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科学面临的难题 _ 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今各自然科 与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借 对学科正式命名并引入中国。...

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中智学, 新的哲学分支 _(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 _(neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 的谬误性, 其中T, I, F为╟-0, 1+╢的标准或非标准子集。 _基本理论:任何观念 _ 趋于被 _ 所中和、削弱和平衡 _(不仅仅是被黑格尔主 的), 达到一种平衡状态。 中智学是中智逻辑学 _(在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 _(模糊 合论的概括总结)、中智概率论和中智统计学 _(分别是经典及非精确概率论、统计学的概括 结) 的基础。 _ 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。 _...

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译者序 _Preface by the Translator ........................................5 作者简介 _Author’s Biography ..........................................9 译者简介 _Biography of the Translator.................................12 原书前言 _查尔斯·李 _.....................................................19 Preface by Charles T. Le 0．引言: 非标准实数单位区间 _.......................................24 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 _.......................................27 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 _........................................90 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 _....................................109 Neutrosophic Set - a unifying field in sets 4．中智概率论 _..........................................................113 ——传统概率论和非精确概率论的概括总结 _ ——以及中智统计学 _ Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 _..............................................117 Addenda: Definitions derived from Neutrosophics...

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1. 科学面临的难题 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以 决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通 新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还 空白, 故借此对学科正式 命名并引入中国。...

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中智学, 新的哲学分支(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 (neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的 作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 F%的谬误性, 其中T, I, F 为╟-0, 1+╢的标准或 非标准子集。 基本理论:任何观念 趋于被 所中和、削弱和平衡 (不仅仅是被黑格尔主张的), 达到一种 平衡状态。 中智学是中智逻辑学 (在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 (模糊集合论的概括总结)、中智概 率论和中智统计学 (分别是经典及非精确概率论、统计学的概括总结) 的基础。 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。...

Table of Contents Details
译者序 Preface by the Translator ..................................5 作者简介 Author’s Biography ..............................9 译者简介 Biography of the Translator...........................12 原书前言 查尔斯·李 ............................................18 Preface by Charles T. Le 0．引言: 非标准实数单位区间 ..............................23 Introduction: The Non-Standard Real Unit Interval 1．中智学——哲学的崭新分支 ..............................26 Neutrosophy - a new branch of philosophy 2．中智逻辑——逻辑学的统一 ...............................83 Neutrosophic Logic - a unifying field in logics 3．中智集合论——集合论的统一 ..............................100 Neutrosophic Set - a unifying field in sets 4．中智概率论 ...........................................103 ——传统概率论和非精确概率论的概括总结 ——以及中智统计学 Neutrosophic Probability - a generalization of classical and imprecise probabilities - and Neutrosophic Statistics 附录: 中智学产生的定义 ..................................106 Addenda: Definitions derived from Neutrosophics...

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A collection of papers concerning Smarandache type functions, numbers, sequences, integer algorithms, paradoxes, experimental geometries, algebraic structures, neutrosophic probability, set, and logic, etc. is published this year....

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This document will describe the current status on the search for factors of Smaranda.che consecutive numbers and their reverse. A complete list up to index 200 will be given, with all known factors. Smarandache numbers are the concatenation of the natural numbers from one up to the given index, and reverse Smaranda.che numbers are the concatenation of the natural numbers from the given index dO\vIJ. to 1....

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As an alternative to the existing logics we propose the Neutrosophic Logic to represent a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined, unknown, incompleteness, inconsistency, redundancy, contradiction. It is a non-classical logic. Eksioglu (1999) explains some of them: “Imprecision of the human systems is due to the imperfection of knowledge that humain receives (observation) from the external world. Imperfection leads to a doubt about the value of a variable, a decision to be taken or a conclusion to be drawn for the actual system. The sources of uncertainty can be stochasticity (the case of intrinsic imperfection where a typical and single value does not exist), incomplete knowledge (ignorance of the totality, limited view on a system because of its complexity) or the acquisition errors (intrinsically imperfect observations, the quantitative errors in measures).”...

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Why after thirty years, should Beckwith’s Hawaiian Mythology be reprinted? Why, for the last twenty-five years, have scholars and amateurs alike sought for either new or used copies of this book which has become a rarity? To begin with, it was the first, and is still the only, scholarly work which charts a pathway through the hundreds of books and articles, many of them obscure and scarce, and through the little-known manuscripts that record the orally transmitted myths, legends, traditions, folktales, and romances of the Hawaiian people. Beckwith herself saw it as a “guide to the native mythology of Hawaii” (p. xxxi), and by mythology she meant “the whole range of story-telling” (p.2). Secondly, from the vantage point of Hawaiian oral narrative the book directs the reader into similar material from peoples elsewhere in Polynesia who are closely related to the Hawaiians, reminding him of relevant narratives from areas west of Polynesia and occasionally even east of Hawaii. The southern Pacific comparison Beckwith offers as “an important link in tracing routes of intercourse during the period of migration of related Polynesian groups...

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This guide to the native mythology of Hawaii has grown out of a childhood and youth spent within sound of the hula drum at the foot of the domelike House of the Sun on the windy island of Maui. There, wandering along its rocky coast and sandy beaches, exploring its windward gorges, riding above the cliffs by moonlight when the surf was high or into the deep forests at midday, we were aware always of a life just out of reach of us latecomers but lived intensely by the kindly, generous race who had chanced so many centuries ago upon its shores. Not before 1914 did the actual shaping of the work begin. The study covers, as any old Hawaiian will discover, less than half the story, but it may serve to start specific answers to the problems here raised and to distinguish the molding forces which have entered into the recasting of such traditional story-telling as has survived the first hundred years of foreign contact. To the general student of mythology the number and length of proper names in an unfamiliar tongue may seem confusing. Hawaiian proper names are rarely made up of a single word but rather form a series of words recalling s...

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Introduction. vii -- Preface. xxxi -- Coming of the Gods. 1 -- Ku Gods. 12 -- The God Lono. 31 -- The Kane Worship. 42 -- Kane and Kanaloa. 60 -- Mythical Lands of the Gods. 67 -- Lesser Gods. 81 -- Sorcery Gods. 105 -- Guardian Gods. 122 -- The Soul after Death. 144 -- The Pele Myth. 167 -- The Pele Sisters. 180 -- Pele Legends. 190 -- Kamapua?a. 201 -- Hina Myths. 214 -- Maui the Trickster. 226 -- Aikanaka-Kaha?i Cycle. 238 -- Wahieloa-Laka Cycle. 259 -- Haumea. 276 -- . Papa and Wakea. 293 -- Genealogies. 307 -- Era of Overturning . 314 -- Mu and Menehune People. 321 -- Runners, Man-Eaters, Dog-Men. 337 -- Hawaiian Mythology - The Moikeha-La?a Migration. 352 -- Hawaiiloa and Paao Migrations. 363 -- Ruling Chiefs. 376 -- Usurping Chiefs. 387 -- Kupua Stories. 403 -- Trickster Stories. 430 -- Voyage to the Land of the Gods. 448 -- Riddling Contests. 455 -- The Kana Legend. 464 -- The Stretching-Tree Kupua. 478 -- Romance of the Swimmer. 489 -- Romance of the Island of Virgins. 498 -- Romances of Match-Making. 506 -- Romances of the Dance. 519 -- Wooing Romances. 526 -- References. 545 -- Index. 555 --...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated together with weak; strong and converse duality theorems are proved. Key Words: Generalized multiobjective fractional programming; Disjunctive programming; Convexity; Concavity; fuzzy parameters Duality. ...

