Bücher veröffentlicht von Springer Basel

This volume is dedicated to Tsuyoshi Ando, a foremost expert in operator theory, matrix theory, complex analysis, and their applications, on the occasion of his 60th birthday. This volume also contains papers on interpolation and completion problems, factorization problems and problems connected with complex analysis.

Kaashoek, "Bitangential interpola tion for input-output operators of time varying systems: the discrete time case" contains solutions of time varying interpolation problems.

One of the key concerns in modern control theory is the design of steering strategies. The implementation of such strategies is done by a regulator. Presented here is a self-contained introduction to the mathematical background of this type of regulator design. The topics selected address the matter of greatest interest to the control community, at present, namely, when the design objective is the reduction of the influence of exogeneous disturbances upon the output of the system. In a first scenario the disturbance signal is regarded as a deterministic time series with known dynamics but unknown parameters. The design objective is then the asymptotic disturbance compensation. In a second scenario, no information about the disturbance signal is available apart from some bounds. Here, in an H-approach, control strategies are worked out which will prove efficient for all such disturbances. The intention of this book is to present ideas and methods on such a level that the beginning graduate student will be able to follow current research. New results are included, especially for nonlinear control systems, and as a service to the reader, an extensive appendix presents topics from linear algebra, invariant manifolds and calculus of variations, information which is hardly to be found in standard textbooks. Contents: Introduction ¿ The problem of output regulation ¿ Introduction ¿ Problem statement ¿ Output regulation via full information ¿ Output regulation via full error feedback ¿ A particular case ¿ Well-posedness and robustness ¿ The construction of a robust regulator ¿ Disturbance attenuation via H-methods ¿ Introduction ¿ Problem statement ¿ A characterization of the L2-gain of a linear system ¿ Disturbance attenuation via full information ¿ Disturbance attenuation via measured feedback ¿ Full information regulators ¿ Problem statement ¿ Time-dependent control strategies ¿ Examples ¿ Time-independent control strategies¿ The local case ¿ Nonlinear observers ¿ Problem statement ¿ Time-dependent observers ¿ Error feedback regulators ¿ Examples ¿ Nonlinear H-techniques ¿ Introduction ¿ Construction of the saddle-point ¿ The local scenario ¿ Disturbance attenuation via linearization ¿ Matrix equations ¿ Linear matrix equations ¿ Algebraic Riccati equations ¿ Invariant manifolds ¿ Existence theorem ¿ Outflowing manifolds ¿ Asymptotic phase ¿ Convergence for T ¹ ¿ A special case ¿ Dichotomies and Lyapunov functions ¿ Hamilton-Jacobi-Bellman-Isaacs equation ¿ Introduction ¿ Method of characteristics ¿ The equation of Isaacs ¿ The Hamiltonian version of Isaacs' equation ¿ Bibliography

A collection of papers on different aspects of operator theory and complex analysis, covering the recent achievements of the Odessa-Kharkov school, where Potapov was very active. The book appeals to a wide group of mathematicians and engineers, and much of the material can be used for advanced courses and seminars.

When the first multigrid conference was held in 1981 there was no doubt about the usefulness of a conference dedicated specially to multigrid, because multigrid was a new and relatively unexplored subject, still in a pioneering stage, and pursued by specialists.

Progress in today's high-technology industries is strongly associated with the development of new mathematical tools. Their contributions, forming the body of this work, cover electric circuit simulation, device simulation and process simulation.

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy.

The English edition differs only slightly from the Russian original. When the Russian edition was being written, these direc tions in game theory had not yet attained their final form, which appeared only in quite recent monographs;

Are demographic and environmental stochas ticity by far more important for the fate of a population or species than genetic stochasticity (genetic drift and inbreeding)?

PREFACE The classic statement of the Riemann boundary problem consists in finding a function (z) which is analytic and bounded in two domains D+ and D-, with a common boundary - a smooth closed contour L admitting a continuous extension onto L both from D+ and D- and satisfying on L the boundary condition +(t) = G(t)-(t) + g(t).

