October 2, 2017
ISBN 9781138402065
With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.
On Non-unitary Representations of the Rotation Group and Magnetic Monopoles. Generalized Derivations of Quantum Polynomials. Abelian Group Gradings on Simple Algebras. Groebner-Shirshov Basis for Lie Algebras. Classification of Solvable Three-Dimensional Lip-Triple Systems. Nonassociative Algebra Structures on Irreducible Representations of the Simple Lie Algebra. On Locally Finite Split Lie Triple Systems. On a Special Kind of Malcev Algebras. New Realizations of Hadronic Supersymmetry Based on Octonions. Application of Octonionic Algebras in Hadronic Physics. Application of Octonionic Algebras in Hardonic Physics. On Flexible Right-Nilalgebras Satisfying x(zy) = y(zx). Lie Algebras: Applications to the Classical Electromagnetic Fields. Helicity Basis and Parity. A New Look at the Freudenthal. On the Theory of Left Loops. Approximation of Locally Compact Groups by Finite Quasigroups. Some Classes of Nonassociative Algebras. Some Results on the Theory of Smooth Bol-Bruck Loops. A Nonzero Element of Degree 7 in the Center of the Free Alternative Algebra. The Identities of the Simple Non-Special Jordan Algebra. Ternary Derivations of Finite Dimensional Real Division Algebras. The Transformation Algebras of Bernstein Graph Algebras. On Composition, Quadratic, and some Triple Systems. Combinatorial Rank of a Frobenius-Lusztig Kernel. On Representations on Right Nilalgebras of Right Nilindex Four and Dimension Four. An Introduction to Associator Quantization. Prosymmetric Spaces. The Exponential Function and the Fundamental Theorem of Algebra for the Cayley Dickson Algebras. Dimension Filtration on Binary Systems. Right Alternative Bimodules. Some Applications of Quasigroups and Loops in Physics. Gravity within the Framework of Nonassociative Geometry. One-to-One Correspondence between Bi-Linear and Triple Product Algebras. Algebras satisfying Local Symmetric Triality Principle. Operads and Nonassociative Deformations. Representations of Quantum Algebras at Roots of 1. Algebras, Hyperalgebras, Nonassociative Bialgebras, and Loops. Algebraic Structures on Lie Algebras, Vinberg Algebras. Algebraic and Differential Structures in Renormalized Perturbation Quantum Field Theory. Survey on Smooth Quasigroups Development. On Kikkawa Spaces. Bol and Bruck Identities in Recent Research. New Example of a Simple Jordan Superalgebra with Associative Even Part. Unital Irreducible Representations of Small Simple Jordan Superalgebras. The Lie Product on the Lie Bialgebra Duals of the Witt and Virasoro Algebras. Derivations and Automorphisms of Free Algebras. On Derivations and Automorphisms of a Lie Algebra. Subrings of Finite Division Rings. Realizaiton of Finite Groups by Nets in Complex Projective Plane.
November 8, 2017
Textbook - 574 Pages - 89 B/W Illustrations
ISBN 9781138740914
Series: Textbooks in Mathematics
Focuses on techniques with requisite theory
Avoids emphasizing abstract vector spaces
Presents a unique chapter on separation of variables of partial differential equations
Emphasizes MATLAB use throughout
Includes several appendixes, including one of Poincare Bendixon theorem, as well as solutions
Elementary Differential Equations presents the standard material in a first course on di?erential equations, including all standard methods which have been a part of the subject since the time of Newton and the Bernoulli brothers. The emphasis in this book is on theory and methods and di?erential equations as a part of analysis.
Differential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented ?rst with theoretical considerations following. Essentially all proofs of the theorems used are included, making the book more useful as a reference.
The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values.
Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for ?nding solutions are included.
Preface; 1 Some Prerequisite Topics; I First Order Scalar Differential Equations, Methods; 2 The Idea Of A Differential Equation; 3 Homogeneous Linear Equations; 4 Nonhomogeneous Equations; 5 Laplace Transform Methods; III Series Methods For Scalar; 6 Power Series; 7 Power Series Methods; IV First Order Linear Systems; 8 First Order Systems Of Differential Equations, Theory; 9 Methods For First Order Systems; V Partial Differential Equations; 10 Boundary Value Problems And Fourier Series; 11 Some Famous Partial Differential Equations; VI Non-linear Systems Of O.D.E.; 12 Theory Of Ordinary Differential Equations; 13 Equilibrium Points And Limit Cycles; 14 The Center Manifold; Appendix A: Calculus Review 381; Appendix B Series, Appendix C Review Of Linear Algebra; Appendix D Theory Of Functions Of Many Variables; Appendix E Spectral Theory; Appendix F Linear Transformations; Appendix G Implicit Function Theorem; Appendix H The Jordan Curve Theorem; Bibliography; Index
November 6, 2017
Reference - 182 Pages
ISBN 9781138562240
This is the first book to examine the interplay between weakly stationary random fields and invariant subspaces
Reviews the current literature and presents
Presents applications to harmonic analysis
Develops the theory for random fields using special representations, such as Wold decompositions, etc
The first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory.
January 31, 2018
Reference - 234 Pages
ISBN 9781498729604
Series: Chapman & Hall/CRC Computer Science & Data Analysis
First book on Chain Event Graphs
Provides a new technology to address discrete asymmetric modelling
Provides a careful description of a new tool for probabilistic elicitation
Written by some major contributors to the development of this class of graphical models, Chain Event Graphs introduces a viable and straightforward new tool for statistical inference, model selection and learning techniques. The book extends established technologies used in the study of discrete Bayesian Networks so that they apply in a much more general setting
As the first book on Chain Event Graphs, this monograph is expected to become a landmark work on the use of event trees and coloured probability trees in statistics, and to lead to the increased use of such tree models to describe hypotheses about how events might unfold.
introduces a new and exciting discrete graphical model based on an event tree
focusses on illustrating inferential techniques, making its methodology accessible to a very broad audience and, most importantly, to practitioners
illustrated by a wide range of examples, encompassing important present and future applications
includes exercises to test comprehension and can easily be used as a course book
introduces relevant software packages
February 13, 2018
Reference
ISBN 9781138442641
Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of moving boundaries in fluid structure couple systems, arteries, shape stabilization level methods, family of moving geometries, and boundary control.
Using numerical analysis, the contributors examine the problems of optimal control theory applied to PDEs arising from continuum mechanics. The book presents several applications to electromagnetic devices, flow, control, computing, images analysis, topological changes, and free boundaries. It specifically focuses on the topics of boundary variation and control, dynamical control of geometry, optimization, free boundary problems, stabilization of structures, controlling fluid-structure devices, electromagnetism 3D, and inverse problems arising in areas such as biomathematics.
Free and Moving Boundaries: Analysis, Simulation and Control explains why the boundary control of physical systems can be viewed as a moving boundary control, empowering the future research of select algebraic areas.