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... 1 =a 2 =1, a 2k+1 =a k+1 -1, a 2k+2 =a k+1 +1 This book can be ordered in paperbound form from: Books on Demand ProQuest Information & Learn... ...ts.htm ISBN: 1-931233-73-X Standard Address Number: 297-5092 Printed in the United States of America 3 Preface This... ...d during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smar... ... function is resolved and an important link to the famous Fermat numbers is established. This work has been reviewed in Zentralblatt für Mathematik,... ...iteration “filters through” from 10 6 until it gets locked onto one of the established invariants or the loop. Table 4. Zσ iteration iteration re... ...Fifth edition 1979. 4. H. Davenport, The Higher Arithmetic, Reprint: Dover Publications, Inc., New York, 1983. 5. C. Dumitrescu and V. Seleacu, S... ...e, Only Problems, Not Solutions, Xiquan Publishing House, Phoenix, Arizona, 1993. 2. K. Kashihara, Comments and Topics on Smarandache Notions and P... ...+…+10 11 =(10 12 -1)/9≡0 (mod 37) This congruence mod 37 has already been established in table 5. It follows that also 30405050403≡0 (mod 37) a... ...arandache F., Only Problems, Not Solutions, Xiquan Publ., Pheonix- Chicago, 1993. 3. Ibstedt H. Surfing on the Ocean of Numbers, Erhus University Pr...
...This book consists of a selection 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 illustra...
...is a representation of an s-manifold illustrating some of the behavior of lines in an s-manifold. This book has been peer reviewed and recommen... ...erine D’Ortona, Mansfield University of Pennsylvania This book can be ordered in microfilm format from: Books on Demand ProQuest Information & ... ...nfo/fabz54. ISBN: 1-931233-44-6 Standard Address Number: 297-5092 Printed in the United States of America 3 Table of Contents Introducti... ... line through P that is parallel to a,” since the existence of parallels can be established from other axioms or postulates. Non-Euclidean geomet... ...nola, R. (1955). Non-Euclidean Geometry (H.S. Carslaw, Trans.). New York: Dover Publications, Inc. (Original work published 1912.) 4. Born, M. (19... ...Born, M. (1962). Einstein’s Theory of Relativity (Revised ed.). New York: Dover Publications, Inc. 5. Boyce, W.E. and DiPrima, R.C. (1992). Elemen... ... Books of the Elements (2 nd ed., Vol. I, T.L. Heath, Trans.). New York: Dover Publications, Inc. (Original work published n.d.) 10. Eves, H. (19... ...pers (Vol. II, pp. 5- 28). University of Kishinev Press. 20. Stillwell, J. (1993). Classical Topology and Combinatorial Group Theory. New York: ...
...A complete understanding of what something is must include an understanding of what it is not. In his paper, “Paradoxist Mathematics” [19], Florentin Smarandache proposed a number of ways in which we could explore “new math concepts and theories, especially if they run counter to the classical ones.” In a manner consis...
...itute of Technology, Madras Chennai – 600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Departm... ...@gmail.com HEXIS Phoenix, Arizona 2005 2 This book can be ordered in a paper bound reprint from: Books on Deman... ...s.htm ISBN: 1931233-98-5 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface ... ... bigraph in general need not be a neutrosophic bipartite bigraph. This is established by the following example. Example 4.2.13: Consider the n... ...ie more often than boy babies even though medical 220 research has long ago established that girls are generally biologically stronger as newborns... ...96/09column.htm 19. Burrow, M. Representation Theory of Finite Groups, Dover Publications, 1993. 20. Carley, K. An Approach for Relating Social Str... ...m 19. Burrow, M. Representation Theory of Finite Groups, Dover Publications, 1993. 20. Carley, K. An Approach for Relating Social Structure to Cog... ...es, D Van Nostrand Co, Princeton, 1958. 51. Harary, F. Graph Theory, Narosa Publications (reprint, Indian edition), New Delhi, 1969. 52. Hart, J.... ...ostrand Co, Princeton, 1953. 58. Jacobson, N. Structure of Rings, Colloquium Publications, 37, American Mathematical Society, 1956. 59. Jang, S.R.,...
...Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduc...
