Applied mathematics Books

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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Book SynopsisCRC Handbook of Percentiles of Non-Central t-Distributions is the first book to provide critical values of non-central t-distributions in an easy-to-use format. The book presents a brief introductory section that outlines properties and applications of non-central t-distributions and then explains the tables. The rest of the book consists of tables. The values listed were produced using cumulative probabilities. CRC Handbook of Percentiles of Non-Central t-Distributions is an essential reference of numerical tables of statistical functions for researchers, practitioners, scientists, and students involved with statistics in the areas of tolerance limits, variable sampling plans, confidence limits on quantiles, confidence limits on proportions, sample coefficient of variation and in computing the power of t-test.Table of ContentsIntroduction: The Critical Values of Non-Central t Distributions. a=0.01, a=0.025, a=0.05, a=0.10, a=0.20, a=0.30, a=0.70, a=0.80, a=0.90, a=0.95, a=0.975, a=0.99. References.

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Book SynopsisStochastic Communities presents a theory of biodiversity by analyzing the distribution of abundances among species in the context of a community. The basis of this theory is a distribution called the J distribution. This distribution is a pure hyperbola and mathematically implied by the stochastic species hypothesis assigning equal probabilities of birth and death within the population of each species over varying periods of time. The J distribution in natural communities has strong empirical support resulting from a meta-study and strong theoretical support from a theorem that is mathematically implied by the stochastic species hypothesis.Trade Review"The science of ecology suffers from a disconnect between theory and direct observation. Mathematicians have thought that simple equations could explain ecology. Field ecologists have assumed the mathematicians are right. Thus, empirical ecological understanding and prediction have suffered. Dewdney is an exceptions; he does field work and he is a mathematician. In his wonderful book, he takes advantage of both parts of ecology. And if Dewdney has done his math right, this book opens a whole new door to understanding biodiversity and its myriad causes."- Daniel Botkin, Professor Emeritus in the Department of Ecology, Evolution, and Marine Biology at the University of California, Santa Barbara, and President of the Center for the Study of the Environment"… development of a theory and guide to sampling, … it will be of great interest to both empirical and theoretical ecologists." - Trends in Ecology and EvolutionTable of ContentsThe J-curve and the J distribution. The J-distribution and its variations. Sampling in practice and in theory. Compiling and analysing field data. Predictions from data. Extending the sample. Stochastic systems and the stochastic community. The metastudy: A review. Fossil J-curves. Summary of theory and open problems. Appendix A: Mathematical Notes and Computer Tools. Appendix B: Results of the metastudy for the J distribution. Appendix C: Results of the test for the J distribution in taxonomic data.

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Book SynopsisIntended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functionals, this book focuses on the preservation of complete symmetry of original differential equations in numerical schemes. This symmetry preservation results in symmetry reduction of the difference model along with that of the original partial differential equations and in order reduction for ordinary difference equations.A substantial part of the book is concerned with conservation laws and first integrals for difference models. The variational approach and Noether type theorems for diTrade ReviewThe book provides a systematic application of Lie groups to difference equations, difference meshes, and difference functionals. Besides the well-explained theoretical background and motivations, there is also a large number of concrete examples discussed in reasonable details. Due to the fairly broad introductory part, the book is indeed self-contained. The main ideas and concepts appear understandable not only to experts.—Vojtech Zadnik, Zentralblatt MATH 1236In recent years "difference geometry" and its applications to integrable systems and mathematical physics have attracted significant attention and this monograph will contribute to the ongoing developments in this general area. It is clearly written and largely self-contained … —Peter J. Vassiliou, Mathematical Reviews, 2012eTable of ContentsIntroduction. Finite differences and transformation groups in space of discrete variables. Invariance of finite difference equations and meshes. Invariant difference models of ordinary differential equations. Invariant difference models of partial differential equations. Combined models, admitting a transformation group. The discrete representation of a differential equation. Invariant variational problem and conservation laws for difference equations.

