R&E Contents

Volume 1

R. T. Rockafellar

The Theory of Subgradients and its Applications to Problems of Optimization. Convex and Nonconvex Functions

115 p., soft cover, ISBN 3-88538-201-6, EUR 10.00, 1981

The author provides in his typical clear and lucid style a detailed exposition of the theory of subgradients. The text can meanwhile be considered classical in convex analysis.

"... opens a new stage in the development of the theory of nonconvex, nondifferentiable optimization".
(Zeitschr. für Angew. Math. und Mechanik)

"The book is highly recommended to anyone interested in modern analysis and optimization theory". (Optima)

Volume 2

J. Dauns

A Concrete Approach to Division Rings

438 p., soft cover, ISBN 3-88538-202-4, EUR 12.00, 1982

This is the first book which treats all types of division rings. Traditionally, the theory of division rings has been based on heavy algebra, thus restricting its accessibility to specialists. In contrast, the first objective of this book is to develop the important basic facts quickly in as straightforward a manner as possible.

In the classical references on division rings the plenitude of theorems contrasts sharply with the paucity of examples illustrating them. Another aim of this book thus is to develop the subject via examples. Many such concrete examples had to be invented and constructed, and are presented here for the first time.

The book begins by considering the classical quaternions, then generalized quaternions, and then cyclic algebras. The author next defines arbitrary crossed products, and finally the universal division algebras. Amitsur's noncrossed product proof is outlined. Along the way, the book covers part of the elementary theory of division algebras and the Brauer group. The second half of this book treats some constructions of infinite-dimensional division algebras. Central to the discussion are twisted polynomial rings. Power series rings and a class of finite extensions termed "pseudolinear" are also covered.

Most chapters of the book can be read independently and do not depend on the rest of the book.

Volume 3

L. Butz

Connectivity in Multi-Factor Designs.
A Combinatorial Approach

200 p., soft cover, ISBN 3-88538-203-2, EUR 10.00, 1982

Designs have to be connected so that contrasts between factor levels can be estimated. This monograph presents useful new characterizations of connectivity, derived through graph theory. It has substantial results to offer on designs for three or more factors and in particular on row-and-column designs. The most useful of these constitute an algorithmic approach to checking whether a design is connected. The algorithm is based on an easily defined digraph, and the maximum number of independent cycles in this graph. The algorithm works economically because complicated digraphs can be reduced by straightforward rules to elementary digraphs without altering the maximum number of independent cycles.

"I found the book extremely interesting and stimulating and was motivated to write a paper on the subject. I can recommend the book to anyone with an interest in the theory of experimental designs".
(J. Opl. Res. Soc.)

"Its new techniques for investigating connectivity are a valuable addition to statistical kowledge, and it should be on the bookshelves of all those whose research interests include connectivity ...".
(Australian J. Statistics)

Volume 4

P. Burmeister, B. Ganter, C. Herrmann, K. Keimel,
W. Poguntke, R. Wille (eds.)

Universal Algebra and its Links with Logic, Algebra, Combinatorics and Computer Science.
Proc. 25th Workshop on Generalized Algebra,
Darmstadt 1983

252 p., soft cover, ISBN 3-88538-204-0, EUR 32.00, 1984

The book consists of survey papers, based on invited lectures.
G. Grätzer: Universal algebra and lattice theory: a story and three research problems;
H. P. Gumm: Geometrical reasoning and analogy in universal algebra;
H. K. Kaiser: Interpolation in universal algebra;
W. Felscher, J. Schulte Möhring: Algebraic and deductive consequence operations;
W. Hodges: On constructing many non-isomorphic algebras;
M. M. Richter: Some aspects of nonstandard methods in general algebra;
V. Weispfennig: Aspects of quantifier elimination in algebra;
H. Werner: Boolean construction and their role in universal algebra and model theory;
P. M. Cohn: Embedding problems for rings and semigroups;
H. Jürgensen: Varietäten von Monoiden, Kongruenzen und Sprachen;
S. Mac Lane: Diagrams, equations, and theories in categories;
R. Quackenbush: Universal algebra and combinatorics;
A. Herzer: Wünsche eines Geometers an die Allgemeine Algebra;
A. Beutelspacher: Universal algebra and combinatorics - a series of problems;
R. H. Möhring: An algebraic decomposition theory for discrete structures;
M. Funk, O. H. Kegel, K. Strambach: On group universality and homogeneity;
H. Andreka, I. Nemeti: Importance of universal algebra for computer science;
L. Kucera, V. Trnkova: The computational complexity of some problems of universal algebra;
H. Reichel: Partial algebras - a sound basis for structural induction.

