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Elimination Methods
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Download or read book Elimination Methods written by D. Wang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.
Book Synopsis Elimination Methods in Polynomial Computer Algebra by : V. Bykov
Download or read book Elimination Methods in Polynomial Computer Algebra written by V. Bykov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. There were several incentives to write the book. First of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta tionary states. Practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. And finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac tical research. The structure of the book is accordingly represented by three main parts: Mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. Nonlinear systems of algebraic equations arise in diverse fields of science. In particular, for processes described by systems of differential equations with a poly nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.
Book Synopsis Methods of Cut-Elimination by : Matthias Baaz
Download or read book Methods of Cut-Elimination written by Matthias Baaz and published by Springer Science & Business Media. This book was released on 2011-01-07 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on cut-elimination in first-order predicate logic from an algorithmic point of view. Instead of just proving the existence of cut-free proofs, it focuses on the algorithmic methods transforming proofs with arbitrary cuts to proofs with only atomic cuts (atomic cut normal forms, so-called ACNFs). The first part investigates traditional reductive methods from the point of view of proof rewriting. Within this general framework, generalizations of Gentzen's and Sch\”utte-Tait's cut-elimination methods are defined and shown terminating with ACNFs of the original proof. Moreover, a complexity theoretic comparison of Gentzen's and Tait's methods is given. The core of the book centers around the cut-elimination method CERES (cut elimination by resolution) developed by the authors. CERES is based on the resolution calculus and radically differs from the reductive cut-elimination methods. The book shows that CERES asymptotically outperforms all reductive methods based on Gentzen's cut-reduction rules. It obtains this result by heavy use of subsumption theorems in clause logic. Moreover, several applications of CERES are given (to interpolation, complexity analysis of cut-elimination, generalization of proofs, and to the analysis of real mathematical proofs). Lastly, the book demonstrates that CERES can be extended to nonclassical logics, in particular to finitely-valued logics and to G\"odel logic.
Book Synopsis On the Poincaré-von Zeipel and Brown-Shook Methods of the Elimination of the Short Period Terms from a Hamiltonian by : Peter Musen
Download or read book On the Poincaré-von Zeipel and Brown-Shook Methods of the Elimination of the Short Period Terms from a Hamiltonian written by Peter Musen and published by . This book was released on 1968 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Multiple Inert Gas Elimination Technique (MIGET) by : Susan R. Hopkins
Download or read book The Multiple Inert Gas Elimination Technique (MIGET) written by Susan R. Hopkins and published by Springer. This book was released on 2017-12-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Multiple Inert Gas Elimination Technique (MIGET) is a complex methodology involving specialized gas chromatography and sophisticated mathematics developed in the early 1970’s. Essentially, nobody possesses knowledge of all its elements except for its original developers, and while some practical and theoretical aspects have been published over the years, none have included the level of detail that would be necessary for a potential user to adopt and understand the technique easily. This book is unique in providing a highly detailed, comprehensive technical description of the theory and practice underlying the MIGET to help potential users set up the method and solve problems they may encounter. But it is much more than a reference manual – it is a substantial physiological and mathematical treatise in its own right. It also has a wide applicability – there is extensive discussion of the common biological problem of quantitative inference. The authors took measured whole-lung gas exchange variables, and used mathematical procedures to infer the distribution of ventilation and blood flow from this data. In so doing, they developed novel approaches to answer the question: What are the limits to what can be concluded when inferring the inner workings from the “black box” behavior of a system? The book details the approaches developed, which can be generalized to other similar distributed functions within tissues and organs. They involve engineering approaches such as linear and quadratic programming, and uniquely use mathematical tools with biological constraints to obtain as much information as possible about a “black box” system. Lastly, the book summarizes the hundreds of research papers published by a number of groups over the decades in a way never before attempted in order to marshal the world’s literature on the topic and to provide in one place the wealth of important discoveries, both physiological a nd clinical, enabled by the technique.
