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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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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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A collection of short prose essays.

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CULTURAL NEWS1 (short prose poem) I queue up at the entry of art. queue for meat, queue for bread (Hurraaah Hurrah How fine is our life!) And I watch how someone builds their tomb in eternity. We beseech you to sit down each as far as possible in literature, we are announced by the hoarse interphone. -No, thanks. I prefer standing up, I find myself answering unquestioned. -But do come, please, come. the poetry is waiting for you - says the interphone, then to me: -Enough, there is no place left, get out....

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About Florentin Smarandache again, by Ion Rotaru 5 Introduction to the Kingdom of Error 9 A few features of the NonExistentialism 10 A common 13 Cultural actuality (short prose - poem) 14 How not to ascend to the High NonSociety 15 News 19 Portrait 20 1st letter of Uncle Vasile the political refugee 21 2nd letter of Uncle Vasile the political refugee 23 3rd letter 25 The letter of Mircea the King-size 26 Leitmotif (short prose without action, without conflict, without subject) 27 Hopes 30 Recollections of which I don’t wish to remember 33 Defect writings (short prose - essay) 35 Introduction in Gibberish 38 Curriculum Vitae 49 The typewriter 50 Landscape with dreams 51 The heroic day of an ordinary man 53 Savu of Lentza 56 Gallant affairs 58 Little history of love (critique short prose) 60 Divorce 62 Uncle Gheorghe’s amazing deeds 64 Genealogy 67 At the swimming place 69 Characterize the character Vitoria Lipan in the novel “The hatchet” 70 RRS 73 Cupboard-which-can-hold-many-people-and-runs-alone-on-railways 74 Shakespeare Alexandru and Beethoven Nicolae 75 Diploma (juridical short prose) 77 Ahmed...

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During my research period in the Summer of 2012 at the Research Institute of Extenics and Innovation Methods, from Guangdong University of Technology, in Guangzhou, China, I have introduced the Linear and Non-Linear Attraction Point Principle and the Network of Attraction Curves, have generalized the 1D Extension Distance and the 1D Dependent Function to 2D, 3D, and in general to n-D Spaces, and have generalized Qiao-Xing Li’s and Xing-Sen Li’s definitions of the Location Value of a Point and the Dependent Function of a Point on a Single Finite Interval from one dimension (1D) to 2D, 3D, and in general n-D spaces. Then I used the Extenics, together with Victor Vlădăreanu, Mihai Liviu Smarandache, Tudor Păroiu, and Ştefan Vlăduţescu, in 2D and 3D spaces in technology, philosophy, and information theory....

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Contribution to Extenics (Preface by Florentin Smarandache): 4 1. Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D, by Florentin Smarandache: 22 2. Applications of Extenics to 2D-Space and 3D-Space, by Florentin Smarandache, Victor Vlădăreanu: 39 3. Generalization of the Dependent Function in Extenics for Nested Sets with Common Endpoints to 2D-Space, 3D-Space, and generally to n-D-Space, by Florentin Smarandache: 52 4. Generalizations in Extenics of the Location Value and Dependent Function from A Single Finite Interval to 2D, 3D, and n-D Spaces, by Florentin Smarandache, Mihai Liviu Smarandache: 60 5. Extention Transformation Used in I Ching, by Florentin Smarandache: 69 6. Extenics in Conventional and Nonconventional [Romanian], by Florentin Smarandache, Tudor Păroiu: 79 7. Extension Communication for Solving the Ontological Contradiction between Communication and Information, by Florentin Smarandache, Ştefan Vlăduţescu: 99-112...

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The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the arguments presented in this book are theoretical, nonetheless we recommend further observation in order to verify or refute the propositions described herein. It is of our hope that this volume could open a new chapter in our knowledge on the formation and structure of Astrophysical systems. ...

