Applied mathematics Books

Book SynopsisOn Gale’s Contribution in Revealed Preference Theory.- Finding Nonlinear Production - Consumption Equilibrium.- Systemic Risk in Financial Systems: Properties of Equilibria.- The Coalitional TU Extensions of Gale-Mas-Colell Economy.- Simple visibility design in network games.- Repeated Games with Tail-Measurable Payoffs.- Calibrated Forecasts: The Minimax Proof.- Getting Permission when Options are Partially Ordered.- Existence of Haar measures: A note on Rudin's fixed-point approach.- Infinite-horizon single-objective and multiobjective optimal control problems in the continuous time framework.- Optimal Growth in a Miniature Two-Sector Model with and without Discounting: A Synthesis.- Production functions with continuum of vintage inputs.- Two country model of trade with international borrowing and lending.- David Gale: Duality and Turnpikes.- Stochastic Dynamical Framework for Risk Managements of SMEs’ Growth: Model, Approach and Quantitative Analysis.- Two turnpike results for a generalized von Neumann-Gale model.- Stability and Weak Setwise Stability in Many-to-Many Matching with Contracts.- A Deferred Acceptance Algorithm for Large Marriage Markets.- Gale-Shapley algorithm revisited: semistability.- Applying the New Concept of Variances with Uncertainty to Cover the Worst Markets.

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Book SynopsisTable of Contents1. Basic Calculations 2. Rig Calculations 3. Pressure Control 4. Fluid Calculations 5. Cementing Calculations 6. Well Hydraulics 7. Drilling Calculations 8. Air and Gas Calculations

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Book SynopsisThis volume presents surveys and research papers on various aspects of modern stability theory, including discussions on modern applications of the theory, all contributed by experts in the field. The volume consists of four sections that explore the following directions in the development of stability theory: progress in stability theory by first approximation; contemporary developments in Lyapunov's idea of the direct method; the stability of solutions to periodic differential systems; and selected applications. Advances in Stability Theory at the End of the 20th Century will interest postgraduates and researchers in engineering fields as well as those in mathematics.Table of ContentsIntroduction to the Series. Preface. Overview. Progress in Stability Theory by the First Approximation. Invariant Foliations for Caratheodory Type Differential Equations. On Exponential Asymptotic Stability for Functional Differential Equations with Causal Operators. Lyapunov Problems on Stability. Contemporary Development of Lyapunov's Ideas of Direct Method. Vector Lyapunov Function: Nonlinear, Time-Varying, Ordinary and Functional Differential Equations. Some Results on Total Stability Properties for Singular Systems. Stability Theory of Voltera Difference Equations. Consistent Lyapunov Methodology for Exponential Stability: PCUP Approach. Advances in Stability Theory of Lyapunov: Old and New. Matrix Lyapunov Functions and Stability Analysis of Dynamical Systems. Stability Theorems in Impulsive Functional Differential Equations with Infinite Delay. The Asymptotic Behavior of Solutions of Stochastic Functional Differential Equations with Finite Delays by Lyapunov-Razumikhin Method. A Non-standard Approach to the Study of the Dynamic System Stability. Stability of Solutions. A Survey of Starzhinskii's Works on Stability of Periodic Motions and Nonlinear Oscillations. Implications of the Stability of an Orbit for Its Omega Limit Set. Some Concepts of Periodic Motions and Stability Originated by Analysis of Homogenous Systems. Stability Criteria for Periodic Solutions of Autonomous Hamiltonian Systems. Selected Applications. Stability in Models of Agriculture-Industry-Environment. Bifurcations of Periodic Solutions of the Three Body Problem. Complex Mechanical Systems: Steady State Motions, Oscillations, Stability. Progress in Stability of Impulsive Systems with Applications to Population Growth Models. Contemporary Development of Lyapunov's Ideas of Direct Method. Stability of Solutions to Periodic Differential Systems. Selected Applications.