Volume 5

Li Weixuan

Optimal Sequential Block Search

218 p., soft cover, ISBN 3-88538-205-9, EUR 10.00, 1984

Sequential block search is a mathematical method to search for the optimal value of a unimodal function. The only prerequisite for this book is preliminary matrix theory.

"... provides a fascinating glimpse at a direction of a branch of Chinese mathematics ... should prove quite valuable algorithmically both for parallel computation and as a start on the time delay problem, which is applicable to serial computation with very expensive function evaluations". (Z. Oper. Res.)

Volume 6

Yu. A. Kutoyants

Parameter Estimation for Stochastic Processes

214 p., soft cover, ISBN 3-88538-206-7, 1984, out of print

The book begins with some elementary concepts from the theory of probability and mathematical statistics and in particular some notions of asymptotic theory of statistical inference. The later chapters deal with asymptotic properties of estimators for various types of continuous time processes. The approach to asymptotic theory used throughout the book is via the log-likelihood ratio process. Many examples illustrate the results.

The approach to the study of asymptotic theory of maximum likelihood and related estimators via stochastic processes as adopted here is also of potiential use in other areas, for instance, nonlinear regression.

The probabilist or the statistician interested in theoretical aspects will appreciate the fact that this book gives a comprehensive treatment of asymptotic theory of statistical inference for several types of continuous time processes. It will be of great interest to mathematicians doing reseach in this area but can also be used for one semester courses for graduate students.

"... gives a comprehensive treatment of asymptotical theory of statistical inference for diffusion and Poisson type processes. It will be of great interest to mathematicians doing research in this area, but can also be used for courses for graduate students".
(Statistics & Decisions)

"... excellent book ...". (Statistics)

Volume 7

M. Jünger

Polyhedral Combinatorics and the Acyclic
Subdigraph Problem

138 p., soft cover, ISBN 3-88538-207-5, EUR 20.00, 1985

Concise introduction to polyhedral combinatorics. The concept is then applied to the acyclic subdigraph problem, a prominent member of the class of NP-hard optimization problems with many practical applications. Solution algorithms are developed within a linear programming framework.

"... excellent study in combinatorial optimization".
(Syst. Anal. Model. Simulation)

Volume 8

G. Reinelt

The Linear Ordering Problem. Algorithms and Applications

168 p., soft cover, ISBN 3-88538-208-3, EUR 20.00, 1985

Instances of the linear ordering problem occur in many practical applications. Examples are the one machine scheduling problem with preference constraints, aggregation of individual preferences in the social sciences, triangulation of input-output matrices in economics, paired comparison ranking in sociology or even tournaments in sports.

This monograph applies methods of polyhedral combinatorics to the linear ordering problem. New results on the facial structure of a polytope related to this problem leads to the "linear ordering polytope". Embedded into a branch and bound framework, a computer implementation of this approach is shown to be able to solve real-world instances of the triangulation problem which could not be solved by previous methods. The optimum triangulation of a large number of European input-output tables makes this book not only an interesting theoretical and computational study in applied mathematics, but also a valuable source for economists.

"The book represents an important contribution to polyhedral combinatorics. ... also valuable for economists". (Optimization).

"This book ... is a convincing documentation of the power and the beauty of the ... cutting plane approach ...". (OR Spectrum)

Volume 9

A. B. Romanowska, J. D. H. Smith

Modal Theory. An Algebraic Approach to Order, Geometry, and Convexity

170 p., soft cover, ISBN 3-88538-209-1, EUR 20.00, 1985

Modal theory is a new algebraic discipline, comparable in scope and intention with the well-established disciplines of linear algebra, lattice theory, and semigroup theory. The topics of modal theory, belonging mostly to universal algebra, have broad connections to the theory of semigroups, semilattices, lattices, convex sets, geometry, and computer science. The value of the work lies in the investigation of general properties of modes and modals (idempotent entropic algebras that are not necessarily associative) and in the analysis of various special cases.

"... is written in a clear and pleasant style and is very readible, even if one is not familiar with the subject. Recommended!"
(Med. Wiskundig Genootschap)

"A new and interesting algebraic structure is investigated". (Monatshefte der Mathematik)

Volume 10

G. Mazzola

Gruppen und Kategorien in der Musik. Entwurf einer mathematischen Musiktheorie

214 p., soft cover, ISBN 3-88538-210-5, EUR 25.00, 1985

Der Autor beschreibt fundamentale Mechanismen der musikalischen Komposition und Interpretation, der Analyse und des Verständnisprozesses durch Begriffe, die dem Paradigma der Mannigfaltigkeit entlehnt sind. Diese Idee der Verknüpfung lokaler Raumteile zu einem globalen Gebilde formalisiert die Vielfalt musikalischer Bedeutung durch die Freiheit, das Ganze in verschiedener Weise aus Teilräumen zusammenzufügen. Während Gruppen affiner Transformationen die Verknüpfungsdaten liefern, führt die Frage nach der Identität eines Musikwerkes über das Yoneda-Lemma zur kategorientheoretischen Klassifikationsproblematik.

