Download or read book Geometry of Subanalytic and Semialgebraic Sets written by Masahiro Shiota and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real analytic sets in Euclidean space (Le. , sets defined locally at each point of Euclidean space by the vanishing of an analytic function) were first investigated in the 1950's by H. Cartan [Car], H. Whitney [WI-3], F. Bruhat [W-B] and others. Their approach was to derive information about real analytic sets from properties of their complexifications. After some basic geometrical and topological facts were established, however, the study of real analytic sets stagnated. This contrasted the rapid develop ment of complex analytic geometry which followed the groundbreaking work of the early 1950's. Certain pathologies in the real case contributed to this failure to progress. For example, the closure of -or the connected components of-a constructible set (Le. , a locally finite union of differ ences of real analytic sets) need not be constructible (e. g. , R - {O} and 3 2 2 { (x, y, z) E R : x = zy2, x + y2 -=I- O}, respectively). Responding to this in the 1960's, R. Thorn [Thl], S. Lojasiewicz [LI,2] and others undertook the study of a larger class of sets, the semianalytic sets, which are the sets defined locally at each point of Euclidean space by a finite number of ana lytic function equalities and inequalities. They established that semianalytic sets admit Whitney stratifications and triangulations, and using these tools they clarified the local topological structure of these sets. For example, they showed that the closure and the connected components of a semianalytic set are semianalytic.
Download or read book Geometry of Subanalytic and Semialgebraic Sets written by Masahiro Shiota and published by Springer Science & Business Media. This book was released on 1997 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subanalytic and semialgebraic sets were introduced for topological and systematic investigations of real analytic and algebraic sets. One of the author's purposes is to show that almost all (known and unknown) properties of subanalytic and semialgebraic sets follow abstractly from some fundamental axioms. Another is to develop methods of proof that use finite processes instead of integration of vector fields. The proofs are elementary, but the results obtained are new and significant - for example, for singularity theorists and topologists. Further, the new methods and tools developed provide solid foundations for further research by model theorists (logicians) who are interested in applications of model theory to geometry. A knowledge of basic topology is required.
Download or read book Real Algebraic and Semi algebraic Sets written by R. Benedetti and published by Editions Hermann. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry of Subanalytic and Semialgebraic Sets written by Masahiro Shiota and published by . This book was released on 1993 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Download or read book Weakly Semialgebraic Spaces written by Manfred Knebusch and published by Springer. This book was released on 2006-11-14 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA(R) or regular paracompact locally semialgebraic spaces over R was studied. The category WSA(R) of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA(R) as a full subcategory. The book provides ample evidence that WSA(R) is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA(R) seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA(R) and WSA(R) as the full subcategory SA(R) of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA(R) with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology.
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Download or read book Constructible Sets in Real Geometry written by Carlos Andradas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic and unified report on the minimal description of constructible sets. It starts at a very basic level (almost undergraduate) and leads up to state-of-the-art results, many of which are published in book form for the very first time. The book contains numerous examples, 63 figures and each chapter ends with a section containing historical notes. The authors tried to keep the presentation as self-contained as it can possibly be.
Download or read book Tame Topology and O minimal Structures written by Lou Van den Dries and published by Cambridge University Press. This book was released on 1998-05-07 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.
Download or read book Algebraic Statistics written by Seth Sullivant and published by American Mathematical Soc.. This book was released on 2018-11-19 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic statistics uses tools from algebraic geometry, commutative algebra, combinatorics, and their computational sides to address problems in statistics and its applications. The starting point for this connection is the observation that many statistical models are semialgebraic sets. The algebra/statistics connection is now over twenty years old, and this book presents the first broad introductory treatment of the subject. Along with background material in probability, algebra, and statistics, this book covers a range of topics in algebraic statistics including algebraic exponential families, likelihood inference, Fisher's exact test, bounds on entries of contingency tables, design of experiments, identifiability of hidden variable models, phylogenetic models, and model selection. With numerous examples, references, and over 150 exercises, this book is suitable for both classroom use and independent study.
Download or read book Real Analytic and Algebraic Geometry written by Fabrizio Broglia and published by Walter de Gruyter. This book was released on 2011-07-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Computer Aided Verification written by Shuvendu K. Lahiri and published by Springer Nature. This book was released on 2020-07-15 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic.
Download or read book Algorithmic and Quantitative Real Algebraic Geometry written by Saugata Basu and published by American Mathematical Soc.. This book was released on 2003-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Tame Geometry with Application in Smooth Analysis written by Yosef Yomdin and published by Springer. This book was released on 2004-02-07 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.
Download or read book SOFSEM 2012 Theory and Practice of Computer Science written by Maria Bielikova and published by Springer. This book was released on 2012-01-18 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012, held in Špindlerův Mlýn, Czech Republic, in January 2012. The 43 revised papers presented in this volume were carefully reviewed and selected from 121 submissions. The book also contains 11 invited talks, 10 of which are in full-paper length. The contributions are organized in topical sections named: foundations of computer science; software and Web engineering; cryptography, security, and verification; and artificial intelligence.
Download or read book SOFSEM 2012 Theory and Practice of Computer Science written by Mária Bieliková and published by Springer Science & Business Media. This book was released on 2012-01-09 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 38th Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2012, held in Špindlerův Mlýn, Czech Republic, in January 2012. The 43 revised papers presented in this volume were carefully reviewed and selected from 121 submissions. The book also contains 11 invited talks, 10 of which are in full-paper length. The contributions are organized in topical sections named: foundations of computer science; software and Web engineering; cryptography, security, and verification; and artificial intelligence.
Download or read book Aportaciones matem ticas written by VV.AA. and published by Ed. Universidad de Cantabria. This book was released on 1991 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
