This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI'2017 - Geometric Science of Information.

Techniques of optimization are applied in many problems in economics, automatic control, engineering, etc. and a wealth of literature is devoted to this subject. The first computer applications involved linear programming problems with simp- le structure and comparatively uncomplicated nonlinear pro- blems: These could be solved readily with the computational power of existing machines, more than 20 years ago. Problems of increasing size and nonlinear complexity made it necessa- ry to develop a complete new arsenal of methods for obtai- ning numerical results in a reasonable time. The lineariza- tion method is one of the fruits of this research of the last 20 years. It is closely related to Newton's method for solving systems of linear equations, to penalty function me- thods and to methods of nondifferentiable optimization. It requires the efficient solution of quadratic programming problems and this leads to a connection with conjugate gra- dient methods and variable metrics. This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.

Targeted audience * Specialists in numerical computations, especially in numerical optimiza tion, who are interested in designing algorithms with automatie result ver ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be. * Mathematicians and computer scientists who are interested in the theory 0/ computing and computational complexity, especially computational com plexity of numerical computations. * Students in applied mathematics and computer science who are interested in computational complexity of different numerical methods and in learning general techniques for estimating this computational complexity. The book is written with all explanations and definitions added, so that it can be used as a graduate level textbook. What this book .is about Data processing. In many real-life situations, we are interested in the value of a physical quantity y that is diflicult (or even impossible) to measure directly. For example, it is impossible to directly measure the amount of oil in an oil field or a distance to a star. Since we cannot measure such quantities directly, we measure them indirectly, by measuring some other quantities Xi and using the known relation between y and Xi'S to reconstruct y. The algorithm that transforms the results Xi of measuring Xi into an estimate fj for y is called data processing.

This book compiles recent developments on sliding mode control theory and its applications. Each chapter presented in the book proposes new dimension in the sliding mode control theory such as higher order sliding mode control, event triggered sliding mode control, networked control, higher order discrete-time sliding mode control and sliding mode control for multi-agent systems. Special emphasis has been given to practical solutions to design involving new types of sliding mode control. This book is a reference guide for graduate students and researchers working in the domain for designing sliding mode controllers. The book is also useful to professional engineers working in the field to design robust controllers for various applications.

This book provides a common theoretical and practical basis to the multifaceted nature of magma mixing. This process represents a fundamental phenomenon both in the evolution of igneous rocks and in triggering explosive volcanic eruptions. The topic is attacked surgically merging field evidence, numerical models, and experiments in order to draw the most complete picture about this natural process. Arguments are discussed in the light of Chaos Theory and Fractal Geometry as new tools to understand the role of magma mixing as a fundamental petrological and volcanological process. The book is intended to be a source of information and a stimulus for new ideas in students, young and possibly more experienced researches.

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.

For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help students apply concepts.

This book features original research papers presented at the International Conference on Computational and Applied Mathematics, held at the Indian Institute of Technology Kharagpur, India during November 23-25, 2018. This book covers various topics under applied mathematics, ranging from modeling of fluid flow, numerical techniques to physical problems, electrokinetic transport phenomenon, graph theory and optimization, stochastic modelling and machine learning. It introduces the mathematical modeling of complicated scientific problems, discusses micro- and nanoscale transport phenomena, recent development in sophisticated numerical algorithms with applications, and gives an in-depth analysis of complicated real-world problems. With contributions from internationally acclaimed academic researchers and experienced practitioners and covering interdisciplinary applications, this book is a valuable resource for researchers and students in fields of mathematics, statistics, engineering, and health care.

The protection of our environment is one of the major problems in the society. More and more important physical and chemical mechanisms are to be added to the air pollution models. Moreover, new reliable and robust control strategies for keeping the pollution caused by harmful compounds under certain safe levels have to be developed and used in a routine way. Well based and correctly analyzed large mathematical models can successfully be used to solve this task. The use of such models leads to the treatment of huge computational tasks. The efficient solution of such problems requires combined research from specialists working in different fields. The aim of the NATO Advanced Research Workshop (NATO ARW) entitled "Advances in Air Pollution Modeling for Environmental Security" was to invite specialists from all areas related to large-scale air pollution modeling and to exchange information and plans for future actions towards improving the reliability and the scope of application of the existing air pollution models and tools. This ARW was planned to be an interdisciplinary event, which provided a forum for discussions between physicists, meteorologists, chemists, computer scientists and specialists in numerical analysis about different ways for improving the performance and the quality of the results of different air pollution models.

