- Mathematics, Applied Mathematics, Graph Theory, Mathematical Combinatorics and Smarandache Multi-space With Applications to Combinatorics, eBranding, Geometry And Topology, and 17 moreTopology, Engineering, Physics, Combinatorics, Education, Philosophy, Social Sciences, Economics, Development Economics, Operations Research, History of Mathematics, Econometrics, Philosophy Of Mathematics, Philosophy of Science, Algebra, Equations, and Topological Graphsedit
Actually, different models characterize things in the world, particularly, animals dependent on the microscopic level. However, there are no a mathematical subfield characterizing animals or human beings ourselves in such a level globally... more
Actually, different models characterize things in the world, particularly, animals dependent on the microscopic level. However, there are no a mathematical subfield characterizing animals or human beings ourselves in such a level globally unless local elements such as points or spaces in classical sciences. Could we establish a mathematics describing animal's microscopic behaviors globally?
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Mathematical science is the human recognition on the evolution laws of things that we can understand with the principle of logical consistency by mathematics, i.e., mathematical reality. So, is the mathematical reality equal to the... more
Mathematical science is the human recognition on the evolution laws of things that we can understand with the principle of logical consistency by mathematics, i.e., mathematical reality. So, is the mathematical reality equal to the reality of thing? The answer is not because there always exists contradiction between things in the eyes of human, which is only a local or conditional conclusion. Such a situation enables us to extend the mathematics further by combinatorics for the reality of thing from the local reality and then, to get a combinatorial reality of thing. This is the combinatorial conjecture for mathematical science, i.e., CC conjecture that I put forward in my postdoctoral report for Chinese Academy of Sciences in 2005, namely any mathematical science can be reconstructed from or made by combinatorialization. After discovering its relation with Smarandache multi-spaces, it is then be applied to generalize mathematics over 1-dimensional topological graphs, namely the mathematical combinatorics that I promoted on science internationally for more than 20 years. This paper surveys how I proposed this conjecture from combinatorial topology, how to use it for characterizing the non-uniform groups or contradictory systems and furthermore, why I introduce the continuity flow G L as a mathematical element, i.e., vectors in Banach space over topological graphs with operations and then, how to apply it to generalize a few of important conclusions in functional analysis for providing the human recognition on the reality of things, including the subdivision of substance into elementary particles or quarks in theoretical physics with a mathematical supporting.
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Science has greatly improved the material civilization, also promoted the spiritual civilization of humans. Even so, can we assert that science is consistent already with the sustainable developing of humans in 21st century? The answer is... more
Science has greatly improved the material civilization, also promoted the spiritual civilization of humans. Even so, can we assert that science is consistent already with the sustainable developing of humans in 21st century? The answer is certainly Not because science is itself only a conditional truth on the reality of things and it is verified by the disposal of wastes in industrial activities led by science over the past hundreds of years. Notice the sustainable developing of humans introduces that humans should live with the nature in harmony, namely all products in human activities must be properly disposed of and not disturb the nature but it is far from this objective until today. Actually, the universal connection between things implies the application of science should be a systemic or combinatorial one, not a solitary or fragmented one, namely it should be discovered the closed systems of substances produced in human activities with an inherited combinatorial structure G L and then, applied it for benefiting humans without intruding to the nature. Such a pattern on science developing is essentially a pattern different from the traditional but a revolution on science, i.e., a biggest problem of science facing to promote human civilization in the 21st century.
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The main purpose of this paper is to survey how to extend classical mathematical non-systems, such as those of algebraic systems with contradictions, algebraic or differential equations with contradictions, geometries with contradictions,... more
The main purpose of this paper is to survey how to extend classical mathematical non-systems, such as those of algebraic systems with contradictions, algebraic or differential equations with contradictions, geometries with contradictions, and generally, classical mathematics systems with contradictions to mathematics by the underlying structure G. All of these discussions show that a non-mathematics in classical is in fact a mathematics underlying a topological structure G, i.e., mathematical combinatorics, and contribute more to physics and other sciences.
