This volume constitutes the proceedings of the third Franco-Japanese symposium on singularities, held in Sapporo in September 2004. It contains not only research papers on the most advanced topics in the field, but also some survey articles which give broad scopes in some areas of the subject. All the articles are carefully refereed for correctness and readability.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

This is the proceedings of the meeting entitled "The 12th MSJ International Research Institute of the Mathematical Society of Japan 2003". The papers cover several important topics in Singularity theory. Especially some of them are survey on motivic integrations, Thom polynomials, complex analytic singularity theory, generic differential geometry etc.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

Since its birth algebraic geometry has been closely related to and deeply motivated by number theory. Particularly the modern study of moduli spaces and arithmetic geometry have many important techniques and ideas in common. With this close relation in mind, the RIMS conference Moduli Spaces and Arithmetic Geometry was held at Kyoto University during September 8-15, 2004 as the 13th International Research Institute of the Mathematical Society of Japan. This volume is the outcome of this conference and consists of thirteen papers by invited speakers, including C Soule, A Beauville and C Faber, and participants. All papers, with two exceptions by C Voisin and Yoshinori Namikawa, treat moduli problem and/or arithmetic geometry. Algebraic curves, Abelian varieties, algebraic vector bundles, connections and D-modules are the subjects of those moduli papers. Arakelov geometry and rigid geometry are studied in arithmetic papers. In the two exceptions, integral Hodge classes on Calabi-Yau threefolds and symplectic resolutions of nilpotent orbits are studied.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America

This book is based on lectures presented over many years to second and third year mathematics students in the Mathematics Departments at Bedford College, London, and King's College, London, as part of the BSc. and MSci. program. Its aim is to provide a gentle yet rigorous first course on complex analysis.Metric space aspects of the complex plane are discussed in detail, making this text an excellent introduction to metric space theory. The complex exponential and trigonometric functions are defined from first principles and great care is taken to derive their familiar properties. In particular, the appearance of , in this context, is carefully explained.The central results of the subject, such as Cauchy's Theorem and its immediate corollaries, as well as the theory of singularities and the Residue Theorem are carefully treated while avoiding overly complicated generality. Throughout, the theory is illustrated by examples.A number of relevant results from real analysis are collected, complete with proofs, in an appendix.The approach in this book attempts to soften the impact for the student who may feel less than completely comfortable with the logical but often overly concise presentation of mathematical analysis elsewhere.

Inequalities from Complex Analysis is a careful, friendly exposition of some rather interesting mathematics. The author begins by defining the complex number field; he gives a novel presentation of some standard mathematical analysis in the early chapters. The development culminates with some results from recent research literature. The book provides complete yet comprehensible proofs as well as some surprising consequences of the results. One unifying theme is a complex variables analogue of Hilbert's seventeenth problem. Numerous examples, exercises and discussions of geometric reasoning aid the reader. The book is accessible to undergraduate mathematicians, as well as physicists and engineers.

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers with comprising edges and other complex cavity features. It is an authoritative account of mathematical developments over the last two decades that provides benchmarks against which solutions obtained by numerical methods can be verified.

The first volume, Canonical Structures in Potential Theory, develops the mathematics, solving mixed boundary potential problems for structures with cavities and edges. The second volume, Acoustic and Electromagnetic Diffraction by Canonical Structures, examines the diffraction of acoustic and electromagnetic waves from several classes of open structures with edges or cavities. Together these volumes present an authoritative and unified treatment of potential theory and diffraction-the first complete description quantifying the scattering mechanisms in complex structures.

This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.

This monograph examines the boundary behavior of holomorphic functions in several complex variables. Moving beyond the early ideas of Fatou and others, Koranyi and then Stein in the late 1960s and early 1970s deepened the study of Fatou-type theorems in several complex variables, showing that in a general context, approach regions of a shape dramatically larger than non-tangential will give rise to a Fatou-type theorem. These have become known as the admissible regions of Koranyi and Stein. It turns out, however, that the admissible approach regions are only optimal on strongly pseudoconvex domains. Considerable effort has been made in the last 20 years to adapt Fatou theory, and the approach regions in particular, to the Levi geometry of a given domain in multidimensional complex space. The work of Di Biase in the late 1990s is devoted to the Nagel--Stein phenomenon, describing a more general notion of approach region that supersedes the classical ideas of non-tangential and admissible. Krantz's work Function Theory of Several Complex Variables (2000), still the only introduction to the subject, focuses on methods based on maximal function estimates. To date, the main open problem, which is the special focus of this book, is the issue of determining the {it optimal natural approach regions} for the almost everywhere convergence to the boundary of certain smoothly bounded pseudoconvex domains. This book provides the proper framework for the eventual solution of the main problem. This work gives an updated, comprehensive, and self-contained exposition of many results that have never appeared in book form. Starting with foundational material, i.e., from the unit disc in one complexvariable, the reader is lead to the latest discoveries in higher dimensions. New results in boundary value issues of holomorphic functions are examined, which in turn point to new open problems. The book may be used by analysts for individual study or by graduate students.

The book is devoted to one of the important areas of theoretical and experimental physics-the calculation of the accuracy of measurements of fundamental physical constants. To achieve this goal, numerous methods and criteria have been proposed. However, all of them are focused on identifying a posteriori uncertainty caused by the idealization of the model and its subsequent computerization in comparison with the physical system. This book focuses on formulating an a priori interaction between the level of a detailed description of a material object (the number of registered quantities) and the lowest uncertainty in measuring a physical constant. It contains the materials necessary for the optimal design of models describing a physical phenomenon. It will appeal to scientists and engineers, as well as university students.

From the reviews of Vols. I-III:

"Since their publication in 1986 J-P. Serre's Collected Papers have already become one of the classical references in mathematical research. This is on the one hand due to the completeness of the collection (132 items) and on the other, of course, due to the beautiful and clear expositions of Serre's papers and their influence on mathematics.

As listed in the preface, the three volumes cover almost all articles published in mathematical journals between 1949 and 1984, the summaries of the author's courses at the CollA]ge de France since 1956, some of his SA(c)minaire notes, and some items not previously published. ...]

The author's notes at the end of each volume giving corrections and important recent progress as well as improvements of the main results represent a highlight of this collection. The mathematical community definitely looks forward to further volume(s) of Serre's outstanding work."

Zentralblatt MATH

This volume presents papers dedicated to Professor Shoshichi Kobayashi, commemorating the occasion of his sixtieth birthday on January 4, 1992.The principal theme of this volume is "Geometry and Analysis on Complex Manifolds". It emphasizes the wide mathematical influence that Professor Kobayashi has on areas ranging from differential geometry to complex analysis and algebraic geometry. It covers various materials including holomorphic vector bundles on complex manifolds, Kahler metrics and Einstein-Hermitian metrics, geometric function theory in several complex variables, and symplectic or non-Kahler geometry on complex manifolds. These are areas in which Professor Kobayashi has made strong impact and is continuing to make many deep invaluable contributions.

This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.