Category: Mystery, Thriller & Suspense

Book Summary :

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Book Summary :

Designing small structures necessitates an a priori understanding of various device behaviors. The way to gain such understanding is to construct, analyze, and interpret the proper mathematical model. Through such models, Modeling MEMS and NEMS illuminates microscale and nanoscale phenomena, thereby facilitating the design and optimization of micro- and nanoscale devices. After some introductory material, a review of continuum mechanics, and a study of scaling, the book is organized around phenomena. Each chapter addresses a sequence of real devices that share a common feature. The authors abstract that feature from the devices and present the mathematical tools needed to model it. They construct, analyze, and interpret a series of models of increasing complexity, then at the end of the chapter, they return to one of the devices described, apply the model to it, and interpret the analysis. In the beginning, the world of microdevices was dominated by experimental work and the development of fabrication techniques. As it matures, optimization and innovative designs are moving to the forefront. Modeling MEMS and NEMS not only provides the practical background and tools needed to design and optimize microdevices but it also helps develop the intuitive understanding that can lead to developing new and better designs and devices.

Book Summary :

This three-volume work contains articles collected on the occasion of Alexander Grothendieck’s sixtieth birthday and originally published in 1990. The articles were offered as a tribute to one of the world’s greatest living mathematicians. Many of the groundbreaking contributions in these volumes contain material that is now considered foundational to the subject. Topics addressed by these top-notch contributors match the breadth of Grothendieck’s own interests, including: functional analysis, algebraic geometry, algebraic topology, number theory, representation theory, K-theory, category theory, and homological algebra.

Book Summary :

"Based on a math course for advanced undergraduates and graduate students at Cal Tech, this brief monograph requires a background in advanced calculus. Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, exponential functions of operators, and problems in partial differential equations. Includes solutions. 1962 edition"--

Book Summary :

* Contains computer algebra worksheets or "recipes" designed using MAPLE (System 10); no prior knowledge of MAPLE is assumed * Effective computational science text for first- and second-year undergraduates in mathematics, physics, engineering, chemistry, economics, biology, and pre-medicine * Examples and problems provide basis for both self-study and on-line course

Book Summary :

In recent years, mathematical techniques applied to novel disciplines within the science and engineering have experienced extraordinary growth. Advanced Mathematical Techniques in Science and Engineering focusses on a detailed range of mathematics applied within various fields of science and engineering for different tasks. Topics of focus include: Analysis of Consensus-Building Time in Social GroupsModeling of intersystem accidents in critical infrastructure systemsStochastic approaches to analysis and modeling of multi-sources and big dataPerformance evaluation of computational DoS attack on access point in Wireless LANsRanking methods for decision-making under uncertaintyUnderstanding time delay based Modeling & Diffusion of technological productsRole of soft computing in science and engineeringComplex system reliability analysis and optimizationTree growth models in forest ecosystems modelling This research book can be used as a reference for students in a final year undergraduate engineering course, such as mechanical, mechatronics, industrial, computer science, information technology, etc. Furthermore, the book can serve as a valuable reference for academics, engineers and researchers in these and related subject areas.

Book Summary :

At first sight discrete and fractional programming techniques appear to be two com pletely unrelated fields in operations research. We will show how techniques in both fields can be applied separately and in a combined form to particular models in location analysis. Location analysis deals with the problem of deciding where to locate facilities, con sidering the clients to be served, in such a way that a certain criterion is optimized. The term "facilities" immediately suggests factories, warehouses, schools, etc. , while the term "clients" refers to depots, retail units, students, etc. Three basic classes can be identified in location analysis: continuous location, network location and dis crete location. The differences between these fields arise from the structure of the set of possible locations for the facilities. Hence, locating facilities in the plane or in another continuous space corresponds to a continuous location model while finding optimal facility locations on the edges or vertices of a network corresponds to a net work location model. Finally, if the possible set of locations is a finite set of points we have a discrete location model. Each of these fields has been actively studied, arousing intense discussion on the advantages and disadvantages of each of them. The usual requirement that every point in the plane or on the network must be a candidate location point, is one of the mostly used arguments "against" continuous and network location models.

Book Summary :

Michael Strevens shows how simplicity can co-exist with the tangled interconnections within complex systems. By looking at the foundations of statistical reasoning about complex systems (gases, ecosystems and even social systems) he provides an understanding of how simplicity emerges from complexity.

Book Summary :

Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions.- G. Wallet: Overstability in Arbitrary Dimension.- F.Diener, M. Diener: Maximal Delay.- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the Case of a Period-doubling Cascade.- E. Benoit: Linear Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: the Zoom.- S.N. Samborski: Rivers from the Point ofView of the Qualitative Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P. van den Berg: Macroscopic Rivers.

Book Summary :

Dealing with Uncertainties is an innovative monograph that lays special emphasis on the deductive approach to uncertainties and on the shape of uncertainty distributions. This perspective has the potential for dealing with the uncertainty of a single data point and with sets of data that have different weights. It is shown that the inductive approach that is commonly used to estimate uncertainties is in fact not suitable for these two cases. The approach that is used to understand the nature of uncertainties is novel in that it is completely decoupled from measurements. Uncertainties which are the consequence of modern science provide a measure of confidence both in scientific data and in information in everyday life. Uncorrelated uncertainties and correlated uncertainties are fully covered and the weakness of using statistical weights in regression analysis is discussed. The text is abundantly illustrated with examples and includes more than 150 problems to help the reader master the subject.

Book Summary :

This advanced textbook on linear algebra and geometry covers a wide range of classical and modern topics. Differing from existing textbooks in approach, the work illustrates the many-sided applications and connections of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. The subjects covered in some

Book Summary :

Covers several research fields dealing with transport. This work covers three main topics including road traffic, granular matter, and biological transport. It considers different points of views including modelling, simulations, experiments, and phenomenological observations.