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Abstract We explore Yang’s Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes and the holographic area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d + 2-dimensions. It is conjectured that QM over Noncommutative spacetimes (Noncommutative QM) may be described by ordinary QMin higher dimensions. Novel Moyal-Yang-Fedosov-Kontsevich star products deformations of the Noncommutative Poisson Brackets are employed to construct star product deformations of scalar field theories. Finally, generalizations of the Dirac-Konstant and Klein-Gordonlike equations relevant to the physics of D-branes and Matrix Models are presented. ...

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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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În literatura românească de călătorie, Florentin Smarandache e un fel de doi într-unul: Juan Sebastian El Cano şi Antonio Pigafetta dimpreună; navigator cărturar, dar totodată un reporter al propriei umbre. Călătoria este pentru Florentin Smarandache un pharmakon: leac şi otravă deopotrivă. Şi îl serveşte ca atare. Cine are curiozitatea să-i deseneze călătoriile pe hartă, va descoperi că nu mai e mult până profesorul de matematici de la New Mexico University va putea exclama, cu vorbele lui Seneca: nec sit terris ultima Thule!...

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We focus our discussions in this book on cities, because in our opinion a city is the smallest economic entity which has ‘self-organizing’ character, in a sense that a city can grow by itself (with minimum intervention). Nonetheless, this book will not discuss the self-organization character itself, but a new concept called ‘Cultural Economy’ development. Cultural Economic here is part of leisure and tourism industry, and depends on taste, advertisement, history, and the quality of being diverse, distinctive, with a large spectrum of varieties....

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Content ................... 3 Prologue ....................... 4 Biography of authors .................. 7 Chapter 1. Historical Precursor ............. 8 Pitfalls of Industrialization Is there alternative to industrialization? A review of economics thinking Box I: Cultural Advantage and Cultural Studies Chapter 2. Cultural Advantage as Alternative ............. 20 De-Industrialization and Emergence of Experience Economy Cultural Advantage, a new proposition Chapter 3. High-Tech/High-Touch and Cultural Advantage ..... 31 To automate or not to automate? How to implement Cultural Advantage in city development Box III: Cultural Advantage and Anthropology Chapter 4. A few examples: Lessons to learn ............. 40 a. Nicosia b. Toronto c. Venice d. Huzhou e. Valencia f. Chicago g. Romanian Lesson h. Eastern Europe Lesson i. Argentina Lesson Chapter 5. Introduction to Poly-Emporium Theory ............. 49 A new proposition: Extended Tobin Tax Bibliography.........60...

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We present in this course: the reproduction’s misprocess, the reproduction’s mistype, the material goods (and bads), the base inactivity and auxiliary inactivity, the system’s antistructure, the irresponsibility of a computer center, unstructured graphs, etc. Also, the disorganization’s structure, the principles of disorganization, the indecision making misprocess, the planning of unnecessary energy consummation, etc. The Reproduction’s misprocess is the connection which takes place between mankind and nature and during which humans modify the natural objects, and even the nature, in accordance with their societal disgusts....

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Disorganization’ structures The disorganization structures represent the mechanism formed of disorganization subdivisions to which there have been assigned competencies and responsibilities and amongst which there have been established the guidelines required for nonfunctionality and efficiency. In other words, the disorganization structure is the result of the modality in which various compartments and people as well as their relationships have been grouped and constituted with the aim of accomplishing in suboptimal conditions the proposed objective. The principal constructive steps in disorganization structure are: 1. The function (position), 2. The compartment, 3. The hierarchy, 4. The relations or subordination....

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Table of Contents................................ 4 Chapter 1 ................................ 7 The reproduction’s misprocess ............................. 7 The reproduction’s mistype ............................. 7 The material goods and bads ............................ 7 The base inactivity and auxiliary inactivity. ........................ 8 Chapter 2 ................................ 8 The reproduction’s incapacity ............................. 8 The system’s antistructure and the approach style of a system ................ 9 Characteristics .................................. 9 Chapter 3. ............................... 11 The systems’ disorganization ............................. 11 The general concept of disorganization. ........................ 11 The scientific disorganizations of enterprises ...................... 11 The micro disorganization level ........................... 13 The macro disorganization level ........................... 13 The level of disorganization’s structure ........................ 13 The level of integrated approach .......................... 13 The disorganization of the informa...