The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.

Honoring Andrei Agrachev's 60th birthday, this volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume, etc.

These proceedings report on the conference "Math Everywhere," celebrating the 60th birthday of the mathematician Vincenzo Capasso. The conference promoted ideas Capasso has pursued and shared the open atmosphere he is known for. Topic sections include: Deterministic and Stochastic Systems. Mathematical Problems in Biology, Medicine and Ecology. Mathematical Problems in Industry and Economics. The broad spectrum of contributions to this volume demonstrates the truth of its title: Math is Everywhere, indeed.

This monograph contributes to the mathematical analysis of systems exhibiting hysteresis effects and phase transitions. Its main part begins with a detailed study of models for scalar rate independent hysteresis in the form of hysteresis operators. Applications to ferromagnetism, elastoplasticity and fatigue analysis are presented, and two representative distributed systems with hysteresis operator are discussed. The attention then shifts to the mechanisms of energy dissipation and transformation that induce a hysteretic behavior in continuous media undergoing phase transitions. After an introduction to phenomenological thermodynamic theories of phase transitions, in particular, the Landau-Ginzburg theory and phase field models, several specific models are discussed in detail. These include Falk's model for the hysteresis in shape memory alloys and the phase field models due to Caginalp and Penrose-Fife. The latter are studied both for conserved and non-conserved order parameters. A chapter presenting a mathematical model for the austenite-pearlite and austenite-martensite phase transitions in eutectoid carbon steels concludes the book.

This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The first volume covers many-particle dynamics, Maxwell models of the Boltzmann equation (including their exact and self-similar solutions), and hydrodynamic limits beyond the Navier-Stokes level.

The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions. The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and Teichmuller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.

The idea for this book originated during the workshop "Model order reduction, coupled problems and optimization" held at the Lorentz Center in Leiden from S- tember 19-23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: fully worked-out examples; many carefully selected and formulated problems; fast Fourier transform methods; a thorough discussion of some important minimization methods; solution of stiff or implicit ordinary differential equations and of differential algebraic systems; modern shooting techniques for solving two-point boundary value problems; and basics of multigrid methods. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. New material on differential equations and the iterative solution of linear equations include: solving differential equations in the presence of discontinuities whose locations are not known at the outset; techniques for sensitivity analyses of differential equations dependent on additional parameters; new advanced techniques in multiple shooting; and Krylov space methods for non-symmetric systems of linear equations.

The requirement of causality in system theory is inevitably accompanied by the appearance of certain mathematical operations, namely the Riesz proj- tion,theHilberttransform,andthespectralfactorizationmapping.Aclassical exampleillustratingthisisthedeterminationoftheso-calledWiener?lter(the linear, minimum means square error estimation ?lter for stationary stochastic sequences [88]). If the ?lter is not required to be causal, the transfer function of the Wiener ?lter is simply given by H(?)=? (?)/? (?),where ? (?) xy xx xx and ? (?) are certain given functions. However, if one requires that the - xy timation ?lter is causal, the transfer function of the optimal ?lter is given by 1 ? (?) xy H(?)= P ,?? (??,?] . + [? ] (?) [? ] (?) xx + xx? Here [? ] and [? ] represent the so called spectral factors of ? ,and xx + xx? xx P is the so called Riesz projection. Thus, compared to the non-causal ?lter, + two additional operations are necessary for the determination of the causal ?lter, namely the spectral factorization mapping ? ? ([? ] ,[? ] ),and xx xx + xx? the Riesz projection P .