Der vorliegende theoretische Ansatz stellt insbesondere Modulationmodelle bereit, die von der Harmonielehre und der Kompositionspraxis gestützt werden. Die Analyse des Allegro-Satzes von Beethovens Hammerklavier-Sonate und die darauf aufbauende Konstruktion eines Sonaten-Hauptsatzes sind prägnante Anwendungen dieser mathematischen Modellbildung.

"Ein faszinierendes Kapitel der angewandten Mathematik, welches sich überaus mutig mit dem (scheinbar?) so diametral gegenüberliegenden Bereich der Musik beschäftigt und sicherlich neue Perspektiven eröffnet". (Monatshefte der Mathematik)

Volume 11

R. Lowen

On the Existence of Natural Non-Topological, Fuzzy Topological Spaces

200 p., soft cover, ISBN 3-88538-211-3, EUR 18.00, 1985

This monograph presents a unified study of several important examples of natural fuzzy topological spaces: the space of probability measures on a separable metrizable topological space, the space of Radon probability measures on a linearly ordered topological space -- which generalizes the so-called fuzzy real line -- and the hyperspace of uppersemicontinuous fuzzy sets on a uniform space.

Volume 12

W. H. Cornish

Antimorphic Action. Categories of Algebraic Structures with Involutions or Anti-Endomorphisms

212 p., soft cover, ISBN 3-88538-212-1, EUR 25.00, 1986

A categorical approach to certain involutions of a Lie algebra, a quadratic Jordan algebra, or a free lattice in a self-dual variety of lattices. Explores properties of the variety formed by those algebras in a variety of finitary algebras expanded by antimorphisms which are acted upon by members of a fixed monoid in a homomorphic or antihomomorphic manner. The deepest results are relevant to algebras obtained from popositional logics.

Volume 13

W. Taylor

The Clone of a Topological Space

100 p., soft cover, ISBN 3-88538-213-X, EUR 20.00, 1986

The set of all continuous selfmaps of a topological space A forms a semigroup, whose properties are well known to reflect those of A in interesting ways. Here we will consider a more general structure, called the clone of A, which consists of all continuous maps from the product of n copies of A to A, n ranging over all integers.

Several theorems are proved indicating how many basic topological properties of A (connectedness, fixed point properties, dimension, etc.) are equivalent to some corresponding algebraic or first order properties of the clone C(A). Most interesting results are obtained for homotopy properties, and for particular spaces A, C(A) can be interpreted as a homotopy group.

Finally this approach is related to the well known theory of the ring C(A) of all continuous real-valued functions from C(A) to R and it is shown that this ring can be interpreted in the clone C(A).

Volume 14

S. Wolfenstein (ed.)

Algebra and Order
Proc. First Int'l Symp. on Ordered Algebraic Structures, Luminy-Marseilles 1984

400 p., soft cover, ISBN 3-88538-214-8, EUR 38.00, 1986

These proceedings present for the first time a complete survey of the current research in this large field. In correspondence to the thematic architecture of the conference the papers are built around lattice ordered groups as the central pillar of strength. Other sections forming also integral parts of the whole concept are: a section on vector lattices and function algebras as a link to functional analysis, a section on real algebraic geometry, and one on ordered semigroups, semirings and related structures.

Volume 15

K. H. Hofmann, R. Wille (eds.)

Symmetry of Discrete Mathematical Structures and Their Symmetry Groups. A Collection of Essays

180 p., soft cover, ISBN 3-88538-215-6, EUR 35.00, 1991

It has been said that, in mathematics, the 20th century became the century of symmetry. The editors make an attempt to elucidate this point of view by presenting five articles on different aspects of this subject:
J. Bokowski: On the geometric flat embedding of abstract complexes with symmetries;
A. Dress: Repetition und Metamorphose - zum Symmetriebegriff in der Mathematik;
K. H. Hofmann: Symmetrie und Homogenität;
E. Schulte, J. M. Wills: Combinatorially regular polyhedra in three-space;
R. Wille: Symmetrie -- Versuch einer Begriffsbestimmung.

The books contains numerous coloured figures and photographs.

Volume 16

Z. Frolik (ed.)

General Topology and its Relations to Modern Analysis
and Algebra VI
Proc. 6th Prague Topological Symposium 1986

736 p., soft cover, ISBN 3-88538-216-4, 1988, out of print

This collection of reviewed articles marks the state-of-the-art in topology. The proceedings of the 5th symposium has also been published by Heldermann Velag as volume 3 of the Sigma Series in Pure Mathematics.