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Book SynopsisStudents and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to control problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.Table of ContentsCompetition and Cooperation: The Social Environment for Economic Activity. Economic Dynamics. Controllable Economic Systems. Ordinary Differential Systems Model of National Economies. Oscillation: Conditions for Economic Boom; Criteria for the Prevention of Depression. Hereditary Economic Systems.

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Book SynopsisLinear non-autonomous equations arise as mathematical models in mechanics, chemistry, and biology. This book explores the preservation of invariant tori of dynamic systems under perturbation. It is a useful contribution to the literature on stability theory and provides a source of reference for postgraduates and researchers.Trade Review"This volume will be of great interest to researchers and students dealing with nonautonomous systems." - Zentralblatt fur Mathematik, Vol. 1026Table of ContentsExponentially Dichotomous Linear Systems of Differential Equations and Lyapunov Functions of Variable Sign. Exponential Dichotomy Criterion for Linear Systems in Terms of Quadratic Forms. Decomposition Over the Whole R Axis of Linear Systems of Differential Equations Exponentially Dichotomous on Semiaxes R+ and R_. Degeneracy of the Quadratic Form Possessing a Definite-Sign Derivative Along the Solutions of the System (1.1.1). Integral Representation of Weakly Regular Systems Bounded on the Whole R Axis. Complement to the Exponentially Dichotomous of Weakly Regular on R Linear Systems. Regularity of Linear Systems of the Block-Triangular Form. Perturbation of the Block-Triangular Form Linear Systems which are Regular and Weakly Regular on the Whole R Axis. Exponentially Dichotomous Linear Systems with Parameters. Comments and References. Linear Extension of Dynamical Systems on a Torus. Necessary Existence Conditions for Invariant Tori. The Green Function. Sufficient Existence Conditions for an Invariant Torus. Existence Conditions for an Exponentially Stable Invariant Torus. Uniqueness Conditions for the Green Function and its Properties. Sufficient Conditions for Exponential Dichotomy of the Invariant Torus. Necessary Conditions for Exponential Dichotomy of the Invariant Torus. Existence Criterion for the Green Function. The Non-Unique Green Function and the Properties of the System Implied by its Existence. Invariant Tori of Linear Extensions with Slowly Changing Phase. Preserving the Green Function Under Small Perturbations of Linear Expansions on a Torus. On the Smoothness of an Exponentially Stable Invariant Torus. On the Dependence of Green Functions on Parameters. Continuity and Differentiability of the Green Function. Invariant Tori of Linear Extensions with a Degenerate Matrix at the Derivatives. Bounded Invariant Manifolds of Dynamical Systems and their Smoothness. Comments and References. Splitability of Linear Extensions of Dynamical Systems on a Torus. Sufficient Conditions for Splitability of Linear Extensions of Dynamical Systems on a Torus. Reversibility of the Theorem on Splitability. On Triangulation and the Relationship of C'-Block Splitability of a Linear System with the Problem on r-frame Complementability up to the Periodic Basis in R^Tn. Reducing on Linearized Systems to a Diagonal Form. On the Relationship of Exponentially Dichotomous Linear Expansions with the Algebraic System Solvability. Three Block Divisibility of Linear Extensions and Lyapunov Functions of Variable Sign. Algebraic Problems of the K-Blocked Divisibility of Linear Extensions on a Torus. Comments and References. Problems of Perturbation Theory of Smooth Invariant Tori of Dynamical Systems. Solution Variations on the Manifold M. Exponential Stability and Dichotomy Conditions for Linear Extensions of Dynamical Systems on a Torus. Roughness Conditions for the Green Function of the Linear Extension of a Dynamical System on a Torus with the Index of Smoothness. A Theorem of Perturbation Theory of an Invariant Torus of a Dynamical System. Green Function for a Linear Matrix Equation. On the Problem of Structure of Some Regular Linear Extensions of Dynamical Systems on a Torus. Invariant Manifolds of Autonomous Differential Equations and Lyapunov Functions with Alternating Signs. Comments and References. Index.

