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Linear Systems, Signal Processing and Hypercomplex Analysis ; Chapman University, November 2017
includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.
Boundary value problems, Weyl Functions, and differential operators
This book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions.
Mathematical Models for Registration and Applications to Medical Imaging
Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume.
Mathematical Analysis I
The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques.
Linear Partial Differential Equations for Scientists and Engineers
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Lectures on Symplectic Geometry
Provides a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.
Jets From Young Stars III : Numerical MHD and Instabilities
This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the Kelvin-Helmholtz, the radiative shock, the pressure driven and the thermal instabilities.
Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke
This volume contains introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers.
Compatible Spatial Discretizations
Compatible spatial discretizations are those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. It offer a snapshot of the current trends and developments in compatible spatial discretizations. The reader will find valuable insights on spatial compatibility from several different perspectives and important examples of applications compatible discretizations in computational electromagnetics, geosciences, linear elasticity, eigenvalue approximations and MHD. The contributions collected in this volume will help to elucidate relations between different methods and concepts and to generally advance our understanding of compatible spatial discretizations for PDEs.
Chaos in Structural Mechanics
This volume introduces and reviews novel theoretical approaches to modeling strongly nonlinear behaviour of either individual or interacting structural mechanical units such as beams, plates and shells or composite systems thereof.
Cells and Robots : Modeling and Control of Large-Size Agent Populations
Cells and Robots is an outcome of the multidisciplinary research extending over Biology, Robotics and Hybrid Systems Theory. It is inspired by modeling reactive behavior of the immune system cell population, where each cell is considered as an independent agent. In our modeling approach, there is no difference if the cells are naturally or artificially created agents, such as robots. This appears even more evident when we introduce a case study concerning a large-size robotic population scenario. Under this scenario, we also formulate the optimal control of maximizing the probability of robotic presence in a given region and discuss the application of the Minimum Principle for partial differential equations to this problem. Simultaneous consideration of cell and robotic populations is of mutual benefit for Biology and Robotics, as well as for the general understanding of multi-agent system dynamics.The text of this monograph is based on the PhD thesis of the first author. The work was a runner-up for the fifth edition of the Georges Giralt Award for the best European PhD thesis in Robotics, annually awarded by the European Robotics Research Network (EURON).
Calcolo stocastico per la finanza = Stochastic Calculation for Finance
Offers an introduction to the mathematical, probabilistic and numerical methods that are the basis of the models for the valuation of derivative instruments, such as options and futures, dealt with in modern financial markets. The book is aimed at readers with scientific training, wishing to develop skills in the field of stochastic calculus applied to finance.
Boundary Integral Equations
This book is devoted to the basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory. It may also serve as the mathematical foundation of the boundary element methods. The latter have recently become extremely popular and efficient computational tools in applications. The authors are well known for their fundamental work on boundary integral equations and related topics. This book is a major scholarly contribution to the modern theory of boundary integral equations and should be accessible and useful to a large community of mathematical analysts, applied mathematicians, engineers and scientists.
Beyond partial differential equations : On linear and Quasi-Linear abstract hyperbolic evolution equations
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups.
Averaging Methods in Nonlinear Dynamical Systems
The authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction.
Asymptotics for Dissipative Nonlinear Equations
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusionsThe types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods.The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it.The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.
Applied Partial Differential Equations : A Visual Approach
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables.
Applicazioni ed esercizi di modellistica numerica per problemi differenziali = Applications and exercises in numerical modeling for differential problems
Contains a collection of exercises related to typical topics in a course on analytical and numerical methods offered in a degree program in Engineering or Mathematics. Starting with exercises in functional analysis and approximation theory, the text develops problems related to the numerical resolution of elliptic, parabolic, and hyperbolic partial differential equations, scalar or vector, in one or more spatial dimensions. Pure diffusion and pure convection problems are therefore addressed, alongside diffusion-transport problems and problems in compressible and incompressible fluid dynamics. Particular emphasis is given to the finite element method for the spatial discretization of the problems considered, although exercises on the finite difference and finite volume methods are also included.
