*Structural Solvability and Controllability*

Author: Kazuo Murota

Publisher: Springer Science & Business Media

ISBN: 3642615864

Category: Mathematics

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### Systems Analysis by Graphs and Matroids

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.

### Matrices and Matroids for Systems Analysis

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

### Decentralized Control of Complex Systems

This book explores optimization, output feedback, manipulative power of graphs, overlapping decompositions and the underlying inclusion principle, and reliability design. An appendix provides efficient graph algorithms. 1991 edition.

### Discrete Images, Objects, and Functions in Zn

The author, who is a well-known expert in the field, presents important new research which generalizes the currently used two-dimensional theory to n dimensions. Voss' book is an indispensable source of information for all those who are involved in the design, implementation, and application of mathematically sound algorithms in image processing; it is written for engineers, mathematicians, and computer scientists.

### Combinatorial and Graph-Theoretical Problems in Linear Algebra

This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph~theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis.

### Moderne Algebra

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

### Graphs, hypergraphs and block systems

### Design and Analysis of Approximation Algorithms

This book is intended to be used as a textbook for graduate students studying theoretical computer science. It can also be used as a reference book for researchers in the area of design and analysis of approximation algorithms. Design and Analysis of Approximation Algorithms is a graduate course in theoretical computer science taught widely in the universities, both in the United States and abroad. There are, however, very few textbooks available for this course. Among those available in the market, most books follow a problem-oriented format; that is, they collected many important combinatorial optimization problems and their approximation algorithms, and organized them based on the types, or applications, of problems, such as geometric-type problems, algebraic-type problems, etc. Such arrangement of materials is perhaps convenient for a researcher to look for the problems and algorithms related to his/her work, but is difficult for a student to capture the ideas underlying the various algorithms. In the new book proposed here, we follow a more structured, technique-oriented presentation. We organize approximation algorithms into different chapters, based on the design techniques for the algorithms, so that the reader can study approximation algorithms of the same nature together. It helps the reader to better understand the design and analysis techniques for approximation algorithms, and also helps the teacher to present the ideas and techniques of approximation algorithms in a more unified way.

### Hybrid Graph Theory and Network Analysis

First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved.

### Catalog of National Bureau of Standards Publications, 1966-1976

### Catalog of National Bureau of Standards Publications, 1966-1976: pt. 1-2. Citations and abstracts

### Optimal Structural Analysis

This second edition of the highly acclaimed and successful first edition, deals primarily with the analysis of structural engineering systems, with applicable methods to other types of structures. The concepts presented in the book are not only relevant to skeletal structures but can equally be used for the analysis of other systems such as hydraulic and electrical networks. The book has been substantially revised to include recent developments and applications of the algebraic graph theory and matroids.

### Matroid Theory and Its Applications

Lectures: T.H. Brylawski: The Tutte polynomial.- D.J.A. Welsh: Matroids and combinatorial optimisation.- Seminars: M. Barnabei, A. Brini, G.-C. Rota: Un’introduzione alla teoria delle funzioni di Möbius.- A. Brini: Some remarks on the critical problem.- J. Oxley: On 3-connected matroids and graphs.- R. Peele: The poset of subpartitions and Cayley’s formula for the complexity of a complete graph.- A. Recski: Engineering applications of matroids.- T. Zaslavisky: Voltage-graphic matroids.