... Research Press Rehoboth, NM 2002 2 This book can be ordered in a paper bound reprint from: Books on Demand ProQuest Informat... ...SBN: 1-931233-69-1 Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface 5 ... ...gs and introduction to Smarandache loop-rings 20 2.3 Smarandache elements in loop rings 30 2.4 Smarandache substructures in loop rings 40 2.5 Gener... ...ifferent future for India's oppressed masses. At the age of twenty, Phule established the first and only school for the girls of untouchable and opp... .... The elements of the form ±g, g ∈ G are trivial units of ZG. [26] has established the alternative analogue of the Zassenhaus conjecture as foll... ...Hung, 50, 241-247 (1987). 28. GOODAIRE, Edgar G., Alternative loop rings, Publications Mathematical Tomus, 30, 31-38 (1983). 29. GOODAIRE, Edgar G.... ... and MUDDDANA, Sekhar V., Experimenting with the identity (xy)z = y(zx), (1993) http://www.cs.clemson.edu/~dpj/albertstuff/albertpapers/xyz.ps 32.... ...NTHA KANDASAMY, W. B., Units in loop rings, U. Sci. Phys. Sci., 5, 86- 88 (1993). 143 60. VASANTHA KANDASAMY, W. B., On strictly right loop rings,...
...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ...ress in Physics retain their rights to use their own articles in any other publications and in any way they see ft. This journal is powered by BaKoMa-... ...ation for Authors and Subscribers Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, i... ...√ P , (11) which is nothing but the standard “quantum potential”, but here established as a mere manifestation of the nondifferen- tiable and fractal ... ...physics: towards a Theory of Scale Relativity. World Scientifc, Singapore, 1993. 2. Nottale L. Chaos, Solitons & Fractals, v. 7, 1996, 877. 3. C´ el´ ... ...ion the general conditions that the required solution must satisfy must be established. Abrams [9] has determined these conditions. I obtain them by o... ...ograms and analysis of its shapes, are described in details in the earlier publications [2, 3, 8]. Measurements of number of events of radioactive dec...
...Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics. All submitted papers should be professional, in good English, containing a b...
...The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Math... ...h the Library of Congress (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathS... .../ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Edito... ...ress in Physics retain their rights to use their own articles in any other publications and in any way they see ft. This journal is powered by BaKoMa-... ...ation for Authors and Subscribers Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, i... ...egion 0<r<2m or division into R and T regions until it has been rigorously established that the said regions are valid to begin with. One cannot treat... ...solution since the boundary on the r-parameter has not yet been rigorously established, but equation (17) provides a way by which the form ofC(D(r)) m... ...p =0, which corresponds to the parameter pointr 0 . Now in addition to the established fact that, in the case of the simple (i .e . non-rotating) poin... ...s. Singapore, World Scientifc, 1994. Brekke L., Freund P. Physics Reports, 1993, v. 1, 231. 21. Ambartzumian R. V. (Ed.) Stochastic and integral geome...
...FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ...ress Rehoboth 1999, 2000, 2003 FLORENTIN SMARANDACHE A UNIFYING FIELD IN LOGICS: NEUTROSOPHIC LOGIC. NEUTROSOPHY, NEUTROSOPHIC SET, NEUTROSOPHIC... ... a new branch of philosophy: 13 2. Neutrosophic Logic - a unifying field in logics: 87 3. Neutrosophic Set - a unifying field in sets: 112 4. Neut... ...hole culture was manipulated by a small group. Only their ideas and their publications counted. We couldn't publish almost anything. Then, I said: L... ...o proper sense, upside-down interpretation of linguistic expressions. In 1993 I did a paradoxist tour to literary associations and universities in B... ...entin Smarandache, Xiquan Publishing House, Phoenix, Chicago, 1991, 1992, 1993; the volume contains very experimental so called , such as: - poems ... ...e spiritual doctrines - although, in its turn, this becomes intrinsically established as another doctrine(!)... for and, at the same time, against ... ... [32] Russell, Bertrand, "Introduction to Mathematical Philosophy", Dover Publications, Inc., New York, 1993. [33] Ryle, Gilbert, "The Concept of M... ... of the growth of the ideas underlying our present atomic knowledge, Dover Publications, Inc., New York, 1959. [73] Hogg, Robert V., Craig, Allen T....
...It was known to me his setting up in 1980’s of a new literary and artistic avant-garde movement that he called “paradoxism”, because I received some books and papers dealing with it in order to review them for the German journal “Zentralblatt fár Mathematik”....
...Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive used of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations....