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Classification of fam ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century.

Dalip J. S. Sirinathsinghii and Ray G. Hill Merck, Sharp & Dohme Research Laboratories, Neuroscience Research Centre, Terlings Park, Eastwick Road, Harlow, Essex CM20 2QR, UK There remains a distinct medical need for new pain therapies. Therefore, it is not surprising that in recent years there has been a major research initiative in both aca­ demic and pharmaceutical laboratories to identify novel pain targets and to devel­ op novel analgesic drugs. It is clear from numerous studies that the NMDA recep­ tor plays a major role in the transmission ofnociceptive information and it has been a subject of extensive investigation over the last decade exploiting the advances of molecular pharmacology and molecular neuroanatomy. As a consequence there has been a rational approach by several laboratories to develop receptor subtype-spe­ cific NMDA antagonists in order to avoid the wide range of side-effects seen with non-selective NMDA ion channel antagonists such as ketamine. This volume brings together contributions from experts in various technological disciplines who have contributed immensely to NMDA receptor research and advanced our understanding of the subunit composition of the NMDA receptor complex, its pharmacology and distribution, its interaction with other neurochemi­ cal systems and the effects on behaviour of NMDA antagonists in rodent models and in the clinic. In consideration of these advances and the prospects of novel NMDA receptor antagonists in the near future for the treatment of pain, this vol­ ume is very timely.

This book deals with statins which have substantially altered the approach to therapy of atherosclerosis and its sequelae. This book not only provides the reader with valuable information but also stimulates further research into the pathogenesis of atherosclerosis and the mechanisms behind the action of effective statins.

Allergic diseases are complex and involve a range of environmental factors interacting with a susceptible genotype.

In March 2000 leading scientists gathered at the Centro Seminariale Monte Verita, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine.

Since the introduction of ciprofloxacin in 1987, fluoroquinolones have expanded far beyond their early role in the treatment of urinary tract infections. Clinical applications beyond genitourinary tract infections include upper and lower respiratory infections, gastrointestinal infections, gynecologic infec­ tions, sexually transmitted diseases, and some skin and soft tissue infections. Their ease of administration, favorable pharmacokinetic properties, excellent tolerability, and efficacy give them enormous potential for use and misuse alike. Quinolones have few common adverse effects, most notably nausea, headache and dizziness. Less frequent but more serious adverse events include prolongation of the corrected QT interval, phototoxicity, liver enzyme abnor­ malities, arthropathy, and cartilage and tendon abnormalities. While possess­ ing many of the favorable properties of intravenous agents, most fluoro­ quinolones offer the convenience of oral administration, thus contributing to decreased health-care costs through increased outpatient therapy and short­ ened hospital stays. With the recent introduction of agents such as gatifloxacin and moxifloxacin, the traditional Gram-negative coverage of fluoroquinolones has been expanded to include Gram-positive organisms, most importantly Streptococcus pneumoniae.

This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators.

The history of mechanics, and more particularly, the history of mechanics applied to constructions, constitutes a field of research that is relatively recent.

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics.

A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001.Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrödinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.

In November 2001 the Mathematical Research Center at Oberwolfach, Germany, hosted the third Conference on Mathematical Models and Numerical Simulation in Electronic Industry. It brought together researchers in mathematics, electrical engineering and scientists working in industry.The contributions to this volume try to bridge the gap between basic and applied mathematics, research in electrical engineering and the needs of industry.

The second part of the present volume collects nonself-adjoint problems on small motions and normal oscillations of a viscous fluid filling a bounded region.

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance.

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance.

The general characteristics of neuropeptides are discussed as a background for the understanding of their role in regulation of physiological systems. The extent of those systems that are crucially affected by neuropeptides is vast and the complexity of their interactions makes the clinical focus on a specific neu­ ropeptide unsatisfactory. The clinical potential of neuropeptides affecting eating disorders, eNS behavioral disorders and the neuroregenerative and neuroprotective action of neuropeptides is discussed. It is probable that suc­ cessful neuropeptide therapeutics will depend upon the application of trans­ lational and combinational research using various ingenious combinations and antagonists, neuropeptide receptor ago­ of neuropeptides, their agonists nists and antagonists, improved methods of delivery and the development of peptides targeted to the genetic profile of individual patients. References 1 DeWied D (1969) Effects of peptide hormones on behavior. In: WF Ganong, L Martini (eds): Frontiers in Neuroendocrinology. Oxford University Press, New York, 97-140 2 Sandman CA, Schally AV, Kastin AJ, Miller L H (1972) A neuroendocrine influence on attention and memory. J Comp Physiol Psychol80: 54-58 3 Kastin AJ, Olson RD, SchaUy A V, Coy DH (1979) CNS effects of peripherally adminis­ tered brain peptides. Life Sci 25: 401-414 4 Strand FL, Saint-Come C, Lee TS, Lee SJ, Kume JA, Zuccarelli LA (1993) An ACTH/MSH 4-10 analog BIM 22015 has neurotrophic and myotrophic attributes during peripheral nerve regeneration. Peptides 14: 287-296 5 Strand FL (1999) Neuropeptides: Regulators ofPhysiologjcal Processes.

For centuries, TK has been used almost exclusively by its creators, that is, indigenous and local communities. Over many generations, indigenous and local communities have accumulated a great deal of TK which has generally been adapted, developed and improved by the generations that followed.

In this book we study orthogonal polynomials and their generalizations in spaces with weighted inner products. These ortho gonal polynomials are called the Szego polynomials associated with the weight w.