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Book SynopsisNonlinear systems with random structures arise quite frequently as mathematical models in diverse disciplines. This monograph presents a systematic treatment of stability theory and the theory of stabilization of nonlinear systems with random structure in terms of new developments in the direct Lyapunov's method. The analysis focuses on dynamic systems with random Markov parameters. This high-level research text is recommended for all those researching or studying in the fields of applied mathematics, applied engineering, and physics-particularly in the areas of stochastic differential equations, dynamical systems, stability, and control theory.Trade Review"This volume will be of interest to researchers and students in stochastic stability theory." - Zentralblatt fur Mathematik, Vol. 1026Table of ContentsIntroductory Remarks. Random Variables and Probability Distributions. Probability Processes and their Mathematical Description. Random Differential Equations. System with Random Structure. Stability Analysis Using Scalar Lyapunov Functions. Stability Concepts for Stochastic Systems. Random Scalar Lyapunov Functions. Conditions of Stability in Probability. Converse Theorems. Stability in Mean Square. Stability in Mean Square of Linear Systems. Stability Analysis Using Multi-component Lyapunov Functions. Vector Lyapunov Functions. Stochastic Matrix-Valued Lyapunov Functions. Stability Analysis in General. Stability Analysis of Systems in Ito's Form. Stochastic Singularly Perturbed Systems. Large-Scale Singularly Perturbed Systems. Stability Analysis by the First-Order Approximation. Stability Criterion by the First-Order Approximation. Stability with Respect to the First-Order Approximation. Stability by First-Order Approximation of Systems with Random Delay. Convergence of Stochastic Approximation Procedure. Stabilization of Controlled Systems with Random Structure. Problems of Stabilization. Optimal Stabilization. Linear-Quadratic Optimal Stabilization. Sufficient Stabilization Conditions for Linear Systems. Optimal Solution Existence. The Small Parameter Method Algorithm. Applications. A Stochastic Version of the Lefschetz Problem. Stability in Probability of Oscillating Systems. Stability in Probability of Regulation Systems. Price Stability in a Stochastic Market Model. References. Index. Lyapunov Functions. Stability Analysis Using Multicomponent Lyapunov Functions. Stability Analysis by the First-order Approximation. Stabilization of Controlled Systems with Random Structure. Applications; References; Index.

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Book SynopsisThe conventional wisdom was that biology influenced mathematics and computer science. But a new approach has taken hold: that of transferring methods and tools from computer science to biology. The reverse trend is evident in Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology and Back. The contributors address the structural (syntactical) view of the domain. Mathematical linguistics and computer science can offer various tools for modeling complex macromolecules and for analyzing and simulating biological issues. This collection is valuable for students and researchers in biology, computer science, and applied mathematics.Table of ContentsLogistics, Languages and Combinatorics. Models of Molecular Computing.

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Book SynopsisThis book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems that appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics, and microelectronics.Table of ContentsThis book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems that appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics, and microelectronics.

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Book SynopsisMathematics and Science for Sport and Exercise introduces students to the basic mathematical and scientific principles underpinning sport and exercise science. It is an invaluable course companion for students who have little prior experience of maths or science, and an ideal revision aid for higher level undergraduate students.The book explains the basic scientific principles that help us to understand sport, exercise and human movement, using a wide range of well-illustrated practical examples. Written by three leading sport scientists with many years experience teaching introductory courses, the book guides beginning students through those difficult to grasp areas of basic maths and science, and identifies the common problems and misconceptions that students often experience. It includes coverage of key areas such as: science of physical states â gas, liquid and solid science of biomechanics, motion and energy mathematical formulae, calculus, and differential equations statistics scientific report writing key concepts such as pressure, torque and velocity self-test features and highlighted key points throughout each chapter. Fully referenced, with guides to further reading, this book is an essential companion for all students on foundation or undergraduate level courses in sport and exercise science, kinesiology, and the human movement sciences.Table of Contents1.Introduction Part1 Physical states 2.Gases 3.Liquids 4.Solids Part 2 Force, pressure, energy and electricity 5.Force and pressure 6.Energy 7.ElectricityPart 3 Scientific transferable skills 8.Data analysis 9.Numerical Calculations 10.Report writing Appendix 1: Health questionnaire Appendix 2: Examples of consent forms Appendix 3: Thermal equivalents of oxygen Appendix 4: Scientific journals in sport and exercise Appendix 5:Measurement concepts