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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 LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Plick Graphs with Crossing Number 1 BY B.BASAVANAGOUD AND V.R.KULLI . . . . . . . . . . . . . . . . . . . . . . 21 Effects of Foldings on Free Product of Fundamental Groups BY M.El-GHOUL, A. E.El-AHMADY, H.RAFAT AND M.ABU-SALEEM. . . . . . . 29 Absolutely Harmonious Labeling of Graphs BY M.SEENIVASAN AND A.LOURDUSAMY . . . . . . . . . . . . . . . . . . . . 40 The Toroidal Crossing Number of K4n BY SHENGXIANG LV, TANG LING AND YUANGQIU HUANG . . . . . . . . . . 52 On Pathos Semitotal and Total Block Graph of a Tree BY MUDDEBIHAL M. H. AND SYED BABAJAN. . . . . . . . . . . . . . . . . . 64 Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate Polynomials Over Ring Zn BY E.ILOJIDE, T.G.JAIYEOLA AND O.O.OWOJORI . . . . . 79 New Characterizations for Bertrand Curves in Minkowski 3-Space BY BAHADDIN BUKCU, MURAT K...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case....

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This monograph is based on a large-scale study among youth in Bangalore, the metropolitan capital of Karnataka. It elaborates various aspects related to tobacco use among youth: consumption of tobacco; perceptions of tobacco use and tobacco users; individual, social and environmental correlates of tobacco use; and status of prevailing tobacco control measures. Apart from the study findings, the monograph reviews and summarises the current literature and provides a nation-wide glimpse of these issues. It concludes by providing some pertinent suggestions on reducing tobacco use among youth....

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1 INTRODUCTION Background and Rationale Aim and Objectives 2 METHODS Study Design and Sampling Data Collection and Analysis Ethical Considerations Sample Characteristics 3 YOUTH AND TOBACCO USE Tobacco Consumption Spending on Tobacco Consumption 4 PERCEPTIONS ABOUT TOBACCO USE Benefits and Harms of Tobacco Use Perceptions About Tobacco Users Attitudes Towards Future Tobacco Use 5 CORRELATES OF TOBACCO USE Reasons for Uptake of Tobacco Use Reasons for Refraining from Tobacco Use Tobacco Use and Use of Other Illicit Substances 6 TOBACCO CONTROL MEASURES Prohibition of Smoking in Public Places Regulation of Tobacco Sale Media Promotion of Tobacco Use Role of the Educational Institutions in Tobacco Control Students’ Suggestions for Tobacco Control 7 RECOMMENDATIONS Role of Educational Institutions in Tobacco Control Strengthening the Implementation of Tobacco Control Legislation...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11 Smarandachely Precontinuous maps and Preopen Sets in Topological Vector Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Path Double Covering Number of Product Graphs BY A. NAGARAJAN, V. MAHESWARI, S. NAVANEETHAKRISHNAN. . . . . . 27 Some Remarks on Fuzzy N-Normed Spaces BY SAYED ELAGAN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 σ-Coloring of the Monohedral Tiling BY M. E. BASHER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 The Forcing Domination Number of Hamiltonian Cubic Graphs BY H.ABDOLLAHZADEH AHANGAR AND PUSHPALATHA L. . . . . . . . . . 53 Permutation Polynomials modulo n, n 6= 2w and Latin Squares BY VADIRAJA BHATTA G. R. and SHANKAR B. R. . . . . . . . . . . . . . . . . 58 Graphoidal Tree d - Cover BY S.SOMASUNDARAM, A.NAGARAJAN AND G.MA...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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On (∈ vq)-Fuzzy Bigroup Abstract: In this paper, we introduce the concept of fuzzy singleton to bigroup, and uses it to define (∈ v q)- fuzzy bigroup and discuss its properties. We investigate whether or not the fuzzy point of a bigroup will belong to or quasi coincident with its fuzzy set if the constituent fuzzy points of the constituting subgroups both belong to or quasi coincident with their respective fuzzy sets, and vise versa. We also prove that a fuzzy bisubset μ is an (∈ vq)-fuzzy subbigroup of the bigroup G if its constituent fuzzy subsets are (∈ vq)-fuzzy subgroups of their respective subgroups among others. Key Words: Bigroups, fuzzy bigroups, fuzzy singleton on bigroup, (∈ vq)- fuzzy subgroups, (∈ vq)- fuzzy bigroup ...

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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 . . . . . . . . . . . . . . . . . . . . . . 08 Separation for Triple-Harmonic Di?erential Operator in Hilbert Space BY E.M.E.ZAYED and S.A.OMRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Classification of Differentiable Graph BY A. El-Abed . . . . . . . . . . . . . . . . . 24 On Equitable Coloring of Helm Graph and Gear Graph BY KALIRAJ.K and VERNOLD VIVIN.J . . . . . . . . . . . . . . . . . . . . . . . . . . 32 On the Roman Edge Domination Number of a Graph BY K. EBADI, E. KHODADADI and L. PUSHPALATHA. . . . . . . . . . . . . . . . . . 38 The Upper Monophonic Number of a Graph BY J.JOHN and S.PANCHALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Some Results on Pair Sum Labeling of Graphs BY R. PONRAJ, J.VIJAYA XAVIER PARTHIPAN and R.KALA . . . . . . . . . . . . . . 53 Weierstrass Formula for Minimal Surface in the Special Three-Dimensional Kenmotsu Manifold K with _-...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Extending Homomorphism Theorem to Multi-Systems Abstract: The multi-laterality of WORLD implies multi-systems to be its best candidate model for ones cognition on nature, which is also included in an ancient book of China, TAO TEH KING written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such systems with combinatorial structures, i.e., combinatorial systems, and shows how to extend the homomorphism theorem in abstract algebra to multi-systems or combinatorial systems. All works in this paper are motivated by a combinatorial speculation of mine which is reformed on combinatorial systems and can be also applied to geometry. Key Words: Homomorphism theorem, multi-system, combinatorial system. ...

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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 T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 On the Time-like Curves of Constant Breadth in Minkowski 3-Space BY SUHA YILMAZ AND MELIH TURGUT. . . . . . . . . . . . . . . . . . . . . 34 On the Basis Number of the Strong Product of Theta Graphs with Cycles BY M.M.M. JARADAT, M.F. JANEM AND A.J. ALAWNEH. . . . . . . . . . . .40 Smarandache Curves in Minkowski Space-time BY MELIH TURGUT AND S¨UHA YILMAZ . . . . . . . . . . . . . . . . . . . . . 51 The Characterization of Symmetric Primitive Matrices with exponent n − 3 BY LICHAO, HUANGFU AND JUNLIANG CAI . . . . . . . . . . . . . . . . . . 56 The Crossing Number of the Circulant Graph C(3k − 1; {1, k}) BY JING WANG AND YUANQIU HUANG. . . . . . . . . . . . . . . . . . . .79 On the Edge Geodetic and k-Edge Geodetic Number of a Graph BY A.P. SANTHAKUMARAN AND S.V. ULLAS CHANDRAN. . . . . . . . . .85 Simple Path Cove...