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Book SynopsisThe rigorous treatment of combustion can be so complex that the kinetic variables, fluid turbulence factors, luminosity, and other factors cannot be defined well enough to find realistic solutions. Simplifying the processes, The Coen & Hamworthy Combustion Handbook provides practical guidance to help you make informed choices about fuels, burners, and associated combustion equipmentand to clearly understand the impacts of the many variables. Editors Stephen B. Londerville and Charles E. Baukal, Jr, top combustion experts from John Zink Hamworthy Combustion and the Coen Company, supply a thorough, state-of-the-art overview of boiler burners that covers Coen, Hamworthy, and Todd brand boiler burners.A Refresher in Fundamentals and State-of-the-Art Solutions for Combustion System ProblemsRoughly divided into two parts, the book first reviews combustion engineering fundamentals. It then uses a building-block approach to present spTrade Review"I consider that the main strength of this book is the elaboration of both ... the theoretical and practical, to make it of great interest and relevance to practicing engineers. The language is simple and the arrangement of chapters is good, moving from theory to practice progressively. Besides various types of burners, all the associated equipment like fans, furnaces, controls, and safeties are all covered, making the topic complete. ... Designers, operators, consulting engineers and also students of heat power should find this book extremely useful."—Kumar Rayaprolu, author of Boilers: A Practical Reference and Boilers for Power and Process"I consider that the main strength of this book is the elaboration of both ... the theoretical and practical, to make it of great interest and relevance to practicing engineers. The language is simple and the arrangement of chapters is good, moving from theory to practice progressively. Besides various types of burners, all the associated equipment like fans, furnaces, controls, and safeties are all covered, making the topic complete. ... Designers, operators, consulting engineers and also students of heat power should find this book extremely useful."—Kumar Rayaprolu, author of Boilers: A Practical Reference and Boilers for Power and ProcessTable of ContentsIntroduction. Engineering Fundamentals. Combustion Fundamentals. Fuels. Oil Atomization. Solid Fuel Combustion in Suspension. Heat Transfer. Fundamentals of Fluid Dynamics. CFD-Based Combustion Modeling. Pollutant Emissions. Noise. Combustion Controls, Burner Management, and Safety Systems. Blowers for Combustion Systems. Burners and Combustion for Industrial and Utility Boilers. Duct Burners. Air Heaters. Marine and Offshore Applications. Appendices. Index.

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Book SynopsisFluid Dynamics via Examples and Solutions provides a substantial set of example problems and detailed model solutions covering various phenomena and effects in fluids. The book is ideal as a supplement or exam review for undergraduate and graduate courses in fluid dynamics, continuum mechanics, turbulence, ocean and atmospheric sciences, and related areas. It is also suitable as a main text for fluid dynamics courses with an emphasis on learning by example and as a self-study resource for practicing scientists who need to learn the basics of fluid dynamics.The author covers several sub-areas of fluid dynamics, types of flows, and applications. He also includes supplementary theoretical material when necessary. Each chapter presents the background, an extended list of references for further reading, numerous problems, and a complete set of model solutions.Trade Review"There is no better way to fall in love with a particular subject then to learn it through problem solving. Sergey Nazarenko has created an important resource for mathematics and physics students and young researchers by introducing basics and techniques of fluid dynamics. Anyone involved in teaching fluid dynamics will treasure this book because it provides a clear path to help convey the beauty, elegance, and sophistication of this enticing area of science."—Professor Natalia Berloff, Department of Applied Mathematics and Theoretical Physics, University of Cambridge and Skolkovo Institute of Science and Technology"This is an excellent book for fluid dynamics students. It gives a good overview of the theory through a large set of worthy example problems. After many classical textbooks on the subject, there is finally one with solved exercises. I fully appreciate the selection of topics."—Professor Miguel Onorato, Physics Department, University of TorinoTable of ContentsFluid Equations and Different Regimes of Fluid Flows. Conservation Laws in Incompressible Fluid Flows. Fluid with Free Surface. Waves and Instabilities. Boundary Layers. Two-Dimensional Flows. Point Vortices and Point Sources. Turbulence. Compressible Flow. Bibliography. Index.

