This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.

"Intelligent Routines II: Solving Linear Algebra and Differential Geometry with Sage" contains numerous of examples and problems as well as many unsolved problems. This book extensively applies the successful software Sage, which can be found free online http: //www.sagemath.org/. Sage is a recent and popular software for mathematical computation, available freely and simple to use. This book is useful to all applied scientists in mathematics, statistics and engineering, as well for late undergraduate and graduate students of above subjects. It is the first such book in solving symbolically with Sage problems in Linear Algebra and Differential Geometry. Plenty of SAGE applications are given at each step of the exposition.

The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it.

This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.

This book focuses on modelling financial information flows and information-based asset pricing framework. After introducing the fundamental properties of the framework, it presents a short information-theoretic perspective with a view to quantifying the information content of financial signals, and links the present framework with the literature on asymmetric information and market microstructure by means of a dynamic, bipartite, heterogeneous agent network. Numerical and explicit analyses shed light on the effects of differential information and information acquisition on the allocation of profit and loss as well as the pace of fundamental price discovery. The dynamic programming method is used to seek an optimal strategy for utilizing superior information. Lastly, the book features an implementation of the present framework using real-world financial data.

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come.

The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director.

More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic.

Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger s successor as director of the Research Institute for Symbolic Computation.

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This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

This book treats state-of-the-art computational methods for power flow studies and contingency analysis. In the first part the authors present the relevant computational methods and mathematical concepts. In the second part, power flow and contingency analysis are treated. Furthermore, traditional methods to solve such problems are compared to modern solvers, developed using the knowledge of the first part of the book. Finally, these solvers are analyzed both theoretically and experimentally, clearly showing the benefits of the modern approach.

The purpose of this book is to provide tools for a better understanding of the fundamental tradeo's and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these int- dependencies to achieve signi?cant performance gains. Two facts prompted us to write it: First, future wireless applications will require a fundamental understanding of the design principles and control mechanisms in wireless networks. Second, the complexity of the network problems simply precludes the use of engineering common sense alone to identify good solutions, and so mathematics becomes the key avenue to cope with central technical problems in the design of wireless networks. In this book, two ?elds of mathematics play a central role: Perron-Frobenius theory for non-negative matrices and optimization theory. This book is a revised and expanded version of the research monograph "Resource Allocation in Wireless Networks" that was published as Lecture Notes in Computer Sciences (LNCS 4000) in 2006. Although the general structure has remained unchanged to a large extent, the book contains - merous additional results and more detailed discussion. For instance, there is a more extensive treatment of general nonnegative matrices and interf- ence functions that are described by an axiomatic model. Additional material on max-min fairness, proportional fairness, utility-based power control with QoS (quality of service) support and stochastic power control has been added.

Any researchers in the field of meshless methods who want to keep up to date with the latest work in the field will find this an essential text.In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics.The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available.This means that engineers in general, applied mathematicians, physicists, and those active in computational mechanics will all find this book a useful reference tool as well. The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon.

In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 "Mathematical Methods for Extracting Quantifiable Information from Complex Systems." This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.

Calculus has been used in solving many scientific and engineering problems. For optimization problems, however, the differential calculus technique sometimes has a drawback when the objective function is step-wise, discontinuous, or multi-modal, or when decision variables are discrete rather than continuous. Thus, researchers have recently turned their interests into metaheuristic algorithms that have been inspired by natural phenomena such as evolution, animal behavior, or metallic annealing.

This book especially focuses on a music-inspired metaheuristic algorithm, harmony search. Interestingly, there exists an analogy between music and optimization: each musical instrument corresponds to each decision variable; musical note corresponds to variable value; and harmony corresponds to solution vector. Just like musicians in Jazz improvisation play notes randomly or based on experiences in order to find fantastic harmony, variables in the harmony search algorithm have random values or previously-memorized good values in order to find optimal solution.

