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Trends in Nonlinear Analysis
Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
The Mathematics of Knots
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Theoretical and Computational Methods in Genome Research
The application ofcomputational methods to solve scientific and practical problems in genome research created a new interdisciplinary area that transcends boundaries tradi tionally separating genetics, biology, mathematics, physics, and computer science. Com puters have, of course, been intensively used in the field of life sciences for many years, even before genome research started, to store and analyze DNA or protein sequences; to explore and model the three-dimensional structure, the dynamics, and the function of biopolymers; to compute genetic linkage or evolutionary processes; and more. The rapid development of new molecular and genetic technologies, combined with ambitious goals to ex...
Semimartingales
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high ...
Multiple Shooting and Time Domain Decomposition Methods
This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
Nonlinear Conservation Laws, Fluid Systems and Related Topics
This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at the 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world''s leading experts in the field. The volume comprises five chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible fluid flows, kinetic theory and conservation laws, to statistical theories for fluid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.
Hemomath
This book illustrates applications of mathematics to various processes (physiological or artificial) involving flowing blood, including hemorheology, microcirculation, coagulation, kidney filtration and dialysis, offering a historical overview of each topic. Mathematical models are used to simulate processes normally occurring in flowing blood and to predict the effects of dysfunctions (e.g. bleeding disorders, renal failure), as well as the effects of therapies with an eye to improving treatments. Most of the models have a completely new approach that makes patient-specific simulations possible. The book is mainly intended for mathematicians interested in medical applications, but it is also useful for clinicians such as hematologists, nephrologists, cardio-surgeons, and bioengineers. Some parts require no specific knowledge of mathematics. The book is a valuable addition to mathematics, medical, biology, and bioengineering libraries.
Emil Artin and Helmut Hasse
This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.
The Impact of Applications on Mathematics
This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.
Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology
Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research, and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behavior has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics, etc. This field of research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are i...
