Contents:
Introduction. Acoustical Oceanography. Propagation I. Observations and Physical Models. Propagation II. Mathematical Models (Part One). Propagation II. Mathematical Models (Part Two). Noise I. Observations and Physical Models. Noise II. Mathematical Models. Reverberation I. Observations and Physical Models. Reverberation II. Observations and Physical Models. Sonar Performance Models. Model Evaluation. Simulation.

Although the use of fuzzy control methods has grown nearly to the level of classical control, the true understanding of fuzzy control lags seriously behind. Moreover, most engineers are well versed in either traditional control or in fuzzy control-rarely both. Each has applications for which it is better suited, but without a good understanding of both, engineers cannot make a sound determination of which technique to use for a given situation.

A First Course in Fuzzy and Neural Control is designed to build the foundation needed to make those decisions. It begins with an introduction to standard control theory, then makes a smooth transition to complex problems that require innovative fuzzy, neural, and fuzzy-neural techniques. For each method, the authors clearly answer the questions: What is this new control method? Why is it needed? How is it implemented? Real-world examples, exercises, and ideas for student projects reinforce the concepts presented.

Developed from lecture notes for a highly successful course titled The Fundamentals of Soft Computing, the text is written in the same reader-friendly style as the authors' popular A First Course in Fuzzy Logic text. A First Course in Fuzzy and Neural Control requires only a basic background in mathematics and engineering and does not overwhelm students with unnecessary material but serves to motivate them toward more advanced studies.

This book contains a sampling of papers presented at the June 2-5, 2002 International Workshop on Bifurcations andamp; Instabilities in Geomechanics (IWBI 2002). The scope of the Workshop includes analytical approaches, numerical methods, and experimental techniques.

Contains a compact disc with nearly 200 microcomputer programs illustrating a wide range of reliability and statistical analyses Mechanical Reliability Improvement provides probability and statistical concepts developed using pseudorandom numbers enumeration-, simulation-, and randomization-based statistical analyses for comparison of the test performance of alternative designs, as well as simulation- and randomization-based tests for examination of the credibility of statistical presumptions and discusses centroid and moment of inertia analogies for mean and variance the organization structure of completely randomized, randomized complete block, and split spot experiment test programs

"Examines classic algorithms, geometric diagrams, and mechanical principles for enhances visualization of statistical estimation procedures and mathematical concepts in physics, engineering, and computer programming."

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs which model real-life situations. Due to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. The book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. The book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations. The book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences. useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering. .

- presents in-depth insights regarding fundamentals associated with big data technologies involved in petroleum streams. - builds on earlier works of researchers and inventors, which is essential source material for students in this area of study. - discusses essential processes and methodologies in petroleum streams that will direct researchers to pursue a practical approach to the field. - sheds light on challenges and problems of individual streams and inert-relation issues, while asking the reader to innovate and ideate upon those issues. - Offers an analysis of the financial aspects and business perspective on the processes to help the reader make constructive and practical decision in the field.

Research in mathematics is much more than solving puzzles, but most people will agree that solving puzzles is not just fun: it helps focus the mind and increases one's armory of techniques for doing mathematics. Mathematical Puzzles makes this connection explicit by isolating important mathematical methods, then using them to solve puzzles and prove a theorem. Features A collection of the world's best mathematical puzzles Each chapter features a technique for solving mathematical puzzles, examples, and finally a genuine theorem of mathematics that features that technique in its proof Puzzles that are entertaining, mystifying, paradoxical, and satisfying; they are not just exercises or contest problems.

This book presents new research in probability theory using ideas from mathematical logic. It is a general study of stochastic processes on adapted probability spaces, employing the concept of similarity of stochastic processes based on the notion of adapted distribution. The authors use ideas from model theory and methods from nonstandard analysis. The construction of spaces with certain richness properties, defined by insights from model theory, becomes easy using nonstandard methods, but remains difficult or impossible without them.