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Book SynopsisBased on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.Table of ContentsMathematical Modeling of N-Body Quantum Scattering Processes Microhydrodynamics of Sharp Corners and Edges Acoustic Scattering by Irregular Obstacles On Generalized Inverse Steklov Problems A Hybrid Root Finder Volterra Type Integral Geometry Problems Inversionof the X-Ray Transform and the Radon Transform with Incomplete Data Reconstructing a Function by means of Integrals over a Family of Conical Surfaces On the use of Wavelet Expansions and the Conjugate Gradient Method for Solving First Kind Integral Equations Optimal Algorithms for the Calculation of Singular Integrals An Order One Approximate Method of Solution of Differential and Integral Equations A Multigrid Method for Solving Reaction-Diffusion Systems Time-Dependent Bending of Plates with Transverse Shear Deformation Polarization Gradient in Piezoelectric Micropolar Elasticity Thermoelastic Stress Separation via Poisson Equation Solution by means of the Boundary Element Method On Neutral Functional Differential Equations with Causal Operations A Semi-Analytic Method for the Study of Acoustic Pulse Propagation in Inhomogeneous Elastic 1-D Media Efficient Finite Elements for the Numerical Approximation of Cylindrical Shells Error Estimates for Computing Fixed Densities of Markov Integral Operators A Modified Monte Carlo Approach to the Approximation of Invariant Measures Acceleration Waves in von Karman Plate Theory Dynamics and Resonance of a Nonlinear Mechanical Oscillator Subjected to Parametric and External Excitation On the Vibration of Helical Springs A Two-Dimensional Numerical Model of Chemotaxis Asymptotic Analysis of Fracture Theory for Layered Composites in Compression (The Plane Problem) Existence and Regularity of Weak Solutions to the Displacement Boundary Value Problem of Nonlinear Elastostatics On Convergence and Uniqueness of Microscale Heat Transfer Equation On Numerical Approximations of a Frictionless Contact Problem for Elastic-Viscoplastic Materials A Panel Clustering Method for 3-D Elastostatics using Spherical Harmonics Extensions of Constrained Least-Squares for Obtaining Regularized Solutions to First-Kind Integral Equations Existence and Nonexistence Results for some Boundary Value Problems at Resonance Analytic Investigation of Thick Anisotropic Plates with Undulating Surfaces On Stoke's Nonlinear Integral Wave Equation - continued.

