Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.

Although there are hundreds of books about MATLAB, there are no books that fully explore its value in the field of business economics. Few books describe how geographic information can be explicitly incorporated in business decisions, or explain how sophisticated MATLAB applications can be provided to users via the Internet using a remote-hosted, thin client environment.

Business, Economics and Finance with MATLAB, GIS and Simulation Models responds by providing a unique overview of sophisticated business and financial applications. This book describes models that have been developed for facing the challenges of finance, retail sales, taxes, location, economic impact, public policy, and other issues that executives, investors, and economists confront on a daily basis. It also offers groundbreaking insight into the many calculation and modeling tools that can be remotely hosted and run over the Internet, resulting in substantial user benefits and cost savings.

Many techniques and models directly incorporate geographic information and GIS into the analysis in a way that was impossible until quite recently. Some techniques, such as fuzzy logic, retail sales, and Simulink economic impact models are described for the first time in print in this book.

By following this blueprint, you will be able to direct tremendously higher amount of computational power toward the challenges that confront your business.

This book presents the state-of-the-art methodology and detailed analytical models and methods used to assess the reliability of complex systems and related applications in statistical reliability engineering. It is a textbook based mainly on the author's recent research and publications as well as experience of over 30 years in this field. The book covers a wide range of methods and models in reliability, and their applications, including: statistical methods and model selection for machine learning; models for maintenance and software reliability; statistical reliability estimation of complex systems; and statistical reliability analysis of k out of n systems, standby systems and repairable systems. Offering numerous examples and solved problems within each chapter, this comprehensive text provides an introduction to reliability engineering graduate students, a reference for data scientists and reliability engineers, and a thorough guide for researchers and instructors in the field.

More than ever before, complicated mathematical procedures are integral to the success and advancement of technology, engineering, and even industrial production. Knowledge of and experience with these procedures is therefore vital to present and future scientists, engineers and technologists.

Mathematical Methods in Physics and Engineering with Mathematica clearly demonstrates how to solve difficult practical problems involving ordinary and partial differential equations and boundary value problems using the software package Mathematica (4.x). Avoiding mathematical theorems and numerical methods-and requiring no prior experience with the software-the author helps readers learn by doing with step-by-step recipes useful in both new and classical applications.

Mathematica and FORTRAN codes used in the book's examples and exercises are available for download from the Internet. The author's clear explanation of each Mathematica command along with a wealth of examples and exercises make Mathematical Methods in Physics and Engineering with Mathematica an outstanding choice both as a reference for practical problem solving and as a quick-start guide to using a leading mathematics software package.

Originally published in 1979. An Input/output database is an information system carrying current data on the intermediate consumption of any product or service by all the specified major firms that consume it. This book begins with a survey of how the interrelationships of an economic system can be represented in a two-dimensional model which traces the output of each economic sector to all other sectors. It talks about how the use of such databases to identify major buyers and sellers can illuminate problems of economic policy at the national, regional, and corporate level and aid in analyzing factors affecting the control of inflation, energy use, transportation, and environmental pollution. The book discusses how advances in database technology, have brought to the fore such issues as the right to individual privacy, corporate secrecy, the public's right of access to stored data, and the use of such information for national planning in a free-enterprise society.

How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed.

Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness.

Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.

'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume. With a focus on mathematics and peppered with a scattering of computer science settings, the entries range from lightly humorous to curiously thought-provoking. Each chapter includes sections and sub-sections that illustrate and supplement the point at hand. Most topics are self-contained within each chapter, and a solid high school mathematics background is all that is needed to enjoy the discussions. There certainly is much to enjoy here.'CHOICEEver notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)?Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques.This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.

This book presents a series of integrated computer programs in Fortran-90 for the dynamic analysis of structures, using the finite element method. Two dimensional continuum structures such as walls are covered along with skeletal structures such as rigid jointed frames and plane grids. Response to general dynamic loading of single degree freedom systems is calculated, and the author also examines multi degree of freedom systems (including earthquake analysis). Each chapter covers a different aspect of analytic theory and the corresponding program segments.
It will be an essential tool for practising structural and civil engineers, whilst also being of interest to academics and postgraduate students.