"Fractals in Biology and Medicine" explores the potential of fractal geometry for describing and understanding biological organisms, their development and growth as well as their structural design and functional properties.

This research monograph contains a study of discrete-time nodes, the discrete counterpart of the theory elaborated by Bart, Gohberg and Kaashoek for the continuous case, discrete-time Lyapunov and Riccati equations, discrete-time Hamiltonian systems in connection with input-output operators and associated Hankel and Toeplitz operators.

Die allgemeine Relativitästheorie lässt sich nur mit Hilfe des Tensorkalküls formulieren. Diesen lernte Einstein 1912 in Form des absoluten Differentialkalküls kennen. Dessen Schöpfer war Gregorio Ricci, dem zusammen mit Sophus Lie und anderen der Ausbau der Theorie der Differentialinvarianten gelang. Der absolute Differentialkalkül passte zur allgemeinen Relativitätstheorie wie ein Schlüssel zum Schloss: der in den Jahren 1884-92 von Ricci entwickelte Kalkül erfüllte in der Tat genau das physikalische Konzept der allgemeinen Relativitätstheorie, das Einstein 1907-15 ausarbeitete. Ein derartiges Zusammenpassen war nur dadurch möglich, weil sowohl Ricci innerhalb der Mathematik als auch Einstein innerhalb der Physik vergleichbare Fragen stellten, nämlich Fragen nach Invarianten bei speziellen Transformationen. Es wird versucht, den historischen Weg so genau wie möglich anhand der Quellen nachzuzeichnen. Neu ist die Herausarbeitung des invariantentheoretischen Aspekts, dem gegenüber die Bedeutung der Differentialgeometrie für die Entwicklung des Tensorkalküls in den Hintergrund treten muss.

Intended for both researchers and practitioners, this book will be a valuable resource for studying and applying recent robust statistical methods. It contains up-to-date research results in the theory of robust statisticsTreats computational aspects and algorithms and shows interesting and new applications.

The theory of Laplace transformation is an important part of the mathematical background required for engineers, physicists and mathematicians. The code is placed in front of the already built-in code of Laplace and z-transformations of Mathematica so that built-in functions not covered by the Package remain available.

Important clinical issues as the outcome of long term treatment with antidepressants, the time of onset of the antidepressant response and the limitations of the antidepressants currently available are covered in this monograph.

In this book we shall study linear functional equations of the form m bu(x) == Lak(X)U(Qk(X)) = f(x), (1) k=l where U is an unknown function from a given space F(X) of functions on a set X, Qk: X -+ X are given mappings, ak and f are given functions. Our approach is based on the investigation of the operators given by the left-hand side of equa­ tion (1). In what follows such operators will be called functional operators. We will pay special attention to the spectral properties of functional operators, first of all, to invertibility and the Noether property. Since the set X, the space F(X), the mappings Qk and the coefficients ak are arbitrary, the class of operators of the form (1) is very rich and some of its individ­ ual representatives are related with problems arising in various areas of mathemat­ ics and its applications. In addition to the classical theory of functional equations, among such areas one can indicate the theory of functional-differential equations with deviating argument, the theory of nonlocal problems for partial differential equations, the theory of boundary value problems for the equation of a vibrating string and equations of mixed type, a number of problems of the general theory of operator algebras and the theory of dynamical systems, the spectral theory of au­ tomorphisms of Banach algebras, and other problems.

This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: - Stability and bifurcation- Geometric mechanics and control theory- Invariant manifolds, attractors and chaos- Fluid mechanics and elasticity- Perturbations and multiscale problems- Hamiltonian dynamics and KAM theoryResearchers and graduate students in dynamical systems and related fields, including engineering, will benefit from the articles presented in this volume.