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Aims and Scope: The International J.Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandachemulti-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,· · · , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretic...

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Abstract: Let G be a group having a partially closed subset S such that S contains the identity element of G and each element in S has an inverse in S. Such subsets of G are called halfsubgroups of G. If a halfsubgroup S generates the group G, then S is called a halfsubgroup generating the group or hsgg in short. In this paper we prove some results on hsggs of a group. Order class of a group are special halfsubgroupoids. Elementary abelian groups are characterized as groups with maximum special halfsubgroupoids. Order class of a group with unity forms a typical halfsubgroup. Key words: halfsubgroup, hsgg, order class of an element. AMS(2000): 20Kxx, 20L05....

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Halfsubgroups BY ARUN S. MUKTIBODH. . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 Flexibility of Embeddings of a Halin Graph on the Projective Plane BY HAN REN and YUN BAI. . . . . . . . . . . . . . . . . . . . . . . . . . . .06 Curvature Equations on Combinatorial Manifolds with Applications to Theoretical Physics BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16 A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .36 A Revision to G¨odel’s Incompleteness Theorem by Neutrosophy BY YUHUA FU and ANJIE FU. . . . . . . . . . . . . . . . . . . . . . . . . . . 45 On the basis Number and the Minimum Cycle Bases of the Wreath Product of Two Wheels BY M.M.M. JARADAT and M.K. AL-QEYYAM . . . . . . . . . . . . . . . . . . 52 Theory of Relativity on the Finsler Spacetime BY SHENGLIN CAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 On the Number of Graceful Trees BY GUANGXUAN WANG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 ...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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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.R.DARAFSHEH AND R.EIZADI ALIKELAYE . . . . 07 Open Alliance in Graphs BY N.JAFARI RAD AND H.REZAZADEH . . . . . . . . . . . . . . . . . . . . . 15 The Forcing Weak Edge Detour Number of a Graph BY A.P.SANTHAKUMARAN AND S.ATHISAYANATHAN . . . . . . . . . . . . . 22 Special Smarandache Curves in the Euclidean Space BY AHMAD T. ALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 The H-Line Signed Graph of a Signed Graph BY R.RANGARAJAN, M. S. SUBRAMANYA AND P. SIVA KOTA REDDY. . . .37 Min-Max Dom-Saturation Number of a Tree BY S. ARUMUGAM AND S. SUDHA . . . . . . . . . . . . . . . . . . . . . . . 45 Embeddings of Circular graph C(2n + 1, 2) (n ≥ 2) on the Projective Plane BY XINQIU LIU, YUANQIU HUANG AND JING WANG. . . . . . . . . . . . .53 A Note On Jump Symmetric n-Sigraph BY H. A.MALATHI AND H. C.SAVITHRI . . . . . . . . . . . . . . . . . . . . 65 New Families of Mean Graphs ...

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Papers concerning any of the Smarandache type functions, sequences, integer algorithms, paradoxes, Non-Euclidean geometries, conjectures, open problems, neutrosophic logic/set/probability, etc. have been selected for this volume. The...

Description Details
Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Abstract: In this paper we find the interrelations and the hidden pattern of the problems faced by the PWDs and their caretakers using Fuzzy Relational Maps (FRMs). Here we have taken the problems faced by the rural persons with disabilities in Melmalayanur and Kurinjipadi 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 attributes and their analysis. The third section gives the suggestions and conclusions derived from the survey as well as the FRM model. Key Words: FRM model, fixed point, hidden pattern, relational matrix, limit cycle. AMS(2000): 04A72....

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Study of the Problems of Persons with Disability (PWD) Using FRMs BY W.B.VASANTHA KANDASAMY, A.PRAVEEN PRAKASH AND K.THIRUSANGU 01 Topological Multi-groups and Multi-fields BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08 Shortest Co-cycle Bases of Graphs BY HAN REN AND JING HAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 On Involute and Evolute Curves of Spacelike Curve with a Spacelike Principal Normal in Minkowski 3 -Space BY BAHADDIN BUKCU AND MURAT KEMAL KARACAN . . . . . . . . . . . . . . . 27 Notes on the Curves in Lorentzian Plane L2 BY S¨ UHA YILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Cycle-Complete Graph Ramsey Numbers r(C4,K9), r(C5,K8) ≤ 33 BY M.M.M. JARADAT AND B.M.N. ALZALEQ . . . . . . . . . . . . . . . . . . . . 42 Smarandache Breadth Pseudo Null Curves in Minkowski Space-time BY MELIH TURGUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Smarandachely k -Constrained labeling of Graphs BY SHREEDHARK, B. SOORYANARAYANA AND RAGHUNATHP . . . . . . . . . . .50 Equiparity Path D...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: maolinfan@163.com Abstract: An interesting symmetry on multiplication of numbers found by Prof.Smarandache recently. By considering integers or elements in groups on graphs, we extend this symmetry on graphs and find geometrical symmetries. For extending further, Smarandache’s or combinatorial systems are also discussed in this paper, particularly, the CC conjecture presented by myself six years ago, which enables one to construct more symmetrical systems in mathematical sciences. Key Words: Smarandache sequence, labeling, Smarandache beauty, graph, group, Smarandache system, combinatorial system, CC conjecture...

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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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Supermagic Coverings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . . . . . . . . . . . 33 Elementary Abelian Regular Coverings of Cube BY FURONG WANG AND LIN ZHANG. . . . . . . . . . . . . . . . . . . . . .49 Super Fibonacci Graceful Labeling of Some Special Class of Graphs BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AND K.NAGARAJAN. . . . . . . . 59 Surface Embeddability of Graphs via Tree-travels BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 Edge Maximal C3 and C5-Edge Disjoint Free Graphs BY M.S.A.BATAINEH AND M.M.M.JARADAT . . . . . . . . . . . . . . . . . . 82 A Note on Admissible Mannheim Curves in Galilean Space G3 BY S.ERSOY, M.AKYIGIT AND M.TOSUN . . . . . . . . . . . . . . . . . . . . 88 The Number of Spanning Trees in Generalized Complete Multipartite Graphs of Fan-Type BY JUNLIANGE CAI AND XIAOLI LIU . . . . . ....

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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§1. Why is the WORLD a Combinatorial One? The multiplicity of the WORLD results in modern sciences overlap and hybrid, also implies its combinatorial structure. To see more clear, we present two meaningful proverbs following. Proverb 1. Ames Room An Ames room is a distorted room constructed so that from the front it appears to be an ordinary cubic-shaped room, with a back wall and two side walls parallel to each other and perpendicular to the horizontally level floor and ceiling. As a result of the optical illusion, a person standing in one corner appears to the observer to be a giant, while a person standing in the other corner appears to be a dwarf. The illusion is convincing enough that a person walking back and forth from the left corner to the right corner appears to grow or shrink. ...

