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...dress Number: 297-5092 Printed in the United States of America 3 Table of Contents Introduction 5 Chapter 1. Smarandache Manifolds 9 s-Manif...

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...Smarandache Production Editor: Gloria Valles Tucson, Arizona 4 Contents Preface……………………………………………………….….. 5 About the cover……...

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...of Rehoboth for e cient handling of this publication. J ozsef S andor 3 Contents Preface 2 Chapter 1. Geometric theorems 8 1 On Smarandache’s Podai...

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...Contents Tangent Space and Derivative Mapping on Time Scale BY EMIN ¨OZYILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Basic Properties Of Second Smarandache Bol Loops BY T.G.JA´IY´E O. L´A . . ....

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...Contents On the Crypto-Automorphism of the Buchsteiner Loops BY J.O.AD´EN´IRN and Y.T.OYEBO. . . . . . . . . . . . . . . . . . . . . . . . .01 Generalizations of Poly-Bernoulli Numbers and Polynomials BY HASSAN JOLANY, M....

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...Contents On the Bicoset of a Bivector Space BY AGBOOLA A.A.A. AND AKINOLA L.S.. . . . . . . . . . . . . . . . . . . . .01 Smarandachely Bondage Number of a Graph BY KARAM EBADI AND L.PUSHPALATHA . . . . . . . . . . . . . ...

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...Contents Extending Homomorphism Theorem to Multi-Systems BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup BY ...

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...njipadi Blocks, Tamil Nadu, India. This paper is organized with the following four sections. Section one is introductory in nature giving the overall contents from the survey made about PWDs in the above said Blocks. Section two gives description of FRM models and the attributes taken for the study related with the PWDs and the caretakers, the FRM model formed using these...

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...Contents Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming BY E.E.AMMAR . . . . . . . . . . . . . . . . . . . . 01 Surface Embeddability of Graphs via Joint Trees BY YANPEI ...

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...Contents On (∈ vq)- Fuzzy Bigroup BY AKINOLA L.S. and AGBOOLA A.A.A. . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Connectivity of Smarandachely Line Splitting Graphs BY B.BASAVANAGOUD and VEENA MATHAD . . . . . ...

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...Contents Lucas Graceful Labeling for Some Graphs BY M.A.PERUMAL, S.NAVANEETHAKRISHNAN AND A.NAGARAJAN . . . . . 01 Sequences on Graphs with Symmetries BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

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...Contents Combinatorial Fields - An Introduction BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 A Spacetime Geodesics of the Schwarzschild Space and Its Deformation Retract BY H. RAFAT...

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...Contents Smarandache-Zagreb Index on Three Graph Operators BY RANJINI P.S. and V.LOKESHA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Total Minimal Dominating Signed Graph BY P.SIVA KOTA REDDY and S.VIJAY ...

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...binatorics, KleinsurfacesorSmarandache geometries. Now we outline the main contents in each chapter. Chapter 1 is preliminary. We introduce the concep... ...ons for improving this book are welcome. L.F.Mao AMSS, Beijing June, 2005 Contents Preface.............................................................. ... The maximum order of an automorphism of a map.........................54 Contents v Chapter 3 On the Automorphisms of a graph on Surfaces..............

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...Contents LETTER I.?ON THE QUAKERS .............................................................................................................................. 6 LETTER II.?ON THE QUAKERS .......................................

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...ity The Pennsylvania State University is an equal opportunity university. Contents LETTER I.—ON THE QUAKERS ............................................

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...Peer-reviewers ii Abstract iii Preface by D. Rapoport iv Contents vi Foreword viii Prologue: Socio-economic impact of New Energy technologies xi Contributors to this volume xiv Short biography of Contributors xv Free energy and Topological Geometrodynamics 1. Nuclear string h...

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...Contents Preface 5 Foreword 6 1 Unsolved Problems in Theoretical Physics 8 1.1. Problems related to elementary particles 8 1.2. Problems related to Unmatter 11 1.3 Some unresolved problems, questions and applications of...

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...Contents Preface to the Second Edition . . . . . . . . . . . . . . . . . . . i Chapter 1. Combinatorial Principle with Graphs . . . . . . . . . . 1 1.1 Multi-sets with operations. . . . . . . . . . . . . . . . . . . . .2 ...

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...ICITY _________ 30 MILITARY STRATEGY _________________ 30 TRANSCENDENT ___ 30 ORDINARILY _______ 30 MEETING __________ 30 GEOPHYSICIST _____ 31 CONTENTS _________ 31 FORECAST _________ 31 COMPLEMENTARY _ 31 COHABITATION ____ 31 VIGOR _____________ 31 THE ARTIST ________ 31 DIRECTION ________ 31 MASOCHISM _______ 32 HIS DAUGTER WAS SO BEAUTIFUL… ___ 32 ENDEAR...

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...Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery o...

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...Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery o...

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...TABLE OF CONTENTS INTRODUCTION 1 THE STORY OF THE ATOM AND CHEMISTRY 7 THE CAVE MAN 7 ABSTRACT ON THE CONCEPT OF PERSPECTIVE AND SENSE OF DUTY 8 THE MIGRATORY AND THE SEDENTARY MAN 9 ABSTRACT ON THE ATOM AND ITS ENERGY 11 TH...