Bücher der Reihe Trends in Mathematics

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general.

Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function.

This collection of course notes from a number theory summer school focus on aspects of Diophantine Analysis, addressed to Master and doctoral students as well as everyone who wants to learn the subject.

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in B¿dlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics.The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Hysteresis and Slow-Fast Systems), which was dedicated to the mathematical theory and applications of multiple scale systems and systems with hysteresis, and held at the Centre de Recerca Matematica (CRM) in Barcelona from June 13th to 17th, 2016.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

Mielnik's geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator.

Hidenori Kimura, renowned system and control theorist, turned 60 years of age in November, 2001. To celebrate this memorable occasion, his friends, collaborators, and former students gathered from all over the world and held a symposium in his honor on November 1 and 2, 2001, at the Sanjo Conference Hall at the University of Tokyo.

Contains selected papers from the ISAAC conference 2007 and invited contributions. This book covers various topics that represent the main streams of research in hypercomplex analysis as well as the expository articles. It is suitable for researchers and postgraduate students in various areas of mathematical analysis.

The workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the advances in the field. This title shows the exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the work in the field.

This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.

The Bialowieza workshops on Geometric Methods in Physics, taking place in the unique environment of the Bialowieza natural forest in Poland, are among the important meetings in the field.

The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables.

Hidenori Kimura, renowned system and control theorist, turned 60 years of age in November, 2001. To celebrate this memorable occasion, his friends, collaborators, and former students gathered from all over the world and held a symposium in his honor on November 1 and 2, 2001, at the Sanjo Conference Hall at the University of Tokyo.

"Categorical Perspectives" consists of introductory surveys as well as articles containing original research and complete proofs devoted mainly to the theoretical and foundational developments of category theory and its applications to other fields. Bentley * G. Castellini * R. El Bashir * H. Husek * L. Melton * G. Schroeder * L. Strecker * A.

Statistics is strongly tied to applications in different scientific disciplines, and the most challenging statistical problems arise from problems in the sciences.

Articles examine the contributions of the great mathematician J. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research.

Provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications.

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering.

Mathematics and Computer Science III contains invited and contributed papers on combinatorics, random graphs and networks, algorithms analysis and trees, branching processes, constituting the Proceedings of the Third International Colloquium on Mathematics and Computer Science, held in Vienna in September 2004.

This volume explores multiscale methods as applied to various areas of physics and to the relative developments in mathematics. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and techniques to test the foundations of quantum mechanics.

Many of our daily-life problems can be written in the form of an optimization problem. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows.

At the heart of Clifford analysis is the study of systems of special partial differential operators that arise naturally from the use of Clifford algebra as a calculus tool. This book focuses on the study of Dirac operators and related ones, together with applications in mathematics, physics and engineering.

Includes contributions, which highlight research in the area of stochastic analysis and mathematical physics, focussing, in particular, on quantum probability. This volume covers topics such as tools for the qualitative analysis of quantum dynamical semigroups, and results on quantum information and quantum large deviations.

This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.

The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables.

This book contains the proceedings of the conference "Fractals in Graz 2001 - Analysis, Dynamics, Geometry, Stochastics" that was held in the second week of June 2001 at Graz University of Technology, in the capital of Styria, southeastern province of Austria.

This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis.

This book presents a selection of papers based on the XXXIII Bialowieza Workshop on Geometric Methods in Physics, 2014.