Book Synopsis Quantifier Elimination and Cylindrical Algebraic Decomposition by : Bob F. Caviness
Download or read book Quantifier Elimination and Cylindrical Algebraic Decomposition written by Bob F. Caviness and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades. This volume is a state-of-the-art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.
Book Synopsis Formal Algorithmic Elimination for PDEs by : Daniel Robertz
Download or read book Formal Algorithmic Elimination for PDEs written by Daniel Robertz and published by Springer. This book was released on 2014-10-13 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigating the correspondence between systems of partial differential equations and their analytic solutions using a formal approach, this monograph presents algorithms to determine the set of analytic solutions of such a system and conversely to find differential equations whose set of solutions coincides with a given parametrized set of analytic functions. After giving a detailed introduction to Janet bases and Thomas decomposition, the problem of finding an implicit description of certain sets of analytic functions in terms of differential equations is addressed. Effective methods of varying generality are developed to solve the differential elimination problems that arise in this context. In particular, it is demonstrated how the symbolic solution of partial differential equations profits from the study of the implicitization problem. For instance, certain families of exact solutions of the Navier-Stokes equations can be computed.
Book Synopsis Finite Element Methods for Engineers by : Roger T Fenner
Download or read book Finite Element Methods for Engineers written by Roger T Fenner and published by World Scientific Publishing Company. This book was released on 2013-01-17 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full FORTRAN programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the FORTRAN language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use on desktops and laptops. Unlike the first edition, the new edition has problems (with solutions) at the end of each chapter. Electronic copies of all the computer programs displayed in the book can be downloaded at: http://www.worldscientific.com/doi/suppl/10.1142/p847/suppl_file/p847_program.zip.
Book Synopsis Hazard Elimination Procedures for Leaded Paints in Housing by : David Waksman
Download or read book Hazard Elimination Procedures for Leaded Paints in Housing written by David Waksman and published by . This book was released on 1973 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Environmental Assessment for the Proposed Elimination of Intermediate Range and Shorter-range Missiles by : Thomas M. Brown
Download or read book Environmental Assessment for the Proposed Elimination of Intermediate Range and Shorter-range Missiles written by Thomas M. Brown and published by . This book was released on 1988 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elements of Photoionization Quantum Dynamics Methods by : Lampros A A Nikolopoulos
Download or read book Elements of Photoionization Quantum Dynamics Methods written by Lampros A A Nikolopoulos and published by Morgan & Claypool Publishers. This book was released on 2019-03-29 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of quantum systems exposed to ultrafast (at the femtosecond time-scale) and strong laser radiation has a highly non-linear character, leading to a number of new phenomena, outside the reach of traditional spectroscopy. The current laser technology makes feasible the probing and control of quantum-scale systems with fields that are as strong as the interatomic Coulombic interactions and time resolution that is equal to (or less than) typical atomic evolution times. It is indispensable that any theoretical description of the induced physical processes should rely on the accurate calculation of the atomic structure and a realistic model of the laser radiation as pulsed fields. This book aims to provide an elementary introduction of theoretical and computational methods and by no means is anywhere near to complete. The selection of the topics as well as the particular viewpoint is best suited for early-stage students and researchers; the included material belongs in the mainstream of theoretical approaches albeit using simpler language without sacrificing mathematical accuracy. Therefore, subjects such as the Hilbert vector-state, density-matrix operators, amplitude equations, Liouville equation, coherent laser radiation, free-electron laser, Dyson-chronological operator, subspace projection, perturbation theory, stochastic density-matrix equations, time-dependent Schrödinger equation, partial-wave analysis, spherical-harmonics expansions, basis and grid wavefunction expansions, ionization, electron kinetic-energy and angular distributions are presented within the context of laser-atom quantum dynamics.