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Book SynopsisThis book explores both non parametric and general statistical ideas by developing non parametric procedures in simple situations.Table of Contents1 Concepts of Statistical Inference and the Binomial Distribution.- 1 Introduction.- 2 Probability Distributions.- 3 Estimators and their Properties.- 3.1 Unbiasedness and Variance.- 3.2 Consistency.- 3.3 Sufficiency.- 3.4 Minimum Variance.- 4 Hypothesis Testing.- 4.1 Tests and their Interpretation.- 4.2 Errors.- 4.3 One-Tailed Binomial Tests.- P-values.- 4.5 Two-Tailed Test Procedures and P-values.- 4.6 Other Conclusions in Two-Tailed Tests.- 5 Randomized Test Procedures.- 5.1 Introduction: Motivation and Examples.- 5.2 Randomized Tests: Definitions.- 5.3 Nonrandomized Tests Equivalent to Randomized Tests.- 5.4 Usefulness of Randomized Tests in Theory and Practice.- 5.5 ?Randomized P-values.- 6 Confidence Regions.- 6.1 Definition and Construction in the Binomial Case.- 6.2 Definition of Confidence Regions and Relationship to Tests in the General Case.- 6.3 Interpretation of Confidence Regions.- 6.4 True Confidence Level.- 6.5 Including False Values and the Size of Confidence Regions.- 6.6 ?Randomized Confidence Regions.- 7 Properties of One-Tailed Procedures.- 7.1 Uniformly Most Powerful One-Tailed Tests.- 7.2 ?Admissibility and Completeness of One-Tailed Tests.- 7.3 Confidence Procedures.- 7.4 ?Proofs.- 8 Choice of Two-Tailed Procedures and their Properties.- 8.1 Test Procedures.- 8.2 Confidence Procedures.- 8.3 ?Completeness and Admissibility of Two-Conclusion Two-Tailed Tests.- 8.4 ?Completeness and Admissibility of Three-Conclusion Two-Tailed Tests.- 9 Appendices to Chapter 1.- A Limits of the Binomial Distribution.- A.1 Ordinary Poisson Approximation and Limit.- A.2 Ordinary Normal Approximation and Limit.- ? Convergence in Distribution and Asymptotic Distributions.- B.1 Convergence of Frequency Functions and Densities.- B.2 Convergence in Distribution.- B.3 Two Central Limit Theorems.- Problems.- 2 One-Sample and Paired-Sample Inferences Based on the Binomial Distribution.- 1 Introduction.- 2 Quantile Values.- 3 The One-Sample Sign Test for Quantile Values.- 3.1 Test Procedures.- 3.2 “Optimum” Properties.- 3.3 ?Proofs.- 4 Confidence Procedures Based on the Sign Test.- 5 Interpolation between Attainable Levels.- 6 The Sign Test with Zero Differences.- 6.1 Discussion of Procedures.- 6.2 Conditional Properties of Conditional Sign Tests.- 6.3 Unconditional Properties of Conditional Sign Tests.- 6.4 ?Proof for One-Sided Alternatives.- 6.5 ?Prooffor Two-Sided Alternatives.- 7 Paired Observations.- 8 Comparing Proportions using Paired Observations.- 8.1 Test Procedure.- 8.2 Alternative Presentations.- 8.3 Example.- 8.4 Interpretation of the Test Results.- 8.5 Properties of the Test.