Computational Methods in Elasticity and Plasticity: Solids and Porous Media presents the latest developments in the area of elastic and elasto-plastic finite element modeling of solids, porous media and pressure-dependent materials and structures. The book covers the following topics in depth: the mathematical foundations of solid mechanics, the finite element method for solids and porous media, the theory of plasticity and the finite element implementation of elasto-plastic constitutive models. The book also includes: -A detailed coverage of elasticity for isotropic and anisotropic solids. -A detailed treatment of nonlinear iterative methods that could be used for nonlinear elastic and elasto-plastic analyses. -A detailed treatment of a kinematic hardening von Mises model that could be used to simulate cyclic behavior of solids. -Discussion of recent advances in the analysis of porous media and pressure-dependent materials in more detail than other books currently available. Computational Methods in Elasticity and Plasticity: Solids and Porous Media also contains problem sets, worked examples and a solutions manual for instructors.

Mathematical algorithms are a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. This book provides a bridge between algebraic geometry and geometric modelling algorithms, formulated within a computer science framework. Apart from the algebraic geometry topics covered, the entire book is based on the unifying concept of using algebraic techniques - properly specialized to solve geometric problems - to seriously improve accuracy, robustness and efficiency of CAD-systems. It provides new approaches as well as industrial applications to deform surfaces when animating virtual characters, to automatically compare images of handwritten signatures and to improve control of NC machines. This book further introduces a noteworthy representation based on 2D contours, which is essential to model the metal sheet in industrial processes. It additionally reviews applications of numerical algebraic geometry to differential equations systems with multiple solutions and bifurcations. Future Vision and Trends on Shapes, Geometry and Algebra is aimed specialists in the area of mathematics and computer science on the one hand and on the other hand at those who want to become familiar with the practical application of algebraic geometry and geometric modelling such as students, researchers and doctorates.

This book presents a comprehensive and detailed study on iterative learning control (ILC) for systems with iteration-varying trial lengths. Instead of traditional ILC, which requires systems to repeat on a fixed time interval, this book focuses on a more practical case where the trial length might randomly vary from iteration to iteration. The iteration-varying trial lengths may be different from the desired trial length, which can cause redundancy or dropouts of control information in ILC, making ILC design a challenging problem. The book focuses on the synthesis and analysis of ILC for both linear and nonlinear systems with iteration-varying trial lengths, and proposes various novel techniques to deal with the precise tracking problem under non-repeatable trial lengths, such as moving window, switching system, and searching-based moving average operator. It not only discusses recent advances in ILC for systems with iteration-varying trial lengths, but also includes numerous intuitive figures to allow readers to develop an in-depth understanding of the intrinsic relationship between the incomplete information environment and the essential tracking performance. This book is intended for academic scholars and engineers who are interested in learning about control, data-driven control, networked control systems, and related fields. It is also a useful resource for graduate students in the above field.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds. This book is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry and applied mathematics. It fills a gap in the literature as the first book to appear on the subject.

This volume contains a collection of papers dedicated to Professor Eckhard Platen to celebrate his 60th birthday, which occurred in 2009. The contributions have been written by a number of his colleagues and co-authors. All papers have been - viewed and presented as keynote talks at the international conference "Quantitative Methods in Finance" (QMF) in Sydney in December 2009. The QMF Conference Series was initiated by Eckhard Platen in 1993 when he was at the Australian - tional University (ANU) in Canberra. Since joining UTS in 1997 the conference came to be organised on a much larger scale and has grown to become a signi?cant international event in quantitative ?nance. Professor Platen has held the Chair of Quantitative Finance at the University of Technology, Sydney (UTS) jointly in the Faculties of Business and Science since 1997. Prior to this appointment, he was the Founding Head of the Centre for Fin- cial Mathematics at the Institute of Advanced Studies at ANU, a position to which he was appointed in 1994. Eckhard completed a PhD in Mathematics at the Technical University in Dresden in 1975 and in 1985 obtained his Doctor of Science degree (Habilitation degree in the German system) from the Academy of Sciences in Berlin where he headed the Stochastics group at the Weierstrass Institute.