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Book SynopsisThe First Pan-China Conference on Differential Equations was held in Kunming, China in June of 1997. Researchers from around the world attended-including representatives from the US, Canada, and the Netherlands-but the majority of the speakers hailed from China and Hong Kong. This volume contains the plenary lectures and invited talks presented at that conference, and provides an excellent view of the research on differential equations being carried out in China.Most of the subjects addressed arose from actual applications and cover ordinary and partial differential equations. Topics include:Table of ContentsPART I: ORDINARY DIFFERENTIAL EQUATIONSAdvances in the Asymptotic and Numerical Solution of Linear Ordinary Differential Equations, F.W.J. OlverSome Unsolved Problems in Asymptotics, R. WongPeriodic Solutions and Heteroclinic Cycles in the Convection Model of a Rotating Fluid Layer, J. Li and X.H. ZhaoThe Equivalence of Exponential Stability for Impulsive Time-Delay Differential Systems, Z.-H. Guan, Y.-C. Zhou, and X.-P. HeConditions for Identity of Bifurcations in Cubic Hamiltonian Systems with Symmetry or Nonsymmetry Perturbations, Z. Liu, H. Cao, and J. LiPART II: PARTIAL DIFFERENTIAL EQUATIONSLong Time Behavior for the Generalized Ginzburg-Landau Equations, B. GuoThe Inverse Scattering Transform for a Variable-Coefficient KdV Equations (with Applications to Shallow Water Waves), H.-H. DaiThe Semigroup Theory and Abstract Linear Equations, G. YangA Unified Approach Towards Nonlinear Parabolic Equations with Strong Reaction in Rn, Y.-W. QiGlobal Existence of Smooth Solution to Boltzmann-Poisson System in Semiconductor Physics, G. Cui and Y. WangAnalytical Methods for a Selection of Elliptic Singular Perturbation Problems, N.M. TemmeExponential Attractors of the Strongly Damped Nonlinear Wave Equations, Z. Dai and B. GuoGeneralized Isovorticity Principle for Ideal Magnetohydrodynamics, V.A. Vladimirov and K.I. IlinScroll Waves in Excitable Media and the Motion of Organization Center, Q. Lu and S. LiuTransport Equations for a General Class of Evolution Equations, M.Z. Guo and X.P. Wanga-Times Integrated Cosine Function, G. YangIdentifying Parameters in Elliptic Systems by Finite Element Methods with Multi-Level Initializing, Y.F. Seid and J. Zou TechniquesMonotone Difference Schemes for Two Dimensional Nonhomogeneous Conservation Laws, T. Tang and Z.-H. Teng

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Book SynopsisThis volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras, including multiplier Hopf algebras and quantum groups.Table of ContentsLifting of Nichols algebras of type A2 and pointed Hopf algebras of order p4; survey of cross product bialgebras; a Morita-Takeuchi context for graded coalgebras; coalgebra-Galois extensions from the extension theory point of view; separable functors for the category of Doi-Hopf modules II; cyclic cohomology of coalgebras, coderivations and De Rham cohomology; Schur-Weyl categories and non-quasiclassical Weyl type formula; a generalized power map for Hopf algebras; associated varieties for classical lie superalgebras; algebraic versions of a finite-dimensional quantum groupoid; quasi-Hopf algebras and the centre of a tensor category; an easy proof for the uniqueness of integrals; the coquasitriangular Hopf algebra associated to a rigid Yang-Baxter coalgebra; on regularity of the algebra of covariants for actions of pointed Hopf algebras on regular commutative algebras; a survey on multiplier Hopf algebras.

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Book SynopsisThis reference illustrates the efficacy of CyclePad software for enhanced simulation of thermodynamic devices and cycles. It improves thermodynamic studies by reducing calculation time, ensuring design accuracy, and allowing for case-specific analyses. Offering a wide-range of pedagogical aids, chapter summaries, review problems, and worked examples, this reference offers a user-friendly and effective approach to thermodynamic processes and computer-based experimentation and design. Thermodynamic Cycles allows students to change any parameter and understand its effect on device performance, run experiments and investigate results, and run valuable sensitivity and cost-benefit analyses.Table of ContentsThermodynamic concepts: intelligent computer-aided software; review of thermodynamic concepts; thermodynamic cyclic systems; cycles; Carnot cycle; Carnot corollaries. Vapour cycles: Carnot vapour cycle; basic Rankine vapour cycle; improvements toRankine cycle; actual Rankine cycle; reheat Rankine cycle; regenerative Rankine cycle; low-temperature Rankine cycles; solar heat engines; geothermal heat engines; ocean thermal energy conversion; solar point heat engine; waste heat engine; vapour cycleworking fluids; kaline cycle; non-azeotropic mixture; Rankine cycle; super-critical cycle; design examples. Gas closed system cycles: Otto cycle; diesel cycle; Atkinson cycle; dual cycle; Lenoir cycle; Stirling cycle; Miller cycle; Wicks cycle; Ralliscycle; design examples. Gas open system cycles: Brayton or Joule cycle; split-shaft gas turbine cycle; improvement to Brayton cycle; reheat and inter-cool Brayton cycle; regenerative Brayton cycle; bleed air Brayton cycle; Feher cycle; Ericsson cycle;Braysson cycle; steam infection gas turbine cycle; Field cycle; Wicks cycle; ice cycle; design examples. Combines cycle and co-generation; combined cycle; triple cycle in series; triple cycle in parallel; cascaded cycle; Brayton/Rankine combined cycle;Brayton/Brayton combined cycle; Rankine/Rankine combined cycle; field cycleo co-generation; design examples. Refrigeration and heat pump open system cycles: Carnot refrigeration and heat pump cycle; basic vapour refrigeration cycle; actual vapourrefrigeration cycle; basic vapour heat pump cycle; actual vapour heat pump cycle working fluids for vapour refrigeration and heat pump systems; cascade and multi-stage vapour refrigeration cycles; domestic refrigerator-freezer and air conditioning-heatpump systems; absorption air-conditioning; Brayton gas refrigeration cycle; Stirling refrigeration cycle; Ericsson refrigeration cycle; liquefaction of gases; non-azeotropic mixture refrigeration cycle; design examples. Finite time thermodynamics: h

