Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics)

( A matroid is an abstract mathematical structure that ca...)

A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "…The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006

http://www.amazon.com/gp/product/3540660240/?tag=2022091-20

Discrete Convex Analysis (Monographs on Discrete Math and Applications) (Monographs on Discrete Mathematics and Applications)

(Discrete Convex Analysis is a novel paradigm for discrete...)

Discrete Convex Analysis is a novel paradigm for discrete optimization that combines the ideas in continuous optimization (convex analysis) and combinatorial optimization (matroid/submodular function theory) to establish a unified theoretical framework for nonlinear discrete optimization. The study of this theory is expanding with the development of efficient algorithms and applications to a number of diverse disciplines like matrix theory, operations research, and economics. This self-contained book is designed to provide a novel insight into optimization on discrete structures and should reveal unexpected links among different disciplines. It is the first and only English-language monograph on the theory and applications of discrete convex analysis. Discrete Convex Analysis provides the information that professionals in optimization will need to "catch up" with this new theoretical development. It also presents an unexpected connection between matroid theory and mathematical economics and expounds a deeper connection between matrices and matroids than most standard textbooks.

http://www.amazon.com/gp/product/0898715407/?tag=2022091-20

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory (Applied Mathematical Sciences)

(Most physical systems lose or gain stability through bifu...)

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

http://www.amazon.com/gp/product/1461426650/?tag=2022091-20

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics)

(Recent technology involves large-scale physical or engine...)

Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.

http://www.amazon.com/gp/product/3540176594/?tag=2022091-20

Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory (Applied Mathematical Sciences)

(This book provides a modern investigation into the bifurc...)

This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods--based on asymptotic, probabilistic, and group-theoretic standpoints--are used to examine experimental and computational data from numerous examples (e.g., soil, sand, kaolin, concrete, domes, etc.). Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.

http://www.amazon.com/gp/product/0387954090/?tag=2022091-20

Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability (Algorithms and Combinatorics)

(Recent technology involves large-scale physical or engine...)

Recent technology involves large-scale physical or engineering systems consisting of thousands of interconnected elementary units. This monograph illustrates how engineering problems can be solved using the recent results of combinatorial mathematics through appropriate mathematical modeling. The structural solvability of a system of linear or nonlinear equations as well as the structural controllability of a linear time-invariant dynamical system are treated by means of graphs and matroids. Special emphasis is laid on the importance of relevant physical observations to successful mathematical modelings. The reader will become acquainted with the concepts of matroid theory and its corresponding matroid theoretical approach. This book is of interest to graduate students and researchers.

http://www.amazon.com/gp/product/0387176594/?tag=2022091-20

Matrices and Matroids for Systems Analysis (Algorithms and Combinatorics) 2000 edition by Murota, Kazuo (2000) Hardcover

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