Related link: http://www.sponpress.com/supportmaterial< /a>
eBook available with sample pages: 0203473469

Fuzzy Cluster Analysis presents advanced and powerful fuzzy clustering techniques. This thorough and self-contained introduction to fuzzy clustering methods and applications covers classification, image recognition, data analysis and rule generation. Combining theoretical and practical perspectives, each method is analysed in detail and fully illustrated with examples. Features include:

• Sections on inducing fuzzy if-then rules by fuzzy clustering and non-alternating optimization fuzzy clustering algorithms
• Discussion of solid fuzzy clustering techniques like the fuzzy c-means, the Gustafson-Kessel and the Gath-and-Geva algorithm for classification problems
• Focus on linear and shell clustering techniques used for detecting contours in image analysis
• Accompanying software and data sets pertaining to the examples presented, enabling the reader to learn through experimentation
• Examination of the difficulties involved in evaluating the results of fuzzy cluster analysis and of determining the number of clusters with analysis of global and local validity measures
• Description of different fuzzy clustering techniques allowing the user to select the method most appropriate to a particular problem

Among the most exciting developments in science today is the design and construction of the quantum computer. Its realization will be the result of multidisciplinary efforts, but ultimately, it is mathematics that lies at the heart of theoretical quantum computer science.

Mathematics of Quantum Computation brings together leading computer scientists, mathematicians, and physicists to provide the first interdisciplinary but mathematically focused exploration of the field's foundations and state of the art. Each section of the book addresses an area of major research, and does so with introductory material that brings newcomers quickly up to speed. Chapters that are more advanced include recent developments not yet published in the open literature.

Information technology will inevitably enter into the realm of quantum mechanics, and, more than all the atomic, molecular, optical, and nanotechnology advances, it is the device-independent mathematics that is the foundation of quantum computer and information science. Mathematics of Quantum Computation offers the first up-to-date coverage that has the technical depth and breadth needed by those interested in the challenges being confronted at the frontiers of research.

Recently molecular biology has undergone unprecedented development generating vast quantities of data needing sophisticated computational methods for analysis, processing and archiving. This requirement has given birth to the truly interdisciplinary field of computational biology, or bioinformatics, a subject reliant on both theoretical and practical contributions from statistics, mathematics, computer science and biology.

• Provides the background mathematics required to understand why certain algorithms work
• Guides the reader through probability theory, entropy and combinatorial optimization
• In-depth coverage of molecular biology and protein structure prediction
• Includes several less familiar algorithms such as DNA segmentation, quartet puzzling and DNA strand separation prediction
• Includes class tested exercises useful for self study
• Source code of programs available on a Web site

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,' discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincare, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

Rapid developments in the field of genetic algorithms along with the popularity of the first edition precipitated this completely revised, thoroughly updated second edition of The Practical Handbook of Genetic Algorithms. Like its predecessor, this edition helps practitioners stay up to date on recent developments in the field and provides material they can use productively in their own endeavors.

For this edition, the editor again recruited authors at the top of their field and from a cross section of academia and industry, theory and practice. Their contributions detail their own research, new applications, experiment results, and recent advances. Among the applications explored are scheduling problems, optimization, multidimensional scaling, constraint handling, and feature selection and classification.

The science and art of GA programming and application has come a long way in the five years since publication of the bestselling first edition. But there still is a long way to go before its bounds are reached-we are still just scratching the surface of GA applications and refinements. By introducing intriguing new applications, offering extensive lists of code, and reporting advances both subtle and dramatic, The Practical Handbook of Genetic Algorithms is designed to help readers contribute to scratching that surface a bit deeper.

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

"This text covers key mathematical principles and algorithms for nonlinear filters used in image processing. Readers will gain an in-depth understanding of the underlying mathematical and filter design methodologies needed to construct and use nonlinear filters in a variety of applications.
The 11 chapters explore topics of contemporary interest as well as fundamentals drawn from nonlinear filtering's historical roots in mathematical morphology and digital signal processing. This book examines various filter options and the types of applications for which they are best suited. The presentation is rigorous, yet accessible to engineers with a solid background in mathematics."

Transfer function form, zpk, state space, modal, and state space modal forms. For someone learning dynamics for the first time or for engineers who use the tools infrequently, the options available for constructing and representing dynamic mechanical models can be daunting. It is important to find a way to put them all in perspective and have them available for quick reference.

It is also important to have a strong understanding of modal analysis, from which the total response of a system can be constructed. Finally, it helps to know how to take the results of large dynamic finite element models and build small MATLAB® state space models.