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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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 On Degree Equitable Sets in a Graph BY A. ANITHA, S. ARUMUGAM AND E. SAMPATHKUMAR . . . . . . . . . . . . 32 Smarandachely k-Constrained Number of Paths and Cycles BY P. DEVADAS RAO, B. SOORYANARAYANA, M. JAYALAKSHMI . . . . . . . . . 48 On Functions Preserving Convergence of Series in Fuzzy n-Normed Spaces BY SAYED ELAGAN AND MOHAMAD RAFI SEGI RAHMAT . . . . . . . . . . . . 61 Achromatic Coloring on Double Star Graph Families BY VERNOLD VIVIN J., VENKATACHALAM M. AND AKBAR ALI M.M. . . . . . 71 Some Results on Super Mean Graphs BY R.VASUKI AND A.NAGARAJAN. . . . . . . . . . . . . . . . . . . . . . . . .82 Chromatic Polynomial of Smarandache νE-Product of Graphs BY KHALIL PARYAB AND EBRAHIM ZARE. . . . . . . . . . . . . . . . . . . .97 Open Distance-Pattern Uniform Graphs BY BIBIN K. JOSE . . . . . . . . . . . . . . . . . ....

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Papers concerning any of the Smarandache type functions, sequences, numbers, algorithms, inferior/superior f-parts, magic squares, palindromes, functional iterations, semantic paradoxes, Non-Euclidean geometries, manifolds, conjectures, open problems, algebraic structures, neutrosophy, neutrosophic logic/set/probability, hypothesis that there is no speed barrier in the universe} quantum paradoxes, etc. have been selected for this volume. Contributors are from Australia, China, England, Germany, India, Ireland, Israel, Italy, Japan, Malaysia, Morocco, Portugal, Romania, Spain, USA. Most of the papers are in English, a few of them are in Spanish, Portuguese, or Gennan....

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In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p -adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert ’s style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen ’s style sequents that was introduced independently by Avron and Pottinger . In particular, we examine Hilbert ’s style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz ’s, Godel ’s, and Product logics....

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1.1 Neutrality concept in logic Every point of view A tends to be neutralized, diminished, balanced by Non-A. At the same time, in between A and Non-A there are infinitely many points of view Neut-A. Let’s note by A an idea, or proposition, theory, event, concept, entity, by Non-A what is not A, and by Anti-A the opposite of A. Neut-A means what is neither A nor Anti-A, i.e. neutrality is also in between the two extremes. ...

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1 Introduction. . . . . . . . . . . . . . . 9 1.1 Neutrality concept in logic . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Neutrality and non-Archimedean logical multiple-validity . . . . 10 1.3 Neutrality and neutrosophic logic . . . . . . . . . . . . . . . . . . 13 2 First-order logical language. . . . . . . . . . . . . . . 17 2.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Hilbert’s type calculus for classical logic . . . . . . . . . . . . . . 20 2.3 Sequent calculus for classical logic . . . . . . . . . . . . . . . . . 22 3 n -valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 27 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Originality of (p + 1)-valued Lukasiewicz’s logics . . . . . . . . . 30 3.3 n-valued Lukasiewicz’s calculi of Hilbert’s type . . . . . . . . . . 32 3.4 Sequent calculi for n-valued Lukasiewicz’s logics . . . . . . . . . . 33 3.5 Hypersequent calculus for 3-valued Lukasiewicz’s propositional logic . . . . . . . . . . . .37 4 Infinite valued Lukasiewicz’s logics. . . . . . . . . . . . . . . 39 4.1 Prelimi...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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Smarandache-Zagreb Index on Three Graph Operators Abstract: Many researchers have studied several operators on a connected graph in which one make an attempt on subdivision of its edges. In this paper, we show how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb index, Zagreb index, graph operators. ...

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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 . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Number of Minimum Dominating Sets in Pn Å~ P2 BY H.B.WALIKAR, K.P. NARAYANKAR and S.S.SHIRAKOL . . . . . . . . . . . . . . . 17 Super Fibonacci Graceful Labeling BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AND K.NAGARAJAN. . . . . . . . . . .22 A Note on Smarandachely Consistent Symmetric n-Marked Graphs BY P.SIVA KOTA REDDY, V. LOKESHA and GURUNATH RAO VAIDYA. . . . . . . . .41 Some Fixed Point Theorems in Fuzzy n-Normed Spaces BY SAYED KHALIL ELAGAN and MOHAMAD RAFI SEGI RAHMAT . . . . . . . . . . 45 A Result of Ramanujan and Brahmagupta Polynomials Described by a Matrix Identity BY R. RANGARAJAN . . . . . . . . . . . . . . . . 57 Biharmonic Slant Helices According to Bishop Frame in E3 BY ESSIN TURHAN and TALAT K¨ORPINAR . . . . . . . . . . . . . . . . . . . . . . 64 Combinatorial Optimization in VLSI Hypergraph Partitioning Using Taguchi Methods...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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On the Bicoset of a Bivector Space Abstract: The study of bivector spaces was first intiated by Vasantha Kandasamy. The objective of this paper is to present the concept of bicoset of a bivector space and obtain some of its elementary properties. Key Words: bigroup, bivector space, bicoset, bisum, direct bisum, inner biproduct space, biprojection. ...

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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 . . . . . . . . . . . . . . . . . . . . . 09 Domination Number in 4-Regular Graphs BY H.Abdollahzadeh Ahangar AND Pushpalatha L. . . . . . . . . . . . . . . . . . 20 Computing Smarandachely Scattering Number of Total Graphs BY AYSUN AYTAC AND ELGIN KILIC. . . . . . . . . . . . . . . . . . . . . . .31 On the 3ψ3 Basic Bilateral Hypergeometric Series Summation Formulas BY K. R.VASUKI AND G.SHARATH. . . . . . . . . . . . . . . . . . . . . . . .41 Minimal Retraction of Space-time and Their Foldings BY A. E. El-AHMADY aND H. RAFAT. . . . . . . . . . . . . . . . . . . . . . . .49 Efficient Domination in Bi-Cayley Graphs BY T. TAMIZH CHELVAM AND SIVAGNANAM MUTHARASU. . . . . . . . . .56 Independent Complementary Distance Pattern Uniform Graphs BY GERMINA K.A. AND BEENA KOSHY. . . . . . . . . . . . . . . . . . . . . .63 On Smarandachely Harmonic Graphs BY D.D.SOMASHEKARA AND C.R.VEENA . . . . . . . . . . . . . . . . . . . . . 75 S...

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Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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The Characterization of Symmetric Primitive Matrices with Exponent n − 2 Junliang Cai Abstract: In this paper the symmetric primitive matrices of order n with exponent n − 2 are completely characterized by applying a combinatorial approach, i.e., mathematical combinatorics ([7]). Key words: primitive matrix, primitive exponent, graph....

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The Characterization of Symmetric Primitive Matrices with Exponent n − 2 BY JUNLIANG CAI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Characterizations of Some Special Space-like Curves in Minkowski Space-time BY MELIH TURGUT AND SUHA YILMAZ . . . . . . . . . . . . . . . . . . . . . . . 17 Combinatorially Riemannian Submanifolds BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Smarandache Half-Groups BY ARUN S.MUKTIBODH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 On Smarandache Bryant Schneider Group of a Smarandache Loop BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Some Properties of Nilpotent Lattice Matrices BY QIYI FAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 On the Crossing Number of the Join of Some 5-Vertex Graphs and Pn BY BO LI, JING WANG AND YUANQIU HUANG . . . . . . . . . . . . . . . . . . 70 Identities by L-summing Method (II) BY MEHDI HASSANI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 On the Basis Numbe...

