The First International Conference on Smarandache Multispace and Multistructure was organized by Prof. Linfan Mao, and i...
Proceedings of the First International Conference on Smarandache Multispace & Multistructure
Edited by Linfan Mao
Beijing University of Civil Engineering and Architecture The Education Publisher Inc. July, 2013
Proceedings of the First International Conference On Smarandache Multispace & Multistructures (28-30 June 2013, Beijing, China) Edited by Linfan Mao
Beijing University of Civil Engineering and Architecture The Education Publisher Inc. July, 2013
This proceedings can be ordered from:
The Educational Publisher Inc. 1313 Chesapeake Ave. Columbus, Ohio 43212, USA Toll Free: 1-866-880-5373 E-mail:
[email protected] Website: www.EduPublisher.com
Peer Reviewers: Said Broumi, University of Hassan II Mohammedia, Hay El Baraka Ben M’sik, Casablanca, Morocco. Linfan Mao, Academy of Mathematics and Systems, Chinese Academy of Sciences, Beijing 100190, P.R.China. Y.P.Liu, Department of Applied Mathematics, Beijing Jiaotong University, Beijing 100044, P.R.China. Jun Zhang, School of Economic and Management Engineering, Beijing University of Civil Engineering and Architecture, P.R.China. Ovidiu Ilie Sandru, Mathematics Department, Polytechnic University of Bucharest, Romania. W. B. Vasantha Kandasamy, Indian Institute of Technology, Chennai, Tamil Nadu, India.
Copyright 2013 Beijing University of Civil Engineering and Architecture, The Education Publisher Inc., The Editor, and The Authors for their papers.
Many books can be downloaded from the following Digital Library of Science: http://fs.gallup.unm.edu/eBooks-otherformats.htm
ISBN: 978-1-59973-229-9 Printed in America
Contents The First International Conference on Smarandache Multispace and Multistructure was held in China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04 The First International Conference on Smarandache Multispace and Multistructure was held in China (In Chinese) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 06 S-Denying a Theory By Florentin Smarandache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08
Smarandache Geometry A geometry with philosophical notion By Linfan Mao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Neutrosophic Transdisciplinarity — Multi-Space & Multi-Structure By Florentin Smarandache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Non-Solvable Equation Systems with Graphs Embedded in Rn By Linfan Mao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Some Properties of Birings By A.A.A.Agboola and B.Davvaz . . . . . . . . . . ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 Surface Embeddability of Graphs via Tree-travels By Yanpei Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Surface Embeddability of Graphs via Joint Trees By Yanpei Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Surface Embeddability of Graphs via Reductions By Yanpei Liu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Recent Developments in Regular Maps By Shaofei Du . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Smarandache Directionally n-Signed Graphs A Survey By P.Siva Kota Reddy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Neutrosophic Diagram and Classes of Neutrosophic Paradoxes, Or To The OuterLimits of Science By Florentin Smarandache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Neutrosophic Groups and Subgroups By Agboola A.A.A., Akwu A.D. and Oyebo Y.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Neutrosophic Rings I By Agboola A.A.A., Akinola A.D. and Oyebola O.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Neutrosophic Degree of a Paradoxicity By Florentin Smarandache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Appendix: The Story of Mine with That of Multispaces (In Chinese) By Linfan Mao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Proceedings of Conference on Multispace & Multistructure
June 28-30, 2013, Beijing
The First International Conference on Smarandache Multispace and Multistructure was held in China In recent decades, Smarandache’s notions of multispace and multistructure were widely spread and have shown much importance in sciences around the world. Organized by Prof.Linfan Mao, a professional conference on multispaces and multistructures, named the First International Conference on Smarandache Multispace and Multistructure was held in Beijing University of Civil Engineering and Architecture of P. R. China on June 28-30, 2013, which was announced by American Mathematical Society in advance.
The Smarandache multispace and multistructure are qualitative notions, but both can be applied to metric and non-metric systems. There were 46 researchers haven taken part in this conference with 14 papers on Smarandache multispaces and geometry, birings, neutrosophy, neutrosophic groups, regular maps and topological graphs with applications to non-solvable equation systems.
Prof.Yanpei Liu reports on topological graphs 1 http://fs.gallup.unm.edu/Multispace.htm
5
News on Conference
Prof.Linfan Mao reports on non-solvable systems of differential equations with graphs in Rn
Prof.Shaofei Du reports on regular maps with developments Applications of Smarandache multispaces and multistructures underline a combinatorial mathematical structure and interchangeability with other sciences, including gravitational fields, weak and strong interactions, traffic network, etc. All participants have showed a genuine interest on topics discussed in this conference and would like to carry these notions forward in their scientific works.
Proceedings of Conference on Multispace & Multistructure
June 28-30, 2013, Beijing
83 Smarandache 50=2-;916/?4 Z_)vpIjU`ymK{6uEhWx &_\ yL-,umKO `N\12HR+dGAUy))mK dy))mK_\YU1b dYKzM %H`' e#;JPov.gÆPo>>B℄D" [L VK℄Bj |BKr'|KrC `e Smarandache B.Æ-Bu | iq i 2013 ) 6 s 28 Nu"[L VK*;AA #;|Krr >R^Po r>( Po ℄ Kr |.L{hPob5P℄'O` [Y ~OX O` Abstract:
What is a multispace? And what is the mathematical combinatorics? Both
of them are the philosophic notions for scientific research. In where, the mathematical combinatorics is such maltispaces underlying combinatorial structures in topological spaces. So these notions are useful approaches for determining the behavior of things in the world by mathematics. I review the multispaces that I known, particularly, the mathematical combinatorics in this paper, and explain why it is important for one understanding things in the world. Some interesting things in preparing the First international Conference on Smarandache multispace and Multistructure are also included.
#jK-))Kj*juBV`9R')) |`Hu.g . g,SnSx}℄f))K{6O`!U))K`9#(ja )#SU u{lPÆK" I_W^GRH $M 3WK%a\Dp_k 3)'HÆt Æ" oA#`.g,! 1_N\R^ Q/'Q{6VVg" *#` .g,O`/4fVYyW
