Elimination Methods
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Elimination Methods
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Author : D. Wang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elimination Methods written by D. Wang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Elimination Methods In Polynomial Computer Algebra
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Author : V. Bykov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Elimination Methods In Polynomial Computer Algebra written by V. Bykov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Methods Of Cut Elimination
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Author : Matthias Baaz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-07
Methods Of Cut Elimination written by Matthias Baaz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-07 with Mathematics categories.
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.
On The Poincar Von Zeipel And Brown Shook Methods Of The Elimination Of The Short Period Terms From A Hamiltonian
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Author : Peter Musen
language : en
Publisher:
Release Date : 1968
On The Poincar Von Zeipel And Brown Shook Methods Of The Elimination Of The Short Period Terms From A Hamiltonian written by Peter Musen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Celestial mechanics categories.
The Multiple Inert Gas Elimination Technique Miget
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Author : Susan R. Hopkins
language : en
Publisher: Springer
Release Date : 2017-12-01
The Multiple Inert Gas Elimination Technique Miget written by Susan R. Hopkins and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-01 with Medical categories.
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.
Quantifier Elimination And Cylindrical Algebraic Decomposition
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Author : Bob F. Caviness
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantifier Elimination And Cylindrical Algebraic Decomposition written by Bob F. Caviness and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
Formal Algorithmic Elimination For Pdes
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Author : Daniel Robertz
language : en
Publisher: Springer
Release Date : 2014-10-13
Formal Algorithmic Elimination For Pdes written by Daniel Robertz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
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.
Elimination Methods In Polynomial Computer Algebra
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Author : V Bykov
language : en
Publisher:
Release Date : 1998-10-31
Elimination Methods In Polynomial Computer Algebra written by V Bykov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-31 with categories.
Hazard Elimination Procedures For Leaded Paints In Housing
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Author : David Waksman
language : en
Publisher:
Release Date : 1973
Hazard Elimination Procedures For Leaded Paints In Housing written by David Waksman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Lead based paint categories.
Environmental Assessment For The Proposed Elimination Of Intermediate Range And Shorter Range Missiles
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Author : Thomas M. Brown
language : en
Publisher:
Release Date : 1988
Environmental Assessment For The Proposed Elimination Of Intermediate Range And Shorter Range Missiles written by Thomas M. Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Environmental impact statements categories.