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A Smarandache multi-space is a union of n different spaces equippedwith different structures for an integer n 2, which can be used for systems both innature or human beings. This textbook introduces Smarandache multi-spaces such asthose of algebraic multi-spaces, including graph multi-spaces, multi-groups, multi-rings,multi-fields, vector multi-spaces, geometrical multi-spaces, particularly map geometrywith or without boundary, pseudo-Euclidean geometry on Rn, combinatorial Euclideanspaces, combinatorial manifolds, topological groups and topological multi-groups, combinatorialmetric spaces, ¿ ¿ ¿, etc. and applications of Smarandache multi-spaces, particularlyto physics, economy and epidemiology. In fact, Smarandache multi-spacesunderlying graphs are an important systematically notion for scientific research in 21stcentury. This book can be applicable for graduate students in combinatorics, topologicalgraphs, Smarandache geometry, physics and macro-economy as a textbook.
A thing is complex, and hybrid with other things sometimes. Then, what is the reality of a thing? 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 maybe local or gradual, not the reality of a thing. Hence, to hold on the reality of things is the main objective of science in the history of human development.
Papers on Mathematics on Non-Mathematics: A Combinatorial Contribution, Fuzzy Cosets and Normal Subgroups and Smarandache Fuzzy Algebra, Smarandache radio mean number, Smarandache friendly index number, Non-Hamiltonian Cubic Planar 3-Connected Graphs, Smarandachely odd sequential labeling, Smarandachely near m-labeling, Smarandachely near m-mean graph, Smarandachely k-dominator coloring, semi-entire equitable dominating graph, etc.
The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences..
Papers on Smarandache Lattice and Pseudo Complement, Smarandache’s Conjecture on Consecutive Primes, Signed Domatic Number of Directed Circulant Graphs, Generalized Quasi-Kenmotsu Manifolds, Geometry on Non-Solvable Equations-A Review on Contradictory Systems, and other topics. Contributors: Octavian Cira, Linfan Mao, N. Kannappa, K. Suresh, F. Smarandache, M. Ali, A. Raheem, A. Q. Baig, M. Javaid, Barnali Laha, Arindam Bhattacharyya, and others.
The Mathematical Combinatorics (International Book Series) is a fully refereed international book series, 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.
The International J. Mathematical Combinatorics is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.
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 Acade- my 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 ow GL 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.