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The Center and Cyclicity Problems: A Computational Algebra Approach
by Valery Romanovski Douglas ShaferUsing a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.
The Center and Focus Problem: Algebraic Solutions and Hypotheses (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by M.N. Popa V.V. PricopThe Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades. A rather essential result is obtained in solving Poincaré's problem. Namely, there are given the upper estimations of the number of Poincaré-Lyapunov quantities, which are algebraically independent and participate in solving the Center and Focus Problem that have not been known so far. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations. Table of Contents 1. Lie Algebra Of Operators Of Centro-Affine Group Representation In The Coefficient Space Of Polynomial Differential Systems 2. Differential Equations For Centro-Affine Invariants And Comitants Of Differential Systems And Their Applications 3. Generating Functions And Hilbert Series For Sibirsky Graded Algebras Of Comitants And Invariants Of Differential Systems 4. Hilbert Series For Sibirsky Algebras And Krull Dimension For Them 5. About The Center And Focus Problem 6. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For The System s(1,m1,…,m`) 7. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For Lyapunov System. Bibliography Appendixes Biographies Popa Mihail Nicolae, holds a Ph.D. from Gorky University (now Nizhny Novgorod, Russia). He has served as Director and Deputy Director of Vladimir Andrunachievici Institute of Mathematics and Computer Science (IMCS)) in the Laboratory of Differential Equations. He is Professor at the State University of Tiraspol (based in Chisinau). His scientific interests are related to the invariant processes in the qualitative theory of differential equations, Lie algebras and commutative graded algebras, generating functions and Hilbert series, orbit theory, Lyapunov stability theory. Pricop Victor Vasile, holds a Ph.D. from Vladimir Andrunachievici Institute of Mathematics and Computer Science. He is professor at the State Institute of International Relations of Moldova. Victor Pricop's scientific interests are related to Lie algebras and graded algebras of invariants and comitants, generating functions and Hilbert series, applications of algebras to polynomial differential systems.
The Center and Focus Problem: Algebraic Solutions and Hypotheses (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by M.N. Popa V.V. PricopThe Center and Focus Problem: Algebraic Solutions and Hypotheses, M. N. Popa and V.V. Pricop, ISBN: 978-1-032-01725-9 (Hardback) This book focuses on an old problem of the qualitative theory of differential equations, called the Center and Focus Problem. It is intended for mathematicians, researchers, professors and Ph.D. students working in the field of differential equations, as well as other specialists who are interested in the theory of Lie algebras, commutative graded algebras, the theory of generating functions and Hilbert series. The book reflects the results obtained by the authors in the last decades. A rather essential result is obtained in solving Poincaré's problem. Namely, there are given the upper estimations of the number of Poincaré-Lyapunov quantities, which are algebraically independent and participate in solving the Center and Focus Problem that have not been known so far. These estimations are equal to Krull dimensions of Sibirsky graded algebras of comitants and invariants of systems of differential equations. Table of Contents 1. Lie Algebra Of Operators Of Centro-Affine Group Representation In The Coefficient Space Of Polynomial Differential Systems 2. Differential Equations For Centro-Affine Invariants And Comitants Of Differential Systems And Their Applications 3. Generating Functions And Hilbert Series For Sibirsky Graded Algebras Of Comitants And Invariants Of Differential Systems 4. Hilbert Series For Sibirsky Algebras And Krull Dimension For Them 5. About The Center And Focus Problem 6. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For The System s(1,m1,…,m`) 7. On The Upper Bound Of The Number Of Algebraically Independent Focus Quantities That Take Part In Solving The Center And Focus Problem For Lyapunov System. Bibliography Appendixes Biographies Popa Mihail Nicolae, holds a Ph.D. from Gorky University (now Nizhny Novgorod, Russia). He has served as Director and Deputy Director of Vladimir Andrunachievici Institute of Mathematics and Computer Science (IMCS)) in the Laboratory of Differential Equations. He is Professor at the State University of Tiraspol (based in Chisinau). His scientific interests are related to the invariant processes in the qualitative theory of differential equations, Lie algebras and commutative graded algebras, generating functions and Hilbert series, orbit theory, Lyapunov stability theory. Pricop Victor Vasile, holds a Ph.D. from Vladimir Andrunachievici Institute of Mathematics and Computer Science. He is professor at the State Institute of International Relations of Moldova. Victor Pricop's scientific interests are related to Lie algebras and graded algebras of invariants and comitants, generating functions and Hilbert series, applications of algebras to polynomial differential systems.