- 8.6 Other Inferences.- 8.7 Cox Model.- 9 Tolerance Regions.- 9.1 Definition.- 9.2 Practical Uses.- 9.3 Construction of Tolerance Regions: Wilks’ Method.- 9.4 Tolerance Regions for Description.- 9.5 Tolerance Regions for Prediction.- 9.6 More General Construction Procedures.- Problems.- 3 One-Sample and Paired-Sample Inferences Based on Signed Ranks.- 1 Introduction.- 2 The Symmetry Assumption or Hypothesis.- 3 The Wilcoxon Signed-Rank Test.- 3.1 Test Procedure and Exact Null Distribution Theory.- 3.2 Asymptotic Null Distribution Theory.- 3.3 Large Sample Power.- 3.4 Consistency.- 3.5 Weakening the Assumptions.- 4 Confidence Procedures Based on the Wilcoxon Signed-Rank Test.- 5 A Modified Wilcoxon Procedure.- 6 Zeros and Ties.- 6.1 Introduction.- 6.2 Obtaining the Signed Ranks.- 6.3 Test Procedures.- 6.4 Warnings and Anomalies: Examples.- 6.5 Comparison of Procedures.- 7 Other Signed-Rank Procedures.- 7.1 Sums of Signed Constants.- 7.2 Signed Ranks and Walsh Averages.- 7.3 Confidence Bounds Corresponding to Signed-Rank Tests.- 7.4 Procedures Involving a Small Number of Walsh Averages.- 8 Invariance and Signed-Rank Procedures.- 8.1 Permutation Invariance.- 8.2 Invariance under Increasing, Odd Transformations.- 9 Locally Most Powerful Signed-Rank Tests 181 Problems.- 4 One-Sample and Paired-Sample Inferences Based on the Method of Randomization.- 1 Introduction.- 2 Randomization Procedures Based on the Sample Mean and Equivalent Criteria.- 2.1 Tests.- 2.2 Weakening the Assumptions.- 2.3 Related Confidence Procedures.- 2.4 Properties of the Exact Randomization Distribution.- 2.5 Modifications and Approximations to the Exact Randomization Procedure.- 3 The General Class of One-Sample Randomization Tests.- 3.1 Definition.- 3.2 Properties.- 4 Most Powerful Randomization Tests.- 4.1 General Case.- 4.2 One-Sided Normal Alternatives.- 4.3 Two-Sided Normal Alternatives.- 5 Obervation-Randomization versus Rank-Randomization Tests.- Problems.- 5 Two-Sample Rank Procedures for Location.- 1 Introduction.- 2 The Shift Assumption.- 3 The Median Test, Other Two-Sample Sign Tests, and Related Confidence Procedures.- 3.1 Reduction of Data to a 2 × 2 Table.- 3.2 Fisher’s Exact Test for 2 × 2 Tables.- 3.3 Ties.- 3.4 Corresponding Confidence Procedures.- 3.5 Power.- 3.6 Consistency.- 3.7 “Optimum” Properties.- 3.8 Weakening the Assumptions.- 4 Procedures Based on Sums of Ranks.- 4.1 The Rank Sum Test Procedure.- 4.2 Null Distribution of the Rank Sum Statistics.- 4.3 Corresponding Confidence Procedures.- 4.4 Approximate Power.- 4.5 Consistency.- 4.6 Weakening the Assumptions.- 4.7 Ties.- 4.8 Point and Confidence Interval Estimation of P(X > Y).- 5 Procedures Based on Sums of Scores.- 6 Two-Sample Rank Tests and the Y — X Differences.- 7 Invariance and Two-Sample Rank Procedures.- 8 Locally Most Powerful Rank Tests.