Polynomial Resolution Theory
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Polynomial Resolution Theory
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Author : William A. Hardy
language : en
Publisher: Trafford Publishing
Release Date : 2005
Polynomial Resolution Theory written by William A. Hardy and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Education categories.
This book is the definitive work on polynomial solution theory. Starting with the simplest linear equations with complex coefficients, this book proceeds in a step by step logical manner to outline the method for solving equations of arbitrarily high degree. Polynomial Resolution Theory is an invaluable book because of its unique perspective on the age old problem of solving polynomial equations of arbitrarily high degree. First of all Hardy insists upon pursuing the subject by using general complex coefficients rather than restricting himself to real coefficients. Complex numbers are used in ordered pair (x,y) form rather than the more traditional x + iy (or x + jy) notation. As Hardy comments, "The Fundamental Theorem of Algebra makes the treatments of polynomials with complex coefficients mandatory. We must not allow applications to direct the way mathematics is presented, but must permit the mathematical results themselves determine how to present the subject. Although practical, real-world applications are important, they must not be allowed to dictate the way in which a subject is treated. Thus, although there are at present no practical applications which employ polynomials with complex coefficients, we must present this subject with complex rather than restrictive real coefficients." This book then proceeds to recast familiar results in a more consistent notation for later progress. Two methods of solution to the general cubic equation with complex coefficients are presented. Then Ferrari's solution to the general complex bicubic (fourth degree) polynomial equation is presented. After this Hardy seamlessly presents the first extension of Ferrari's work to resolving the general bicubic (sixth degree) equation with complex coefficients into two component cubic equations. Eight special cases of this equation which are solvable in closed form are developed with detailed examples. Next the resolution of the octal (eighth degree) polynomial equation is developed along with twelve special cases which are solvable in closed form. This book is appropriate for students at the advanced college algebra level who have an understanding of the basic arithmetic of the complex numbers and know how to use a calculator which handles complex numbers directly. Hardy continues to develop the theory of polynomial resolution to equations of degree forty-eight. An extensive set of appendices is useful for verifying derived results and for rigging various special case equations. This is the 3rd edition of Hardy's book.
Number Theory And Polynomials
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Author : James Fraser McKee
language : en
Publisher: Cambridge University Press
Release Date : 2008-05-08
Number Theory And Polynomials written by James Fraser McKee and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-08 with Mathematics categories.
Contributions by leading experts in the field provide a snapshot of current progress in polynomials and number theory.
Positive Trigonometric Polynomials And Signal Processing Applications
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Author : Bogdan Dumitrescu
language : en
Publisher: Springer
Release Date : 2018-07-21
Positive Trigonometric Polynomials And Signal Processing Applications written by Bogdan Dumitrescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-21 with Technology & Engineering categories.
This book gathers the main recent results on positive trigonometric polynomials within a unitary framework. The book has two parts: theory and applications. The theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The applications part is organized as a collection of related problems that use systematically the theoretical results.
Theory And Applications Of Satisfiability Testing Sat 2012
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Author : Alessandro Cimatti
language : en
Publisher: Springer
Release Date : 2012-06-18
Theory And Applications Of Satisfiability Testing Sat 2012 written by Alessandro Cimatti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-18 with Computers categories.
This book constitutes the refereed proceedings of the 15th International Conference on Theory and Applications of Satisfiability Testing, SAT 2012, held in Trento, Italy, in June 2012. The 29 revised full papers, 7 tool papers, and 16 poster papers presented together with 2 invited talks were carefully reviewed and selected from 112 submissions (88 full, 10 tool and 14 poster papers). The papers are organized in topical sections on stochastic local search, theory, quantified Boolean formulae, applications, parallel and portfolio approaches, CDCL SAT solving, MAX-SAT, cores interpolants, complexity analysis, and circuits and encodings.
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.
Computational Complexity Theory
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Author : Steven Rudich, Avi Wigderson
language : en
Publisher: American Mathematical Soc.
Release Date :
Computational Complexity Theory written by Steven Rudich, Avi Wigderson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Computational Complexity Theory
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Author : Steven Rudich
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Computational Complexity Theory written by Steven Rudich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computers categories.
Computational Complexity Theory is the study of how much of a given resource is required to perform the computations that interest us the most. Four decades of fruitful research have produced a rich and subtle theory of the relationship between different resource measures and problems. At the core of the theory are some of the most alluring open problems in mathematics. This book presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on computational complexity. The first week gives a general introduction to the field, including descriptions of the basic mo.
Mine Planning And Equipment Selection 2004
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Author : Monika Hardygóra
language : en
Publisher: CRC Press
Release Date : 2004-08-15
Mine Planning And Equipment Selection 2004 written by Monika Hardygóra and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-08-15 with Technology & Engineering categories.
Spearheading the promotion of international technology transfer in the fields of mine planning, mining systems design, equipment selection and operation techniques, the International Symposium on Mine Planning and Equipment Selection is recognised by the mining society as a key annual event in highlighting developments within the field. Here in this volume, proceedings from the thirteenth annual symposium concentrate on the following major topics: * open pit and underground mine planning, modelling and design * geomechanics * mining and processing methods * design, monitoring and maintenance of mine equipment * simulation, optimalization and control of technological processes * management, mine economics and financial analysis * health, safety and environmental protection. Including 147 papers from leading experts and authorities, Mine Planning and Equipment Selection undoubtedly provides valuable information and insight for a range of engineers, scientists, researchers and consultants involved in the planning, design and operation of underground and surface mines.
Lessons From Learning
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Author : Robert Lewis
language : en
Publisher: North Holland
Release Date : 1994
Lessons From Learning written by Robert Lewis and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Computers categories.
The last thirty years have produced a widely varying series of research experiments and innovative practices in the uses of computer and communications technologies to support teaching and learning. Relatively recently, enough experience has been accumulated to justify significant investment in implementing systems across a broad range of educational and training domains. Much of this experience has been pragmatic and attempts to place the activity within a substantive cognitive framework have not met with much success. Lessons have been learnt from the experience but there are many complex issues of knowledge representation, acquisition and long-term accommodation linked to the role of human actors and technological tools.This publication divides its exploration of the intricacies of the field into four key areas. Theme A takes a cognitive psychologist's approach to learning processes. It is concerned with the ways in which knowledge is stored or represented inside the human mind; it is also concerned with knowledge acquisition and knowledge structures and their relation to learning environment design. Theme B takes an educationalist's perspective of learning. It takes the learner as the focus and examines learning styles, teaching styles, collaborative learning, etc. Theme C focuses on the design of learning tasks and environments, with considerations of design principles of exploratory or expressive materials. It is strongly domain orientated. Theme D focuses on knowledge architectures as they can be created in a machine and so includes the formalisms and models required in artificial intelligence applications to learning.In addition to providing a comprehensive consideration of the problems faced and solutions so far achieved, it is hoped the book will stimulate further research and funding in an area that simply cannot be ignored.
Developments In Language Theory
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Author : Werner Kuich
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-03-27
Developments In Language Theory written by Werner Kuich 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 2002-03-27 with Computers categories.
This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Developments in Language Theory, DLT 2001, held in Vienna, Austria, in July 2001. The 24 revised full papers presented together with 10 revised invited papers were carefully selected during two rounds of reviewing and revision from a total of 64 papers submitted. Among the topics covered are grammars and acceptors, efficient algorithms for languages, combinatorial and algebraic properties, decision problems, relations to complexity theory, logic, picture description and analysis, DNA computing, cryptography, and concurrency.