Central Asia at the End of the Transition
by Boris Z. RumerFor better or worse, the former Soviet republics of Central Asia have largely completed their post-independence transitions. Over more than a decade, they have established themselves as independent states whose internal regimes and external relations have characteristic patterns and vulnerabilities both individually and as a group. The purpose of this volume is to assess both what has been accomplished and the trends of development in the region, especially its leading states. How sound are the foundations of this "bulwark against the spread of terrorism" in Eurasia?
Central Asia at the End of the Transition
by Boris Z. RumerFor better or worse, the former Soviet republics of Central Asia have largely completed their post-independence transitions. Over more than a decade, they have established themselves as independent states whose internal regimes and external relations have characteristic patterns and vulnerabilities both individually and as a group. The purpose of this volume is to assess both what has been accomplished and the trends of development in the region, especially its leading states. How sound are the foundations of this "bulwark against the spread of terrorism" in Eurasia?
Central Configurations, Periodic Orbits, and Hamiltonian Systems (Advanced Courses in Mathematics - CRM Barcelona)
by Jaume Llibre Richard Moeckel Carles SimóThe notes of this book originate from three series of lectures given at the Centre de Recerca Matemàtica (CRM) in Barcelona. The first one is dedicated to the study of periodic solutions of autonomous differential systems in Rn via the Averaging Theory and was delivered by Jaume Llibre. The second one, given by Richard Moeckel, focusses on methods for studying Central Configurations. The last one, by Carles Simó, describes the main mechanisms leading to a fairly global description of the dynamics in conservative systems.The book is directed towards graduate students and researchers interested in dynamical systems, in particular in the conservative case, and aims at facilitating the understanding of dynamics of specific models. The results presented and the tools introduced in this book include a large range of applications.
Central European Functional Programming School: Third Summer School, CEFP 2009, Budapest, Hungary, May 21-23, 2009 and Komárno, Slovakia, May 25-30, 2009, Revised Selected Lectures (Lecture Notes in Computer Science #6299)
by Zoltán Horváth Rinus Plasmeijer Viktoria ZsókThis volume presents the revised lecture notes of selected talks given at the Third Central European Functional Programming School, CEFP 2009, held in May 2009 in Komárno, Slovakia. It was co-organized with the TFP 2009 conference. The summer school included a three days warm-up session organized in Budapest, Hungary also in May, 2009. The 11 revised full papers presented were carefully reviewed and selected. The lectures cover a wide range of topics such as design patterns, semantics, types, and advanced programming in various functional programming languages.
Central European Functional Programming School: Second Summer School, CEFP 2007, Cluj-Napoca, Romania, June 23-30, 2007, Revised Selected Lectures (Lecture Notes in Computer Science #5161)
by Anna SoósThis volume presents the revised lecture notes of selected talks given at the second Central European Functional Programming School, CEFP 2007, held June 23–30, 2007 at Babe¸ s-Bolyai University, Cluj-Napoca, Romania. The summer school was organized in the spirit of the advanced progr- ming schools. CEFP focuses on involving an ever-growing number of students, researchers,andteachersfromcentral,andeasternEuropeancountries.We were glad to welcome the invited lecturers and the participants: 15 professors and 30 students from 9 di?erent universities. The intensive program o?ered a creative and inspiring environment and a great opportunity to present and exchange ideas in new topics of functional programming. The lectures covereda wide range of topics like interactive work ?ows for the Web, proving properties of lazy functional programs, lambda calculus and - stract lambda calculus machines, programming in ? mega, object-oriented fu- tional programming, and refactoring in Erlang. We are very grateful to the lecturers and researchers for the time and the e?ort they devoted to the talks and the revised lecture notes. The lecture notes were each carefully checked by reviewers selected from experts of functional programming. Afterwards the papers were revised once more by the lecturers. This revision process guaranteed that only high-quality papers are accepted in the volume of the lecture notes.
