Series on Knots and Everything
250pp Jun 2018
ISBN: 978-981-3233-52-2 (hardcover)
In this richly illustrated book, Dr Jorma Kyppo explores the history of board games dating back to Ancient Egypt, Mesopotamia, India and China. He provides a description of the evolution and various interpretations of chess. Furthermore, the book offers the study of the old Celtic and Viking board games and the old Hawaiian board game Konane, as well as a new hypothesis about the interpretation of the famous Cretan Phaistos Disk. Descriptions of several chess variations, including some highlights of the game theory and tiling in different dimensions, are followed by a multidimensional symmetrical n-person strategy game model, based on chess. Final chapter (Concluding remarks) offers the new generalizations of the Euler-Poincare's Characteristic, Pi and Fibonacci sequence.
Game Theory and N-Person Games
Tiling in Different Dimensions
Schlafli Symbol
Honeycombs
Kissing Number
Packing Problems
The History and Prehistory of Chess
Mehen, An Ancient n-Person Game
The Royal Game of Ur
Ashtapada
Hnefatafl, Latrunculi and Petteia
Go and Liubo
Konane
Chaturaji, the Four-Person Chaturanga
Xiangqi, Chinese Chess
Shogi, the Japanese Chess
Evolution of Chess
Was the Phaistos Disk a Game?
Later Chess Variations
Ancient N-Handed Chess Games
Seven Armies Game
Marinelli's Three-Handed Chess
A Hexagonal Three-Person Chess by Siegmund Wellisch
Basic Model of Universal Chess
Trichess
Chess without a Board
Extensions of Universal Chess
Extensions of Chess on Large Square Boards
The Extension to Dimension N
Symmetric N-person Chess
A Model Based on the Multinomial Formula
Embedding Chess in the Simplex Platform
The Symmetric 4-Player Model on 3-Simplex Board
Symmetric 5-Player Model on 4-Simplex Board
The Symmetric 6-Player Model on 5-Simplex Board
Symmetric n-Player Model on (n?1)-Simplex Board
Multi-Simplex Chess
Concluding Remarks
The Number of a Graph
Strategy Networks of Small Chess-Like Games
Generalization of Euler?Poincare Characteristic
Odd and Even Euclidean Dimensions
Generalized Pi
Generalizations of the Fibonacci Sequence
Readership: Researchers in combinatorics, complex manifolds and topology, game theory.
450pp Jul 2018
ISBN: 978-981-3238-30-5 (hardcover)
The book provides exercises and problems with solutions in Galois Theory and its applications: Finite fields, Permutation polynomials, Derivations and Algebraic number Theory.
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Polynomials, Fields, Generalities
Algebraic Extention, Algebraic Closure
Separability, Inseparability
Normal Extensions
Galois Extensions, Galois Groups
Finite Fields
Permutation Polynomials
Transcendental Extensions, Linearly Disjoint Extensions, Luroth's Theorem
Multivariate Polynomials
Integral Elements, Algebraic Number Theory
Derivations
Readership: Undergraduate and graduate students in Galois group theory.
Series on Knots and Everything
500pp Nov 2018
ISBN: 978-981-3237-39-1 (hardcover)
Focused on concrete examples and constructions and using extensive computer generated three-dimensional graphics, this book serves as a guide to methods and examples of higher dimensional knotting. The book has modest mathematical requirements, has been written with non-specialists in mind and contains considerable background information.
Knotting whether fanciful or practical has been of interest to many ? from sculptors to sailors and in more modern times of interest to mathematicians, biologists and physicists as well. Spaces of dimensions greater than three are also of widespread interest in the arts, sciences and engineering as well as mathematics. Knotting and linking of circles can aid us to understand three dimensionality. So, it is natural to consider knotting in order to understand higher dimensions.
Knotting in 4-dimensional space involves surfaces ? spheres, tori, Klein bottles and others while in five dimensions one looks primarily at similar tangling and self-tangling of three dimensional objects.
Visualization is an important part of this journey and techniques for higher dimensions, especially in 4-dimensional space, are discussed in detail.
Introduction: Background Including Classical Knots and Links in 3-Space and Basics of Geometric Topology
Why Knotting Surfaces in Four Dimensions is the "Right" Way to Generalize Knotting of Circles in Three Dimensions
How to Visualize Surfaces in 4-Dimensional Space
Wild Knotting and the Division of Knot Theory Divisions into Topological, Locally Flat, Smooth and Piecewise Linear Knottings
Examples and Construction Methods for Knottings of Spheres, Torii, Projective Planes, Klein Bottles, etc.
How to Tell If Two Knottings are Equivalent ? "Motions" and "Moves" of Surfaces in 4-Space
Higher Dimensional Knotting (5-Space and Higher Dimensions)
Some Things Get Easy, Some Get Hard
High Dimensional Lattice Knots
Readership:
Graduate students and researchers in geometric topology, manifolds and cell complexes, scientists and engineers who want a concrete introduction to high dimensional construction and visualization.
300pp Jun 2018
ISBN: 978-981-3235-00-7 (hardcover)
The book is devoted to limit theorems for nonconventional sums and arrays. Asymptotic behavior of such sums were first studied in ergodic theory but recently it turned out that main limit theorems of probability theory such as central, local and Poisson limit theorems can also be obtained for such expressions. In order to obtain sufficiently general local limit theorem we develop also thermodynamic formalism type results for random complex operators which is one of novelties of the book.
Nonconventional Limit Theorems:
Stein's Method for Nonconventional Sums
Local Limit Theorem
Nonconventional Arrays
Random Transformations
Thermodynamic Formalism for Random Complex Operators:
Ruelle-Perron-Frobenius Theorem Via Cone Contractions
Application to Random Locally Expanding Covering Maps
Pressure, Asymptotic Variance and Complex Gibbs Measures
Application to Random Complex Integral Operators
Fiberwise Limit Theorems
Readership:
vanced graduate students and researchers in probability theory and stochastic processes and dynamical systems and ergodic theory.
300pp Nov 2018
ISBN: 978-981-3238-36-7 (hardcover)
According to the fundamental concept "adjunctions" in category theory, the Micro and Macro in nature can be connected in a coherent way, which constitutes quite an effective theoretical and mathematical machinery that has not been commonly recognized. On the basis of this concept, many important problems in physics and mathematics can be viewed from quite different and fresh angles, which facilitate deep understanding and the satisfactory solution of those problems.
Introduction: What is Quantum Theory?
Quantum-Classical Correspondence/ Micro-Macro Duality/ Quadrality Scheme
Applications of Micro-Macro Duality & Quadrality Scheme
Micro-Macro Duality & Sector Structures
Quantum Field Theory: Scattering Processes of Quantum Fields & Micro-Macro Duality
Towards New Horizons
Readership:
Graduate students and researchers in quantum theory, mathematical physics, neural networks, pattern recognition.