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In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

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1.2 The basics of neutrosophy Neutrosophy studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It considers that every idea tends to be neutralized, balanced by ideas; as a state of equilibrium. Neutrosophy is the basis of neutrosophic logic, neutrosophic set which generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Neutrosophic Logic is a multiple-valued logic in which each proposition is estimated to have percentages of truth, indeterminacy, and falsity in T, I, and F respectively, where T, I, F are standard or non-standard subsets included in the non-standard unit interval ] −0, 1+[. It is an extension of fuzzy, intuitionistic, paraconsistent logics. ...

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Preface of the Editor 4 Chapter 1 PROBLEM STATEMENT . THE BASICS OF NEUTROSOPHY 1.1 Problem statement 5 1.2 The basics of neutrosophy 8 1.3 Neutrosophic subjects 13 1.4 Neutrosophic logic. The origin of neutrosophy 14 1.5 Definitions of neutrosophic 16 Chapter 2 TRAJECTORIES AND PARTICLES 2.1 Einstein’s basic space-time 18 2.2 Standard set of trajectories and particles. A way to expand the set 22 2.3 Introducing trajectories of mixed isotropic/non-isotropic kind 28 2.4 Particles moving along mixed isotropic/non-isotropic trajectories 31 2.5 S-denying the signature conditions. Classification of the expanded spaces 35 2.6 More on an expanded space-time of kind IV 45 2.7 A space-time of kind IV: a home space for virtual photons 52 2.8 A space-time of kind IV: non-quantum teleportation of photons 55 2.9 Conclusions 59 Chapter 3 ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD 3.1 Disentangled and entangled particles in General Relativity. Problem statement 61 3.2 Incorporating entangled states into General Relativity 64 3.3 Quantum Causality Threshold in General Relativity 69 3.4 Conclusions 72 Biblio...

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We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters and 6 appendices. The first chapter just recalls the definition of four fuzzy models used in this book and gives illustration of some of them. Chapter two introduces the new n-adaptive fuzzy models. Chapter three uses for the first time 2 adaptive fuzzy models to study psychological and sociological problems about HIV/AIDS. Chapter four gives an outline of the interviews. Chapter five gives the suggestions and conclusion based on our study. Of the 6 appendices four of them are C-program made to make the working of the fuzzy model simple....

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In this chapter for the first time we introduce the new class of n-adaptive fuzzy models (n a positive integer and n ≥ 2) and illustrate it. These n-adaptive fuzzy models can analyze a problem using different models so one can get in one case the hidden pattern, in one case the maximum time period in some case output state vector for a given input vector and so on. So this new model has the capacity to analyze the problem in different angles, which can give multiple suggestions and solutions about the problem. This chapter has two sections. Section one defines the new model gives illustrations and section two defines some special n-adaptive models and proposes some problems....

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Chapter One SOME BASIC FUZZY MODELS WITH ILLUSTRATIONS 1.1 Fuzzy matrices and their applications 9 1.2 Definition and illustration of Fuzzy Relational Maps (FRMs) 16 1.3 Some basic concepts of BAM with illustration 20 1.3.1 Some basic concepts of BAM 22 1.3.2 Use of BAM Model to study the cause of vulnerability to HIV/AIDS and factors for migration 28 1.4 Introduction to Fuzzy Associative Memories (FAM) 35 Chapter Two ON A NEW CLASS OF N-ADAPTIVE FUZZY MODELS WITH ILLUSTRATIONS 2.1 On a new class of n-adaptive fuzzy models with illustrations 39 2.2 Some special n-adaptive models 49 Chapter Three USE OF 2-ADAPTIVE FUZZY MODEL TO ANALYZE THE PUBLIC AWARENESS OF HIV/AIDS 3.1 Study of the psychological and social problems the public have about HIV/AIDS patients using CETD matrix 52 3.2 Use of 2 adaptive fuzzy model to analyze the problem 72 Chapter Four PUBLIC ATTITUDE AND AWARENESS ABOUT HIV/AIDS 4.1 Introduction 77 4.2 Interviews 81 Chapter Five CONCLUSIONS 167 Appendix 1. Questionnaire 177 2. Table of Statistics 191 3. C-program for CETD and RTD Matrix 198 4. C-program for FRM 202 5. C-program for CFRM 2...

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Hinduism Today Releases a Special Issue on Balinese Hindus The April/May/June 2012 issue of our flagship magazine focuses on the Hinduism of Bali, where we experience the people and explore the philosophy and temple culture of this unique Hindu outpost. If you ask the Balinese, they will tell you theirs is the real, the ancient and the true form of the faith! They may well be right. Our Delhi correspondent flew to the island and spent two weeks among the Balinese, diving ever deeper into their special expression of Sanatana Dharma and their tightly-knit and proudly Hindu community. To get us started, he relates the history of how Hindus settled on this unlikely island and later uncovers the little-known Lontar palm-leaf manuscripts which reflect Bali's connection with ancient India. An expatriate Australian married to a Balinese shares her keen insider-outsider cultural insights, and there is a rich sampling of the Hindu arts, music, painting and dance which permeate Bali's way of life. Dare we speak about Nyepi, the day of silence, when all of Bali comes to a complete stop? Yes, everyone, even the tourists, enjoy a day wit...

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DISCLAIMER . . . . . . . . . . . . . . . . . . . . . . . ii FOREWORD . . . . . . . . . . . . . . . . . . . . . . . vii ABOUT THE AUTHOR . . . . . . . . . . . . . . . . . ix PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . xi 1 PREPARING TO TALK . . . . . . . . . . . . . . . . 1 Types of Speaking . . . . . . . . . . . . . . . . . . 2 Briefing . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Teaching Lecture . . . . . . . . . . . . . . . . . . . . 2 Speech . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Audience . . . . . . . . . . . . . . . . . . . . . . . . . 3 Audience Analysis . . . . . . . . . . . . . . . . . . . 4 Audience Attitude . . . . . . . . . . . . . . . . . . . .5 Subject . . . . . . . . . . . . . . . . . . . . . . . . . . .6 Selecting the Subject . . . . . . . . . . . . . . 6 Narrowing the Subject . . . . . . . . . . . . . . 8 Choosing a Title . . . . . . . . . . . . . . . . . 8 Objectives . . . . . . . . . . . . . . . . . . . . . . . 9 General Responses . . . . . . . . . . . . . . . . 9 Specific Responses . . . . . . . . . . . . . . . . 9 Gathering Material . . . . . . . . . . ....

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As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classical logic, but as you will see in the book, there are two intermediate steps between them. Neutrosophic logic is yet another idea generated by Florentin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to quantum me...

