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41

Sep 23, 2013
09/13

by
Linfan Mao

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As we known, the {\it Seifert-Van Kampen theorem} handles fundamental groups of those topological spaces $X=U\cup V$ for open subsets $U, V\subset X$ such that $U\cap V$ is arcwise connected. In this paper, this theorem is generalized to such a case of maybe not arcwise-connected, i.e., there are $C_1$, $C_2$,$..., C_m$ arcwise-connected components in $U\cap V$ for an integer $m\geq 1$, which enables one to find fundamental groups of combinatorial spaces by that of spaces with theirs underlying...

Source: http://arxiv.org/abs/1006.4071v1

83
83

Nov 20, 2015
11/15

by
Linfan Mao

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Applying this result, this paper discusses the →G-flow solutions on Schrodinger equation, Klein-Gordon 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: G-flow, equations of particles

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68

Nov 20, 2015
11/15

by
Linfan Mao

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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, non-solvable equations

Integral theory on these smoothly combinatorial manifolds are introduced. Some classical results, such as those of Stokes’ theorem and Gauss’ theorem are generalized to smoothly combinatorial manifolds in this paper.

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37

Sep 19, 2013
09/13

by
Linfan Mao

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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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45

Sep 18, 2013
09/13

by
Linfan Mao

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A tendering is a negotiating process for a contract through by a tenderer issuing an invitation, bidders submitting bidding documents and the tenderer accepting a bidding by sending out a notification of award. As a useful way of purchasing, there are many norms and rulers for it in the purchasing guides of the World Bank, the Asian Development Bank, $...$, also in contract conditions of various consultant associations. In China, there is a law and regulation system for tendering and bidding....

Source: http://arxiv.org/abs/math/0605495v1

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63

Sep 20, 2013
09/13

by
Linfan Mao

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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

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.

160
160

Nov 8, 2015
11/15

by
LINFAN MAO

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A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician’s interesting. Its function and role in mathematics are widely accepted by mathematicians today.

Topics: combinatorial map, surface

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2.0

Apr 2, 2021
04/21

by
Linfan Mao

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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 non-orientable 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...

64
64

Sep 18, 2013
09/13

by
Linfan Mao

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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 non-orientable surfaces. A number of results for the enumeration of unrooted maps underlying a graph on orientable and non-orientable surfaces are discovered. An elementary classification for...

Source: http://arxiv.org/abs/math/0505318v1

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42

Sep 20, 2013
09/13

by
Linfan Mao; Yanpei Liu

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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 non-equivalent orientable or non-orientable 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 non-orientable surfaces, formulae for the number of non-equivalent maps of $\Gamma$ on surfaces (orientable,...

Source: http://arxiv.org/abs/math/0607791v1

0
0.0

Nov 30, 2021
11/21

by
Linfan Mao

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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 multi-space model for bidding is...

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4.0

Apr 2, 2021
04/21

by
Linfan Mao

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7.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 7

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73

Sep 18, 2013
09/13

by
Linfan Mao

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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,...

Source: http://arxiv.org/abs/math/0606702v2

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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63

Sep 22, 2013
09/13

by
Linfan Mao

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A manifold $M^n$ inherits a labeled $n$-dimensional graph $\widetilde{M}[G^L]$ structure consisting of its charts. This structure enables one to characterize fundamental groups of manifolds, classify those of locally compact manifolds with finite non-homotopic loops by that of labeled graphs $G^L$. As a by-product, this approach also concludes that {\it every homotopy $n$-sphere is homeomorphic to the sphere $S^n$ for an integer $n\geq 1$}, particularly, the Perelman's result for $n=3$.

Source: http://arxiv.org/abs/1004.1231v2

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86

Nov 20, 2015
11/15

by
Linfan MAO

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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, GL-system, non-solvable system of equations

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66

Nov 20, 2015
11/15

by
Linfan MAO

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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 multi-space solutions for equations, for instance, the Einstein’s gravitational...

Topics: Banach space, topological graph, conservation flow, topological graph, differential flow,...

Topological and differential structures such as those of d-pathwise connected, homotopy classes, fundamental d-groups in topology and tangent vector fields, tensor fields, connections, Minkowski norms in differential geometry on these finitely combinatorial manifolds are introduced. Some classical results are generalized to finitely combinatorial manifolds. Euler-Poincare characteristic is discussed and geometrical inclusions in Smarandache geometries for various geometries are also presented...

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51

Sep 20, 2013
09/13

by
Linfan Mao

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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 $1\leq j\leq s(p)\leq m$. Topological and differential structures...

Source: http://arxiv.org/abs/math/0612760v1

A complex system S consists m components, maybe inconsistence with m ≥ 2, such as those of biological systems or generally, interaction systems and usually, a system with contradictions, which implies that there are no a mathematical subfield applicable.

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3.0

Apr 25, 2021
04/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

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14

Apr 25, 2021
04/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

11
11

Apr 30, 2021
04/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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: Smarandache geometries, Smarandache curves

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9.0

Apr 30, 2021
04/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology

10
10.0

May 2, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

7
7.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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: Smarandache geometries, Smarandache curves

9
9.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

10
10.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 10

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

7
7.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 7

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

5
5.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 5

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

4
4.0

May 5, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

9
9.0

May 6, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 9

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves

8
8.0

May 7, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

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16

May 7, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

11
11

May 7, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 11

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

5
5.0

May 9, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 5

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

9
9.0

May 8, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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...

Topics: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

8
8.0

May 7, 2021
05/21

by
Linfan Mao (Editor in Chief)

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The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences 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: Smarandache geometries, Smarandache curves, graphs, combinatorial maps, topology, differential...

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...

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8.0

Apr 2, 2021
04/21

by
Linfan Mao

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9.0

Apr 2, 2021
04/21

by
Linfan Mao

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0
0.0

Nov 30, 2021
11/21

by
Linfan Mao

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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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8.0

Apr 2, 2021
04/21

by
Linfan Mao

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Papers on Extending Homomorphism Theorem to Multi-Systems, A Double Cryptography Using the Smarandache Keedwell Cross Inverse Quasigroup, the Time-like Curves of Constant Breadth in Minkowski 3-Space, Actions of Multi-groups on Finite Sets, and other topics.

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Apr 2, 2021
04/21

by
Linfan Mao

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3.0

Apr 2, 2021
04/21

by
Linfan Mao

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4.0

Apr 2, 2021
04/21

by
Linfan Mao

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6.0

Apr 2, 2021
04/21

by
Linfan Mao

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