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The book contains some of the most important results on the analysis of polynomials and their derivatives. Besides the fundamental results which are treated with their proofs, the book also provides an account of the most recent developments concerning extremal properties of polynomials and their derivatives in various metrics with an extensive analysis of inequalities for trigonometric sums and algebraic polynomials, as well as their zeros. The final chapter provides some selected applications of polynomials in approximation theory and computer aided geometric design (CAGD). One can also find in this book several new research problems and conjectures with sufficient information concerning the results obtained to date towards the investigation of their solution. Contents:PrefaceGeneral Concept of Algebraic PolynomialsSelected Polynomial InequalitiesZeros of PolynomialsInequalities Connected with Trigonometric SumsExtremal Problems for PolynomialsExtremal Problems of Markov-Bernstein TypeSome Applications of PolynomialsSymbol IndexName IndexSubject Index Readership: Mathematicians and mathematical physicists. keywords:Algebraic Polynomials;Trigonometric Polynomials;Zeros;Extremal Problems;Trigonometric Sums;Positivity and Monotonicity;Distribution of Zeros;Bounds for Polynomial Zeros;Incomplete Polynomials;Polynomials with Minimal Norm;Markov-Bernstein Inequalities;Approximation;Symmetric Functions;Orthogonal Polynomials;Nonnegative Polynomials “The topics are tastefully selected and the results are easy to find. Although this book is not really planned as a textbook to teach from, it is excellent for self-study or seminars. This is a very useful reference book with many results which have not appeared in a book form yet. It is an important addition to the literature.” Journal of Approximation Theory “I find the book to be well written and readable. The authors have made an attempt to present the material in an integrated and self-contained fashion and, in my opinion, they have been greatly successful. The book would be useful not only for the specialist mathematician, but also for those researchers in the applied and computational sciences who use polynomials as a tool.” Mathematical Reviews “This is a remarkable book, offering a cornucopia of results, all connected by their involvement with polynomials. The scope of the volume can be conveyed by citing some statistics: there are 821 pages, 7 chapters, 20 sections, 108 subsections, 95 pages of references (distributed throughout the book), a name index of 16 pages, and a subject index of 19 pages … The book is written in a gentle style: one can open it anywhere and begin to understand, without encountering unfamiliar notation and terminology. It is strongly recommended to individuals and to libraries.” Mathematics of Computation “This book contains some of the most important results on the analysis of polynomials and their derivatives … is intended, not only for the specialist mathematician, but also for those researchers in the applied sciences who use polynomials as a tool.” Sever S Dragomir “This is a well-written book on a widely useful topic. It is strongly recommended not only to the mathematical specialist, but also to all those researchers in the applied and computational sciences who make frequent use of polynomials as a tool. Of course, libraries will also benefit greatly by including this book in their cherished collection.” Mathematics Abstracts “There is no doubt that this is a very useful work compiling enormous researches carried out on the subject … This is a well-written book on a widely useful topic.” Zentralblatt für Mathematik

An International Statistical Conference on Linear Inference was held in Poznan, Poland, on June 4-8, 1984. The conference was organized under the auspices of the Polish Section of the Bernoulli Society, the Committee of Mathematical Sciences and the Mathematical Institute of the ,Polish Academy of Sciences. The purpose of the meeting was to bring together scientists from vari ous countries working in the diverse areas of statistical sciences but showing great interest in the advances of research on linear inference taken in its broad sense. Thus, the conference programme included ses sions on Gauss-Markov models, robustness, variance components~ experi mental design, multiple comparisons, multivariate models, computational aspects and on some special topics. 38 papers were read within the vari ous sessions and 5 were presented as posters. At the end of the confer ence a lively general discussion session was held. The conference gathered more than ninety participants from 16 countries, representing both parts of Europe, North America and Asia. Judging from opinions expressed by many participants, the conference was quite suc cessful, well contributing to the dissemination of knowledge and the stimulation of research in different areas linked with statistical li near inference. If the conference was really a success, it was due to all its participants who in various ways were devoting their time and efforts to make the conference fruitful and enjoyable.

This book addresses the identification of the shape of penetrable periodic media by means of scattered time-harmonic waves. Mathematically, this is about the determination of the support of a function which occurs in the governing equations. Our theoretical analysis shows that this problem can be strictly solved for acoustic as well as for electromagnetic radiation by the so-called Factorization Method. We apply this method to reconstruct a couple of media from numerically simulated field data.

This book provides a comprehensive practical treatment of the modelling of electrical power systems, and the theory and practice of fault analysis of power systems covering detailed and advanced theories as well as modern industry practices. The continuity and quality of electricity delivered safely and economically by today’s and future’s electrical power networks are important for both developed and developing economies. The correct modelling of power system equipment and correct fault analysis of electrical networks are pre-requisite to ensuring safety and they play a critical role in the identification of economic network investments. Environmental and economic factors require engineers to maximise the use of existing assets which in turn require accurate modelling and analysis techniques. The technology described in this book will always be required for the safe and economic design and operation of electrical power systems. The book describes relevant advances in industry such as in the areas of international standards developments, emerging new generation technologies such as wind turbine generators, fault current limiters, multi-phase fault analysis, measurement of equipment parameters, probabilistic short-circuit analysis and electrical interference. *A fully up-to-date guide to the analysis and practical troubleshooting of short-circuit faults in electricity utilities and industrial power systems *Covers generators, transformers, substations, overhead power lines and industrial systems with a focus on best-practice techniques, safety issues, power system planning and economics *North American and British / European standards covered

Reprint of the original, first published in 1889.

This volume is based on contributions from the First International Conference on “Recent Advances in Natural Language Processing” (RANLP’95) held in Tzigov Chark, Bulgaria, 14-16 September 1995. This conference was one of the most important and competitively reviewed conferences in Natural Language Processing (NLP) for 1995 with submissions from more than 30 countries. Of the 48 papers presented at RANLP’95, the best (revised) papers have been selected for this book, in the hope that they reflect the most significant and promising trends (and latest successful results) in NLP. The book is organised thematically and the contributions are grouped according to the traditional topics found in NLP: morphology, syntax, grammars, parsing, semantics, discourse, grammars, generation, machine translation, corpus processing and multimedia. To help the reader find his/her way, the authors have prepared an extensive index which contains major terms used in NLP; an index of authors which lists the names of the authors and the page numbers of their paper(s); a list of figures; and a list of tables. This book will be of interest to researchers, lecturers and graduate students interested in Natural Language Processing and more specifically to those who work in Computational Linguistics, Corpus Linguistics and Machine Translation.

Using lasers to induce and probe surface processes has the advantages of quantum state specificity, species selectivity, surface sensitivity, fast time-resolution, high frequency resolution, and accessibility to full pressure ranges. These advantages make it highly desirable to use light to induce, control, or monitor surface chemical and physical processes. Recent applications of laser based techniques in studying surface processes have stimulated new developments and enabled the understanding of fundamental problems in energy transfer and reactions. This volume will include discussions on spectroscopic techniques, energy transfer, desorption dynamics, and photochemistry.