Research Interests: Mathematics, Algebra, Geometry And Topology, Mathematics Education, Combinatorics, and 6 moreAMS, Equations, D, C, A, and Topological Graphs
Let V be a Banach space over a field F. A − → G-flow is a graph − → G embedded in a topological space S associated with an injective mappings L : u v → L(u v) ∈ V such that L(u v) = −L(v u) for ∀(u, v) ∈ X − → G holding with conservation... more
Let V be a Banach space over a field F. A − → G-flow is a graph − → G embedded in a topological space S associated with an injective mappings L : u v → L(u v) ∈ V such that L(u v) = −L(v u) for ∀(u, v) ∈ X − → G holding with conservation laws u∈N G (v) L (v u) = 0 for ∀v ∈ V − → G , where u v denotes the semi-arc of (u, v) ∈ X − → G , which is an abstract model, also a mathematical object for things embedded in a topological space, or matters happened in the world. 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 equations. A generalization of so...
Discusses Smarandache geometries, including those of map geometries, planar map geometries and pseudo-plane geometries, in which the Finsler geometry, particularly the Riemann geometry appears as a special case of these Smarandache... more
Discusses Smarandache geometries, including those of map geometries, planar map geometries and pseudo-plane geometries, in which the Finsler geometry, particularly the Riemann geometry appears as a special case of these Smarandache geometries.
As the time enters the 21st century, sciences such as those of theoretical physics, complex system and network, cytology, biology and economy developments change rapidly, and meanwhile, a few global questions constantly emerge, such as... more
As the time enters the 21st century, sciences such as those of theoretical physics, complex system and network, cytology, biology and economy developments change rapidly, and meanwhile, a few global questions constantly emerge, such as those of local war, food safety, epidemic spreading network, environmental protection, multilateral trade dispute, more and more questions accompanied with the overdevelopment and applying the internet, · · · , etc. In this case, how to keep up mathematics with the developments of other sciences? Clearly, today's mathematics is no longer adequate for the needs of other sciences. New mathematical theory or techniques should be established by mathematicians. Certainly, solving problem is the main objective of mathematics, proof or calculation is the basic skill of a mathematician. When it develops in problem-oriented, a mathematician should makes more attentions on the reality of things in mathematics because it is the main topic of human beings.
A combinatorial field WG is a multi-field underlying a graph G, established on a smoothly combinatorial manifold. This paper first presents a quick glance to its mathematical basis with motivation, such as those of why the WORLD is... more
A combinatorial field WG is a multi-field underlying a graph G, established on a smoothly combinatorial manifold. This paper first presents a quick glance to its mathematical basis with motivation, such as those of why the WORLD is combinatorial? and what is a topological or differentiable combinatorial manifold? After then, we explain how to construct principal fiber bundles on combinatorial manifolds by the voltage assignment technique, and how to establish differential theory, for example, connections on combinatorial manifolds. We also show applications of combinatorial fields to other sciences in this paper.
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 in USA quarterly comprising 460 pages approx. per volume, which... more
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 in USA quarterly comprising 460 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.
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A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical... more
A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics.
Research Interests: Mathematics and Embedding
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising... more
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series with ISBN number on each issue, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. <br>
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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 in USA quarterly comprising 100-150 pages approx. per volume,... more
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 in USA quarterly comprising 100-150 pages approx. per volume, which publishes original researchpapers 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. <br>
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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 in USA quarterly comprising 100-150 pages approx. per volume,... more
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 in USA quarterly comprising 100-150 pages approx. per volume, which publishes original researchpapers 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. <br>
Aims and Scope: 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 in USA quarterly comprising 100-150 pages... more
Aims and Scope: 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 in USA 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;
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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,... more
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 sym- metrical systems in mathematical sciences.
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Our WORLD is a multiple one both shown by the natural world and human beings. For example, the observation enables one knowing that there are infinite planets in the universe. Each of them revolves on its own axis and has its own seasons.... more
Our WORLD is a multiple one both shown by the natural world and human beings. For example, the observation enables one knowing that there are infinite planets in the universe. Each of them revolves on its own axis and has its own seasons. In the human society, these rich or poor, big or small countries appear and each of them has its own system. All of these show that our WORLD is not in homogenous but in multiple. Besides, all things that one can acknowledge is determined by his eyes, or ears, or nose, or tongue, or body or passions, i.e., these six organs, which means theWORLD consists of have and not have parts for human beings. For thousands years, human being has never stopped his steps for exploring its behaviors of all kinds.