Presenting state-of-the-art methods in the area, the book begins with a presentation of weak discrete time approximations of jump-diffusion stochastic differential equations for derivatives pricing and risk measurement. Using a moving least squares reconstruction, a numerical approach is then developed that allows for the construction of arbitrage-free surfaces. Free boundary problems are considered next, with particular focus on stochastic impulse control problems that arise when the cost of control includes a fixed cost, common in financial applications. The text proceeds with the development of a fear index based on equity option surfaces, allowing for the measurement of overall fear levels in the market. The problem of American option pricing is considered next, applying simulation methods combined with regression techniques and discussing convergence properties. Changing focus to integral transform methods, a variety of option pricing problems are considered. The COS method is practically applied for the pricing of options under uncertain volatility, a method developed by the authors that relies on the dynamic programming principle and Fourier cosine series expansions. Efficient approximation methods are next developed for the application of the fast Fourier transform for option pricing under multifactor affine models with stochastic volatility and jumps. Following this, fast and accurate pricing techniques are showcased for the pricing of credit derivative contracts with discrete monitoring based on the Wiener-Hopf factorisation. With an energy theme, a recombining pentanomial lattice is developed for the pricing of gas swing contracts under regime switching dynamics. The book concludes with a linear and nonlinear review of the arbitrage-free parity theory for the CDS and bond markets.

Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

The focus from most Virtual Reality (VR) systems lies mainly on the visual immersion of the user. But the emphasis only on the visual perception is insufficient for some applications as the user is limited in his interactions within the VR. Therefore the textbook presents the principles and theoretical background to develop a VR system that is able to create a link between physical simulations and haptic rendering which requires update rates of 1\,kHz for the force feedback. Special attention is given to the modeling and computation of contact forces in a two-finger grasp of textiles. Addressing further the perception of small scale surface properties like roughness, novel algorithms are presented that are not only able to consider the highly dynamic behaviour of textiles but also capable of computing the small forces needed for the tactile rendering at the contact point. Final analysis of the entire VR system is being made showing the problems and the solutions found in the work

An important objective of the study of mathematics is to analyze and visualize phenomena of nature and real world problems for its proper understanding. Gradually, it is also becoming the language of modem financial instruments. To project some of these developments, the conference was planned under the joint auspices of the Indian Society of Industrial and Applied mathematics (ISlAM) and Guru Nanak Dev University (G. N. D. U. ), Amritsar, India. Dr. Pammy Manchanda, chairperson of Mathematics Department, G. N. D. U., was appointed the organizing secretary and an organizing committee was constituted. The Conference was scheduled in World Mathematics Year 2000 but, due one reason or the other, it could be held during 22. -25. January 2001. How ever, keeping in view the suggestion of the International Mathematics union, we organized two symposia, Role of Mathematics in industrial development and vice-versa and How image of Mathematics can be improved in public. These two symposia aroused great interest among the participants and almost everyone participated in the deliberations. The discussion in these two themes could be summarized in the lengthy following lines: "Tradition of working in isolation is a barrier for interaction with the workers in the other fields of science and engineering, what to talk of non-academic areas, specially the private sector of finance and industry. Therefore, it is essential to build bridges within in stitutions and between institutions."

Praise for The Mathematics of Derivatives

"The Mathematics of Derivatives provides a concise pedagogical discussion of both fundamental and very recent developments in mathematical finance, and is particularly well suited for readers with a science or engineering background. It is written from the point of view of a physicist focused on providing an understanding of the methodology and the assumptions behind derivative pricing. Navin has a unique and elegant viewpoint, and will help mathematically sophisticated readers rapidly get up to speed in the latest Wall Street financial innovations."
--David Montano, Managing Director JPMorgan Securities

"A stylish and practical introduction to the key concepts in financial mathematics, this book tackles key fundamentals in the subject in an intuitive and refreshing manner whilst also providing detailed analytical and numerical schema for solving interesting derivatives pricing problems. If Richard Feynman wrote an introduction to financial mathematics, it might look similar. The problem and solution sets are first rate."
--Barry Ryan, Partner Bhramavira Capital Partners, London

"This is a great book for anyone beginning (or contemplating), a career in financial research or analytic programming. Navin dissects a huge, complex topic into a series of discrete, concise, accessible lectures that combine the required mathematical theory with relevant applications to real-world markets. I wish this book was around when I started in finance. It would have saved me a lot of time and aggravation."
--Larry Magargal