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Book SynopsisThe computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively simple terms, this book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering. Boundary integral equation methods (BIEM''s) have certain advantages over other procedures for solving such problems: BIEM''s are powerful, applicable to a wide variety of situations, elegant, and ideal for numerical treatment. Certain fundamental constructs in BIEM''s are also essential ingredients in boundary element methods, often used by scientists and engineers.However, BIEM''s are also sometimes more difficult to use in plane cases than in their three-dimensional counterparts. Consequently, the full, detailed BIEM treatment of two-dimensional problTrade Review"The text is written clearly and the proofs are given in detail." M. Aron, Proceedings of the Edinburgh Mathematical Society, Vol. 44, 445-448, 2001 "…the book offers a comprehensive treatment of the subject matter and constitutes a very useful source of information for mathematicians and other scientists interested in boundary integral equation methods. M. Aron, Proceedings of the Edinburgh Mathematical Society, Vol. 44, 445-448, 2001Table of ContentsIntroduction. The Laplace Equation. Plane Strain. Bending of Elastic Plates. Which Method?NTI/Sales Copy

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Book SynopsisAlthough the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation.The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipative terms, leading to new explicit and exact solutions. He also shows that the method is applicable to a variety of nonlinear problems.First discovered in virtual reality, nonlinear waves and solitons in solids are finally moving into the genuine reality of physics, mechanics, and engineering. Strain Solitons in Solids and How to Construct Them shows how to balance the mathematics of the problem with the application of the results to experiments and ultimately to generating and observing solitons in solids.Table of ContentsNonlinear Waves in Elastic Solids. Mathematical Description of General Deformation Wave Problem. Direct Methods and Formal Solutions. Nonlinear Strain Waves in Elastic Wave Guides. Waves in Non-Homogeneous Wave Guide. Numerical Simulation and Experiments. References. Index.

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Book SynopsisThe increasing power of computer resources along with great improvements in observational data in recent years have led to some remarkable and rapid advances in astrophysical fluid dynamics. The subject spans three distinct but overlapping communities whose interests focus on (1) accretion discs and high-energy astrophysics; (2) solar, stellar, and galactic magnetic fields; and (3) the geodynamo, planetary magnetic fields, and associated experiments. This book grew out of a special conference sponsored by the London Mathematical Society with the support of EPSRC that brought together leading researchers in all of these areas to exchange ideas and review the status of the field.The many interesting problems addressed in this volume concern:Table of ContentsAccretion Discs. Discs with Mhd Turbulence and Their Response to Orbiting Planets. Mixing at the Surface of White Dwarf Stars. Pulsar Magnetospheres. Magnetic Fields in Galaxies. Self-Consistent Mean Field Electrodynamics in Two and Three Dimensions. The Solar Tachocline: Formation, Stability and Its Role in the Solar Dynamo. Magnetoconvection. Alfvén Waves Within the Earth's Core. Turbulence Models and Plane Layer Dynamos. Planetary and Stellar Dynamos: Challenges for Next Generation Models. Convection in Rotating Spherical Fluid Shells and Its Dynamo States. Laboratory Experiments on Liquid Metal Dynamos and Liquid Metal Mhd Turbulence. Index.

