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On the basis of the agreement signed between UNESCO and the Government of the Republic of Poland the International Institute for Cell and Molecular Biology of UNESCO was officially inaugurated in October 1995 in Warsaw, Poland, as part of the activity of the Global Network for Molecular and Cell Biology (MCBN) of UNESCO.

Inequalities continue to play an essential role in mathematics. Since the seminal work Inequalities (1934) of Hardy, Littlewood and P6lya mathematicians have laboured to extend and sharpen the earlier classical inequalities.

About one half of the papers in this volume are based on lectures which were pre sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov. OT72 which appears frequently in this volume, refers to Volume 72 in the series Operator Theory: Advances and Applications.

most polynomial growth on every half-space Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x,O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e- ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt,E* ®E), locally given by 00 K(x,y; t) = L>-IAk(~k ® 'Pk)(X,y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::>- k. k=O Now, using, e. g. , the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for­ malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

The intensive study of molecular events leading to cellular transformation in tissue culture or in intact organisms culminated in the identification of 100 or more genes that can be defined as oncogenes or tumor suppressor genes.

The Potsdam Institute for Climate Impact Research (PIK) was founded in 1992 as a "Blue List" research institute, with the Federal Ministry for Education, Science, Research and Technology and the Ministry for Science, Research and Culture of the federal state of Brandenburg each provid ing half ofthe funding.

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 1997. This book is a self-contained exposition of the spectral theory of Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients.

Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures.

This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.

After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10.

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares.

This book is devoted to the theory of entire Hermitian operators, an important branch of functional analysis harmoniously combining the methods of operator theory and the theory of analytic functions.

Pseudo-differential operators belong to the most powerful tools in the analysis of partial differential equations. Basic achievements in the early sixties have initiated a completely new understanding of many old and important problems in analy­ sis and mathematical physics. The standard calculus of pseudo-differential and Fourier integral operators may today be considered as classical. The development has been continuous since the early days of the first essential applications to ellip­ ticity, index theory, parametrices and propagation of singularities for non-elliptic operators, boundary-value problems, and spectral theory. The basic ideas of the calculus go back to Giraud, Calderon, Zygmund, Mikhlin, Agranovich, Dynin, Vishik, Eskin, and Maslov. Subsequent progress was greatly stimulated by the classical works of Kohn, Nirenberg and Hormander. In recent years there developed a new vital interest in the ideas of micro­ local analysis in connection with analogous fields of applications over spaces with singularities, e.g. conical points, edges, corners, and higher singularities. The index theory for manifolds with singularities became an enormous challenge for analysists to invent an adequate concept of ellipticity, based on corresponding symbolic structures. Note that index theory was another source of ideas for the later development of the theory of pseudo-differential operators. Let us mention, in particular, the fundamental contributions by Gelfand, Atiyah, Singer, and Bott.

This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" .

This is the second volume of the procedings of the second European Congress of Mathematics. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. II: J.

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets.

The present work is a continuation of the work initiated in Autumn 1991, which resulted in the book, published by Birkhauser Verlag in 1994, entitled: Methods for Risk Assessment of Transgenic Plants.

George Boole (1815-1864) is well known to mathematicians for his research and textbooks on the calculus, but his name has spread world-wide for his innovations in symbolic logic and the development and applications made since his day.

The Eighth International Conference of the Inflammation Research Association was held on October 27 to 31, 1996 at Hershey Lodge and Convention Center in Hershey, Pennsylvania.

In modern ecotoxicology, fish have become the major vertebrate model, and a tremendous body of information has been accumulated. This volume attempts to summarize our present knowledge in several fields of primary ecotoxicological interest ranging from the use of (ultra)structural modifications of selected cell systems as sources of biomarkers for environmental impact over novel approaches to monitoring the impact of xenobiotics with fish in vitro systems such as primary and permanent fish cell cultures, the importance of early life-stage tests with fish, the bioaccumulation of xenobiotics in fish, the origin of liver neoplastic lesions in small fish species, immunocytochemical approaches to monitoring effects in cytochrome P450-related biotransformation, the impact of heavy metals in soft water systems, the environmental toxicology of organotin compounds, oxidative stress in fish by environmental pollutants to effects by estrogenic substances in aquatic systems.

"Methods in Pulmonary Research" presents a comprehensive review of methods used to study physiology and the cell biology of the lung.

Consisting of 23 refereed contributions, this volume offers a broad and diverse view of current research in control and estimation of partial differential equations. Topics addressed include, but are not limited to - control and stability of hyperbolic systems related to elasticity, linear and nonlinear;

The Proceedings of the Fourth International Metallothionein Meeting (MT-97) feature the latest research on metallothionein. This is an increasingly important, multi-disciplinary area of study that has benefitted from recent advances in concepts and methodologies from other fields.

The search for simple types of immune mechanisms in less complex but still evolutionary successful animals is promising and may contribute to better understanding of highly complex immune adaptive responses in mammals.

Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process.

On September 1-7, 1996 a conference on Groups and Geometries took place in lovely Siena, Italy. The conference concerned a broad range of topics in group theory and geometry, with emphasis on recent results and open problems. the structure and properties of groups of Lie type over finite and algebraically closed fields of finite characteristic, 3.

This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday. The book begins with his biography and list of publications.

This volume brings readers up to date on different aspects of operator theory and its applications, including mathematical physics, hydrodynamics, magnetohydrodynamics, quantum mechanics, astrophysics as well as the theory of networks and systems.