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Different from the system in classical mathematics, a Smarandache system is a contradictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in... more
Different from the system in classical mathematics, a Smarandache system is a contradictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems exist extensively in the world, particularly, in our daily life. In this paper, we discuss such a kind of Smarandache system, i.e., non-solvable ordinary differential equation systems by a combinatorial approach, classify these systems and characterize their behaviors, particularly, the global stability, such as those of sum-stability and prod-stability of such linear and non-linear differential equations. Some applications of such systems to other sciences, such as those of globally controlling of infectious diseases, establishing dynamical equations of instable structure, particularly, the n-body problem and understanding global stability of matters with multilateral properties can be also found.
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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... more
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.
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This paper discusses the G-flow solutions on Schr¨odinger 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... more
This paper discusses the G-flow solutions on Schr¨odinger 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.
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Different from the homogenous systems, a Smarandache system is a contra- dictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple... more
Different from the homogenous systems, a Smarandache system is a contra- dictory system in which an axiom behaves in at least two different ways within the same system, i.e., validated and invalided, or only invalided but in multiple distinct ways. Such systems widely exist in the world. In this report, we discuss such a kind of Smarandache sys- tem, i.e., non-solvable equation systems, such as those of non-solvable algebraic equations, non-solvable ordinary differential equations and non-solvable partial differential equations by topological graphs, classify these systems and characterize their global behaviors, partic- ularly, the sum-stability and prod-stability of such equations. Applications of such systems to other sciences, such as those of controlling of infectious diseases, interaction fields and flows in network are also included in this report.
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This paper surveys the applications of Smarandache's notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper. Topics... more
This paper surveys the applications of Smarandache's notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper. Topics covered in this paper include: (1)What is a Smarandache System? (2)Vertex-Edge Labeled Graphs with Applications: (i)Smarandachely k-constrained labeling of a graph; (ii)Smarandachely super m-mean graph; (iii)Smarandachely uniform k-graph; (iv)Smarandachely total coloring of a graph; (3)Covering and Decomposing of a Graph: (i)Smarandache path k-cover of a graph; (ii)Smarandache graphoidal tree d-cover of a graph; (4)Furthermore.
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Certainly, a Smarandache multispace or multisystem S is a union of m distinct spaces or systems S1, S2, • • • , Sm which is an appropriate model on things T in the universe because of the limitation of humans ourselves and a thing T is... more
Certainly, a Smarandache multispace or multisystem S is a union of m distinct spaces or systems S1, S2, • • • , Sm which is an appropriate model on things T in the universe because of the limitation of humans ourselves and a thing T is complex, even overlap with other things. However, nearly all observation data on T is a multiple one S which implies Si and Sj are entangled if Si Sj = ∅, we have to disentangle Si from Sj, 1 ≤ i = j ≤ m for hold on the reality of thing T. Thus, disentangling a multi-space S to self-enclosed spaces or systems S1, S2, • • • , Sm is interesting, also valuable in hold on the reality of things in the universe. The main purpose of this paper is to discuss the disentangling ways on a Smarandache multispace or multisystem if we assume that each self-enclosed space or system of Si, 1 ≤ i ≤ m is endowed with mathematical elements such as those of topological, geometrical, algebraic structures or generally, each space or system of Si has a character χi different from others for integers 1 ≤ i ≤ m. As it happens, this problem is equivalent to Schrödinger's cat of quantum mechanics in the case of m = 2, which are extensively applied in quantum teleportation for preparation, distribution and measurement of the entangled pairs of particles and prospecting us to design a general key carrier on the Smarandachely entangling pairs in commutation.
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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 in USA quarterly comprising 460 pages approx. per volume, which... more
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 in USA quarterly comprising 460 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.
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The science's function is realizing the natural world, developing our society in coordination with natural laws and the mathematics provides the quantitative tool and method for solving problems helping with that understanding.... more
The science's function is realizing the natural world, developing our society in coordination with natural laws and the mathematics provides the quantitative tool and method for solving problems helping with that understanding. Generally, understanding a natural thing by mathematical ways or means to other sciences are respectively establishing mathematical model on typical characters of it with analysis first, and then forecasting its behaviors, and finally, directing human beings for hold on its essence by that model.
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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... more
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 orientable and non-orientable surfaces are discovered. An elementary classification for the closed s-manifolds is found. Open problems related the combinatorial maps with the differential geometry, Riemann geometry and Smarandache geometries are also presented in this monograph for the further applications of the combinatorial maps to the classical mathematics.