Principles of Learning and Memory presents state-of-the-art reviews that cover the experimental analysis of behavior, as well as the biological basis of learning and memory, and that overcome traditional borders separating disciplines.

Heat shock proteins (HSP) have received ample interest by immunologists over recent years. Since then, the raised presence of immunity to HSPs in virtually all conditions of inflammation, including autoimmune diseases, transplant rejection and atherosclerosis, has emphasised the critical significance of immunity to HSPs in inflammatory diseases.

Noise is a rich concept playing an underlying role in human activity. Consideration of the noise phenomenon in arts and sciences, respectively, makes the distinction between both domains more obvious. Artists create "deliberate noise"`; the masterpieces of literature, music, modern fine art etc. are those where a clear idea, traditionally related to such concepts as love, is presented under a skilful veil of "deliberate noise". On the contrary, sciences fight against noise; a scientific discovery is a law of nature extracted from a noisy medium and refined.This book discusses the methods of fighting against noise. It can be regarded as a mathematical view of specific engineering problems with known and new methods of control and estimation in noisy media.The main feature of this book is the investigation of stochastic optimal control and estimation problems with the noise processes acting dependently on the state (or signal) and observation systems. While multiple early and recent findings on the subject have been obtained and challenging problems remain to be solved, this subject has not yet been dealt with systematically nor properly investigated. The discussion is given for infinite dimensional systems, but within the linear quadratic framework for continuous and finite time horizon. In order to make this book self-contained, some background material is provided.Consequently, the target readers of this book are both applied mathematicians and theoretically oriented engineers who are designing new technology, as well as students of the related branches. The book may also be used as a reference manual in that part of functional analysis that is needed for problems of infinite dimensional linear systems theory.

The seminar on Stochastic Analysis and Mathematical Physics of the Ca­ tholic University of Chile, started in Santiago in 1984, has being followed and enlarged since 1995 by a series of international workshops aimed at pro­ moting a wide-spectrum dialogue between experts on the fields of classical and quantum stochastic analysis, mathematical physics, and physics. This volume collects most of the contributions to the Fourth Interna­ tional Workshop on Stochastic Analysis and Mathematical Physics (whose Spanish abbreviation is "ANESTOC"; in English, "STAMP"), held in San­ tiago, Chile, from January 5 to 11, 2000. The workshop style stimulated a vivid exchange of ideas which finally led to a number of written con­ tributions which I am glad to introduce here. However, we are currently submitted to a sort of invasion of proceedings books, and we do not want to increase our own shelves with a new one of the like. On the other hand, the editors of conference proceedings have to use different exhausting and com­ pulsive strategies to persuade authors to write and provide texts in time, a task which terrifies us. As a result, this volume is aimed at smoothly start­ ing a new kind of publication. What we would like to have is a collection of books organized like our seminar.

Over the last years, stochastic analysis has had an enormous progress with the impetus originating from different branches of mathematics: PDE's and the Malliavin calculus, quantum physics, path space analysis on curved manifolds via probabilistic methods, and more. This volume contains selected contributions which were presented at the 8th Silivri Workshop on Stochastic Analysis and Related Topics, held in September 2000 in Gazimagusa, North Cyprus. The topics include stochastic control theory, generalized functions in a nonlinear setting, tangent spaces of manifold-valued paths with quasi-invariant measures, and applications in game theory, theoretical biology and theoretical physics. Contributors: A.E. Bashirov, A. Bensoussan and J. Frehse, U. Capar and H. Aktuglul, A.B. Cruzeiro and Kai-Nan Xiang, E. Hausenblas, Y. Ishikawa, N. Mahmudov, P. Malliavin and U. Taneri, N. Privault, A.S. Üstünel

This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Operator Theoretical Methods in Diffraction Theory;

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 volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems.

Consisting of 16 refereed original contributions, this volume presents a diversified collection of recent results in control of distributed parameter systems. Topics addressed include - optimal control in fluid mechanics - numerical methods for optimal control of partial differential equations - modeling and control of shells - level set methods - mesh adaptation for parameter estimation problems - shape optimization Advanced graduate students and researchers will find the book an excellent guide to the forefront of control and estimation of distributed parameter systems.

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." -Zentralblatt Math"This monograph contains a wealth of information many topologists will find very handy.

Euklid, der Geometer aus Alexandria, und sein uberwiegend geometrisches literarisches Werk bilden den Mittelpunkt dieses Buches zur Geschichte der Mathematik. Es ist bis heute nicht mit letzter Sicherheit geklart, ob es einen Mathematiker mit dem Namen Euklid wirklich gegeben, wann er gelebt hat und ob die ihm zugeschriebenen Lehrbucher zur Mathematik und zur mathematischen Physik tatsachlich nur von ihm verfasst wurden. Trotz dieser Einschrankungen breitet der Autor das derzeit verfugbare Wissen uber die voreuklidische griechische Mathematik, die Traditionslinien der euklidischen Geometrie und die uber Jahrhunderte andauernde Wirkungsgeschichte der euklidischen Werke umfassend aus. Dabei wird an vielen Stellen deutlich, wie unzureichend unsere Kenntnisse uber die Rezeptionsgeschichte und wie luckenhaft das antike Quellenmaterial auch nach zweitausend Jahren immer noch sind. Das Buch spurt den vielfaltigen historischen und interkulturellen Aspekten und Facetten der Mathematik nach.

The significance of foundational debate in mathematics that took place in the 1920s seems to have been recognized only in circles of mathematicians and philosophers. A period in the history of mathematics when mathematics and philosophy, usually so far away from each other, seemed to meet.