A Century of State Murder?: Death and Policy in Twentieth Century Russia
by Michael Haynes Rumy HusanRussia has one of the lowest rates of adult life expectancy in the world. Average life expectancy for a man in America is 74; in Russia, it is just 59. Birth rates and population levels have also plummeted. These excess levels of mortality affect all countries that formed the former Soviet bloc. Running into many millions, they raise comparisons with the earlier period of forced transition under Stalin. *BR**BR*This book seeks to put the recent history of the transition into a longer term perspective by identifying, explaining and comparing the pattern of change in Russia in the last century. It offers a sharp challenge to the conventional wisdom and benign interpretations offered in the west of what has happened since 1991. *BR**BR*Mike Haynes and Rumy Husan have produced the first and most complete and accurate account of Russian demographic crisis from the Revolution to the present.
A Certain Ambiguity: A Mathematical Novel
by Gaurav Suri Hartosh Singh BalWhile taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.
A Certain Ambiguity: A Mathematical Novel (PDF)
by Gaurav Suri Hartosh Singh BalWhile taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry. As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex. Moving and enlightening, A Certain Ambiguity is a story about what it means to face the extent--and the limits--of human knowledge.
Certain Number-Theoretic Episodes In Algebra, Second Edition (Chapman & Hall/CRC Pure and Applied Mathematics)
by Sivaramakrishnan RThe book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Certain Number-Theoretic Episodes In Algebra, Second Edition (Chapman & Hall/CRC Pure and Applied Mathematics #Vol. 237)
by Sivaramakrishnan RThe book attempts to point out the interconnections between number theory and algebra with a view to making a student understand certain basic concepts in the two areas forming the subject-matter of the book.
Certificates of Positivity for Real Polynomials: Theory, Practice, and Applications (Developments in Mathematics #69)
by Victoria PowersThis book collects and explains the many theorems concerning the existence of certificates of positivity for polynomials that are positive globally or on semialgebraic sets. A certificate of positivity for a real polynomial is an algebraic identity that gives an immediate proof of a positivity condition for the polynomial. Certificates of positivity have their roots in fundamental work of David Hilbert from the late 19th century on positive polynomials and sums of squares. Because of the numerous applications of certificates of positivity in mathematics, applied mathematics, engineering, and other fields, it is desirable to have methods for finding, describing, and characterizing them. For many of the topics covered in this book, appropriate algorithms, computational methods, and applications are discussed. This volume contains a comprehensive, accessible, up-to-date treatment of certificates of positivity, written by an expert in the field. It provides an overview of both the theory and computational aspects of the subject, and includes many of the recent and exciting developments in the area. Background information is given so that beginning graduate students and researchers who are not specialists can learn about this fascinating subject. Furthermore, researchers who work on certificates of positivity or use them in applications will find this a useful reference for their work.
Certified Kubernetes Administrator (cka) Exam Guide: Validate Your Knowledge Of Kubernetes And Implement It In A Real-life Production Environment
by Brendan Burns Melony Qin Mark Whitby Alessandro VozzaValidate your knowledge of Kubernetes and implement it in a real-life production environment
Certified Programs and Proofs: Third International Conference, CPP 2013, Melbourne, VIC, Australia, December 11-13,2013, Proceedings (Lecture Notes in Computer Science #8307)
by Georges Gonthier Michael NorrishThis book constitutes the refereed proceedings of the Third International Conference on Certified Programs and Proofs, CPP 2013, colocated with APLAS 2013 held in Melbourne, Australia, in December 2013. The 18 revised regular papers presented together with 1 invited lecture were carefully reviewed and selected from 39 submissions. The papers are organized in topical sections on code verification, elegant proofs, proof libraries, certified transformations and security.
Certified Programs and Proofs: Second International Conference, CPP 2012, Kyoto, Japan, December 13-15, 2012, Proceedings (Lecture Notes in Computer Science #7679)
by Chris Hawblitzel Dale MillerThis book constitutes the refereed proceedings of the Second International Conference on Certified Programs and Proofs, CPP 2012, held in Kyoto, Japan, in December 2012. The 18 revised regular papers presented were carefully reviewed and selected from 37 submissions. They deal with those topics in computer science and mathematics in which certification via formal techniques is crucial.
