الصفحة 2
الصفحة 2
Finite Difference Computing with PDEs : A Modern Software Approach
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.
Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
The theory of random Schrödinger operators is devoted to the mathematical analysis of quantum mechanical Hamiltonians modeling disordered solids. Apart from its importance in physics, it is a multifaceted subject in its own right, drawing on ideas and methods from various mathematical disciplines like functional analysis, selfadjoint operators, PDE, stochastic processes and multiscale methods. The present text describes in detail a quantity encoding spectral features of random operators: the integrated density of states or spectral distribution function. Various approaches to the construction of the integrated density of states and the proof of its regularity properties are presented.
Digital Simulation in Electrochemistry
The book shows how to numerically solve the parabolic partial differential equations (pdes) encountered in electroanalytical chemistry. It does this in a didactic manner, by first introducing the basic equations to be solved and some model systems as text cases, for which solutions exist. Then it treats basic numerical approximation for derivatives and techniques for the numerical solution of ordinary differential equations, from which the more complicated methods for pdes can be derived. The major implicit methods are described in detail, and the handling of homogeneous chemical reactions, including coupled and nonlinear cases, is detailed. More advanced techniques are presented briefly, as well as some commercially available program packages.
Differential Geometry and Analysis on CR Manifolds
The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric acheivements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry.Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory.
Deformable Models : Theory and Biomaterial Applications
Deformable Models: Theory and Biomaterial Applications is the second installation in the two-volume set Deformable Models which provides a wide cross-section of the methods and algorithms of variational and PDE methods in biomedical image analysis. The chapters are written by well-known researchers in this field, and the presentation style goes beyond an intricate abstraction of the theory into real application of the methods and description of the algorithms that were implemented. As such these chapters will serve the main goal of the editors of the volumes in bringing down to earth the latest in variational and PDE methods in modeling of soft tissues, covering the theory, algorithms, and applications of level sets and deformable models in medical image analysis.
Deformable Models : Biomedical and Clinical Applications
Deformable Models: Biomedical and Clinical Applications is the first entry in the two-volume set which provides a wide cross-section of the methods and algorithms of variational and Partial-Differential Equations (PDE) methods in biomedical image analysis. The chapters of Deformable Models: Biomedical and Clinical Applications are written by the well-known researchers in this field, and the presentation style goes beyond an intricate abstraction of the theory into real application of the methods and description of the algorithms that were implemented. As such these chapters will serve the main goal of the editors of these two volumes in bringing down to earth the latest in variational and PDE methods in modeling of soft tissues.
Cross-Cultural Assessment of Psychological Trauma and PTSD
Recent advances in trauma treatment, coupled with ongoing traumatic world events, point to a critical need for global standards in assessment. But despite the best intentions of Western psychology, one model does not fit all cultures. Cross-Cultural Assessment of Psychological Trauma and PTSD addresses key issues in the field to help fill this knowledge gap. Focusing equally on theoretical concepts, culturally valid assessment methods, and cultural adaptation in trauma and resilience, 29 experts present the cutting edge of research and strategies. Extended case examples (including West Africans in Austria, Hmong in the U.S., and Aboriginal people in Australia) illustrate an informative range of symptom profiles, comorbid conditions, and coping skills, as well as secondary traumas that can occur in asylum seekers.
Control of Turbulent and Magnetohydrodynamic Channel Flows : Boundary Stabilization and State Estimation
This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions. Efforts in flow control over the last few years have led to a wide range of developments in many different directions, but most implementable developments thus far have been obtained using discretized versions of the plant models and finite-dimensional control techniques. In contrast, the design methods examined in this book are based on the “continuum” version of the backstepping approach, applied to the PDE model of the flow.
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 modeling of the human brain : From magnetic resonance images to finite element simulation
This book bridges common tools in medical imaging and neuroscience with the numerical solution of brain modelling PDEs. The connection between these areas is established through the use of two existing tools, FreeSurfer and FEniCS, and one novel tool, the SVM-Tk, developed for this book. The reader will learn the basics of magnetic resonance imaging and quickly proceed to generating their first FEniCS brain meshes from T1-weighted images.
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.
Issues in Bioinvasion Science: EEI 2003 : a Contribution to the Knowledge on Invasive Alien Species
Biological invasions are a global problem whose local impact can be of great magnitude. The prevention and minimization of the impact of invasive alien species has become a priority because of their negative impact on biodiversity, economy and public health. Issues in Bioinvasion Science contains key contributions of this conference. The themes included cut across different aspects of non-native species invasions. This volume is essential reading for anyone seeking an understanding of non-native species invasions.
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.
Compact Riemann Surfaces : An Introduction to Contemporary Mathematics
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory.
A Concise Course on Stochastic Partial Differential Equations
Concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations.