This text gathers, revises and explains the newly developed Adomian decomposition method along with its modification and some traditional techniques.

Handbook of Alternative Data in Finance, Volume I motivates and challenges the reader to explore and apply Alternative Data in finance. The book provides a robust and in-depth overview of Alternative Data, including its definition, characteristics, difference from conventional data, categories of Alternative Data, Alternative Data providers, and more. The book also offers a rigorous and detailed exploration of process, application and delivery that should be practically useful to researchers and practitioners alike. Features Includes cutting edge applications in machine learning, fintech, and more Suitable for professional quantitative analysts, and as a resource for postgraduates and researchers in financial mathematics Features chapters from many leading researchers and practitioners.

Artificial intelligence (AI) and digital engineering have become prevalent in business, industry, government, and academia. However, the workforce still has a lot to learn on how to leverage them. This handbook presents the preparatory and operational foundations for the efficacy, applicability, risk, and how to take advantage of these tools and techniques. "Handbook of Mathematical and Digital Engineering Foundations for Artificial Intelligence: A Systems Methodology" provides a guide for using digital engineering platforms for advancing AI applications. The book discusses an interface of education and research in the pursuit of AI developments and highlights the facilitation of advanced education through AI and digital engineering systems. It presents an integration of soft and hard skills in developing and using AI and offers a rigorous systems approach to understanding and using AI. This handbook will be the go-to resource for practitioners and students on applying systems methodology to the body of knowledge of understanding, embracing, and using digital engineering tools and techniques.

Containing more than 1,000 entries, the Dictionary of Classical and Theoretical Mathematics focuses on mathematical terms and definitions of critical importance to practicing mathematicians and scientists. This single-source reference provides working definitions, meanings of terms, related references, and a list of alternative terms and definitions. The dictionary is one of five constituent works that make up the casebound CRC Comprehensive Dictionary of Mathematics.

The use of lasers for various applications in materials processing has grown rapidly in recent years. Lasers are by nature particularly well suited to automation, but to ensure repeatability and reliability, the engineers employing them must not simply rely on numerical analysis software. They must have a firm grasp on the physical principles involved.

Mathematics of Thermal Modelling: An Introduction to the Theory of Laser Material Processing introduces the mathematics needed to formulate and exploit the physical principles important to modelling various aspects of laser material processing. The author shows how to gain insight by constructing and analyzing simple models. He demonstrates how to extract qualitative information from the models, how the underlying principles can be extended to more complex modelling, and how these principles can be applied to processes such as laser welding, surface treatment, drilling, and cutting.

Written at a level accessible to graduate students, this book shows that simple mathematical investigation-- based primarily on analytical methods backed by relatively simple numerical methods--can greatly illuminate the processes being studied. Regardless of the stage of your career development, if you are confronting the modelling of thermal process in this field for the first time, Mathematics of Thermal Modelling will build the foundation you need.

This textbook is created from the author's successful, Advanced Engineering Mathematics. The previous volume is now split into two books to offer more flexibility. Reviewers have endorsed the split. The author's best-selling book, Green's Functions, is distilled here, as well as coverage of complex variables, Z and Hilbert transforms, probability and random processes, and a unique coverage of Ito's stochastic calculus. The topics are driven by applications and MatLab is used throughout. This book offers flexibility in a course where many competitors are now over 1000 pages and very expensive. This second book covers topics normally taught in the second or third term of an AEM course.

