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Applied Mathematical Modelling of Engineering Problems

The subject of the book is the "know-how" of applied mathematical modelling: how to construct specific models and adjust them to a new engineering environment or more precise realistic assumptions; how to analyze models for the purpose of investigating real life phenomena; and how the models can extend our knowledge about a specific engineering process. Two major sources of the book are the stock of classic models and the authors' wide experience in the field. The book provides a theoretical background to guide the development of practical models and their investigation. It considers general modelling techniques, explains basic underlying physical laws and shows how to transform them into a set of mathematical equations. The emphasis is placed on common features of the modelling process in various applications as well as on complications and generalizations of models. The book covers a variety of applications: mechanical, acoustical, physical and electrical, water transportation and contamination processes; bioengineering and population control; production systems and technical equipment renovation. Mathematical tools include partial and ordinary differential equations, difference and integral equations, the calculus of variations, optimal control, bifurcation methods, and related subjects.

Mathematical models and methods provide a rigorous, systematic, and
quantitative description of various real-world (physical, chemical, biological)
phenomena. They help to understand and analyse the essential qualitative
features of these ...

Classical and Quantum Orthogonal Polynomials in One Variable

The first modern treatment of orthogonal polynomials from the viewpoint of special functions is now available in paperback.

He defined the functions sm(u, q) and cm(u, a) as the solutions to the coupled
system s'(u) = c2(u) - as(u), c'(u) = -s2(u) + ac(u), (21.9.48) subject to the initial
conditions s(0) = 0, c(0) = 1. In this notation, s = sm, c = cm. In his doctoral
dissertation ...

Recueil de Modèles Aléatoires

Ce recueil puise sa source dans les cours de master de mathématiques appliquées et de préparation à l’épreuve de modélisation de l’agrégation de mathématiques. Le parti pris de cet ouvrage est de polariser la rédaction par les modèles plutôt que par les outils, et de consacrer chaque chapitre à un modèle. Le premier public visé est celui des enseignants-chercheurs en probabilités, débutants ou confirmés. De nombreux chapitres peuvent également bénéficier directement à des étudiants de master ou préparant l’agrégation. This collection was inspired by applied mathematics Master classes in stochastic modeling. The focus is on models rather than on tools, and each chapter is devoted to a specific model. Though the book is primarily intended for academics in the field of probability theory, beginners and experienced researchers alike, many chapters will also benefit students preparing to pursue their Master degree in mathematics.

De nombreux chapitres peuvent également bénéficier directement à des étudiants de master ou préparant l’agrégation. This collection was inspired by applied mathematics Master classes in stochastic modeling.

Constructions of Lie Algebras and their Modules

This book deals with central simple Lie algebras over arbitrary fields of characteristic zero. It aims to give constructions of the algebras and their finite-dimensional modules in terms that are rational with respect to the given ground field. All isotropic algebras with non-reduced relative root systems are treated, along with classical anisotropic algebras. The latter are treated by what seems to be a novel device, namely by studying certain modules for isotropic classical algebras in which they are embedded. In this development, symmetric powers of central simple associative algebras, along with generalized even Clifford algebras of involutorial algebras, play central roles. Considerable attention is given to exceptional algebras. The pace is that of a rather expansive research monograph. The reader who has at hand a standard introductory text on Lie algebras, such as Jacobson or Humphreys, should be in a position to understand the results. More technical matters arise in some of the detailed arguments. The book is intended for researchers and students of algebraic Lie theory, as well as for other researchers who are seeking explicit realizations of algebras or modules. It will probably be more useful as a resource to be dipped into, than as a text to be worked straight through.

When the involution in D is of first kind, one has for x € M", v and w é W, X *($v,w)
= xp(v & w) — # t((w, v) + (v,v)")x x y(v 2 v - # tow,v) + (v,v)")x k sk = -8 *($v,v - 8 ) –
4. t((w, v) + (w, v) )x S u, (v,w)y * − x °v,w + x (-8 (v,w) Egg - *****{41, mitri) k * A.

Structure and Properties of Clusters: from a few Atoms to Nanoparticles

This volume on Clusters brings together contributions from a large number of specialists. A central element for all contributions is the use of advanced computational methodologies and their application to various aspects of structure, reactivity and properties of clusters. The size of clusters varies from a few atoms to nanoparticles. Special emphasis is given to bringing forth new insights on the structure and properties of these systems with an eye towards potential applications in Materials Science. Overal, the volume presents to the readers an amazing wealth of new results. Particular subjects include water clusters, Silicon, Iron, Nickel and Gold clusters, carbon-titanium microclusters and nanoparticles, fullerenes, carbon nanotubes, chiral carbon nanotubes, boron nanoclusters and more.

[10] M. L. Kimble, A. W. Castleman, Jr., R. Mitri, C. Bürgel, and V. Bonacoic'-
Koutecky", Reactivity of Atomic Gold Anions toward Oxygen and the Oxidation of
CO: Experiment and Theory, Journal of the American Chemical Society 126, ...

Basic Hypergeometric Series

This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain its comprehensiveness.

... Sudler [1966], Sylvester [1882], and Wright [1965]. Concerning theta functions,
see Adiga et al. [1985], Askey [1989c], Bellman [1961], and Jensen's use of theta
functions in Pólya [1927] to derive necessary and sufficient conditions for the ...

An Accompaniment to Higher Mathematics

Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.

In particular, he observes that Pólya's heuristic strategies actually are whole
categories of related strategies, and that attempts by students to implement them
from Pólya's general descriptions founder at least in part on this lack of detail (
see ...