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Parapedagogy is the science which studies the techniques of instruction and destruction and the deconfiguration of personality. It is concerned with non goals, discontents, anti principles, methods and disorganization forms of the education. In the misseducation research other disciplines are involved, such as the inhuman anatomy and psychology (especially the mass brain washing), the anti sociology of education which studies the psycho-asocial-anti-cultural medium and its sad influence over the personality. ...

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The parapedagogy definition The parapedagogy is the science which studies the techniques of instruction and destruction and the deconfiguration of personality. It is concerned with non goals, discontents, principles, methods and disorganization forms of the instruction and misseducation. The fundamental research in parapedagogy has the main goal to discover the laws and principles of parapedagogy, to establish an idealistic philosophy of the misseducation guideline in the misprocess of reconfiguration of the inhuman personality. The applicative research is preoccupied with student’s individuality, to detect and develop the inaptitude, anti talents, and the discovery of methods and procedures, which would decrease the school efficiency in its misprocess. In the parapedagogy research other disciplines are involved, such as the inhuman anatomy and psychology (especially the brain washing in mass), the sociology of misseducation which studies the psycho-asocial-anti-cultural medium and its influence over the personality. The historic and dialectic immaterialism constitutes the theoretical and methodological base of the parapedagogy res...

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Table of Discontents .................................5 Chapter 1 – Misseducation and Parapedagogy............... 10 Misseducation and parapedagogy...........................10 The miss concept of misseducation..........................13 Chapter 2 - The parapedagogic research.................. 14 The parapedagogy definition.............................14 The non‐objectives of parapedagogy research......................14 Research methods in parapedagogy..........................14 The biological bases of the psychological under development...............18 The role of the environment in personality disconfiguration................19 The rapport between maturity, learning, under‐development...............19 Chapter 3 - Knowledge about student’s personality .............20 The phases of intellectual under‐development......................20 The miss‐concepts of individual, person and personality..................21 The psychological miss‐concept of personality ......................22 Chapter 4 – Programs of study and characterization ............ 26 The main characteristics ...............................29 CHOLERIC...

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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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A book on the contrasts between the eastern Asian culture versus the western culture on topics such as education, medicine, science, and politics.

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Is oriental culture a kind of science? There lies a crucial difference in that Western science seeks the exterior solutions outside the heart. However, our ancient sages illustrated that humans are an integral part of the universe, and all the phenomena never skip out of the heart. And very fortunately, many wise men did succeed in cultivating their hearts to testify to the profound truth. So our Eastern classics focus on our inner cultivation. However people, including the overwhelming majority of the Chinese, would regard such education as being an extra (to life or science). Please contact the corresponding Taiwan or Singapore websites, where there are plenty of English versions of texts and videos of Buddhism, to request the standard translation. “What is Dao (Tao)? It is the natural principle all over the universe, the natural order, the essentiality of nature. The great universe has its order and rule, where the education of ancient sages roots. Education stems from here, and a human being has to obey the natural principle –Dao. In our Chinese notion of the integral of humans and nature; heaven, earth and human are...

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On the Cultural Contrast: East-West, preface by F. Liu .……………………………….4 Abstract by the Translator to the Chinese Translation of Neutrosophics………………12 Preface by the Translator to the Chinese Translation of Neutrosophics………………13 Biography of the Translator…………………………………………………………….18 Publication Review by F. Liu…………………………………………………………22 Annotation in the Chinese Translation of Neutrosophics………………………………27 Neutrosophic Dialogues………………………………………………………………51 Absolute Truth……………………………………………………………………………68 Science, Destiny, and Buddhism……………………………………………………….…79 Call for Papers…………………………………………………………………………….94 Neutrosophy and Dialectic, postface by Anthony Mansueto.…………………………….95...

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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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The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu....

