Diese Einfuhrung in die Welt der Wavelets ist gedacht fur Studierende der Mathematik in oberen Semestern, aber auch fur mathematisch interessierte Ingenieure. Sie hat zum Ziel, die notwendigen mathematischen Grundlagen und die eigentlichen Wavelet-Konstruktionen sowie die zugehorigen Algorithmen im Zusammenhang darzustellen. Die (fur Studierende) abstrakten Inhalte der "hoheren Analysis" werden konkret an Beispielen mathematisch durchsichtig gemacht, z.B. an signaltechnische Erfahrungen von Anwendern. Zahlreiche Figuren und durchgerechnete Beispiele bereichern den Band."

The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently.
It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this...

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the...

Band VII der Buchreihe "Moeller, Leitfaden der Elektrotechnik" hatte bisher die Aufgabe, Band I in fUr Studenten wiinschenswerter Weise durch "Beispiele zu Grundlagen der Elektrotechnik" zu erganzen. Diese Beispiele werden zukiinftig weitgehend in Band I integriert sein. Andererseits hat in der Zwischenzeit der pro grammierbare Taschenrechner eine neue Entwicklung fUr das L6sen elektrotech nischer Aufgaben eingeleitet. Es lag daher nahe, Band VII auf diese veranderte Be handlungsweise auszurichten und so ein Lehrbuch fUr das zweckmaBige Anwenden von Taschenrechnern in der Elektrotechnik zu...

This text introduces at a moderate speed and in a thorough way the basic concepts of the theory of stochastic integrals and Ito calculus for sem i martingales. There are many reasons to study this subject. We are fascinated by the contrast between general measure theoretic arguments and concrete probabilistic problems, and by the own flavour of a new differential calculus. For the beginner, a lot of work is necessary to go through this text in detail. As areward it should enable her or hirn to study more advanced literature and to become at ease with a couple of seemingly frightening...

The aims of this book are threefold:
We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most important results from the theory of homogeneous Markov chains on finite state spaces.
Chains are called rapidly mixing if all of the associated walks, regardles of where they started, behave similarly already after comparitively few steps: it is impossible from observing the chain to get information on the starting position or the number...

This book is based on a lecture course that I gave at the University of Regensburg. The purpose of these lectures was to explain the role of Kahler differential forms in ring theory, to prepare the road for their application in algebraic geometry, and to lead up to some research problems. The text discusses almost exclusively local questions and is therefore written in the language of commutative alge bra. The translation into the language of algebraic geometry is easy for the reader who is familiar with sheaf theory and the theory of schemes. The principal goals of the monograph are: To...

This book is a slightly augmented version of a set of lec tures on optimization which I held at the University of Got tingen in the winter semester 1983/84. The lectures were in tended to give an introduction to the foundations and an im pression of the applications of optimization theory. Since in finite dimensional problems were also to be treated and one could only assume a minimal knowledge of functional analysis, the necessary tools from functional analysis were almost com pletely developed during the course of the semester. The most important aspects of the course are the duality theory...