Sums Of Even Powers Of Real Linear Forms
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Author | : Bruce Arie Reznick |
Publisher | : American Mathematical Soc. |
Total Pages | : 169 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : 0821825232 |
Download Sum of Even Powers of Real Linear Forms Book in PDF, Epub and Kindle
This work initiates a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms and the resulting implications in real algebraic geometry, number theory, combinatorics, functional analysis, and numerical analysis. The proofs utilize elementary techniques from linear algebra, convexity, number theory, and real algebraic geometry and many explicit examples and relevant historical remarks are presented.
Author | : Bruce Reznick |
Publisher | : |
Total Pages | : 155 |
Release | : 1992 |
Genre | : |
ISBN | : |
Download Sums of even powers of real linear forms Book in PDF, Epub and Kindle
Author | : Krishnaswami Alladi |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2013-08-13 |
Genre | : Mathematics |
ISBN | : 1461474884 |
Download Quadratic and Higher Degree Forms Book in PDF, Epub and Kindle
In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas. Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.
Author | : Anthony Iarrobino |
Publisher | : Springer |
Total Pages | : 365 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540467076 |
Download Power Sums, Gorenstein Algebras, and Determinantal Loci Book in PDF, Epub and Kindle
This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and algebraic geometry, including the theories of determinantal varieties, of classifying spaces of Gorenstein-Artin algebras, and of Hilbert schemes of zero-dimensional subschemes. Of the many concrete examples given, some are calculated with the aid of the computer algebra program "Macaulay", illustrating the abstract material. The final chapter considers open problems. This book will be of interest to graduate students, beginning researchers, and seasoned specialists. Prerequisite is a basic knowledge of commutative algebra and algebraic geometry.
Author | : Saugata Basu |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821828630 |
Download Algorithmic and Quantitative Real Algebraic Geometry Book in PDF, Epub and Kindle
Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ``Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.
Author | : Charles N. Delzell |
Publisher | : American Mathematical Soc. |
Total Pages | : 320 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821808044 |
Download Real Algebraic Geometry and Ordered Structures Book in PDF, Epub and Kindle
This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
Author | : Petter Brändén |
Publisher | : Springer Science & Business Media |
Total Pages | : 413 |
Release | : 2011-09-01 |
Genre | : Mathematics |
ISBN | : 3034801424 |
Download Notions of Positivity and the Geometry of Polynomials Book in PDF, Epub and Kindle
The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.
Author | : Jiawang Nie |
Publisher | : SIAM |
Total Pages | : 484 |
Release | : 2023-06-15 |
Genre | : Mathematics |
ISBN | : 1611977606 |
Download Moment and Polynomial Optimization Book in PDF, Epub and Kindle
Moment and polynomial optimization is an active research field used to solve difficult questions in many areas, including global optimization, tensor computation, saddle points, Nash equilibrium, and bilevel programs, and it has many applications. The author synthesizes current research and applications, providing a systematic introduction to theory and methods, a comprehensive approach for extracting optimizers and solving truncated moment problems, and a creative methodology for using optimality conditions to construct tight Moment-SOS relaxations. This book is intended for applied mathematicians, engineers, and researchers entering the field. It can be used as a textbook for graduate students in courses on convex optimization, polynomial optimization, and matrix and tensor optimization.
Author | : Lenore Blum |
Publisher | : Springer Science & Business Media |
Total Pages | : 456 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461207010 |
Download Complexity and Real Computation Book in PDF, Epub and Kindle
The classical theory of computation has its origins in the work of Goedel, Turing, Church, and Kleene and has been an extraordinarily successful framework for theoretical computer science. The thesis of this book, however, is that it provides an inadequate foundation for modern scientific computation where most of the algorithms are real number algorithms. The goal of this book is to develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing. Along the way, the authors consider such fundamental problems as: * Is the Mandelbrot set decidable? * For simple quadratic maps, is the Julia set a halting set? * What is the real complexity of Newton's method? * Is there an algorithm for deciding the knapsack problem in a ploynomial number of steps? * Is the Hilbert Nullstellensatz intractable? * Is the problem of locating a real zero of a degree four polynomial intractable? * Is linear programming tractable over the reals? The book is divided into three parts: The first part provides an extensive introduction and then proves the fundamental NP-completeness theorems of Cook-Karp and their extensions to more general number fields as the real and complex numbers. The later parts of the book develop a formal theory of computation which integrates major themes of the classical theory and which is more directly applicable to problems in mathematics, numerical analysis, and scientific computing.
Author | : Arthur Erdélyi |
Publisher | : American Mathematical Soc. |
Total Pages | : 60 |
Release | : 1957 |
Genre | : Airy functions |
ISBN | : 0821812254 |
Download Asymptotic Forms of Whittaker's Confluent Hypergeometric Functions Book in PDF, Epub and Kindle