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The main objective of this was to understand the basic psychological and social problems faced by the PWDs and their caretakers. To interpret the collected data, tabulations and analysis were made. Efforts were made to highlight the inferences in each table and in few places comments were made in order to use it for fuzzy analysis. Following is the list of organizations and the total population from 5 blocks is listed below....

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Preface 6 Chapter One INTRODUCTION TO BASIC CONCEPTS 11 Chapter Two ANALYSIS OF THE COLLECTED DATA OF THE PWDS FROM MELMALAYANUR AND KURINJI PADI BLOCKS IN TAMIL NADU 13 Chapter Three THE NEW FUZZY COGNITIVE RELATIONAL MAPS (FCRMS) BIMODEL 29 Chapter Four ANALYSIS OF THE SOCIO ECONOMIC PROBLEMS FACED BY THE PWDS USING (SFCMS) 47 4.1 Application of FCMs Models to Social and Psychological Problems 48 4.2 Expert Opinion of PWDs using Special FCMs to Analyse the Problem of PWDs 50 4.3 The Expert Opinion of the caretakers of the PWDs using SFCM 59 4.4 The Expert Opinion of the NGOs working with the PWDs using Special FCM Model 62 Chapter Five THE STUDY OF INTERRELATED PROBLEMS FACED BY THE PWDS AND THE CARE TAKERS 73 5.1 Introduction 73 5.2 Experts Opinion from a Public Person Living in Melmalayanur Block 77 5.3 Expert Opinion of PWDs using FRMs 84 5.4 Expert Opinion of Caretakers of the PWDs using FRM 87 5.5 Expert Opinion of the NGOs working with the PWDs using the FRM model 93 Chapter Six ANALYSIS OF PROBLEMS OF RURAL PWDs USING THE NEW FCRM BIMODEL 99 6.1 Expert Opinion of the Caretaker and a PWD using the ...

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The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem....

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1.2 Definition of Fuzzy Cognitive Maps In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts. Example 1.2.1: In Tamil Nadu (a southern state in India) in the last decade several new engineering colleges have been approved and started. The resultant increase in the production of engineering graduates in these years is disproportionate with the need of engineering graduates. ...

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Dedication 5 Preface 6 Chapter One BASIC CONCEPTS 1.1 Definition of Interval Matrices and Examples 8 1.2 Definition of Fuzzy Cognitive Maps 9 1.3 An Introduction to Neutrosophy 13 1.4 Some Basic Neutrosophic Structures 16 1.5 Some Basic Notions about Neutrosophic Graphs 22 1.6 On Neutrosophic Cognitive Maps with Examples 28 1.7 Definition and Illustration of Fuzzy Relational Maps (FRMs) 33 1.8 Introduction to Fuzzy Associative Memories 40 1.9 Some Basic Concepts of BAM 43 1.10 Properties of Fuzzy Relations and FREs 49 1.11 Binary Neutrosophic Relations and their Properties 56 Chapter Two INTRODUCTION TO FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES AND THEIR GENERALIZATIONS 2.1 Fuzzy Interval Matrices 68 2.2 Interval Bimatrices and their Generalizations 76 2.3 Neutrosophic Interval Matrices and their Generalizations 92 Chapter Three FUZZY MODELS AND NEUTROSOPHIC MODELS USING FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES 3.1 Description of FCIMs Model 118 3.2 Description and Illustration of FRIM Model 129 3.3 Description of FCIBM model and its Generalization 139 3.4 FRIBM model and i...

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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 issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems or other mathematical problems. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume....

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Abstract : Let k be any ¯xed positive integer, n be any positive integer, Sk(n) denotes the smallest positive integer m such that m! is divisible by kn: In this paper, we use the elementary methods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it. Keywords : F. Smarandache problem, primitive numbers, asymptotic formula. ...