- 8.1 Most Powerful and Locally Most Powerful Rank Tests Against Given Alternatives.- 8.2 The Class of Locally Most Powerful Rank Tests.- Problems.- 6 Two-Sample Inferences Based on the Method of Randomization.- 1 Introduction.- 2 Randomization Procedures Based on the Difference Between Sample Means and Equivalent Criteria.- 2.1 Tests.- 2.2 Weakening the Assumptions.- 2.3 Related Confidence Procedures.- 2.4 Properties of the Exact Randomization Distribution.- 2.5 Approximations to the Exact Randomization Distribution.- 3 The Class of Two-Sample Randomization Tests.- 3.1 Definition.- 3.2 Properties.- 4 Most Powerful Randomization Tests.- 4.1 General Case.- 4.2 One-Sided Normal Alternatives.- 4.3 Two-Sided Normal Alternatives.- Problems.- 7 Kolmogorov-Smirnov Two-Sample Tests.- 1 Introduction.- 2 Empirical Distribution Function.- 3 Two-Sample Kolmogorov-Smirnov Statistics.- 4 Null Distribution Theory.- 4.1 An Algorithm for the Exact Null Distribution.- 4.2 Relation Between One-Tailed and Two-Tailed Procedures.- 4.3 Exact Formulas for Equal Sample Sizes.- 4.4 Asymptotic Null Distributions.- 5 Ties.- 6 Performance.- 7 One-Sample Kolmogorov-Smirnov Statistics.- Problems.- 8 Asymptotic Relative Efficiency.- 1 Introduction.- 2 Asymptotic Behavior of Tests: Heuristic Discussion.- 2.1 Asymptotic Power of a Test.- 2.2 Nuisance Parameters.- 2.3 Asymptotic Relative Efficiency of Two Tests.- 3 Asymptotic Behavior of Point Estimators: Heuristic Discussion.- 3.1 Estimators of the Same Quantity.- 3.2 Relation of Estimators and Tests.- 3.3 Estimators of Different Quantities.- 4 Asymptotic Behavior of Confidence Bounds.- 5 Example.- 6 Definitions of Asymptotic Relative Efficiency.- 6.1 Introduction.- 6.2 Tests.- 6.3 Estimators.- 6.4 Confidence Bounds.- 6.5 Confidence Intervals.- 6.6 Summary.- 7 Pitman’s Formula.- 8 Asymptotic Relative Efficiencies of One-Sample Procedures for Shift Families.- 8.1 The Shift Model.- 8.2 Asymptotic Relative Efficiencies for Specific Shift Families.- 8.3 Bounds on Asymptotic Relative Efficiencies for Shift Families.- 8.4 ?Asymptotically Efficient Signed-Rank Procedures.- 9 Asymptotic Relative Efficiency of Procedures for Matched Pairs.- 9.1 Assumptions.- 9.2 Bounds for Asymptotic Efficiencies for Matched Pairs.- 10 Asymptotic Relative Efficiency of Two-Sample Procedures for Shift Families.- 11 Asymptotic Efficiency of Kolmogorov-Smirnov Procedures.- 11.1 One-Sided Tests.- 11.2 Two-Sided Tests.- Problems.- Tables.- Table A Cumulative Standard Normal Distribution.- Table B Cumulative Binomial Distribution.- Table C Binomial Confidence Limits.- Table D Cumulative Probabilities for Wilcoxon Signed-Rank Statistic.- Table E Cumulative Probabilities for Hypergeometric Distribution.- Table F Cumulative Probabilities for Wilcoxon Rank Sum Statistic.- Table G Kolmogorov-Smirnov Two-Sample Statistic.

