Download or read book On the Unboundedness of the Set of Integral Points in a Polyhedral Region written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1974 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integer Points in Polyhedra written by Alexander Barvinok and published by European Mathematical Society. This book was released on 2008 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.
Download or read book Research in Progress written by and published by . This book was released on 1975 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Decomposition in Integer Programming written by Stanford University. Department of Operations Research. Systems Optimization Laboratory and published by . This book was released on 1976 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Resource Decomposition: A Conceptual Outline; Branching in the Rudimentary Branch-and-Bound Algorithm; Computing Bounds: Single Linking Constraint Case; Computing Bounds: Multiple Linking Constraints Case; Computational Results; and Conclusions, Extensions, and Areas for Future Research.
Download or read book Generalized Convexity Generalized Monotonicity and Applications written by Andrew Eberhard and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.
Download or read book Integer Points in Polyhedra Geometry Number Theory Representation Theory Algebra Optimization Statistics written by Matthias Beck and published by American Mathematical Soc.. This book was released on 2008 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a cross section of recent advances connected to lattice-point questions. Topics range from commutative algebra to optimization, from discrete geometry to statistics, from mirror symmetry to geometry of numbers. The book is suitable for resarchers and graduate students interested in combinatorial aspects of the above fields.
Download or read book Integral Convex Polyhedra and an Approach to Integralization written by Murray Edelberg and published by . This book was released on 1970 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many combinatorial optimization problems may be formulated as integer linear programming problems, that is, problems of the form: given a convex polyhedron P contained in the non-negative orthant of n-dimensional space, find an integer point in P which maximizes (or minimizes) a given linear objective function. Well known linear programming methods would suffice to solve such a problem if: (1) P is an integral convex polyhedron, or (2) P is transformed into the integral convex polyhedron that is the convex hull of the set of integer points in P, a process which is called integralization. This thesis provides some theoretical results concerning integral convex polyhedra and the process of integralization. Necessary and sufficient conditions for a convex polyhedron P to have the integral property are derived in terms of the system of linear inequalities defining P.A number-theoretic method for integralizing two-dimensional convex polyhedra is developed which makes use of a generalization of the division theorem for integers. The method is applicable to a restricted class of higher dimensional polyhedra as well. (Author).
Download or read book Status of Energy Policy Research at Stanford written by Stanford University. Institute for Energy Studies and published by . This book was released on 1980 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Index written by and published by . This book was released on 1975 with total page 1262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computing the Continuous Discretely written by Matthias Beck and published by Springer. This book was released on 2015-11-14 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: This richly illustrated textbook explores the amazing interaction between combinatorics, geometry, number theory, and analysis which arises in the interplay between polyhedra and lattices. Highly accessible to advanced undergraduates, as well as beginning graduate students, this second edition is perfect for a capstone course, and adds two new chapters, many new exercises, and updated open problems. For scientists, this text can be utilized as a self-contained tooling device. The topics include a friendly invitation to Ehrhart’s theory of counting lattice points in polytopes, finite Fourier analysis, the Frobenius coin-exchange problem, Dedekind sums, solid angles, Euler–Maclaurin summation for polytopes, computational geometry, magic squares, zonotopes, and more. With more than 300 exercises and open research problems, the reader is an active participant, carried through diverse but tightly woven mathematical fields that are inspired by an innocently elementary question: What are the relationships between the continuous volume of a polytope and its discrete volume? Reviews of the first edition: “You owe it to yourself to pick up a copy of Computing the Continuous Discretely to read about a number of interesting problems in geometry, number theory, and combinatorics.” — MAA Reviews “The book is written as an accessible and engaging textbook, with many examples, historical notes, pithy quotes, commentary integrating the mate rial, exercises, open problems and an extensive bibliography.” — Zentralblatt MATH “This beautiful book presents, at a level suitable for advanced undergraduates, a fairly complete introduction to the problem of counting lattice points inside a convex polyhedron.” — Mathematical Reviews “Many departments recognize the need for capstone courses in which graduating students can see the tools they have acquired come together in some satisfying way. Beck and Robins have written the perfect text for such a course.” — CHOICE
Download or read book Government Reports Annual Index written by and published by . This book was released on 1985 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Management Science written by and published by . This book was released on 1976 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes special issues: The Professional series in the management sciences.
Download or read book Operations Research Proceedings 2003 written by Dino Ahr and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers referring to lectures presented at the symposium "Operations Research 2003" (OR03) held at the Ruprecht Karls-Universitiit Heidelberg, September 3 - 5, 2003. This international con ference took place under the auspices of the German Operations Research So ciety (GOR) and of Dr. Erwin Teufel, prime minister of Baden-Wurttemberg. The symposium had about 500 participants from countries all over the world. It attracted academians and practitioners working in various field of Opera tions Research and provided them with the most recent advances in Opera tions Research and related areas in Economics, Mathematics, and Computer Science. The program consisted of 4 plenary and 13 semi-plenary talks and more than 300 contributed papers selected by the program committee to be presented in 17 sections. Due to a limited number of pages available for the proceedings volume, the length of each article as well as the total number of accepted contributions had to be restricted. Submitted manuscripts have therefore been reviewed and 62 of them have been selected for publication. This refereeing procedure has been strongly supported by the section chairmen and we would like to express our gratitude to them. Finally, we also would like to thank Dr. Werner Muller from Springer-Verlag for his support in publishing this proceedings volume.
Download or read book Multidimensional Signals Circuits and Systems written by Krzysztof Galkowski and published by CRC Press. This book was released on 2001-05-10 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although research on general multidimensional systems theory has been developing rapidly in recent years, this is the first research text to appear on the subject since the early 1980s. The text describes the current state of the art nD systems and sets out a number of open problems, and gives several different perspectives on the subject. It presents a number of different solutions to major theoretical problems as well as some interesting practical results. The book comprises of a selection of plenary and other lectures given at The First International Workshop on Multidimensional (nD) Systems (NDS-98) held in 1998 in Poland, and is written by leading world specialists in the field.
Download or read book Government Reports Announcements written by and published by . This book was released on 1974 with total page 1210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Government Reports Announcements Index written by and published by . This book was released on 1974 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial Reciprocity Theorems An Invitation to Enumerative Geometric Combinatorics written by Matthias Beck and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial reciprocity is a very interesting phenomenon, which can be described as follows: A polynomial, whose values at positive integers count combinatorial objects of some sort, may give the number of combinatorial objects of a different sort when evaluated at negative integers (and suitably normalized). Such combinatorial reciprocity theorems occur in connections with graphs, partially ordered sets, polyhedra, and more. Using the combinatorial reciprocity theorems as a leitmotif, this book unfolds central ideas and techniques in enumerative and geometric combinatorics. Written in a friendly writing style, this is an accessible graduate textbook with almost 300 exercises, numerous illustrations, and pointers to the research literature. Topics include concise introductions to partially ordered sets, polyhedral geometry, and rational generating functions, followed by highly original chapters on subdivisions, geometric realizations of partially ordered sets, and hyperplane arrangements.
