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Parallel lines are very important objects in Euclid plane geometry and its behaviors can be gotten by one's intuition. But in a planar map geometry, a kind of the Smarandache geometries, the sutation is complex since it may contains elliptic or hyperbolic points. This paper concentrates on the behavior of parallel bundles, a generazation of parallel lines in plane geometry and obtains characteristics for for parallel bundles.
Source: http://arxiv.org/abs/math/0506386v1
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A Smarandache multispace is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining classical of a group with Smarandache multispaces, the conception of a multigroup space is introduced in this paper, which is a generalization of the classical algebraic structures, such as the group, filed, body, $...$, etc.. Similar to groups, some characteristics of a multigroup space are obtained in this paper.
Source: http://arxiv.org/abs/math/0510427v1
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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A Smarandache multispace is a union of n various spaces equipped with different structures for an integer n >= 2, which can be used for both discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multispaces and includes three parts. The first part is on algebraic multispaces, with structures such as those of multigroups, multirings, multivector spaces, multimetric spaces, multioperation...
This book is for students and young scholar, words of a mathematician, also a physicist and an economic scientist to them through by the experience himself and his philosophy. By recalling each of his growth and success steps, i.e., beginning as a construction worker, obtained a certification of undergraduate learn by himself and a doctor’s degree in university, promoting mathematical combinatorics for contradictory system on the reality of things and economic systems, and after then...
A Smarandache geometry is a geometry which has at least one Smarandachely denied axiom(1969), i.e., an axiom behaves in at least two different ways within the same space, i.e., validated and invalided, or only invalided but in multiple distinct ways and a Smarandache nmanifold is a nmanifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2manifolds on surfaces,...
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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This book is for young students, words of one mathematician, also being a physicist and an engineer to young students. By recalling each of his growth and success steps, beginning as a construction worker, obtained a certification of undergraduate learn by himself and a doctor’s degree in university, after then continuously overlooking these obtained achievements, raising new scientific objectives in mathematics and physics by Smarandache’s notion and combinatorial principle for his...
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For an integer $m\geq 1$, a combinatorial manifold $\widetilde{M}$ is defined to be a geometrical object $\widetilde{M}$ such that for $\forall p\in\widetilde{M}$, there is a local chart $(U_p,\phi_p)$ enable $\phi_p:U_p\to B^{n_{i_1}}\bigcup B^{n_{i_2}}\bigcup...\bigcup B^{n_{i_{s(p)}}}$ with $B^{n_{i_1}}\bigcap B^{n_{i_2}}\bigcap...\bigcap B^{n_{i_{s(p)}}}\not=\emptyset$, where $B^{n_{i_j}}$ is an $n_{i_j}$ball for integers $1\leq j\leq s(p)\leq m$. Integral theory on these smoothly...
Source: http://arxiv.org/abs/math/0703400v1
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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A Smarandache multispace is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This is the third part on multispaces concertrating on Smarandache geometries, including those of map geometries, planar map geometries and pseudoplane geometries. In where, the Finsler geometry, particularly the Riemann geometry appears as a...
Source: http://arxiv.org/abs/math/0604482v1
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A Smarandache multispace is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This is second part on multispaces. Many conceptions in graphs are generalized by Smarandache's notion, such as multivoltage graphs, Cayley graphs of a finite multigroup,multiembedding of a graph in an $n$manifold, graph phase, $...$, etc.....
Source: http://arxiv.org/abs/math/0604481v1
A Smarandache multispace is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This monograph concentrates on characterizing various multispaces including three parts altogether. The first part is on algebraic multispaces with structures, such as those of multigroups, multirings, multivector spaces, multimetric spaces,...
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A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism groups of a Klein surface and a Smarandache manifold, also applied to the enumeration of unrooted maps on orientable and nonorientable surfaces. A number of results for the automorphism groups of maps, Klein surfaces and Smarandache manifolds and the enumeration of unrooted maps underlying a graph on...
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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Applying this result, this paper discusses the →Gflow solutions on Schrodinger equation, KleinGordon equation and Dirac equation, i.e., the field equations of particles, bosons or fermions, answers previous questions by ”yes“, and establishes the many world interpretation of quantum mechanics of H. Everett by purely mathematics in logic, i.e., mathematical combinatorics.