Certified Programs and Proofs: First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011, Proceedings (Lecture Notes in Computer Science #7086)
by Jean-Pierre Jouannaud Zhong ShaoThis book constitutes the referred proceedings of the First International Conference on Certified Programs and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011. The 24 revised regular papers presented together with 4 invited talks were carefully reviewed and selected from 49 submissions. They are organized in topical sections on logic and types, certificates, formalization, proof assistants, teaching, programming languages, hardware certification, miscellaneous, and proof perls.
Certified Reduced Basis Methods for Parametrized Partial Differential Equations (SpringerBriefs in Mathematics)
by Jan S Hesthaven Gianluigi Rozza Benjamin StammThis book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
CFD-Modellierung: Grundlagen und Anwendungen bei Strömungsprozessen
by Rüdiger SchwarzeIn diesem kompakten Lehrbuch legt der Autor die Methodik der numerischen Simulation von Strömungsprozessen dar. Nach einer konzisen Erläuterung der Grundlagen lernen Leser das Potenzial der Methodik anhand von Anwendungsbeispielen kennen. Demonstriert werden sowohl einfache wie komplexe Probleme. Während Leser die einfachen Problemstellungen mithilfe von Open-Source-Softwarepaketen selbst bearbeitet können, sind die komplexen Beispiele aus aktuellen grundlagenorientierten und aus anwendungsnahen Forschungsprojekten des Autors abgeleitet.
Cfe Advanced Higher Maths Practice Papers For Sqa Exams (Practice Papers For Sqa Exam Revision Ser.)
by Leckie and Leckie and Leckie Craig Lowther Dominic Kennedy Graeme NolanExam Board: SQA Level: Advanced Higher Subject: Maths First Teaching: 2015, First Exam: 2016 Get ready for your CfE Advanced Higher Maths exam with these brand new practice papers that look just like the SQA exam - the best way to prepare for the big day! Get ready for your CfE Advanced Higher Maths exam with these brand new practice papers that look just like the SQA exam - the best way to prepare for the big day! Give yourself the best chance to excel with these original and full practice papers Build your confidence with the type and level of questions you can expect in your SQA exam Detailed answers to all of the questions show you exactly how your exam will be marked Hints and tips throughout explain how to approach different types of question A topic index shows you where to find questions for any areas you'd like to practise specifically
Cfe Advanced Higher Maths Student Book (PDF)
by Anita Leckie Clare Ford Craig Lowther Deirdre Murray John Ballantyne Monica KirsonExam Board: SQA Level: Higher Subject: Maths First Teaching: 2015, First Exam: 2016 The Advanced Higher Maths Student Book helps teachers and students map their route through the CfE programme, providing comprehensive and authoritative guidance for the course. Full coverage of the new Advanced Higher course specifications with list of learning intentions Attractive layout with clear text features Key questions highlight crucial concepts and techniques that need to be grasped by students in order to progress to the next learning intention What the examiner/assessor is looking for to help teachers & students feel secure End of unit material - unit assessment, exam-style questions with worked answers and examiners commentary, self-assessment Student Books give a practical, supportive approach to help deliver the new curriculum and offer a blend of sound teaching and learning with assessment guidance.
CfE Higher Mathematics Practice Papers for SQA Exams (Practice Papers for SQA Exams) (PDF)
by Leckie And LeckieThis book contains practice exam papers, which mirror the actual SQA exam as much as possibl.
CfE Higher Maths Student Book (PDF)
by Andrew Thompson Craig Lowther Stuart Welsh Claire Anderson Robin ChristieThe Higher Maths Student Book helps teachers and students map their route through the CfE programme, providing comprehensive and authoritative guidance for the course.
CfE Higher Maths Success Guide (Success Guide) (PDF)
by Ken NisbetPrepare to excel in your CfE Higher SQA exam with this Success Guide - the first choice for Scottish students! Success Guides really work because: Topics in user-friendly sections help plan revision Examples throughout explain new ideas clearly Quick Tests provide the practice that experts say is required for recall.