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Complex Variables with Applications
Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a two-dimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. It explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics, using geometry to illustrate analytic concepts and employing analysis to unravel geometric notions. The engaging exposition is replete with discussions, remarks, questions, and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. This focus involves a careful examination of the methods and assumptions underlying various alternative routes that lead to the same destination.
Complex Nonlinearity : Chaos, Phase Transitions, Topology Change and Path Integrals
The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism.
Complex Effects in Large Eddy Simulations
This volume contains a collection of expert views on the state of the art in Large Eddy Simulation (LES) and its application to complex ?ows. Much of the material in this volume was inspired by contributions that were originally presented at the symposium on Complex E?ects in Large Eddy Simulation held in Lemesos (Limassol), Cyprus, between September 21st and 24th, 2005.
Complex decision making : Theory and practice
The increasingly complex environment of today's world, characterized by technological innovation and global communication, generates myriads of possible and actual interactions while limited physical and intellectual resources severely impinge on decision makers, be it in the public or private domains. At the core of the decision-making process is the need for quality information that allows the decision maker to better assess the impact of decisions in terms of outcomes, nonlinear feedback processes and time delays on the performance of the complex system invoked.
Complex Analysis : In the Spirit of Lipman Bers
In this book, the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory.
Complex analysis
The guiding principle of this presentation of ``Classical Complex Analysis'' is to proceed as quickly as possible to the central results while using a small number of notions and concepts from other fields. Thus the prerequisites for understanding this book are minimal; only elementary facts of calculus and algebra are required.
Comparative genomics ; Vol. 3678 : RECOMB 2005 International Workshop, RCG 2005, Dublin, Ireland, September 18-20, 2005, Proceedings
This book constitutes the refereed proceedings of the RECOMB 2005 Satellite Workshop, the 3rd RECOMB Comparative Genomics meeting RCG 2005, held in Dublin, Ireland in September 2005. The 14 revised full papers presented were carefully reviewed and selected from 21 initial submissions. The papers address a broad variety of aspects and components of the field of comparative genomics, ranging from new quantitative discoveries about genome structure and process to theorems on the complexity of computational problems inspired by genome comparison.
Comparative genomics ; Vol. 3388 : RECOMB 2004 International Workshop, RCG 2004, Bertinoro, Italy, October 16-19, 2004, Revised Selected Papers
This papers investigates the problem of conservation of combinatorial structures in genome rearrangement scenarios. We give a characterization of a class of scenarios that conserve all common intervals, called commuting scenarios, and a characterization of permutations for which commuting scenarios exist. We show that measuring conservation of common intervals can be useful tool in assessing the quality of rearrangement scenarios, by investigating in detail three specific scenarios involving the mouse, rat and human X chromosomes.
Compact Riemann Surfaces : An Introduction to Contemporary Mathematics
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory.
Compact Lie Groups
This book covers the structure and representation theory of compact Lie groups. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.
Communications and Discoveries from Multidisciplinary Data
In this book, we aim at urging the development of data-based methods and methodologies for interdisciplinary and creative communications for solving emerging social problems. The reader shall view the direction to combine three methodological frameworks: data mining, data sharing, and communication in the contexts of sciences and businesses.
Classification - the ubiquitous challenge ; Proceedings of the 28th annual conference of the Gesellschaft für Klassifikation e.V., University of Dortmund, March 9-11, 2004
This volume contains revised versions of selected papers presented duringthe 28th Annual Conference of the Gesellschaft f ̈ur Klassifikation (GfKl), theGerman Classification Society. contributed papers by authors from 18countries were presented at the conference in 52 parallel sessions representingthe whole field addressed by the title of the conference “Classification: TheUbiquitous Challenge”. Among these 52 sessions the VOC organized sessionson Mixture Modelling, Optimal Scaling, Multiway Methods, and Psychomet-rics with 18 papers. Overall, presentation of the papers in this volume is arranged in the fol-lowing parts:I. (Semi-)Plenary PresentationsII. Classification and Data AnalysisIII. Applications, andIV. Contest: Social Milieus in Dortmund
Classical Nucleation Theory in Multicomponent Systems
Nucleation is the initial step of every first-order phase transition, and most phase transitions encountered both in everyday life and industrial processes are of the first-order. Using an elegant classical theory based on thermodynamics and kinetics, this book provides a fully detailed picture of multi-component nucleation. As many of the issues concerning multi-component nucleation theory have been solved during the last 10-15 years, it also thoroughly integrates both fundamental theory with recent advances presented in the literature. It covered are: the basic relevant thermodynamics and statistical physics; modelling a molecular cluster as a spherical liquid droplet; predicting the size and composition of the nucleating critical clusters; kinetic models for cluster growth and decay; calculating nucleation rates; and a full derivation and application of nucleation theorems that can be used to extract microscopic cluster properties from nucleation rate measurements.