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J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for generalized Euler numbers 9 H. Li and Q. Yang : Some properties of the LCM sequence 14 M. Liu : On the generalization of the primitive number function 18 Z. Lv : On the F. Smarandache LCM function and its mean value 22 Q. Wu : A conjecture involving the F. Smarandache LCM function 26 S. Xue : On the Smarandache dual function 29 N. Yuan : A new arithmetical function and its asymptotic formula 33 A. Muktibodh, etc. : Sequences of pyramidal numbers 39 R. Zhang and S. Ma : An e±cient hybrid genetic algorithm for continuous optimization problems 46 L. Mao : An introduction to Smarandache multi-spaces and mathematical combinatorics 54 M. Selariu : Smarandache stepped functions 81 X. Zhang and Y. Zhang : Sequences of numbers with alternate common di®erences 93 Y. Zhang : On the near pseudo Smarandache function 98 A. Muktibodh : Smarandache mukti-squares 102...

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Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

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0. In 1999, the second author of this remarks published a book over 30 of Smarandache's problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20 problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28]. In [16] Florentin Smarandache formulated 105 unsolved problems, while in [10] C.Dumitresu and V. Seleacu formulated 140 unsolved problems of his. The second book contains almost all the problems from [16], but now each problem has unique number and by this reason in [1, 28] and here the authors use the numeration of the problems from [10]. In the text below the following notations are used....

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V. Mladen and T. Krassimir : Remarks on some of the Smarandache's problem. Part 2 1 W. Kandasamy : Smarandache groupoids 27 L. Ding : On the primitive numbers of power P and its mean value properties 36 D. Torres and V. Teca : Consecutive, reversed, mirror, and symmetric Smarandache sequence of triangular numbers 39 D. Ren : On the square-free number sequence 46 T. Ramaraj and N. Kannappa : On ¯nite Smarandache near-rings 49 X. Kang : Some interesting properties of the Smarandache function 52 L. Mao : On Automorphism Groups of Maps, Surfaces and Smarandache Geometries 55 L. Ding : On the mean value of Smarandache ceil function 74 M. Le : An equation concerning the Smarandache function 78 M. Bayat, H. Teimoori and M. Hassani : An extension of ABC-theorem 81 J. Ma : An equation involving the Smarandache function 89 C. Chen : Inequalities for the polygamma functions with application 91 W. Vasantha and M. Chetry : On the number of Smarandache zero-divisors and Smarandache weak zero-divisors in loop rings 96 M. Le : The function equation S(n) = Z(n) 109 Z. Li : On the Smarandache Pseudo-number Sequences 111 D. Mehendale :...

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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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The antiwar of our entire nation is defined as being the army-impeded forces, skirmishing shoulder to shoulder with the civilian population, with the purpose of defeating all non-aggressors, for securing our country’s slavery and dependency. The defeat in this battle is assured through a moral inferiority of our population - the right cause of this antiwar -, the lack of heroism of our state’s citizens, by applying an adequate blundering, using our geographical disadvantages, and the international public humiliation. ...

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The battle and its non-goal. The battle is an ensemble of skirmishes of the subunits and units, which take place in a disorganized manner using armament and fighting techniques, for the expressed desire to enforce the enemy. The battle cannot take place on the ground, in the air, or on the water, in an open paradoxist cooperation with all-military denominations, and using their armament’s procedures with the goal of empowering the non-aggressor enemy. The battle is not the only way for obtaining the miscarriage. The battle’s goal is not the destruction or the capture of enemy’s groups, or the capture and holding on of critical portions of terrain. While in anti-defense, the defeat with fewer forces of the enemy’s superior forces would be done with our old-fashioned technique: ...

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Instruction Notebooks...............................3 Table of Contents .................................4 1 The Non-Tactical Instruction...........................10 Non-Assignment 1. ...............................10 The battle and its non-goal. ...........................12 The principles of non-organizing the battle’s actions. .................13 Non-Assignment 2...............................13 The disorganization principle of the subunits of unpatriotic guards. ............15 The subunits of the other branches of the military, their non-role, and their non-missions. ....15 The non-role and non-missions unsustainable by the other branches of the military. ......16 Not understanding the modern military ......................17 General principles disregarding the non-actions conducted by the subunits of a non-modern military in the inoffensive battles............................18 The anti-defense forms............................20 The non-roles and the non-missions of the fight units. .................20 The non-insurance for battle...........................20 The content of the battle’s non-insurance, its goal...