"Artificial Boundary Method" systematically introduces the artificial boundary method for the numerical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrodinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for researchers working in the fields of computational mathematics and mechanical engineering.
Prof. Houde Han works at Tsinghua University, China; Prof. Xiaonan Wu works at Hong Kong Baptist University, China."

This book focuses on the nonlinear behaviour of thin-wall shells (single- and multilayered with delamination areas) under various uniform and non-uniform loadings.
The dependence of critical (buckling) load upon load variability is revealed to be highly non-monotonous, showing minima when load variability is close to the eigenmode variabilities of solution branching points of the respective nonlinear boundary problem.
A novel numerical approach is employed to analyze branching points and to build primary, secondary, and tertiary bifurcation paths of the nonlinear boundary problem for the case of uniform loading. The load levels of singular points belonging to the paths are considered to be critical load estimates for the case of non-uniform loadings.

This book collects up-to-date papers from world experts in a broad variety of relevant applications of approximation theory, including dynamical systems, multiscale modelling of fluid flow, metrology, and geometric modelling to mention a few. The 14 papers in this volume document modern trends in approximation through recent theoretical developments, important computational aspects and multidisciplinary applications. The book is arranged in seven invited surveys, followed by seven contributed research papers. The surveys of the first seven chapters are addressing the following relevant topics: emergent behaviour in large electrical networks, algorithms for multivariate piecewise constant approximation, anisotropic triangulation methods in adaptive image approximation, form assessment in coordinate metrology, discontinuous Galerkin methods for linear problems, a numerical analyst's view of the lattice Boltzmann method, approximation of probability measures on manifolds. Moreover, the diverse contributed papers of the remaining seven chapters reflect recent developments in approximation theory, approximation practice and their applications. Graduate students who wish to discover the state of the art in a number of important directions of approximation algorithms will find this a valuable volume. Established researchers from statisticians through to fluid modellers will find interesting new approaches to solving familiar but challenging problems. This book grew out of the sixth in the conference series on "Algorithms for Approximation", which took place from 31st August to September 4th 2009 in Ambleside in the Lake District of the United Kingdom.

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7-10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.

Optimization is a field important in its own right but is also integral to numerous applied sciences, including operations research, management science, economics, finance and all branches of mathematics-oriented engineering. Constrained optimization models are one of the most widely used mathematical models in operations research and management science.

This book gives a modern and well-balanced presentation of the subject, focusing on theory but also including algorithims and examples from various real-world applications. The text is easy to read and accessible to anyone with a knowledge of multi-dimensional calculus, linear algebra and basic numerical methods. Detailed examples and counter-examples are provided--as are exercises, solutions and helpful hints, and Matlab/Maple supplements.

The intended readership is advanced undergraduates, graduates, and professionals in any of the applied fields.

This book uses numerical analysis as the main tool to investigate methods in machine learning and neural networks. The efficiency of neural network representations for general functions and for polynomial functions is studied in detail, together with an original description of the Latin hypercube method and of the ADAM algorithm for training. Furthermore, unique features include the use of Tensorflow for implementation session, and the description of on going research about the construction of new optimized numerical schemes.

This book presents an original combination of three well-known methodological approaches for nonlinear data analysis: recurrence, networks, and fuzzy logic. After basic concepts of these three approaches are introduced, this book presents recently developed methods known as fuzzy recurrence plots and fuzzy recurrence networks. Computer programs written in MATLAB, which implement the basic algorithms, are included to facilitate the understanding of the developed ideas. Several applications of these techniques to biomedical problems, ranging from cancer and neurodegenerative disease to depression, are illustrated to show the potential of fuzzy recurrence methods. This book opens a new door to theorists in complex systems science as well as specialists in medicine, biology, engineering, physics, computer science, geosciences, and social economics to address issues in experimental nonlinear signal and data processing.