Functions as a self-study guide and textbook containing over 110 examples and 165 problem sets with answers, a comprehensive solutions manual, and computer programs that clarify arithmetic concepts-ideal for a two-semester course in structural dynamics, analysis and design of seismic structures, matrix methods of structural analysis, numerical methods in structural engineering, and advanced structural mechanics and design This book uses state-of-the-art computer technology to formulate displacement method with matrix algebra, facilitating analysis of structural dynamics and applications to earthquake engineering and UBC and IBC seismic building codes. Links code provisions to analytical derivations and compares individual specifications across codes, including the IBC-2000 With 3700 equations and 660 drawings and tables, Matrix Analysis of Structural Dynamics: Applications and Earthquake Engineering examines vibration of trusses, rigid and elastic frames, plane grid systems, and 3-D building systems with slabs, walls, bracings, beam-columns, and rigid zones presents single and multiple degree-of-freedom systems and various response behaviors for different types of time-dependent excitations outlines determinant, iteration, Jacobian, Choleski decomposition, and Sturm sequence eigensolution methods details proportional and nonproportional damping, steady-state vibration for undamped harmonic excitation, and transient vibration for general forcing function includes P-? effects, elastic media, coupling vibrations, Timoshenko theory, and geometric and material nonlinearity illustrates free and forced vibrations of frameworks and plates stressing isoparametric finite element formulation offers several numerical integration methods with solution criteria for error and stability behavior details models and computer calculations for bracings, RC beams and columns, coupling bending, and shear of low-rise walls and more Matrix Analysis

This book introduces acoustic wave theories using a reader-friendly matrix-based linear algebra approach. It will enable the reader to take advantage of software tools such as MATLAB (commercial codes) and OCTAVE (open-source codes) to gain better and deeper understanding of the underlying physics quickly. In this aspect, this text can be regarded as a practical introduction of the acoustic wave theories in an easy-to-follow linear algebra format using matrix manipulations instead of an abstract approach relying on tensor manipulations. The book also uses case studies to demonstrate how the fundamentals on acoustic waves discussed throughout the book are applied in device designs and analyses such that the connections and interdependences between the underlying sciences and the observed behavior and performances can be better appreciated by the reader. To achieve this, all problems for illustrations, examples, case studies, and device analyses are developed and solved based on the mathematical foundations laid out in the book.

Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the advantage these books offer the astute reader. Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses. As a high-level industry executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial industry and two decades in education where he taught in highly respected graduate programs. Readers should be quantitatively literate and familiar with the developments in the first books in the set. The set offers a linear progression through these topics, though each title can be studied independently since the collection is extensively self-referenced. Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes, develops several approaches to an integration theory. The first two approaches were introduced in the Chapter 1 of Book I to motivate measure theory. The general theory of integration on measure spaces will be developed in Book V, and stochastic integrals then studies on Book VIII. Book III Features: Extensively referenced to utilize materials from earlier books. Presents the theory needed to better understand applications. Supplements previous training in mathematics, with more detailed developments. Built from the author's five decades of experience in industry, research, and teaching. Published and forthcoming titles in the Robert Reitano Quantitative Finance Series: Book I: Measure Spaces and Measurable Functions. Book II: Probability Spaces and Random Variables, Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes Book IV: Distribution Functions and Expectations Book V: General Measure and Integration Theory Book VI: Densities, Transformed Distributions, and Limit Theorems Book VII: Brownian Motion and Other Stochastic Processes Book VIII: Itô Integration and Stochastic Calculus 1 Book IX: Stochastic Calculus 2 and Stochastic Differential Equations Book 10: Applications and Classic Models

The text focuses on mathematical modeling and applications of advanced techniques of machine learning, and artificial intelligence, including artificial neural networks, evolutionary computing, data mining, and fuzzy systems to solve performance and design issues more precisely. Intelligent computing encompasses technologies, algorithms, and models in providing effective and efficient solutions to a wide range of problems including the airport's intelligent safety system. It will serve as an ideal reference text for senior undergraduate, graduate students, and academic researchers in fields including industrial engineering, manufacturing engineering, computer engineering, and mathematics. The book- Discusses mathematical modeling for traffic, sustainable supply chain, vehicular Ad-Hoc networks, internet of things networks with intelligent gateways. Covers advanced machine learning, artificial intelligence, fuzzy systems, evolutionary computing, data mining techniques for real-world problems. Presents applications of mathematical models in chronic diseases such as kidney and coronary artery diseases. Highlights advances in mathematical modeling, strength, and benefits of machine learning and artificial intelligence, including driving goals, applicability, algorithms, and processes involved. Showcases emerging real-life topics on mathematical models, machine learning, and intelligent computing using an interdisciplinary approach. The text presents emerging real-life topics on mathematical models, machine learning, and intelligent computing in a single volume. It will serve as an ideal text for senior undergraduate, graduate students, and researchers in diverse fields domains including industrial and manufacturing engineering, computer engineering, and mathematics.

