Enrique Castillo

Juan R. Ruiz-Tolosa

This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

From Vectors to Tensors

This book is a comprehensive guide to extreme value theory in engineering. Written for the end user with intermediate and advanced statistical knowledge, it covers classical methods as well as recent advances. A collection of 150 examples illustrates the theoretical results and takes the reader from simple applications through complex cases of dependence.

Extreme Value Theory in Engineering

Antonio J. Conejo

Pablo Pedregal

Ricardo García

Natalia Alguacil

Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools inengineering and the applied sciences. In this book, the authorsdeal with mathematical programming models both linear and nonlinearand across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis,the authors focus on the power of modeling methods for solvingpractical problems-clearly showing the connection between physicaland mathematical realities-while also describing and exploring themain concepts and tools at work. This highly computational coverageincludes: * Discussion and implementation of the GAMS programmingsystem * Unique coverage of compatibility * Illustrative examples that showcase the connection between modeland reality * Practical problems covering a wide range of scientificdisciplines, as well as hundreds of examples and end-of-chapterexercises * Real-world applications to probability and statistics, electricalengineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineeringand Science is practically suited for use as a professionalreference for mathematicians, engineers, and applied or industrialscientists, while also tutorial and illustrative enough foradvanced students in mathematics or engineering.

Building and Solving Mathematical Programming Models in Engineering and Science

Alfonso Fernandez-Canteli

This book is an attempt to provide a uni?ed methodology to derive models for fatigue life. This includes S-N, ?-N and crack propagation models. This is not a conventional book aimed at describing the fatigue fundamentals, but rather a book in which the basic models of the three main fatigue approaches, the stress-based, the strain-based and the fracture mechanics approaches, are contemplated from a novel and integrated point of view. On the other hand, as an alternative to the preferential attention paid to deterministic models based on the physical, phenomenological and empirical description of fatigue, their probabilistic nature is emphasized in this book, in which stochastic fatigue and crack growth models are presented. This book is the result of a long period of close collaborationbetween its two authors who, although of di?erent backgrounds, mathematical and mechanical, both have a strong sense of engineering with respect to the fatigue problem. When the authors of this book ?rst approached the fatigue ?eld in 1982 (twenty six years ago), they found the following scenario: 1. Linear, bilinear or trilinear models were frequently proposed by relevant laboratoriesandacademiccenterstoreproducetheW ̈ ohler?eld. Thiswas the case of well known institutions, which justi?ed these models based on clientrequirementsorpreferences. Thisledtotheinclusionofsuchmodels and methods as, for example, the up-and-down, in standards and o?cial practical directives (ASTM, Euronorm, etc.), which have proved to be unfortunate.

A Unified Statistical Methodology for Modeling Fatigue Damage

Ali S. Hadi

Jose M. Gutierrez

Artificial intelligence and expert systems have seen a great deal of research in recent years, much of which has been devoted to methods for incorporating uncertainty into models. This book is devoted to providing a thorough and up-to-date survey of this field for researchers and students.

Expert Systems and Probabilistic Network Models

Angel Cobo

Francisco Jubete

Rosa Eva Pruneda

A unique, applied approach to problem solving in linear algebra Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for: * Checking the equivalence of two systems * Solving a system in certain selected variables * Modifying systems of equations * Solving linear systems of inequalities * Using the new exterior point method * Modifying a linear programming problem With few prerequisites, but with plenty of figures and tables, end-of-chapter exercises as well as Java and Mathematica programs available from the authors' Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics.

Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming

Orthogonal Sets and Polar Methods in Linear Algebra

Roberto Minguez

Raquel Garcia-Bertrand

Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.

Engineering and Science Applications

Decomposition Techniques in Mathematical Programming

N. Balakrishnan

Jose-Maria Sarabia Alegria

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

Enrique Castillo

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