Tamoxifen is a pioneering medicine for the treatment and prevention of breast cancer. It is the first drug targeted therapy in cancer to be successful. Tamoxifen targets the tumor estrogen receptor. The therapy is known to have saved the lives of millions of women over the past 40 years.This monograph, written by V. Craig Jordan - known as the "e;father of tamoxifen"e; - and his Tamoxifen Team at the Georgetown University Washington DC, illustrates the journey of this milestone in medicine. It includes a personal interview with V. Craig Jordan about his four decades of discovery in breast cancer research and treatment. V. Craig Jordan was there for the birth of tamoxifen as he is credited for reinventing a "e;failed morning after contraceptive"e; to become the "e;gold standard"e; for the treatment of breast cancer. He contributed to every aspect of tamoxifen application in therapeutics and all aspects of tamoxifen's pharmacology. He discovered the selective estrogen receptor modulators (SERMs) and explored the new biology of estrogen-induced apoptosis.

The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important.Fractal Symmetry of Protein Exterior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Although these ideas are entirely mathematical, mathematical expositions have been avoided, unless the use of some expressions becomes absolutely obligatory. A first chapter introduce into fractal dimensions, protein exteriors and to methods to study the roughness of surfaces. The main topics covered in the following chapters include: protein-protein interaction interfaces; protein surface-roughness and local shape as well as adhesion on protein and other rough biomolecular surfaces.

The essential question that fractal dimensions attempt to answer is about the scales in Nature. For a system as non-idealistic and complex as a protein, studying scale-invariance becomes particularly important.Fractal Symmetry of Protein Interior investigates the diverse facets of the various scales at which we describe protein biophysical and biochemical phenomena. Following a thorough introduction to fractal dimensions, fractal-dimension-based approaches, that have been employed to study protein interior biophysical properties, are described. The focus is on the question "e;which scales are scale-invariant?"e; Investigations related to scaling of biophysical and biochemical behaviors may one day help us to formulate a fundamental theory about protein biophysics; which, in turn, may help us to understand fundamental principles of proteins.

Concentration analysis provides, in settings without a priori available compactness, a manageable structural description for the functional sequences intended to approximate solutions of partial differential equations.

The following five chapters concentrate on proteins, their structure, folding and function, the electrochemistry of redox proteins and voltammetric methods.

The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied.

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)".

In this volume outstanding specialists review the state of the art in nervous system research for all main invertebrate groups. Novel techniques in molecular and developmental biology are creating new perspectives that point toward a theoretical foundation for a modern organismic biology.

gar discusses recent studies of the SF gene promoter that may be relevant to understanding the detailed molecular mechanism(s) by which soluble factors regulate SF production. Polverini and Nickoloff discuss another mechanism by which SF may enhance tumor growth, ie., stimulation of angiogenesis, the formation of new blood vessels from pre-existing microvessels. Angiogenesis is required for continued growth of most solid tumors, and provides a mechanism by which the stroma may continue to grow along with the tumor cells. Although endothelial cells are stromal cells, they express a number of epithelial characteristics including (i) epithelial-like tight junctions and junctional proteins; (ii) the ability to organize into flat­ tened tubular structures; (iii) the c-met receptor protein; and (iv) biologic responsiveness to SF. It is, perhaps, not surprising that vascular endothe­ lial cells may both produce and respond to SF in different situations. 'Epithelialness' may be defined in two ways: (i) expression of generic epithelial structures and proteins (eg., specialized junctions, junctional proteins [eg., cadherins, ZOl], cytokeratins); and (ii) production of specific differentiated products (eg., milk proteins by mammary epithelia, renin by renal tubular epithelia of the juxtaglomerular apparatus). Recent studies suggest that SF Ic-met signalling may mediate epithelia­ mesenchyme interconversion, in part by modifying some of the generic epithelial characteristics. Nusrat discusses the effects of SF on the epithelial junctional apparatus. Relatively little is known about whether and how SF regulates cell-specific differentiation.

This book is based on two keywords: Bioradical and ESR. Research on the structure and function of bioradicals has been attrac ting growing attention in the field of biological science, and comprehensive investigations from many fields are helping to understand the real features of these species.