Automorphism groups survey similarities on mathematical systems, which appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, · · · and theoretical physics, theoretical chemistry, etc.. In geometry,... more
Automorphism groups survey similarities on mathematical systems, which appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, · · · and theoretical physics, theoretical chemistry, etc.. In geometry, configurations with high symmetry born symmetrical patterns, a kind of beautiful pictures in aesthetics. Naturally, automorphism groups enable one to distinguish systems by similarity. More automor-phisms imply more symmetries of that system. This fact has established the fundamental role of automorphism groups in modern sciences. So it is important for graduate students knowing automorphism groups with applications. The first edition of this book is in fact consisting of my post-doctoral reports in Chi-nese Academy of Sciences in 2005, not self-contained and not suitable as a textbook for graduate students. Many friends of mine suggested me to extend it to a textbook for graduate students in past years. That is the initial motivation of this editi...
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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... more
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. However, few works on the mathematical model of a tendering and its evaluation can be found in publication. The main purpose of this paper is to construct a Smarandache multi-space model for a tendering, establish an evaluation system for bidding based on those ideas in the references [7] and [8] and analyze its solution by applying the decision approach for multiple objectives and value engineering. Open problems for pseudo-multi-spaces are also presented in the final section.
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As we known, the Seifert-Van Kampen theorem handles fundamental groups of those topological spaces X = U ∪ V for open subsets U, V ⊂ X such that U ∩ V is arcwise connected. In this paper, this theorem is generalized to such a case of... more
As we known, the Seifert-Van Kampen theorem handles fundamental groups of those topological spaces X = U ∪ V for open subsets U, V ⊂ X such that U ∩ V is arcwise connected. In this paper, this theorem is generalized to such a case of maybe not arcwise-connected, i.e., there are C1, C2,···, Cm arcwise-connected components in U ∩ V for an integer m ≥ 1, which enables one to find fundamental groups of combinatorial spaces by that of spaces with theirs underlying topological graphs, particularly, that of compact manifolds by their underlying graphs of charts.
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An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently, i.e., validated and Invalided, or only invalidated but in at least two distinct ways. And a Smarandache multi-space is a union of n... more
An axiom is said smarandachely denied (S-denied) if in the same space the axiom behaves differently, i.e., validated and Invalided, or only invalidated but in at least two distinct ways. And a Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n≧2. This paper studies them.
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The main purpose of this paper is to extend Banach or Hilbert spaces to Banach or Hilbert continuity flow spaces over topological graphs and establish differentials on continuity flows for characterizing their globally change rate.
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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... more
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 nmanifold 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, called map geometries was presented by the author in [9]− [10] and [12]. However, few observations for cases of n ≥ 3 are found on the journals. As a kind of Smarandache geometries, a general way for constructing dimensional n pseudo-manifolds are presented for any integer n ≥ 2 in this paper. Connection and principal fiber bundles are also defined on these manifolds. Following these constructions, nearly all existent geometries, such as those of Euclid geometry, LobachevshyBolyai geometry, Riema...
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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 a bijection with a bijection between linear continuous functionals and... more
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 a bijection with a bijection between linear continuous functionals and elements, which enables one to solve linear functional equations in such extended space, particularly, solve algebraic, differential or integral equations on a topological graph, find multi-space solutions on equations, for instance, the Einstein’s gravitational equations.
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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 non-solvable equations on that thing... more
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 non-solvable equations on that thing for human beings. Notice that all contradictions are artificial, not the nature of things. Thus, holding on reality of things forces one extending contradictory systems in classical mathematics to a compatible one by combinatorial notion, particularly, action flow on differential equations, which is in fact an embedded oriented graph −→ G in a topological space S associated with a mapping L : (v, u) → L(v, u), 2 end-operators Avu : L(v, u) → L A+vu(v, u) and Auv : L(u, v) → L A+uv(u, v) on a Banach space B with L(v, u) = −L(u, v) and Avu(−L(v, u)) = −L A+vu(v, u) for ∀(v, u) ∈ E ( −→ G ) holding with conservation laws ∑ u∈NG(v) L + vu (v, u) = 0, ∀v ∈ V ( −→ G ) . The main purpose of this paper is to survey the powerful role of action flows to mathem...
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The universality of contradiction and connection of things in nature implies that a thing is nothing else but a labeled topological graph GL with a labeling map L.
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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... more
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 combinatorial manifolds are introduced. Some classical results, such as those of {\it Stokes'} theorem and {\it Gauss'} theorem are generalized to smoothly combinatorial manifolds in this paper.
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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... more
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.