Multiplicative Differential Equations: Volume I is the first part of a comprehensive approach to the subject. It continues a series of books written by the authors on multiplicative, geometric approaches to key mathematical topics. This volume begins with a basic introduction to multiplicative differential equations and then moves on to first and second order equations, as well as the question of existence and unique of solutions. Each chapter ends with a section of practical problems. The book is accessible to graduate students and researchers in mathematics, physics, engineering and biology.

Model theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950's, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory. The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they can be studied independently of one another. This second volume contains introductions to real-valued logic and applications, abstract elementary classes and applications, interconnections between model theory and function spaces, nonstucture theory, and model theory of second-order logic. Features A coherent introduction to current trends in model theory. Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together. Suitable as a reference for advanced undergraduate, postgraduates, and researchers. Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature. The various chapters in the book can be studied independently.

Contents:
Part I Introduction to Computational Fluid Dynamics 1. Introduction 2. Governing Equations 3. Classification of Partial Differential Equations 4. Well Posed Problems 5. Numerical Methods 6. The Finite Difference Method
Part II The Finite Analytic Method 7. Basic Principles 8. The One-Dimensional Case 9. The Two-Dimensional Case 10. The Tree-Dimensional Case 11. Stability of Convergence 12. Hyperbolic PDEs 13. Explicit Finite Analytic Method
Part III 14. Introduction to Grid Generation 15. Elliptic Grid Generation 16. Equations in E and n Coordinates 17. Diagonal Cartesian Method 18. FA Method on Diagonal Cartesian Coordinates
Part IV Computational Considerations 19. Velocity , Pressure and Staggered Grids 20. Non-staggered Grid Methods 21. Boundary Conditions
Applications of the FA Method 22. Turbulent Flows 23. Turbulent Heat Transfer 24. Complex Domain Flows 25. Conjugate Heat Transfer
A The One-Dimensional Case
B The Two-Dimensional Case

Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

'Lighting Engineering: Applied Calculations' describes the mathematical background to the calculation techniques used in lighting engineering and links them to the applications with which they are used. The fundamentals of flux and illuminance, colour, measurement and optical design are covered in detail. There are detailed discussions of specific applications, including interior lighting, road lighting, tunnel lighting, floodlighting and emergency lighting. The authors have used their years of experience to provide guidance for common mistakes and useful techniques including worked examples and case studies.
The last decade has seen the universal application of personal computers to lighting engineering on a day-to-day basis. Many calculations that were previously impracticable are therefore now easily accessible to any engineer or designer who has access to an appropriate computer program. However, a grasp of the underlying calculation principles is still necessary in order to utilise these technologies to the full.
Written by two of the leading authorities on this subject, 'Lighting Engineering' is essential reading for practising lighting engineers, designers and architects, and students in the field of lighting.
* Provides you with detailed calculations and shows you how to apply them in practical situations
* Benefit from the author teams' acknowledged expertise in the field
* Learn to utilise new technologies to the full

Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?

Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do not exist.

Regardless of your specific field-physical science, social science, or statistics, practitioner or theorist-Fitting Statistical Distributions is required reading. It includes wide-ranging applications illustrating the methods in practice and offers proofs of key results for those involved in theoretical development. Without it, you may be using obsolete methods, wasting time, and risking incorrect results.