Book Synopsis Third International Symposium on Domain Decomposition Methods for Partial Differential Equations by : Tony F. Chan
Download or read book Third International Symposium on Domain Decomposition Methods for Partial Differential Equations written by Tony F. Chan and published by SIAM. This book was released on 1990-01-01 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fatigue Study: The Elimination of Humanity's Greatest Unnecessary Waste by : Lillian Moller Gilbreth
Download or read book Fatigue Study: The Elimination of Humanity's Greatest Unnecessary Waste written by Lillian Moller Gilbreth and published by Good Press. This book was released on 2022-08-21 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fatigue Study: The Elimination of Humanity's Greatest Unnecessary Waste: A First Step in Motion Study" by Lillian Moller Gilbreth and Frank B. Gilbreth was written in 1916, but had retained much of its relevance even over a century later. Written by a psychologist and an engineer, this helped shape people's understanding of how the human mind and motion are interconnected.
Book Synopsis Elimination Practice by : Dongming Wang
Download or read book Elimination Practice written by Dongming Wang and published by World Scientific. This book was released on 2004 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomial Elimination at Work; The Epsilon Library; The CharSets Package; The TriSys and SiSys Modules; The GEOTHER Environment; Relevant Elimination Tools; Solving Polynomial Systems; Automated Theorem Proving and Discovering in Geometry; Symbolic Geometric Computation; Selected Problems in Computer Mathematics.
Book Synopsis Automated Reasoning with Analytic Tableaux and Related Methods by : Neil V. Murray
Download or read book Automated Reasoning with Analytic Tableaux and Related Methods written by Neil V. Murray and published by Springer. This book was released on 2003-07-31 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the International Conference on Analytic Tableaux and Related Methods, TABLEAUX'99, held in Saratoga Springs, NY, USA, in June 1999. The volume presents 18 revised full papers and three system descriptions selected from 41 submissions. Also included are system comparisons and abstracts of an invited paper and of two tutorials. All current issues surrounding mechanization of reasoning with tableaux and similar methods are addressed - ranging from theoretical foundations to implementation and systems development and applications, as well as covering a broad variety of logic calculi. As application areas, formal verification of software and computer systems, deductive databases, knowledge representation, and systems diagnosis are covered.
Book Synopsis The Routledge Handbook of Planning Research Methods by : Elisabete A. Silva
Download or read book The Routledge Handbook of Planning Research Methods written by Elisabete A. Silva and published by Routledge. This book was released on 2014-08-21 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Routledge Handbook of Planning Research Methods is an expansive look at the traditions, methods, and challenges of research design and research projects in contemporary urban planning. Through case studies, an international group of researchers, planning practitioners, and planning academics and educators, all recognized authorities in the field, provide accounts of designing and implementing research projects from different approaches and venues. This book shows how to apply quantitative and qualitative methods to projects, and how to take your research from the classroom to the real world. The book is structured into sections focusing on Beginning planning research Research design and development Rediscovering qualitative methods New advances in quantitative methods Turning research into action With chapters written by leading scholars in spatial planning, The Routledge Handbook of Planning Research Methods is the most authoritative and comprehensive handbook on the topic, providing both established and ground breaking coverage of spatial planning research methods. The book is an invaluable resource for undergraduate and graduate level students, young professionals and practitioners in urban, regional, and spatial planning.
Book Synopsis Innovations and Advances in Computer Sciences and Engineering by : Tarek Sobh
Download or read book Innovations and Advances in Computer Sciences and Engineering written by Tarek Sobh and published by Springer Science & Business Media. This book was released on 2010-03-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: Innovations and Advances in Computer Sciences and Engineering includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computer Science, Software Engineering, Computer Engineering, and Systems Engineering and Sciences. Innovations and Advances in Computer Sciences and Engineering includes selected papers form the conference proceedings of the International Conference on Systems, Computing Sciences and Software Engineering (SCSS 2008) which was part of the International Joint Conferences on Computer, Information and Systems Sciences and Engineering (CISSE 2008).