Topics: Gflow, equations of particles
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On SMARANDACHE GEOMETRIES & MAP THEORY WITH APPLICATIONS.
Topics: Automorphism groups of maps, surfaces and Smarandache geometries
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There is a bidding law and regulation system in China. For getting or issue a contract, a contractor or an employer should understand all these laws and regulations first and then know how they work. This book contains the main materials of this kind for a construction contract, and contains four chapters. Chapter 1 is a survey of bidding for a construction contact. The laws and regulations for bidding in China are interpreted in this chapter. A Smarandache multispace model for bidding is...
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A map is a connected topological graph $\Gamma$ cellularly embedded in a surface. In this paper, applying Tutte's algebraic representation of map, new ideas for enumerating nonequivalent orientable or nonorientable maps of graph are presented. By determining automorphisms of maps of Cayley graph $\Gamma={\rm Cay}(G:S)$ with ${\rm Aut} \Gamma\cong G\times H$ on locally, orientable and nonorientable surfaces, formulae for the number of nonequivalent maps of $\Gamma$ on surfaces (orientable,...
Source: http://arxiv.org/abs/math/0607791v1
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A natural behavior is used to characterize by differential equation established on human observations, which is assumed to be on one particle or one field complied with reproducibility. However, the multilateral property of a particle P and the mathematical consistence determine that such an understanding is only local, not the whole reality on P, which leads to a central thesis for knowing the nature, i.e. how to establish a physical equation with a proper interpretation on a thing. As it is...
Topics: human observations, nonsolvable equations
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The main purpose of this paper is to extend Banach spaces on topological graphs with operator actions and show all of these extensions are also Banach space with unique correspondence in elements on linear continuous functionals, which enables one to solve linear functional equations in such extended space, particularly, solve algebraic, differential or integral equations on a topological graph, i.e., find multispace solutions for equations, for instance, the Einstein’s gravitational...
Topics: Banach space, topological graph, conservation flow, topological graph, differential flow,...
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A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold, also applied to the enumeration of unrooted maps on orientable and nonorientable surfaces. A number of results for the enumeration of unrooted maps underlying a graph on orientable and nonorientable surfaces are discovered. An elementary classification for...
Source: http://arxiv.org/abs/math/0505318v1
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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A Smarandache multispace is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multispaces with linear vector spaces in classical linear algebra, the conception of multivector spaces is introduced. Some characteristics of a multivector space are obtained in this paper.
Source: http://arxiv.org/abs/math/0510479v1
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences.
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are Smarandache geometries and their enumertion are obtained. Open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are also presented in this paper.
Source: http://arxiv.org/abs/math/0506232v1
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences. Topics in detail to be covered...
Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...
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Linfan Mao (Editor in Chief)
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The International J. Mathematical Combinatorics (ISSN 19371055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published quarterly comprising 100150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multispaces, Smarandache geometries, mathematical combinatorics, nonEuclidean geometry and topology and their applications to other sciences.
Topics: Smarandache geometries, Smarandache curves
On a geometrical view, the conception of map geometries is introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surfaces. Some open problems related combinatorial maps with the Riemann geometry and Smarandache geometries are presented.
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to find combinatorial behavior for objectives. Recently, such research works appeared on journals for mathematics and theoretical physics on cosmos. The main purpose of this paper is to survey these thinking and ideas for mathematics and cosmological physics,...
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The universality of contradiction implies that the reality of a thing is only hold on observation with level dependent on the observer standing out or in and lead respectively to solvable equation or nonsolvable equations on that thing for human beings.
Topics: action flows, nonsolvable systems
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A Smarandache multispace is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. This is the 4th part of multispaces considering applications of multispaces to theoretical physics, including the relativity theory, the Mtheory and the cosmology. Multispace models for $p$branes and cosmos are constructed and some questions...
Source: http://arxiv.org/abs/math/0604483v1
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As a powerful technique for holding relations in things, combinatorics has experienced rapidly development in the past century, particularly, enumeration of configurations, combinatorial design and graph theory. However, the main objective for mathematics is to bring about a quantitative analysis for other sciences, which implies a natural question on combinatorics.
Topics: CC conjecture, Smarandache system, GLsystem, nonsolvable system of equations