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CMMI High Maturity is something every software organization is interested in! Attaining Maturity Level 5 rating means world class processes in place in that organization. Though it’s everyone’s interest, there is less details available in the world on how to practically implement CMMI ML5 and how to interpret the High Maturity practices. This book is an attempt to decode the high maturity practices with clear sample cases for all the High maturity process areas, there by connecting the dots of Implementation. This book explains the practicality of implementation of CMMI ML5 and has given specific guidance in many cases. Obviously it is not the whole of CMMI or the whole of everything, however may be this is the only book which offers highest possible insight in CMMI High Maturity Implementation. What it offers: • Complete guide as an End to End CMMI High Maturity Implementation • Practical interpretation of CMMI Practices • Sample cases covering CMMI Dev and CMMI SVC Models v1.3 • Basic Statistical Concepts Required for Implementing High Maturity • Clarity in definition and difference between important terms • Connects the E...

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CMMI High Maturity Handbook Indian Edition Vishnuvarthanan Moorthy Copyright © 2015 Vishnuvarthanan Moorthy All rights reserved. DEDICATION TO THE SUPREME POWER!. CONTENTS 1 High Maturity an Introduction 1 2 Prerequisites for High Maturity Pg 5 3 Planning High Maturity Implementation Pg 8 4 SMART Business Objectives and Aligned Processes Pg 17 5 Measurement System and Process Performance Models Pg 29 6 Process Performance Baselines Pg 70 7 Define and Achieve Project Objectives and QPPOs Pg 93 8 Causal Analysis in Projects to Achieve Results Pg 113 9 Driving Innovation/Improvements to Achieve Results Pg 131 10 Succeeding in High Maturity Appraisals Pg 150 11 Reference Books, Links and Contributors Pg 154 1 HIGH MATURITY AN INTRODUCTION CMMI High Maturity Level is one of the Prestigious Rating any IT/ITES Companies would be interested in getting. The Maturity Level 4 and 5 achievement is considered as “High Maturity” since the Organizations understand their own process performance and its impact on Business performance. In addition, they bring world class pra...

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High Maturity an Introduction 1 Prerequisites for High Maturity Pg 5 Planning High Maturity Implementation Pg 8 SMART Business Objectives and Aligned Processes Pg 17 Measurement System and Process Performance Models Pg 29 Process Performance Baselines Pg 70 Define and Achieve Project Objectives and QPPOs Pg 93 Causal Analysis in Projects to Achieve Results Pg 113 Driving Innovation/Improvements to Achieve Results Pg 131 Succeeding in High Maturity Appraisals Pg 150 Reference Books, Links and Contributors Pg 154 ...

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Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. Most of these applications target the theory of relativity and quantum physics, but other sections of physics are also possible to be considered....

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We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV....

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Preface, by Dmitri Rabounski ............................5 General Relativity, Gravitation, and Cosmology................6 S-Denying of the Signature Conditions Expands General Relativity’s Space, by Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Progress in Physics, 13-19, Vol. 3, 2006.......7 Positive, Neutral, and Negative Mass-Charges in General Relativity, by Larissa Borissova and Florentin Smarandache, Progress in Physics, 51-54, Vol. 3, 2006. .............14 Extension of the Big Bang Theory, by Florentin Smarandache, Bulletin of Pure and Applied Sciences, 139-140, Vol. 23D, No. 2, 2004. .....................18 What Gravity Is. Some Recent Considerations, by Vic Christianto and Florentin Smarandache, Progress in Physics, 63-67, Vol. 3, 2008. .......................20 A Few Remarks on the Length of Day: A Cosmological Perspective, by Vic Christianto, Matti Pitkaneny, and Florentin Smarandache, Progress in Physics, L3-L4, Vol. 1, 2009............25 Quantum Physics and Statistics .......................27 A Note on Unified Statistics Including Fermi-Dirac, Bose-Einstein, and Tsallis Statistic...

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This book examines the economics of the postal sector through three lenses: snapshot and trends, models, and opportunities. In the years to come, the Universal Postal Union plans to develop its role as a knowledge centre for the postal sector from these perspectives. At this time of radical transformation of the postal sector, it is important to understand how the sector has evolved historically, how it is connected with the economic system, and where it is heading. This book thus first presents a long-run view, focusing on incumbent operators over the last three decades, and then describes their development in the last five to ten years. It also offers a real-time picture based on daily “big postal data”, revealing one of the greatest opportunities for the sector in terms of forecasting and product design....

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PREFACE Bishar A. Hussein ACKNOWLEDGEMENTS INTRODUCTION Development strategies for the postal sector: an economic perspective José Ansón and Matthias Helble CHAPTER 1 Postal economics and statistics for strategy analysis – The long view José Ansón and Matthias Helble CHAPTER 2 Postal economics and statistics for strategy analysis – The short view Joëlle Toledano Bialot CHAPTER 3 Status of the postal service 20 years after the green paper: a Franco-European perspective José Ansón, Rudy Cuadra, Altamir Linhares, Guillermo Ronderos and Joëlle Toledano Bialot CHAPTER 4 The economics of postal delivery in developing countries: learning from the Latin American and Sub-Saharan African experiences José Ansón, Rudy Cuadra, Altamir Linhares,Guillermo Ronderos and Joëlle Toledano Bialot CHAPTER 5 Postal regulation in Sub-Saharan Africa Marie-Odile Pilley CHAPTER 6 Financial inclusion, postal banking and the future postal economic model José Ansón and Joëlle Toledano Bialot CHAPTER 7 Big postal data, now casting and the global pulse of the economy José Ansón and Matthias He...

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Female spouse of one’s brother is called `sister-in-law`; similarly the sister of one’s spouse is sister-in-law. Again, the wife of one’s brother-in-law is also called sister-in-law, subject however to the condition that the said brother-in-law is not the husband of one’s own sister. Thus, in Indian society, we find a vast variety of sister-in-law. However, one factor of commonality is often found in the cases where at both ends of this relationship, we have females. The say that this factor provides sauce to our family life, by swift maneuvers of their inimical or endearing postures towards each other. The author has picked up every variety of this relationship from the middle-class stratum of Indian society, while sketching his story for this fictional narration. However, in a given situation, we feel like addressing or being addressed as `MUY DEAR SISTER-IN-LAW`. To take the story forward, the author has tried his best to strew certain suchlike expressions coming forth sporadically, uttered by one or the other character, irrespective of his/her sex....

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Perched in his wheelchair, at the moment on 30th June, 2007, this erstwhile lover of Maya Dua is expecting Vibha Ratra ..... Of course, this infirm oldie his first ever acquaintance with Vibha Ratra took place, when his family ... Our mother, though surprised to be getting acquainted by her son to Mrs Wilson as the bride's mother, chose to maintain silence about her knowledge of that lady's `swarthy` reputation in the residential vicinity, during their adolescence. Instead of consoling his father in a socially approved manner, the arrogant son had yelled out at the top of his voice, "Papa, you have had enough of her during the past 45 years. In case, you still need a woman's company, there is no dearth of this lot to provide warmth to your body. The following day, while exiting from the faculty meet, Vibha marked that Dr Rawat looked eager to join her, while she was proceeding towards the group of some junior teachers of her department, already waiting for their head of the department. Really, it's an agonizing account," Madhukar ejaculated following a long sigh. After a short while, he resumes, "You can bank upon, this humble fr...

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This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given....