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Book SynopsisOn the job or in the field, when facing a problem with differential equations and boundary conditions, most likely you don't have time to read through several publications in search of a method that may or may not solve your problem. Organized for quick and easy access to practical solutions, Analytical and Approximate Methods in Transport Phenomena is a reference for the day-to-day problems encountered when working with variables in heat, mass, or momentum transfer. This text is organized differently from usual resources on applied mathematics for engineers. First, it introduces a new classification system of the problem based on just three numbers, so locating the appropriate solution method is quick and easy. Second, the author presents mathematical methods with applications in mind, introducing examples, as well as common or possible solutions, before presenting any mathematical theory or method. This allows you to identify the issue you need to resolve, then apply theTable of ContentsProblems 111; One Variable, 1st Order, 1st Kind Boundary Condition. Problems 112; One Variable, 1st Order, 2nd Kind Boundary Condition. Problems 113; One Variable, 1st Order, 3rd Kind Boundary Condition. Problems 121; One Variable, 2nd Order, 1st Kind Boundary Condition. Problems 122; One Variable, 2nd Order, 2nd Kind Boundary Condition. Problems 123; One Variable, 2nd Order, 3rd Kind Boundary Condition. Problems 211; Two Variables, 1st Order, 1st Kind Boundary Condition. Problems 212; Two Variables, 1st Order, 2nd Kind Boundary Condition, Problems 213; Two Variables, 1st Order, 3rd Kind Boundary Condition, Problems 221; Two Variables, 2nd Order, 1st Kind Boundary Condition, Problems 222; Two variables, 2nd Order, 2nd Kind Boundary Condition. Problems 223; Two Variables, 2nd Order, 3rd Kind Boundary Condition. Problems 311; Three Variables, 1st Order, 1st Kind Boundary Condition. Problems 312; Three Variables, 1st Order, 2nd Kind Boundary Condition. Problems 313; Three Variables, 1st Order, 3rd Kind Boundary Condition. Problems 321; Three Variables, 2nd Order, 1st Kind Boundary Condition. Appendices.

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Book SynopsisAn ideal textbook for civil and environmental, mechanical, and chemical engineers taking the required Introduction to Fluid Mechanics course, Fluid Mechanics for Civil and Environmental Engineers offers clear guidance and builds a firm real-world foundation using practical examples and problem sets. Each chapter begins with a statement of objectives, and includes practical examples to relate the theory to real-world engineering design challenges. The author places special emphasis on topics that are included in the Fundamentals of Engineering exam, and make the book more accessible by highlighting keywords and important concepts, including Mathcad algorithms, and providing chapter summaries of important concepts and equations.Table of ContentsIntroduction. Fluid Statics. Continuity Equation. Energy Equation. Momentum Equation. Flow Resistance Equations. Dimensional Analysis. Pipe Flow. Open Channel Flow. External Flow. Dynamic Similitude and Modeling. Appendix A: Physical Properties of Common Fluids. Appendix B: Geometric Properties of Common Shapes. References. Bibliography. Index..