Chiral Soliton Models for Baryons
This concise research monograph introduces and reviews the concept of chiral soliton models for baryons. In these models, baryons emerge as (topological) defects of the chiral field. The many applications shed light on a number of bayron properties, ranging from static properties via nucleon resonances and deep inelastic scattering to even heavy ion collisions. As far as possible, the theoretical investigations are confronted with experiment. Conceived to bridge the gap between advanced graduate textbooks and the research literature, this volume also features a number of appendices to help nonspecialist readers to follow in more detail some of the calculations in the main text.
Chemical Kinetics and Reaction Dynamics
Chemical Kinetics and Reaction Dynamics brings together the major facts and theories relating to the rates with which chemical reactions occur from both the macroscopic and microscopic point of view. This book helps the reader achieve a thorough understanding of the principles of chemical kinetics and includes: *Detailed stereochemical discussions of reaction steps / *Classical theory based calculations of state-to-state rate constants / *A collection of matters on kinetics of various special reactions such as micellar catalysis, phase transfer catalysis, inhibition processes, oscillatory reactions, solid-state reactions, and polymerization reactions at a single source. / The growth of the chemical industry greatly depends on the application of chemical kinetics, catalysts and catalytic processes.
Challenges for Computational Intelligence
Computational Intelligence (CI) is used as a name to cover many existing branches of science, with artificial neural networks, fuzzy systems and evolutionary computation forming its core. In recent years CI has been extended by adding many other subdisciplines and it became quite obvious that this new field also requires a series of challenging problems that will give it a sense of direction. Without setting up clear goals and yardsticks to measure progress on the way many research efforts are wasted.The book written by top experts in CI provides such clear directions and the much-needed focus on the most important and challenging research issues, showing a roadmap how to achieve ambitious goals.
Centrifugal Pumps
This book gives an unparalleled, up-to-date, in-depth treatment of all kinds of flow phenomena encountered in centrifugal pumps including the complex interactions of fluid flow with vibrations and wear of materials.
Casting : An Analytical Approach
For a long time, the die cast industry has used trial and error as a leading development method, resulting in tremendous growth in the utilisation of available CFD (computational fluid dynamics) software. This software allows the development of better products that maximise the advantages the die cast process has to offer. Casting: An Analytical Approach will refresh knowledge of the governing laws of the fluid dynamics that have an effect on die cast die and die cast process design. MATLAB® (MathWorks, Inc.) and Visual Basic® (Microsoft) code are listed in Casting: An Analytical Approach for every stage of product, die and die cast process design; providing better understanding of die and process design and simplifying calculations of the die cast die as well as the die cast process. Gas ventilation system calculations and fundamentals of compressible gas flow are also included.
Carbon Inventory Methods Handbook for Greenhouse Gas Inventory, Carbon Mitigation and Roundwood Production Projects
Carbon Inventory Methods Handbook provides detailed step-by-step information on sampling procedures, field and laboratory measurements, application of remote sensing and GIS techniques, modeling, and calculation procedures along with sources of data for carbon inventory. The unique feature of this handbook is that it provides practical guidance on carbon inventory methods for four kinds of projects, namely, 1) development, implementation and monitoring of carbon mitigation in forest, agriculture and grassland sectors, 2) national greenhouse gas inventory in agriculture, forest, and other land-use categories, 3) forest, grassland and agroforestry development and 4) commercial and community forestry roundwood production.
Calculus of variations and nonlinear partial differential equations : With a historical overview by Elvira Mascolo : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 27 - July 2, 2005
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
