... Standard Address Number: 297-5092 Printed in the United States of America 3 CONTENTS Preface 5 Chapter One BASIC ... ...s 23 Chapter Three APPLICATION OF BIMATRICES TO NEW FUZZY MODELS 3.1. Definition of Fuzzy Cognitive Maps 71 3.2. Fuzzy Cognitive Bimaps... ...y Cognitive Maps 71 3.2. Fuzzy Cognitive Bimaps and their Applications 76 3.3. Fuzzy Cognitive Trimaps and their Applications 102 4 3.4. Def... ...ons 102 4 3.4. Definition and Illustration of Fuzzy Relational Maps 121 3.5. Fuzzy Relational Bimaps and their Applications 124 3.6. Fuzzy R... ...eutrosophic graphs 151 4.2 Neutrosophic Bigraphs and their Properties 158 4.3 Neutrosophic Cognitive Bimaps and their Generalizations 188 4.4 Ne... ...tional Neural Network Society, Annual Meeting World Congress Neural Networks, June 1994. 32. Craiger, J.P., and M.D. Coovert. Modeling Dynamic Soc... ...lds, International Neural Network Society, World Congress on Neural Networks, June 1994. 36. Dickerson, J.A., and B. Kosko. Virtual Worlds as Fuzzy... ... Computer Sciences (JTC-CSCC '95), Sept. 18-21 1996, v E79-A, no. 6, 921-927, June 1996. 83. Lee, K.C., H.S. Kim, and S.C. Chu. A Fuzzy Cognitive ... ...andasamy, Department of Mathematics, Indian Institute of Technology, Chennai, June 1998. 180. Voyevodin, V.V. Linear Algebra, Mir Publishers, 1983....

... my late ant Jolanda who surely would have appreciated this work of mine. 3 INTRODUCTION I have met the Smarandache's world for the first time about ... ...n which is defined for positive integers argument. Euler's function (n) j [3] is such, as are n!, º ß n , 2 n etc. The functions which are interes... ...s the number of positive integers n k £ which are relatively prime to n [3]. In the figure 1.1, the growth of function Zt(n) versus n is showed. As ... ...like the square root of n. (Fig. 1.2) In fact according to Walfisz result [3] the sum of first m values of Euler function is given by: 3 4 3 2 2 2 m ... ...of Euler function is given by: 3 4 3 2 2 2 m 1 k ) (ln(ln(m)) ln(m) O(m m 3 (k) + = = p j and then the Zt(n) asymptotic behaviour is decribed... ... of mathematics in 1725 in St. Petersburg, Russia. In a letter to Euler on June 7, 1742, He speculated that every even number is the sum of three prim...

...results for the Klein surfaces and s-manifolds are obtained in the Section 3. The Section 4 concerns the order of an automorphism of Klein surfaces an... ...en in this section are better than those of results already known. Chapter 3 presents a necessary and sufficient condition for a group of a graph being ... ...Any suggestions for improving this book are welcome. L.F.Mao AMSS, Beijing June, 2005 Contents Preface.................................................. ...ssification of Klein surfaces and s-manifolds ..............................3 §2 Map and embedding of a graph on surface.................................. ...embedding of a graph on surfaces.......................................6 2.3 Map and rooted map on surface............................................... ... as a combinatorial model of Klein surfaces and s-manifolds .......... 12 §3 The semi-arc automorphism group of a graph with application to maps enume... ...also a senior engineer and a consultor in Guoxin Tendering Co., Ltd. until June,2003. Then he works in the Academy of Mathematics and Systems of Chine...

...Address Number: 297-5092 Printed in the United States of America 3 BEGIN THE ADVENTURE How to Break the Light Barrier by A.D. 207... ...……………. 11 Ch.2. The Human Barrier ……………………………………………………………. 14 Ch.3. An Overview ………………………………………………………………….. 18 Ch.4. Acceleration Due t... ...a tenacious hold on the scientific community as well. Robert L. Forward: [3] It is difficult to go to the stars. They are far away, and the spe... ...ce and Technolgy,1993, Vol.16, No. 4, pp. 297-303, ISSN 0155-7785. [3] Robert L.Forward, “The Stars Our Destination? The Feasibility of Interst... ...akes of Reason Rule Our Minds, 1994, ISBN 0-471-58126-7. 18 Chapter 3 An Overview Einstein's postulates of relativity as translated fr... ...for sending information. Landauer's original announcement appears in the June 28, 1996, issue of Science. He suggested methods that might be used ... ...n a 1972 paper, was presented at the Universidad de Blumenau, Brazil, May-June 1993, in a Tour Conference on "Paradoxism in Literature and Science"; ... ...Science": "Is There a Speed Barrier?", Universidade de Blumenau, May 31 - June 20, 1993. [15] Smarandache, Florentin, "Definitions, Solved and Uns...

...Prefaces. 6 -- Ch.1. Introduction . 11 -- Ch.2. The Human Barrier. 14 -- Ch.3. An Overview. 18 -- Ch.4. Acceleration Due to Light Pressure. 21 -- Ch.5. Light Sailing is Not All There Is. 27 -- Ch.6. Einstein's Light Barrier. 32 -- Ch.7. The Phase One Experiment: The First Starship. 37 -- Ch.8. The P...