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Book SynopsisMathematics does not exist in isolation but is linked inextricably to the physical world. At the 2003 International Congress of Industrial and Applied Mathematics, leading mathematicians from around the globe gathered for a symposium on the Mathematics of Real World Problems, which focused on furthering the establishment and dissemination of those links.Presented in four parts, Mathematical Models and Methods for Real World Systems comprises chapters by those invited to this symposium. The first part examines mathematics for technology, exploring future challenges of mathematical technology, offering a wide-ranging definition of industrial mathematics, and explaining the mathematics of type-II superconductors. After lucid discussions on theoretical and applied aspects of wavelets, the book presents classical and fractal methods for physical problems, including a fractal approach to porous media textures and using MATLAB to model chaos in the motion of a satellite. The final section surveys recent trends in variational methods, focusing on areas such as elliptic inverse problems, sweeping processes, and the BBKY hierarchy of quantum kinetic equations.By virtue of its abstraction, mathematics allows the transfer of ideas between fields of applications. Mathematical Models and Methods for Real World Systems clearly demonstrates this and promotes the kind of cross-thinking that nurtures creativity and leads to further innovation.Table of ContentsMATHEMATICS FOR TECHNOLOGY: Mathematics as a Technology-Challenges for the Next Ten Years. Industrial Mathematics-What Is It? Mathematical Models and Algorithms for Type-II Superconductors. WAVELET METHODS FOR REAL-WORLD PROBLEMS: Wavelet Frames and Multiresolution Analysis. Comparison of a Wavelet-Galerkin Procedure with a Crank-Nicolson-Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass. Trends in Wavelet Applications. Wavelet Methods for Indian Rainfall Data. Wavelet Analysis of Tropospheric and Lower Stratospheric Gravity Waves. Advanced Data Processes of Some Meteorological Parameters. Wavelet Methods for Seismic Data Analysis and Processing. CLASSICAL AND FRACTAL METHODS FOR PHYSICAL PROBLEMS: Gradient Catastrophe in Heat Propagation with Second Sound. Acoustic Waves in a Perturbed Layered Ocean. Non-Linear Planar Oscillation of a Satellite Leading to Chaos under the Influence of Third-Body Torque. Chaos Using MATLAB in the Motion of a Satellite under the Influence of Magnetic Torque. A New Analysis Approach to Porous Media Texture- Mathematical Tools for Signal Analysis in a Context of Increasing Complexity. TRENDS IN VARIATIONAL METHODS: A Convex Objective Functional for Elliptic Inverse Problems. The Solutions of BBGKY Hierarchy of Quantum Kinetic Equations for Dense Systems. Convergence and the Optimal Choice of the Relation Parameter for a Class of Iterative Methods. On a Special Class of Sweeping Process.

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Book SynopsisOne of the first things a student of partial differential equations learns is that it is impossible to solve elliptic equations by spatial marching. This new book describes how to do exactly that, providing a powerful tool for solving problems in fluid dynamics, heat transfer, electrostatics, and other fields characterized by discretized partial differential equations. Elliptic Marching Methods and Domain Decomposition demonstrates how to handle numerical instabilities (i.e., limitations on the size of the problem) that appear when one tries to solve these discretized equations with marching methods. The book also shows how marching methods can be superior to multigrid and pre-conditioned conjugate gradient (PCG) methods, particularly when used in the context of multiprocessor parallel computers. Techniques for using domain decomposition together with marching methods are detailed, clearly illustrating the benefits of these techniques for applications in engineering, applied mathemTrade Review"Together with an important historical perspective, this book uses the domain decomposition connection to develop and explore the nature of marching methods. Interesting analytical and anecdotal comparisons are made with direct methods and multigrid techniques, told by a scientist who has obviously has much experience with real practical problems."-Mathematical Reviews, 99aTable of ContentsBasic Marching Methods for 2D Elliptic ProblemsHigh-Order EquationsExtending the Mesh Size: Domain DecompositionBanded Approximations to Influence MatricesMarching Methods in 3DPerformance of the 2D GEM CodeVectorization and ParallelizationSemidirect Methods for Nonlinear Equations of Fluid DynamicsComparison to Multigrid MethodsAppendix A - Marching Schemes and Error Propagation for Various Discrete LaplaciansAppendix B - Tridiagonal Algorithm for Periodic Boundary ConditionsAppendix C - Gauss Elimination as a Direct SolverSubject IndexTOC for NTI/Flyer

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Book SynopsisAn Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand''s representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann''s double commutant theorem, Kaplansky''s density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

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