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The Chapter 7 of my book: Combinatorial Theory on the Universe, including the topics on logical consistency, quantum entanglement, limited mathematics, contradictory reality and group-system stability, etc.
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Bidding is a kind of purchasing behavior of microeconomics in a market. However, lots of people do not understand why we need bidding and how to purchase goods by bidding in a market, which results in sometimes only the form or procedure... more
Bidding is a kind of purchasing behavior of microeconomics in a market. However, lots of people do not understand why we need bidding and how to purchase goods by bidding in a market, which results in sometimes only the form or procedure of bidding remained but the departure of the procurement purpose in China. Based on the microeconomics, this book introduces the bidding principle by explaining its ideas and rules in cases analyzing from the macro to the micro and from the easy to the difficult cases. Meanwhile, it analyzes the causes of collusive bidding, win a bid by fraud or linked a unit illegally, spiteful low price in human's social attribute and moral cultivation with countermeasure, and also presents how to construct an orderly market of bidding in China, which refers to researchers on fields of bidding, contact management and market construction, and also to the employed professionals in bidding. Certainly, it contributes also a textbook or reference to students in bidding or contact management.
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The Mathematical Combinatorics (International Book Series) is a fully refereed international book series, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 pages approx. per volume,... more
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 110-160 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.
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Research Interests: Mathematics and Topology
This is the Chapter 11 of my book Combinatorial Theory on the Universe, which introduces the Chinese notions of unity of humans with the heaven, everything's law, etc., the meridians on human body of Chinese medicine with mathematics... more
This is the Chapter 11 of my book Combinatorial Theory on the Universe, which introduces the Chinese notions of unity of humans with the heaven, everything's law, etc., the meridians on human body of Chinese medicine with mathematics and the soul or essence of Chinese science.
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Holding on a thing is essentially to recognize the cause and effect in its evolving. The combinatorial notion implied in words of the sophist in the fable of the blind men with an elephant, is a philosophical notion for humans recognizing... more
Holding on a thing is essentially to recognize the cause and effect in its evolving. The combinatorial notion implied in words of the sophist in the fable of the blind men with an elephant, is a philosophical notion for humans recognizing things with only the local recognition of things. Under this notion, this book surveys the quantitative understanding of things. It starts with some ultimate questions on universe usually raised by children, explains the systematic recognition of things including the reference frame, relativity principle, system with synchronization, non-harmonious systems with non-solvable equations, complex networks, etc., establishes the model of continuity flow, a kind of mathematics over topological graph and comments the role of science in the harmonious coexistence of humans with the nature, which is a systematic review on mathematical science and philosophy, suitable for researchers in mathematics and applied mathematics, systems science, complex systems, complex networks and philosophy of science.
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An International Journal on Mathematical Combinatorics
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Vol.3,2020 of International Journal of Mathematical Combinatorics (ISSN 1937-1055)
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The Vol.4,2019 of International Journal of Mathematical Combinatorics.
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An international book series on Mathematical Combinatorics, Vol.2, 2019
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The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings is local or gradual, and mainly the mathematical... more
The reality of a thing is its state of existed, exists, or will exist in the world,
independent on the understanding of human beings, which implies that the reality holds on
by human beings is local or gradual, and mainly the mathematical reality, not the reality of
a thing. Is our mathematical theory can already be used for understanding the reality of all
things in the world? The answer is not because one can not holds on the reality in many fields.
For examples, the elementary particle system or ecological system, in which there are no a
classical mathematical subfield applicable, i.e., a huge challenge now is appearing in front of
modern mathematicians: To establish new mathematics adapting the holds on the reality of
things. I research mathematics with reality beginning from 2003 and then published papers on
fields, such as those of complex system and network, interaction system, contradictory system,
biological populations, non-solvable differential equations, and elementary established an entirely
new envelope theory for this objective by flows, i.e., mathematical combinatorics, or mathematics
over graphs, which is an appropriated way for understanding the reality of a thing because it is
complex, even contradictory. This book collects my mainly papers on mathematics with reality
of a thing from 2007 – 2017 and most of them are the plenary or invited reports in international
conferences.
independent on the understanding of human beings, which implies that the reality holds on
by human beings is local or gradual, and mainly the mathematical reality, not the reality of
a thing. Is our mathematical theory can already be used for understanding the reality of all
things in the world? The answer is not because one can not holds on the reality in many fields.
