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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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126
126

Jul 20, 2013
07/13

by
Linfan Mao

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A Smarandache multi-space 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 paper is the first part on characterizing multi-spaces. Various algebraic multi-spaces with structures such as those of multi-groups, multi-rings, multi-vector spaces, multi-metric spaces, multi-operation systems are discussed and new results...

Source: http://arxiv.org/abs/math/0604480v1

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6.0

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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3.0

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...

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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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5.0

Apr 2, 2021
04/21

by
Linfan Mao

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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 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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6.0

Apr 2, 2021
04/21

by
Linfan Mao

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2.0

Apr 2, 2021
04/21

by
Linfan Mao

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5
5.0

May 9, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 5

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favorite 0

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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...

86
86

Jul 20, 2013
07/13

by
Linfan Mao

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A Smarandache multi-space 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 multi-spaces. Many conceptions in graphs are generalized by Smarandache's notion, such as multi-voltage graphs, Cayley graphs of a finite multi-group,multi-embedding of a graph in an $n$-manifold, graph phase, $...$, etc.....

Source: http://arxiv.org/abs/math/0604481v1

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41

Sep 23, 2013
09/13

by
Linfan Mao

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A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with classical metric spaces, the conception of multi-metric space is introduced. Some characteristics of a multi-metric space are obtained and Banach's fixed-point theorem is generalized in this paper.

Source: http://arxiv.org/abs/math/0510480v1

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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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57

Sep 20, 2013
09/13

by
Linfan Mao

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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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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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3.0

Apr 2, 2021
04/21

by
Linfan Mao

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3
3.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 3

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40

Sep 23, 2013
09/13

by
Linfan Mao

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A Smarandache multi-space is a union of $n$ spaces $A_1,A_2,..., A_n$ with some additional conditions holding. Combining Smarandache multi-spaces with rings in classical ring theory, the conception of multi-ring spaces is introduced. Some characteristics of a multi-ring space are obtained in this paper.

Source: http://arxiv.org/abs/math/0510478v1

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10.0

Apr 2, 2021
04/21

by
Linfan Mao

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3
3.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 3

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favorite 0

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3
3.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 3

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favorite 0

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comment 0

6
6.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 6

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favorite 0

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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...

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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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

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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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2.0

Apr 2, 2021
04/21

by
Linfan Mao

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comment 0

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4.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 4

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favorite 0

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2
2.0

Apr 2, 2021
04/21

by
Linfan Mao

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eye 2

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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...

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...

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.

81
81

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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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,...

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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

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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

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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

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48

Sep 19, 2013
09/13

by
Linfan Mao

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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 n-manifold is a n-manifold that support a Smarandache geometry. Iseri provided a construction for Smarandache 2-manifolds by equilateral triangular disks on a plane and a more general way for Smarandache 2-manifolds on surfaces,...

Source: http://arxiv.org/abs/math/0610307v1

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9.0

Apr 2, 2021
04/21

by
Linfan Mao

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46

Sep 20, 2013
09/13

by
Linfan Mao; Yanpei Liu; Feng Tian

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A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on its vertices. Applying a scheme for enumerating maps on surfaces with a given underlying graph, the numbers of unrooted complete maps on orientable or non-orientable surfaces are obtained.

Source: http://arxiv.org/abs/math/0607790v1

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47

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

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117

Jul 20, 2013
07/13

by
Linfan Mao

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A Smarandache multi-space 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 multi-spaces considering applications of multi-spaces to theoretical physics, including the relativity theory, the M-theory and the cosmology. Multi-space models for $p$-branes and cosmos are constructed and some questions...

Source: http://arxiv.org/abs/math/0604483v1

8
8.0

May 8, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 8

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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 2, 2021
05/21

by
Linfan Mao (Editor in Chief)

texts

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eye 10

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comment 0

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 6, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 7

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comment 0

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

5
5.0

May 3, 2021
05/21

by
Linfan Mao (Editor in Chief)

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eye 5

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comment 0

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

Apr 30, 2021
04/21

by
Linfan Mao (Editor in Chief)

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eye 8

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comment 0

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

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.