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Book Synopsis1 Introduction.- 1.1 The Classical Sampling Theorem.- 1.2 Non-Uniform Sampling and Frames.- 1.3 Outline of the Book.- 2 On the Transmission Capacity of the Ether and Wire in Electrocommunications.- I Sampling, Wavelets, and the Uncertainty Principle.- 3 Wavelets and Sampling.- 4 Embeddings and Uncertainty Principles for Generalized Modulation Spaces.- 5 Sampling Theory for Certain Hilbert Spaces of Bandlimited Functions.- 6 Shannon-Type Wavelets and the Convergence of Their Associated Wavelet Series.- II Sampling Topics from Mathematical Analysis.- 7 Non-Uniform Sampling in Higher Dimensions: From Trigonometric Polynomials to Bandlimited Functions.- 8 The Analysis of Oscillatory Behavior in Signals Through Their Samples.- 9 Residue and Sampling Techniques in Deconvolution.- 10 Sampling Theorems from the Iteration of Low Order Differential Operators.- 11 Approximation of Continuous Functions by RogosinskiType Sampling Series.- III Sampling Tools and Applications.- 12 Fast Fourier Transforms for Nonequispaced Data: A Tutorial.- 13 Efficient Minimum Rate Sampling of Signals with Frequency Support over Non-Commensurable Sets.- 14 Finite-and Infinite-Dimensional Models for Oversampled Filter Banks.- 15 Statistical Aspects of Sampling for Noisy and Grouped Data.- 16 Reconstruction of MRI Images from Non-Uniform Sampling and Its Application to Intrascan Motion Correction in Functional MRI.- 17 Efficient Sampling of the Rotation Invariant Radon Transform.- References.Trade Review"The introduction (Chapter 1) gives an excellent overview of the history and development of sampling theory. It shows that the WSK sampling theory has roots in many classical areas of mathematics, such as harmonic analysis, number theory, and interpolation theory. Many famous mathematicians, such as Cauchy, Borel, Hadamard, and de la Vallee-Poussin contributed directly or indirectly to its development. The introduction then proceeds to show how sampling theory is connected to more recent topics in mathematical analysis, such as wavelets, Gabor systems, density theorems, frames, and sampling in locally compact abelian groups." —Mathematical Reviews "Engineers and mathematicians working in wavelets, signal processing, and harmonic analysis, as well as scientists and engineers working on applications as varied as medical imaging and synthetic aperture radar, will find the book to be a modern and authoritative guide to sampling theory." —Publicationes MathematicaeTable of ContentsIntroduction, On the transmission capacity of the 'ether' and wire in electrocommunications, Part I: Sampling, wavelets, and the uncertainty principle, Wavelets and sampling, Embeddings and uncertainty principles for generalized modulation spaces, Sampling theory for certain hilbert spaces of bandlimited functions, Shannon-type wavelets and the convergence of their associated wavelet series, Part II: Sampling topics from mathematical analysis, Non-uniform sampling in higher dimensions: From trigonometric polynomials to bandlimited functions, The analysis of oscillatory behavior in signals through their samples, Residue and sampling techniques in deconvolution, Sampling theorems from the iteration of low order differential operators, Approximation of continuous functions by Rogosinski-Type sampling series, Part III: Sampling tools and applications, Fast fourier transforms for nonequispaced data: A tutorial, Efficient minimum rate sampling of signals with frequency support over non-commensurable sets, Finite and infinite-dimensional models for oversampled filter banks, Statistical aspects of sampling for noisy and grouped data, Reconstruction of MRI images from non-uniform sampling, application to Intrascan motion correction in functional MRI, Efficient sampling of the rotation invariant radon transform

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Book SynopsisSolve the DVA/FVA Overlap Issue and Effectively Manage Portfolio Credit RiskCounterparty Risk and Funding: A Tale of Two Puzzles explains how to study risk embedded in financial transactions between the bank and its counterparty. The authors provide an analytical basis for the quantitative methodology of dynamic valuation, mitigation, and hedging of bilateral counterparty risk on over-the-counter (OTC) derivative contracts under funding constraints. They explore credit, debt, funding, liquidity, and rating valuation adjustment (CVA, DVA, FVA, LVA, and RVA) as well as replacement cost (RC), wrong-way risk, multiple funding curves, and collateral. The first part of the book assesses today's financial landscape, including the current multi-curve reality of financial markets. In mathematical but model-free terms, the second part describes all the basic elements of the pricing and hedging framework. Taking a more practical slant, the third pTrade Review"… a fresh take on mitigation of counterparty risk … [the book] gives a ground-up approach for analysis and managing of risks associated with non-payment of promised cash flows due to the default by a party in an over-the-counter derivative transaction. It should be of value to researchers, graduate students, financial quants, managers in banks, CVA desks, and members of supervisory bodies."