Volume 17

E.-A. Behrens

Arithmetical Completely Simple Semigroups

143 p., soft cover, ISBN 3-88538-217-2, EUR 25.00, 1989

To develop a non-commutative arithmetic for partially ordered semigroups the author defines arithmetical completely simple semigroups and applies them to the integral normal ideals in the central simple algebras Q over the quotient field of a Dedekind ring under a generalized multiplication. On the set I of the maximal orders in Q he introduces a partial order relation, the finer properties of which describe the arithmetic of Q.

Volume 19

A. Romanowska, J. D. H. Smith (eds.)

Universal Algebra and Quasigroup Theory

250 p., soft cover, ISBN 3-88538-219-9, EUR 35.00, 1992

The two fields of universal algebra and quasigroup theory have long enjoyed a symbiotic relationship. Universal algebraic principles reveal that quasigroup theory may achieve the depth and applicability of group theory. On the other hand, concepts from quasigroup theory (such as centrality and isotopy) are now having a marked influence on the general course of universal algebra. The 10 papers in this volume present results ranging across the spectrum from universal algebra to quasigroup theory, the fruit of recent interaction between schools in Central Europe and North America. For more details see the Contents.

Volume 20

K. Denecke, H.-J. Vogel (eds.)

General Algebra and Applications

240 p., soft cover, ISBN 3-88538-220-2, EUR 40.00, 1993

This collection of 20 articles is related to the following topics: Equational theory of universal algebra; Mal'cev conditions; Arithmetical affine complete varieties; Theory of clones; Duality theory and category equivalences; Lattice theory and applications; Partial algebras; Classical structures. For more details see the Contents.

Volume 21

K. Denecke, O. Lüders (eds.)

General Algebra and Discrete Mathematics

272 p., soft cover, ISBN 3-88538-221-0, EUR 38.00, 1995

Algebraic structures such as semigroups, lattices, Boolean algebras, function algebras, and relation algebras, or ordered algebraic structures, form a structural background of such fields of Discrete Mathematics as formal languages, the theory of automata, theoretical computer science, and graph theory. The 20 papers of this collection survey and further develop this field. For more details see the Contents.

Volume 22

W. Krabs

Optimal Control of Undamped Linear Vibrations

188 p., soft cover, ISBN 3-88538-222-9, EUR 40.00, 1995

Considered are vibrating systems with finitely many and infinitely many degrees of freedom which are undamped and linear. The first can be described by linear systems of ordinary differential equations of second order without first order terms. The control of the systems is performed by exterior forces on the right hand side of the equations and is called lumped control. In the case of infinitely many degrees of freedom the vibrating systems are described by linear partial differential equations of second order with respect to the time under linear boundary conditions. There are two kinds of control: distributed control where the control is performed by an exterior force on the right hand side of the differential equation and boundary control which is applied to one or more boundary conditions.

The main purpose of this book is to investigate the vibrating systems under the aspect of null-controllability. In particular the relationship between time-minimal null-controllability with norm bounded controls and minimum norm null-controls on fixed time intervals is studied because it is the key for a numerical solution.
Distributed control of partial differential equations is uniformly treated within the framework of abstract wave equations for Hilbert space valued functions which also comprises the case of lumped control of vibrating systems with finitely many degrees of freedom. The corresponding control problems are approximately solved with the aid of Galerkin's method and by applying duality results for certain minimum norm problems.

Volume 23

K. A. Baker, R. Wille (eds.)

Lattice Theory and its Applications. In Celebration of Garrett Birkhoff's 80th Birthday

268 p., soft cover, ISBN 3-88538-223-7, EUR 42.00, 1995

The 15 articles in this volume are elaborations of selected lectures by leading experts held at a conference which was organized on the occasion of G. Birkhoff's 80th birthday. The contributions survey pure and applied lattice theory and contain substantial new results. For more details see the Contents.

Volume 24

E. Martin Peinador, J. Nunez Garcia (eds.)

Nuclear Groups and Lie Groups

258 p., soft cover, ISBN 3-88538-224-5, EUR 36.00, 2001

The 14 articles in this volume are elaborations of selected lectures by leading experts held at a conference at the University Complutense of Madrid in September 1999. For more details see the Contents.

Volume 25

I. Bajo, E. Sanmartin (eds.)

Recent Advances in Lie Theory

406 p., soft cover, ISBN 3-88538-225-3, EUR 44.00, 2002

Lie Theory is known to play a crucial role in many fields of Mathematics and Physics. Apart from their obvious geometric and algebraic importance, Lie groups and Lie algebras have turned out to be of fundamental significance in Differential Equations, Quantum Mechanics, Algebraic Geometry, Topology and the Theory of Special Functions. The aim of this book is to provide the reader with a general view of recent research directions, represented in 23 articles, in most of these topics.
For more details see the Contents.