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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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In the volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems. There are a few papers which are not directly related to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3. Y. Wang and Z. Sheng, Two formulas for x^n in terms of Chebyshev polynomials. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume....

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On Algebraic Multi-Vector Spaces Abstract A Smarandache multi-space is a union of n spaces A1;A2;An with some additional conditions hold. Combining these Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of multi-vector spaces are obtained in this paper. Keywords Vector, multi-space, multi-vector space, dimension of a space. x1. Introduction These multi-spaces was introduced by Smarandache in under his idea of hybrid mathematics: combining different fields into a unifying field, which can be formally defined with mathematical words by the next definition. ...

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L. Mao : On Algebraic Multi-Vector Spaces 1 L. Liu and W. Zhou : On conjectures concerning class number of binary quadratic forms 7 W. Zhai and H. Liu : On square-free primitive roots mod p 15 X. Pan : A new limit theorem involving the Smarandache LCM sequence 20 M. Le : The Smarandache Perfect Numbers 24 N. Yuan : On the solutions of an equation involving the Smarandache dual function 27 J. Wang : Mean value of a Smarandache-Type Function 31 H. Yang and R. Fu : On the mean value of the Near Pseudo Smarandache Function 35 W. Liang : An Identity of Stirling Numbers of the Second Kind 40 R. Ma : On the F.Smarandache LCM Ratio Sequence 44 L. Mao : On Algebraic Multi-Ring Spaces 48 Y. Han : On the Product of the Square-free Divisor of a Natural Number 55 P. Zhang : Some identities on k-power complement 60 Y. Wang and Z. Sheng : Two Formulas for xn being Represented by Chebyshev Polynomials 64 X. Chen : Two Problems About 2-Power Free Numbers 70 X. Ma : The Asymptotic Formula of P n·x log Pad(n) 72 Q. Tian : On the K-power free number sequence 77 C. Lv : On a generalized equation of Smarandache and its integer sol...

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NonNovel is indeed a novel of drawer, carried year after year in the bottomless sack of the exile. This fierce parabola about totalitarianism, about alienation, guilty obedience and lie, opportunism, cruelty, violence, monstrosity, written in a strong tensioned and lacking bashfulness style, situates Florentin Smarandache closer by Orwell, Konwicki, Koestler, Baconsky, and marks a new dimension of the Paradoxism....

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Mybreathin gstops Mybrea thingstops Myb reath ings tops Mybreathingstops Mybreat hin gsto ps M ybreath ingstops My breathing stops

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WARNING!: 5 Mister Editor (a letter arrived at the editorial office): 6 I: 7 Dedication: 10 The Adventures of Hon Hyn: 11 Happenings from Wodania: 23 II: 26 About patriotism: 28 The royal feast: 29 The press: 30 Post Office: 31 The State control: 32 Non-values’ Epoch: 36 Pluralism: 43 A leader not like anyone else: 45 Invisible barriers: 46 The graduates’ allocation: 49 The lunatic asylum: 50 The abolishing of the difference between man and animal: 56 III: 59 The Earthquake: 60 Modern gallinacean: 62 The crop of pea: 63 The peasantry: 64 The intellectuality: 66 A little meditation does not hurt: 67 The Fonfoist Party: 69 An unsafe life was provided to us: 70 A certain kind of speech: 72 The Fonfoist Society: 83 “We will live here in abundance”: 87 The multilateral development of personality: 93 The Police and the Revolution: 95 Imposing buildings of prisons: 97 Football: 99 Public genuflection: 100 The contemporary history: 102 Hon Hyn’s visit to Paris: 103 The National Museum: 104 The Management of the Economical Systems: 105 A few notions of psychology: 106 (editor’s note): 109 The wise po...

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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................................