### Journal of Combinatorics, Information & System Sciences

### Pattern Recognition on Oriented Matroids

Pattern Recognition on Oriented Matroids covers a range of innovative problems in combinatorics, poset and graph theories, optimization, and number theory that constitute a far-reaching extension of the arsenal of committee methods in pattern recognition. The groundwork for the modern committee theory was laid in the mid-1960s, when it was shown that the familiar notion of solution to a feasible system of linear inequalities has ingenious analogues which can serve as collective solutions to infeasible systems. A hierarchy of dialects in the language of mathematics, for instance, open cones in the context of linear inequality systems, regions of hyperplane arrangements, and maximal covectors (or topes) of oriented matroids, provides an excellent opportunity to take a fresh look at the infeasible system of homogeneous strict linear inequalities – the standard working model for the contradictory two-class pattern recognition problem in its geometric setting. The universal language of oriented matroid theory considerably simplifies a structural and enumerative analysis of applied aspects of the infeasibility phenomenon. The present book is devoted to several selected topics in the emerging theory of pattern recognition on oriented matroids: the questions of existence and applicability of matroidal generalizations of committee decision rules and related graph-theoretic constructions to oriented matroids with very weak restrictions on their structural properties; a study (in which, in particular, interesting subsequences of the Farey sequence appear naturally) of the hierarchy of the corresponding tope committees; a description of the three-tope committees that are the most attractive approximation to the notion of solution to an infeasible system of linear constraints; an application of convexity in oriented matroids as well as blocker constructions in combinatorial optimization and in poset theory to enumerative problems on tope committees; an attempt to clarify how elementary changes (one-element reorientations) in an oriented matroid affect the family of its tope committees; a discrete Fourier analysis of the important family of critical tope committees through rank and distance relations in the tope poset and the tope graph; the characterization of a key combinatorial role played by the symmetric cycles in hypercube graphs. Contents Oriented Matroids, the Pattern Recognition Problem, and Tope Committees Boolean Intervals Dehn–Sommerville Type Relations Farey Subsequences Blocking Sets of Set Families, and Absolute Blocking Constructions in Posets Committees of Set Families, and Relative Blocking Constructions in Posets Layers of Tope Committees Three-Tope Committees Halfspaces, Convex Sets, and Tope Committees Tope Committees and Reorientations of Oriented Matroids Topes and Critical Committees Critical Committees and Distance Signals Symmetric Cycles in the Hypercube Graphs

### Graphs

This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.

### The Design and Analysis of Algorithms

The design and analysis of algorithms is one of the two essential cornerstone topics in computer science (the other being automata theory/theory of computation). Every computer scientist has a copy of Knuth's works on algorithms on his or her shelf. Dexter Kozen, a researcher and professor at Cornell University, has written a text for graduate study of algorithms. This will be an important reference book as well as being a useful graduate-level textbook.

### Submodular Functions and Optimization

The importance of submodular functions has been widely recognized in recent years in combinatorial optimization. This is the first book devoted to the exposition of the theory of submodular functions from an elementary technical level to an advanced one. A unifying view of the theory is shown by means of base polyhedra and duality for submodular and supermodular systems. Among the subjects treated are: neoflows (submodular flows, independent flows, polymatroidal flows), submodular analysis (submodular programs, duality, Lagrangian functions, principal partitions), nonlinear optimization with submodular constraints (lexicographically optimal bases, fair resource allocation). Special emphasis is placed on the constructive aspects of the theory, which lead to practical, efficient algorithms.

### Submodular Functions and Optimization

It has widely been recognized that submodular functions play essential roles in efficiently solvable combinatorial optimization problems. Since the publication of the 1st edition of this book fifteen years ago, submodular functions have been showing further increasing importance in optimization, combinatorics, discrete mathematics, algorithmic computer science, and algorithmic economics, and there have been made remarkable developments of theory and algorithms in submodular functions. The 2nd edition of the book supplements the 1st edition with a lot of remarks and with new two chapters: "Submodular Function Minimization" and "Discrete Convex Analysis." The present 2nd edition is still a unique book on submodular functions, which is essential to students and researchers interested in combinatorial optimization, discrete mathematics, and discrete algorithms in the fields of mathematics, operations research, computer science, and economics. Key features: - Self-contained exposition of the theory of submodular functions. - Selected up-to-date materials substantial to future developments. - Polyhedral description of Discrete Convex Analysis. - Full description of submodular function minimization algorithms. - Effective insertion of figures. - Useful in applied mathematics, operations research, computer science, and economics. - Self-contained exposition of the theory of submodular functions. - Selected up-to-date materials substantial to future developments. - Polyhedral description of Discrete Convex Analysis. - Full description of submodular function minimization algorithms. - Effective insertion of figures. - Useful in applied mathematics, operations research, computer science, and economics.

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*Structural Solvability and Controllability*

Author: Kazuo Murota

Publisher: Springer Science & Business Media

ISBN: 3642615864

Category: Mathematics

Page: 284

View: 2520

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Publisher: Springer Science & Business Media

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Page: 483

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ISBN: 1461383544

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Publisher: Springer-Verlag

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*proceedings of the Symposium on Combinatorial Analysis held in Zielona Góra, September, 1976*

Author: Zdzisław Skupień,Wyższa Szkoła Inżynierska w Zielonej Górze. Instytut Matematyki i Fizyki

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Publisher: John Wiley & Sons

ISBN: 0470033290

Category: Mathematics

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*Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna (Como), Italy, August 24 - September 2, 1980*

Author: A. Barlotti

Publisher: Springer Science & Business Media

ISBN: 9783642111105

Category: Mathematics

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*Theory and Algorithms*

Author: K. Thulasiraman,M. N. S. Swamy

Publisher: John Wiley & Sons

ISBN: 1118030257

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Page: 480

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