—hedgeweek.com, July 2014"The landscape of the rates and credit markets has changed so drastically since the 2008 crisis that older textbooks are barely relevant and, from an analytic perspective, appropriate methods have to be rethought from scratch. The present volume is one of the best contributions in this direction, featuring a clear description of the various ‘value adjustments,’ new models for portfolio credit risk, a unified analytic framework based on BSDEs, and detailed treatment of numerical methods."—Mark Davis, Imperial College London"Understanding the subtle interconnections between credit and funding is key to a modern valuation of derivatives. This timely contribution, written by world-class academics who are also well-recognized experts in the field, offers a rigorous and comprehensive treatment of the main theories underpinning the new valuation principles. Numerical examples are also provided to help the reader grasp key concepts and ideas of the advanced models and techniques here presented. Overall, an excellent textbook. Brigo’s dialogue is the icing on the cake."—Fabio Mercurio, Head of Derivatives Research, Bloomberg LP"A big hooray for this book on CVA, DVA, FVA/LVA, RVA, TVA, and other three letter acronyms (TLA!)."—Peter Carr, PhD, Managing Director, Morgan Stanley, and Executive Director, NYU Courant Master of Science Program in Mathematics in FinanceTable of ContentsFinancial Landscape. Model-Free Developments. Reduced-Form BSDE Modeling. Dynamic Copula Models. Further Developments. Mathematical Appendix. Index.

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Book SynopsisActuarial Models: The Mathematics of Insurance, Second Edition thoroughly covers the basic models of insurance processes. It also presents the mathematical frameworks and methods used in actuarial modeling. This second edition provides an even smoother, more robust account of the main ideas and models, preparing students to take exams of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS).New to the Second Edition Revises all chapters, especially material on the surplus process Takes into account new results and current trends in teaching actuarial modeling Presents a new chapter on pension models Includes new problems from the 2011-2013 CAS examinations Like its best-selling, widely adopted predecessor, this edition is designed for students, actuaries, mathematicians, and researchers interested in insurance processes and economic and social models. The authTable of ContentsPreliminary Facts from Probability and Interest. Comparison of Random Variables. Preferences of Individuals. An Individual Risk Model for a Short Period. A Collective Risk Model for a Short Period. Random Processes and Their Applications I. Random Processes and Their Applications II. Global Characteristics of the Surplus Process. Survival Distributions. Life Insurance Models. Annuity Models. Premiums and Reserves. Pensions Plans. Risk Exchange: Reinsurance and Coinsurance. Appendix. References. Answers to Exercises. Index.

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Book SynopsisSince the start of modern computing, the studies of living organisms have inspired the progress in developing computers and intelligent machines. In particular, the methods of search and foraging are the benchmark problems for robotics and multi-agent systems. The highly developed theory of search and screening involves optimal search plans that are obtained by standard optimization techniques while the foraging theory addresses search plans that mimic the behavior of living foragers.Search and Foraging: Individual Motion and Swarm Dynamics examines how to program artificial search agents so that they demonstrate the same behavior as predicted by the foraging theory for living organisms. For cybernetics, this approach yields techniques that enable the best online search planning in varying environments. For biology, it allows reasonable insights regarding the internal activity of living organisms performing foraging tasks.The book discusses foraTrade Review"The book is valuable reading both for teaching inspiration as well as for research insights into optimization, modeling, mathematical biology, and robot programming."—Zentralblatt MATH 1327Table of ContentsIntroduction. Methods of Optimal Search and Screening. Methods of Optimal Foraging. Models of Individual Search and Foraging. Coalitional Search and Swarm Dynamics. Remarks on Swarm Robotic Systems for Search and Foraging. Conclusion. Bibliography. Index.

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