Vibration Simulation Using MATLAB and ANSYS answers all those needs. Using a three degree-of-freedom (DOF) system as a unifying theme, it presents all the methods in one book. Each chapter provides the background theory to support its example, and each chapter contains both a closed form solution to the problem-shown in its entirety-and detailed MATLAB code for solving the problem.

Bridging the gap between introductory vibration courses and the techniques used in actual practice, Vibration Simulation Using MATLAB and ANSYS builds the foundation that allows you to simulate your own real-life problems.

Features

o Demonstrates how to solve real problems, covering the vibration of systems from single DOF to finite element models with thousands of DOF
o Illustrates the differences and similarities between different models by tracking a single example throughout the book
o Includes the complete, closed-form solution and the MATLAB code used to solve each problem
o Shows explicitly how to take the results of a realistic ANSYS finite element model and develop a small MATLAB state-space model
o Provides a solid grounding in how individual modes of vibration combine for overall system response

Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.

What's new in the Second Edition?

Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The author has also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. He discusses three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:
* Proof Theory
* Propositional Structures
* Frames
* Decidability
* Coda
Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered:
* Proof Theory
* Propositional Structures
* Frames
* Decidability
* Coda
Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.

The author of the "Programmer's Toolbox" column shows how to use powerful math functions to achieve optimal real-time performance in programming. Along the way, readers will gain new understanding of math fundamentals, learn how to write more robust software for real-time systems, and discover how to implement math algorithms efficiently and accurately. The toolkit is bundled with a CD-ROM containing an arsenal of math algorithms to make the learning process easy and fun.

Are some areas of fast Fourier transforms still unclear to you? Do the notation and vocabulary seem inconsistent? Does your knowledge of their algorithmic aspects feel incomplete? The fast Fourier transform represents one of the most important advancements in scientific and engineering computing. Until now, however, treatments have been either brief, cryptic, intimidating, or not published in the open literature. Inside the FFT Black Box brings the numerous and varied ideas together in a common notational framework, clarifying vague FFT concepts. Examples and diagrams explain algorithms completely, with consistent notation. This approach connects the algorithms explicitly to the underlying mathematics. Reviews and explanations of FFT ideas taken from engineering, mathematics, and computer science journals teach the computational techniques relevant to FFT. Two appendices familiarize readers with the design and analysis of computer algorithms, as well. This volume employs a unified and systematic approach to FFT. It closes the gap between brief textbook introductions and intimidating treatments in the FFT literature. Inside the FFT Black Box provides an up-to-date, self-contained guide for learning the FFT and the multitude of ideas and computing techniques it employs.

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

"Covers design methods for optimal (or quasioptimal) control algorithms in the form of synthesis for deterministic and stochastic dynamical systems-with applications in aerospace, robotic, and servomechanical technologies. Providing new results on exact and approximate solutions of optimal control problems."

The subject of this book is the analysis and design of digital devices that implement computer arithmetic. The book's presentation of high-level detail, descriptions, formalisms and design principles means that it can support many research activities in this field, with an emphasis on bridging the gap between algorithm optimization and hardware implementation. The author provides a unified view linking the domains of digital design and arithmetic algorithms, based on original formalisms and hardware description languages.

A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures.

The book is suitable for researchers and students engaged with hardware design in computer science and engineering.

A feature of the book is the large number of examples and the implementation details provided. While the author does not avoid high-level details, providing for example gate-level designs for all matrix/combinational arithmetic structures.

The book is suitable for researchers and students engaged with hardware design in computer science and engineering.

Digital Signal Processing Algorithms describes computational number theory and its applications to deriving fast algorithms for digital signal processing. It demonstrates the importance of computational number theory in the design of digital signal processing algorithms and clearly describes the nature and structure of the algorithms themselves. The book has two primary focuses: first, it establishes the properties of discrete-time sequence indices and their corresponding fast algorithms; and second, it investigates the properties of the discrete-time sequences and the corresponding fast algorithms for processing these sequences.
Digital Signal Processing Algorithms examines three of the most common computational tasks that occur in digital signal processing; namely, cyclic convolution, acyclic convolution, and discrete Fourier transformation. The application of number theory to deriving fast and efficient algorithms for these three and related computationally intensive tasks is clearly discussed and illustrated with examples.
Its comprehensive coverage of digital signal processing, computer arithmetic, and coding theory makes Digital Signal Processing Algorithms an excellent reference for practicing engineers. The authors' intent to demystify the abstract nature of number theory and the related algebra is evident throughout the text, providing clear and precise coverage of the quickly evolving field of digital signal processing.