For examples, the elementary particle system or ecological system, in which there are no a
classical mathematical subfield applicable, i.e., a huge challenge now is appearing in front of
modern mathematicians: To establish new mathematics adapting the holds on the reality of
things. I research mathematics with reality beginning from 2003 and then published papers on
fields, such as those of complex system and network, interaction system, contradictory system,
biological populations, non-solvable differential equations, and elementary established an entirely
new envelope theory for this objective by flows, i.e., mathematical combinatorics, or mathematics
over graphs, which is an appropriated way for understanding the reality of a thing because it is
complex, even contradictory. This book collects my mainly papers on mathematics with reality
of a thing from 2007 – 2017 and most of them are the plenary or invited reports in international
conferences.
Research Interests:
The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings is local or gradual, and mainly the mathematical... more
The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings is local or gradual, and mainly the mathematical reality, not the reality of a thing. Is our mathematical theory can already be used for understanding the reality of all things in the world? The answer is not because one can not holds on the reality in many fields. For examples, the elementary particle system or ecological system, in which there are no a classical mathematical subfield applicable, i.e., a huge challenge now is appearing in front of modern mathematicians: To establish new mathematics adapting the holds on the reality of things. I research mathematics with reality beginning from 2003 and then published papers on fields, such as those of complex system and network, interaction system, contradictory system, biological populations, non-solvable differential equations, and elementary established an entirely
new envelope theory for this objective by flows, i.e., mathematical combinatorics, or mathematics over graphs, which is an appropriated way for understanding the reality of a thing because it is complex, even contradictory. This book collects my mainly papers on mathematics with reality of a thing from 2007 – 2017 and most of them are the plenary or invited reports in international conferences.
new envelope theory for this objective by flows, i.e., mathematical combinatorics, or mathematics over graphs, which is an appropriated way for understanding the reality of a thing because it is complex, even contradictory. This book collects my mainly papers on mathematics with reality of a thing from 2007 – 2017 and most of them are the plenary or invited reports in international conferences.
Research Interests:
There are 2 contradictory views on our world, i.e., continuous or discrete, which results in that only partially reality of a thing T can be understood by one of continuous or discrete mathematics because of the uni-versality of... more
There are 2 contradictory views on our world, i.e., continuous or discrete, which results in that only partially reality of a thing T can be understood by one of continuous or discrete mathematics because of the uni-versality of contradiction and the connection of things in the nature, just as the philosophical meaning in the story of the blind men with an elephant.
Research Interests:
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Research Interests:
Actually, different views result in different models on things in the universe. We usually view a microcosmic object to be a geometrical point and get into the macrocosmic for finding the truth, particularly the universe which results in... more
Actually, different views result in different models on things in the universe. We usually view a microcosmic object to be a geometrical point and get into the macrocosmic for finding the truth, particularly the universe which results in a topological skeleton or complex network. Thus, all the known is local by ourselves and we always apply a local knowledge on the global. Whether a local knowledge can applies to things without boundary? The answer is negative because we can not get the global conclusion only by a local knowledge in logic. Such a fact implies also that our knowledge on a thing maybe only true locally. Can we hold on the reality of all things in the universe globally? The answer is uncertain for the limitation or local understanding of human beings on things in the universe which naturally causes the science's dilemma: it gives the knowledge on things but locally or partially in the universe. Then, how can we globally hold on the reality of things in the universe? And what is the right way for applying scientific conclusions, i.e., technology? Clearly, different answers on such questions lead to different sciences with applications, maybe improper to the universe. However, if we all conform to a criterion, i.e., the coexistence of human beings with that of the nature, we will consciously review science with that of applications and get a right orientation on science's development.
Research Interests:
All issues of international Journal of Mathematical Combinatorics (ISSN 1937-1055) can be download freely on the website of Academy of Mathematical Combinatorics & Applications (AMCA) following: www.mathcombin.com on the column... more
All issues of international Journal of Mathematical Combinatorics (ISSN 1937-1055) can be download freely on the website of Academy of Mathematical Combinatorics & Applications (AMCA) following: www.mathcombin.com on the column International J.Math.Combin. form its founded issue in 2007 to the last issue Vol.4,2015.
Research Interests:
Proceedings of the
International Conference on Discrete Mathematics and its Applications, Manonmaniam Sundaranar University, January 18-21, 2018.
International Conference on Discrete Mathematics and its Applications, Manonmaniam Sundaranar University, January 18-21, 2018.