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2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1}, or Boolean Logic from British mathematician George Boole (1815-64), was named by the philosopher Quine (1981) “sweet simplicity.” [57] But this typical binary logic is not without problems. In the light of aforementioned ‘garment analogue’, we can compare this binary logic with a classic black-and-white tuxedo. It is timeless design, but of course you will not wear it for all occasions. Aristotle himself apparently knew this problem; therefore he introduced new terms ‘contingency’ and ‘possibility’ into his modal logic [5]. And then American logician Lewis first formulated these concepts of logical modality. ...

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Contents Foreword 6 1 Introduction: Paradoxes, Lukasiewicz, Multi-Valued logic 7 2 Lukasiewicz Multi-Valued Logic: History and Introduction to Multi-Valued Algebra 10 2.1. Introduction to trivalent logic and plurivalent logic 10 2.2. History of Lukasiewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valued Logic and Quantum Mechanics 15 2.5. Exercise 17 3 Neutrosophy 25 3.1. Introduction to Neutrosophy 25 3.2. Introduction to Non-Standard Analysis 26 3.3. Definition of Neutrosophic Components 27 3.4. Formalization 28 3.5. Evolution of an Idea 30 3.6. Definition of Neutrosophic Logic 31 3.7. Differences between Neutrosophic Logic and IFL 32 3.8. Operations with Sets 33 3.9. Generalizations 34 4 Schrödinger Equation 39 4.1. Introduction 39 4.2. Quantum wave dynamics and classical dynamical system 43 4.3. A new derivation of Schrödinger-type Equation 45 5 Solution to Schrödinger’s Cat Paradox 47 5.1. Standard interpretation 47 5.2. Schrödinger’s Cat Paradox 48 5.3. Hidden-variable hypothesis 50 5.4. Hydrodynamic viewpoint and diffusion i...

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Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion....

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Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Generalized belief functions . . . . . . 20 1.2.4 The classic DSm rule of combination . . . . . 21 1.2.5 The hybrid DSm rule of combination . . . . . 22 1.2.6 Examples of combination rules . . . . . . 24 1.2.7 Fusion of imprecise beliefs . . . . . . 29 1.3 Proportional Conflict Redistribution rule . . . . . 33 1.3.1 PCR formulas . . . . . . . . . 34 1.3.2 Examples . . . . . . . . . 35 1.3.3 Zadeh’s example . . . . . . . . 39 1.4 Uniform and partially uniform redistribution rules . . . 41 1.5 RSC Fusion rules . . . . . . . . . 43 1.6 The generalized pignistic transformation (GPT) . . . . 45 1.6.1 The classical pignistic transformation . . . . 45 1.6.2 Notion of DSmcardinality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic In...

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This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose them in order to share ideas and motivate new debates with people interested in new reasoning methods and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence....

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Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive rule . . . . . . . . . 6 1.2.3 The disjunctive rule . . . . . . . . . 8 1.2.4 Dempster’s rule of combination . . . . . . . 8 1.2.5 Smets’ rule of combination . . . . . . . 9 1.2.6 Yager’s rule of combination . . . . . . . 9 1.2.7 Dubois & Prade’s rule of combination . . . . . . 9 1.2.8 The hybrid DSm rule . . . . . . . . 10 1.3 The general weighted operator (WO) . . . . . . . 11 1.4 The weighted average operator (WAO) . . . . . . . 12 1.4.1 Definition . . . . . . . . . 12 1.4.2 Example for WAO . . . . . . . . . 13 1.4.3 Limitations of WAO . . . . . . . . . 13 1.5 Daniel’s minC rule of combination . . . . . . . 14 1.5.1 Principle of the minC rule . . . . . . . 14 1.5.2 Example for minC . . . . . . . . . 15 1.6 Principle of the PCR rules . . . . . . . . . 20 1.7 The...

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In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for developing mathematical sciences of 21st century, which means that we can combine different fields into a union one and then determines its behavior quantitatively. It is this notion that urges me to research mathematics and physics by combinatorics, i.e., mathematical combinatorics beginning in 2004 when I was a post-doctor of Chinese Academy of Mathematics and System Science. It finally brought about me one self-contained book, the first edition of this book, published by InfoQuest Publisher in 2009. This edition is a revisited edition, also includes the development of a few topics discussed in the first edition....

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1.5 ENUMERATION TECHNIQUES 1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X....

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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 1.1.1 Set . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Boolean algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Multi-Set . . . . . . . . . . . . . . . . . . . . . . . . . .8 1.2 Multi-posets . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 Partially ordered set . . . . . . . . . . . . . . . . . . . . .11 1.2.2 Multi-Poset . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Countable sets . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Countable set . . . . . . . . . . . . . . . . . . . . 16 1.4 Graphs . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.4.2 Subgraph . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.3 Labeled graph. . . . . . ...

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Female spouse of one’s brother is called `sister-in-law`; similarly the sister of one’s spouse is sister-in-law. Again, the wife of one’s brother-in-law is also called sister-in-law, subject however to the condition that the said brother-in-law is not the husband of one’s own sister. Thus, in Indian society, we find a vast variety of sister-in-law. However, one factor of commonality is often found in the cases where at both ends of this relationship, we have females. The say that this factor provides sauce to our family life, by swift maneuvers of their inimical or endearing postures towards each other. The author has picked up every variety of this relationship from the middle-class stratum of Indian society, while sketching his story for this fictional narration. However, in a given situation, we feel like addressing or being addressed as `MUY DEAR SISTER-IN-LAW`. To take the story forward, the author has tried his best to strew certain suchlike expressions coming forth sporadically, uttered by one or the other character ,irrespective of his/her sex. ...

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Perched in his wheelchair, at the moment on 30th June, 2007, this erstwhile lover of Maya -law. Of course, this infirm oldie his first ever acquaintance with Vibha Ratra took place, when his family ... Our mother, though surprised to be getting acquainted by her son to Mrs Wilson as the bride's mother, chose to maintain silence about her knowledge of that lady's `swarthy` reputation in the residential vicinity, during their adolescence. Instead of consoling his father in a socially approved manner, the arrogant son had yelled out at the top of his voice, "Papa, you have had enough of her during the past 45 years. In case, you still need a woman's company, there is no dearth of this lot to provide warmth to your body. The following day, while exiting from the faculty meet, Vibha marked that Dr Rawat looked eager to join her, while she was proceeding towards the group of some junior teachers of her department, already waiting for their head of the department. Really, it's an agonizing account," Madhukar ejaculated following a long sigh. After a short while, he resumes, "You can bank upon, this humble friend for all support, wheneve...

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This book is devoted to an emerging branch of Information Fusion based on new approach for modeling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theoretical investigations while Part 2 presents several applications of this new theory. We hope that this first book on DSmT will stir up some interests to researchers and engineers working in data fusion and in artificial intelligence. Many simple but didactic examples are proposed throughout the book. As a young emerging theory, DSmT is probably not exempt from improvements and its development will continue to evolve over the years. We just want through this book to propose a new look at the Information Fusion problematic and open a new track to attack the combination of information....

