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An Introduction to Sato's Hyperfunctions
This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.
Algebraic Geometry
Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings, and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting thenecessary background along the way. Originally published in Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes andalgebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces.
An Introduction to Algebraic Geometry
This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.
Best Approximation by Linear Superpositions (approximate Nomography)
This book deals with problems of approximation of continuous or bounded functions of several variables by linear superposition of functions that are from the same class and have fewer variables. The main topic is the space of linear superpositions D considered as a sub-space of the space of continous functions C(X) on a compact space X. Such properties as density of D in C(X), its closedness, proximality, etc. are studied in great detail. The approach to these and other problems based on duality and the Hahn-Banach theorem is emphasized. Also, considerable attention is given to the discussion of the Diliberto-Straus algorithm for finding the best approximation of a given function by linear superpositions.
Uncountably Categorical Theories
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
Theory of Entire and Meromorphic Functions
This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.
Embeddings and Immersions
This book covers fundamental techniques in the theory of -imbeddings and -immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on -imbeddings and -manifolds. The Smale-Hirsch theorem is presented as a generalization of the classification of -imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.Nothing provided
Asymptotic Methods in the Theory of Gaussian Processes and Fields
This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.
