Matematik for ingeniører

We describe in this book, new methods for analysis and design of hybrid intelligent systems using soft computing techniques. Soft Computing (SC) consists of several computing paradigms, including fuzzy logic, neural networks, and genetic algorithms, which can be used to produce powerful hybrid intelligent systems for solving problems in pattern recognition, time series prediction, intelligent control, robotics and automation. Hybrid int- ligent systems that combine several SC techniques are needed due to the complexity and high dimensionality of real-world problems. Hybrid int- ligent systems can have different architectures, which have an impact on the efficiency and accuracy of these systems, for this reason it is very - portant to optimize architecture design. The architectures can combine, in different ways, neural networks, fuzzy logic and genetic algorithms, to achieve the ultimate goal of pattern recognition, time series prediction, - telligent control, or other application areas. This book is intended to be a major reference for scientists and en- neers interested in applying new computational and mathematical tools to design hybrid intelligent systems. This book can also be used as a textbook or major reference for graduate courses like the following: soft computing, intelligent pattern recognition, computer vision, applied artificial intel- gence, and similar ones. We consider that this book can also be used to get novel ideas for new lines of research, or to continue the lines of research proposed by the authors of the book.

The contributors present the main results and techniques of their specialties in an easily accessible way accompanied with many references: historical, hints for complete proofs or solutions to exercises and directions for further research. This volume contains applications which have not appeared in any collection of this type. The book is a general source of information in computation theory, at the undergraduate and research level.

Evolutionary design of intelligent systems is gaining much popularity due to its capabilities in handling several real world problems involving optimization, complexity, noisy and non-stationary environment, imprecision, uncertainty and vagueness. This edited volume 'Engineering Evolutionary Intelligent Systems' deals with the theoretical and methodological aspects, as well as various evolutionary algorithm applications to many real world problems originating from science, technology, business or commerce. This volume comprises of 15 chapters including an introductory chapter which covers the fundamental definitions and outlines some important research challenges. Chapters were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed.

Hybridization of evolutionary algorithms is getting popular due to their capabilities in handling several real world problems involving complexity, noisy environment, imprecision, uncertainty and vagueness. This edited volume is targeted to present the latest state-of-the-art methodologies in "e;Hybrid Evolutionary Algorithms"e;. This book deals with the theoretical and methodological aspects, as well as various applications to many real world problems from science, technology, business or commerce. This volume comprises of 14 chapters including an introductory chapter giving the fundamental definitions and some important research challenges. Chapters were selected on the basis of fundamental ideas/concepts rather than the thoroughness of techniques deployed.

The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys- tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec- tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "e;mode of evolution"e; or "e;law of motion"e; because of random changes of the "e;environment"e; or in a "e;medium"e;. So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.

Special tools are required for examining and solving optimization problems. The main tools in the study of local optimization are classical calculus and its modern generalizions which form nonsmooth analysis. The gradient and various kinds of generalized derivatives allow us to ac- complish a local approximation of a given function in a neighbourhood of a given point. This kind of approximation is very useful in the study of local extrema. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for solving these problems. The simplest and most well-known area of global and simultaneously local optimization is convex programming. The fundamental tool in the study of convex optimization problems is the subgradient, which actu- ally plays both a local and global role. First, a subgradient of a convex function f at a point x carries out a local approximation of f in a neigh- bourhood of x. Second, the subgradient permits the construction of an affine function, which does not exceed f over the entire space and coincides with f at x. This affine function h is called a support func- tion. Since f(y) ~ h(y) for ally, the second role is global. In contrast to a local approximation, the function h will be called a global affine support.

This book discusses heat transfer in underground energy systems. It covers a wide range of important and practical topics including the modeling and optimization of underground power cable systems, modeling of thermal energy storage systems utilizing waste heat from PV panels cooling. Modeling of PV pannels with cooling. While the performance of energy systems which utilize heat transfer in the ground is not yet fully understood, this book attempts to make sense of them. It provides mathematical modeling fundaments, as well as experimental investigation for underground energy systems. The book shows detailed examples, with solution procedures. The solutions are based on the Finite Element Method and the Finite Volume Method. The book allows the reader to perform a detailed design of various underground energy systems, as well as enables them to study the economic aspects and energy efficiency of underground energy systems. Therefore, this text is of interest to researchers, students, and lecturers alike.

"Computational Methods for Nonlinear Dynamical Systems proposes novel ideas and develops highly efficient and accurate methods for solving nonlinear dynamical systems, drawing inspiration from the weighted residual method and the asymptomatic method. The book also introduces global estimation methods and local computational methods for nonlinear dynamical systems. Starting from the classic asymptomatic, finite difference and weighted residual methods, typical methods for solving nonlinear dynamical systems are considered. All proposed are new high-performance methods, such as time-domain collocation and local variational iteration. These proposed methods can be used both for real-time simulation and for the analysis of nonlinear dynamics in aerospace engineering. This book summarizes and develops computational methods for strongly nonlinear dynamical systems and considers the practical application of the methods within aerospace engineering, making it an essential resource for those working in this area."--

This textbook, now in its fourth edition, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, it features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Unlike other books on stochastic methods that specialize in a specific field of applications, this volume examines the ways in which similar stochastic methods can be applied across di¿erent ¿elds.Beginning with the fundamentals of probability, the authors go on to introduce the theory of stochastic processes, the Itô Integral, and stochastic differential equations. The following chapters then explore stability, stationarity, and ergodicity. The second half of the book is dedicated to applications to a variety of fields, including finance, biology, and medicine. Some highlights of this fourth edition include a more rigorous introduction to Gaussian white noise, additional material on the stability of stochastic semigroups used in models of population dynamics and epidemic systems, and the expansion of methods of analysis of one-dimensional stochastic di¿erential equations.An Introduction to Continuous-Time Stochastic Processes, Fourth Edition is intended for graduate students taking an introductory course on stochastic processes, applied probability, stochastic calculus, mathematical finance, or mathematical biology. Prerequisites include knowledge of calculus and some analysis; exposure to probability would be helpful but not required since the necessary fundamentals of measure and integration are provided. Researchers and practitioners in mathematical finance, biomathematics, biotechnology, and engineering will also find this volume to be of interest, particularlythe applications explored in the second half of the book.