KOGAION REVIEW
romanian literary monthly

Florentin Smarandache’s new books

1) “Quantization in Astrophysics, Brownian Motion, and Supersymmetry”, editors: F. Smarandache, V. Christianto, 516 pages, MathTiger, Chennai, Tamil Nadu, India, $56.65, 2007, ISBN: 978-81-902190-9-9.

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years.

Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the arguments presented in this book are theoretical, nonetheless we recommend further observation in order to verify or refute the propositions described herein. It is of our hope that this volume could open a new chapter in our knowledge on the formation and structure of Astrophysical systems.

The present book is also intended for young physics and math fellows who perhaps will find the arguments

described here are at least worth pondering.

Papers by A. Rubcic, J. Rubcic, M. Pitkanen, Fu Yuhua, C. Castro, J. Mahecha, M. Pavsic, J. A. Nieto, J. F. Gonzalez, D. L. Rapoport, Gao Shan, M. Pereira, A. Yefremov, F. Smarandache, V. Christianto.

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2)

“Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists”, by W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral, 352 p., 2007, Los Angeles, $40.00.

This book gives the basic notions of fuzzy matrix theory and its applications to simple models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of mathematicians has conditioned students of sociology in such a manner that they averse to using mathematical tools.

Six simple types of fuzzy models that make use of fuzzy matrices are given. These models are distinct because they are time dependent and can even be used for statistical data.

The Fuzzy Cognitive Maps model gives the hidden pattern. Fuzzy Relational Maps model not only gives the inter-relations between two sets of disjoint attributes. The Bidirectional Associative Memories model analyzes data depending on the time-period while the Fuzzy Associative memories model can give the gradation of importance of each attribute. Finally, the Fuzzy Relational Equation model is capable of giving a solution closer to the redicted solution. All the methods are illustrated through elaborate examples of particular social problems.

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