences, Vol. 17E, No.1, 1998, p. 149-151 [6] F. Russo, Some... ...ot of sequences in number theory. Several concepts of number theory can be applied to the set of Smarandache sequences as has already been done for ex... ...n k k Su n Sm 1 ) ( ) ( 49 where Su(k) is the Smarandache Mobius function applied to any Smarandache sequence a(k). As example see the fig. 2.4 where... ...che sequence a(k). As example see the fig. 2.4 where the function has been applied to Smarandache power sequence [2]. Problem 17. Is there any Smara...

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...This work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the classical notions of Benthamite utility and the normative utility paradigm offered by the von Neumann-Morgenstern expected utility theory; exploring its major pitfa...

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... work covers a substantial mosaic of related concepts in utility theory as applied to financial decision-making. It reviews some of the classical not... ...els, our approach is predominantly numerate and substantiated by rigorous mathematics rather than being merely normative or speculative. The... ... While countless research papers have been written and published on the mathematics of option pricing formulation, surprisingly little work has be... ...sure for the spread of coordinates of a utility increment vector. He also applied the differential form of entropy expression in continous form to a... ...le from a basket of commodities. We have illustrated the concepts with an applied finance perspective whereby we have used this methodological appro... ...ured products. In particular, principles of Shannon-Fano coding have been applied to the coding of structured product information for transmission fr... ...s in which tools and concepts from mathematical information theory can be applied in utility analysis in general and to analyzing investor utility p... .... Numerical Methods and Software. Prentice-Hall Series in Computational Mathematics, New Jersey: Prentice-Hall, 1989. Khoshnevisan, M., S. Bhatt... ...78. Lyuu, Yuh-Dauh. Financial Engineering and Computation – Principles, Mathematics, Algorithms. Cambridge University Press, U.K., 2002. Mark...

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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... ...s a place to start, in that there are many different functions that can be applied. For example, the iteration cycle could be altered by starting wit... ...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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...A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today. On the last century, many works are concentrated on the combinatorial pro...

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...ress Rehoboth, NM 2005 Linfan MAO Institute of Systems Science Academy of Mathematics and Systems Chinese Academy of Sciences Beijing 100080, P.R.Chi... ...lib.umi.com/bod/search/basic Peer Reviewers: F.Tian and X.D.Hu, Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100080, P.R.C... ...of Sciences, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.Chi... ...ces, Beijing 100080, P.R.China. Y.P.Liu and R.X.Hao, Department of Applied Mathematics, Beijing Jiaotong Uni- versity, Beijing 100044, P.R.China. S.Bh... ... S.Bhattacharya, Alaska Pacific University, AK, USA. H.Iseri, Department of Mathematics and Computer Information Science, Mansfield University, Mansfield... ...S.ChimientiandM.Bencze, Smarandacheparadoxistgeometry,Bulletin of Pure and Applied Sciences, Delhi, India, Vol.17E, No.1(1998), 123-1124. [17] J.Edmon... ...ao and Y.P.Liu, Group action approach for enumerating maps on sur- faces,J.Applied Math. & Computing, vol.13, No.1-2,201-215. [47] L.F.Mao and Y.P.Liu... ...rationresearchinjournals. He was born in December 31,1962and got his BA in applied mathematics in Peking University in 1995 learnt by himself. In 2002... ...he automorphism groups of a Klein surface and a Smarandache manifold, also applied to the enumeration of unrooted mapsonorientableandnon-orientablesur...

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...E FUZZY AND NEUTROSOPHIC MODELS W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, ... ....in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: s... ...y discovered many times since it may quite properly be regarded as an area of applied mathematics. The 152 subject finds its place in the work of ... ...ered many times since it may quite properly be regarded as an area of applied mathematics. The 152 subject finds its place in the work of Euler. S... ...examples we make it clear that all unsupervised data need not have NCMs to be applied to it. Only data which have the relation between two nodes to ... ...de, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, March 2000. 6.... ...ics, Masters Dissertation, Guide: Dr. W. B. Vasantha Kandasamy, Department of Mathematics, Indian Institute of Technology, Chennai, April 2001. 9.... ...Model, Proc. of the 9 th National Conf. of the Vijnana Parishad of India on Applied and Industrial Mathematics held at Netaji Subhas Inst. of Tech...