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Preamble xi Prefaces xiii I Advances on DSmT 1 1 Presentation of DSmT 3 1.1 Introduction . . . . . 3 1.2 Short introduction to the DST . . . . 5 1.2.1 Shafer’s model and belief functions . . . 5 1.2.2 Dempster’s rule of combination . . . 5 1.2.3 Alternatives to Dempster’s rule of combination . . . 6 1.2.4 The discounting of sources of evidence . . . 10 1.3 Foundations of the DSmT . . . . 11 1.3.1 Notion of free and hybrid DSm models . . . 11 1.3.2 Notion of hyper-power set D_ . . . 13 1.3.3 Generalized belief functions . . . . 15 1.3.4 The classic DSm rule of combination . . . 16 1.3.5 The hybrid DSm rule of combination . . . 17 1.3.6 On the refinement of the frames . . . 18 1.3.7 On the combination of sources over different frames . . . 20 1.4 Comparison of different rules of combinations . . . 21 1.4.1 First example . . . . . 21 1.4.2 Second example . . . . 25 1.4.3 Third example . . . . 26 1.4.4 Fourth example . . . . 27 1.4.5 Fifth example . . . . . 27 1.5 Summary . . . . . 29 1.6 References . . . . . 31 2 The generation of hyper-power sets 37 2.1 Introduction . . . . . 37 2.2 Definition of hyper-po...

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On preservation of the Western rights, freedoms and quality of life in 21st century and beyond

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Systemic approach to life of the highly cultured people provides them with higher level of happiness simply because their lives are better organized, risks are covered, reserves are maintained, dangers avoided, contacts established and so on so forth. Culture is not something that comes only with DNA, but genetic pre-disposition towards culture exists without doubt. Otherwise there would be no examples of people raising themselves above the scum they were born in and reaching high levels of society. Understanding of the elements of high culture, its systemic approach to organizing one’s life, can be practiced by virtually everybody. One just needs to want to elevate themselves and work towards that goal, which may involve getting better training and education, moving to a different neighborhood, getting a different job, spending time on more important things rather than on leisure, quitting drinking and smoking, refusing drugs, taking care of health, concentrating on the upbringing of the children and helping them in their adult life, babysitting grand-children, watching over quality of food supply and keeping the family ...

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Table of Contents Introduction iii Table of Contents iv About this book ix Who should not read this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Who is this book for? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Response to our critics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x About the authors xiii I What do we want to preserve and why? 1 1 Foreword 3 2 Measuring the quality of life 5 2.1 Individual happiness and self-fulfillment . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Individual rights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Social harmony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Checks and balances 11 3.1 Acceptable personal risk and responsibility . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 What is worth to fight for? 15 4.1 Security of the person . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2 Personal and societal wealth . . . . . . . . . . . . ....

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What this Book is About There is a commonly held view that the incidence and scale of disasters is increasing in the modern world although some disagreement on whether the incidence of events, such as Tsunamis, earthquakes, fires, floods etc., that can give rise to disasters is increasing. The view is understandable, both population and their built environment are increasing so more is at risk and this trend of increased risk will continue while populations continue to rise. As the World Bank Independent Evaluation Group (IEG) enumerates this: ‘Natural disasters are becoming more costly: in constant dollars, disaster costs between 1990 and 1999 were more than 15 times higher ($652 billion in material losses) than they were between 1950 and 1959 ($38 billion at 1998 values) The human cost is also high: over the 1984–2003 period, more than 4.1 billion people were affected by natural disasters. The number affected has grown, from 1.6 billion in the first half of that period (1984–93) to almost 2.6 billion in the second half (1994-2003), and has continued to increase. Although disasters caused by natural events occur throughout...

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List of figures, table & Abbreviations ix Acknowledgements x What this Book is About 1 Chapter 1 - Key Concepts 7 Disaster Risk Reduction 7 Risk 10 Fast and Slow Onset Disasters 11 Resilience 12 Systems Thinking 13 Self-organising Systems 18 A System for Disaster Risk Reduction 21 Evaluation of Natural Disasters 22 Chapter 2 –Components of Disasters and NRM 27 Economic Analysis – Five Forms of Capital 27 The Significance of Context 31 Ecosystems Functional Analysis ...

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Etymologically, aphorism + floral = aph(L)orism, which is a short reflection written on a floral design, or a short poetry accompanied by an artistic background. They are colorful contemplations. Maximus in minimis (Lat.) means very much in very little [max in min], or condensed thought, or ideating essence. They are actually maxims, adages, sayings mostly in one line (uni-stich) with a title, as a metaphoric statement, a breathing momentum that oils our soul....

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Nonchalantly : The wind with its mantle steps lightly. Skin Condition : The Sun has spots too. At what time? When it rains, God cries. Atmosphere : Blue, as the sky dirtied by clouds. Bright : A balcony full of Sun. Natural disaster : The swans look drunk on the fetid lake. Surprisingly : The crow is a beautiful black. Elegant woman : A bird high on her legs. Most powerful chess piece : You are a queen but only in the dark. Medicinal plant : You’re a flower but amongst weeds. Force that attracts food : The stomach’s gravitation pulls me to food....

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Passion.......................................................................23 Worthless.....................................................................23 Tired of you....................................................................23 Tittle-tattle....................................................................23 Talk is cheep...................................................................24 Give the man what he doesn’t have.................................................24 Novel for (non) writers...........................................................24 Desolate......................................................................24 Did I have the pleasure...........................................................24 Sloppy work....................................................................25 Despicable.....................................................................25 Wanted.......................................................................25 Talking in vain..................................................................25 Use caplets.....................................................

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The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues through these bi-verses closed in a new lyric exact formula, but with an opening to essence. For this kind of procedural poems one can elaborate mathematical algorithms and implement them in a computer: but, it is preferable a machine with … soul!...

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I M M O D E S T With the shame Shamelessness U N D E C I D E D Fighting Himself J A Z Z ( I ) Melodious Anarchy J A Z Z ( I I ) Anarchic Melody...

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Fore/word and Back/word _________ 3 The making of the distich : _____ 3 Characteristics: ______________ 3 Historical considerations: _____ 5 Types of Paradoxist distiches ___ 8 1. Clichés paraphrased: ___ 8 2. Parodies: _____________ 8 3. Reversed formulae: ____ 8 4. Double negation _______ 8 5. Double affirmation, ____ 8 6. Turn around on false tracks: _________________ 8 7. Hyperboles (exaggerated): __________________ 8 8. With nuance changeable from the title: ________ 8 9. Epigrammatic: ________ 8 10. Pseudo-paradoxes: ___ 8 11. Tautologies: ________ 9 12. Redundant: _________ 9 13. Based on pleonasms: _ 9 14. or on anti-pleonasms: 9 15. Substitution of the attribute in collocations ___ 9 16. Substitution of the complement in collocations 9 17. Permutation of various parts of the whole: ___ 9 18. The negation of the clichés ______________ 10 19. Antonymization (substantively, adjectively, etc.) ________________ 10 20. Fable against the grain: _________________ 10 21. Change in grammatical category (preserving substitutions’ homonymy): ________________ 10 22. Epistolary or colloquia style: _________...

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The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

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This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

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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 of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................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................................

Description Details
The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors...

Excerpt Details
This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

Table of Contents Details
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 of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................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................................