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...election of papers most of which were produced during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smarandache’s wellknown publication Only Problems, Not Solutions. All topics are independent of one another and can be read separately. Findings are illustrated with diagrams and tables. ...

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.... They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smarandache’s wellknown publicatio... ...tracted worddabcdabcda is then studied. The analysis of concatenations is applied to number sequences and many interesting properties are found. I... ...o different operators. This leads to a situation were the iteration process applied to a member of a cycle may generate a member of another cycle as... ... member of another cycle as described in table 2. Table 2. A Zσ iteration applied to an element belonging to one cycle may generate an element bel... ...e correspondence between a number n to which the sequence of iterations is applied and the cycle that it will generate. Henceforth the iteration fu... ...t I hope to have contributed some light reading in the area of recreational mathematics. References: 1. H. Ibstedt, Surfing on the Ocean of N... ...ired by questions asked by Charles Ashbacher in the Journal of Recreational Mathematics, vol. 29.2. It concerns the Smarandache Deconstructive Seque... ...cerning the Smarandache Deconstructive Sequence, Journal of Recreational Mathematics, Vol 29, Number 2 – 1998, Baywood Publishing Company,Inc. ...

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... Fuzzy and Neutrosophic Models W. B. Vasantha Kandasamy Department of Mathematics Indian Institute of Technology, Madras Chennai – 600036, In... ...n web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, NM 87301, USA e-mail: sma... ...mia Technica Militaria, Bucharest, Romania. Dr. B.S. Kirangi, Department of Mathematics and Computer Science, University of Mysore, Karnataka, India... ...iscovered many times, since it may quite properly be regarded as an area of applied mathematics. Euler (1707-1782) became the father of graph theor... ...d many times, since it may quite properly be regarded as an area of applied mathematics. Euler (1707-1782) became the father of graph theory. In 18... ... these five types of cases lot of indeterminacy is involved, so when NCM is applied certainly it will lead to better results. Example 3.7.9: Use o... ... the reader to model this problem using NCM and compare it when only FCM is applied; complete discussions using FCM is given in [65] as taken from [... ...th tools like the FCM and the NCM. Next we shall see how best NCM can be applied in medical diagnosis. FCMs have found applications in many medic... ...or nodes to be divided into two (or more) disjoint classes. FRMs cannot be applied when the nodes or attributes under consideration in a data canno...

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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... ...s 199 2.11 Semantics of implication operators and fuzzy relational products applied to HIV/AIDS patients 211 Chapter Three SOME NEW AND BA... ...egular matrix multiplication. However the multiplication and addition that are applied to these combinations in the matrix multiplication are repla... ...ogramming methods, such as the simplex and interior-point algorithms, cannot be applied to this problem. [58] denote the solution set of problem (1... ... that dominates, z is a dominated criterion vector. The idea of dominance is applied to the criterion vectors whereas the idea of efficiency is a... ...nts can therefore be set aside from the problem. The genetic operators are then applied to this reduced problem. Without loss of generality, we assu... ...al, and thus one defines the neutrosophic set. One gives 227 examples from mathematics, physics, philosophy, and applications of the neutrosoph...

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...e Florentin Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US... ...andache Star Function", SNJ, Vol.11, No. 1-2-3, 2000. 6. Problem 2/31, Mathematics & Informatics Quarterly, 3/99 Volume 9, Sept' 99, Bulgaria. ... ...u, “Smarandache Partition Type and Other Sequences”, Bulletin of Pure and Applied Sciences, Vol. 16 E(No. 2) 1997, page 240. 12. Amarnath Murthy, ... ...age 240. 12. Amarnath Murthy, “On The Infinitude of Prime Numbers”, The Mathematics Education, India, Vol. XXIX, No. 1, March, 1995. 13. Felice... ... b 3 k) = a 1 b 1 + a 2 b 2 + a 3 b 3 If this same idea was applied to ordinary algebra (a + b) ( c + d ) = ac + bd. ---------... ... 6. “The Florentine Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US... ...0. " The Florentine Smarandache Special Collection”, Archives of American Mathematics, Centre for American History, University of Texas at Austin, US...