Nagoya Mathematical Journal
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Published: 2009
Total Pages: 756
ISBN-13:
DOWNLOAD EBOOKIssue for Mar. 1970 dedicated to Professor Katuzi Ono on his 60th birthday with portrait, sketch of his life, and list of mathematical papers.
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The Lefschetz Properties
Author: Tadahito Harima
Publisher: Springer
Published: 2013-08-23
Total Pages: 268
ISBN-13: 3642382061
DOWNLOAD EBOOKThis is a monograph which collects basic techniques, major results and interesting applications of Lefschetz properties of Artinian algebras. The origin of the Lefschetz properties of Artinian algebras is the Hard Lefschetz Theorem, which is a major result in algebraic geometry. However, for the last two decades, numerous applications of the Lefschetz properties to other areas of mathematics have been found, as a result of which the theory of the Lefschetz properties is now of great interest in its own right. It also has ties to other areas, including combinatorics, algebraic geometry, algebraic topology, commutative algebra and representation theory. The connections between the Lefschetz property and other areas of mathematics are not only diverse, but sometimes quite surprising, e.g. its ties to the Schur-Weyl duality. This is the first book solely devoted to the Lefschetz properties and is the first attempt to treat those properties systematically.
On Stochastic Differential Equations
Author: Kiyosi Itô
Publisher: American Mathematical Soc.
Published: 1951
Total Pages: 56
ISBN-13: 0821812041
DOWNLOAD EBOOKIntegral Representations
Author: I. Reiner
Publisher: Springer
Published: 2006-11-15
Total Pages: 284
ISBN-13: 3540350071
DOWNLOAD EBOOKEquimultiplicity and Blowing Up
Author: Manfred Herrmann
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 646
ISBN-13: 3642613497
DOWNLOAD EBOOKContent and Subject Matter: This research monograph deals with two main subjects, namely the notion of equimultiplicity and the algebraic study of various graded rings in relation to blowing ups. Both subjects are clearly motivated by their use in resolving singularities of algebraic varieties, for which one of the main tools consists in blowing up the variety along an equimultiple subvariety. For equimultiplicity a unified and self-contained treatment of earlier results of two of the authors is given, establishing a notion of equimultiplicity for situations other than the classical ones. For blowing up, new results are presented on the connection with generalized Cohen-Macaulay rings. To keep this part self-contained too, a section on local cohomology and local duality for graded rings and modules is included with detailed proofs. Finally, in an appendix, the notion of equimultiplicity for complex analytic spaces is given a geometric interpretation and its equivalence to the algebraic notion is explained. The book is primarily addressed to specialists in the subject but the self-contained and unified presentation of numerous earlier results make it accessible to graduate students with basic knowledge in commutative algebra.
Singularities of the Minimal Model Program
Author: János Kollár
Publisher: Cambridge University Press
Published: 2013-02-21
Total Pages: 381
ISBN-13: 1107035341
DOWNLOAD EBOOKAn authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.
Rational and Nearly Rational Varieties
Author: János Kollár
Publisher: Cambridge University Press
Published: 2004-04-22
Total Pages: 246
ISBN-13: 9780521832076
DOWNLOAD EBOOKThe most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.
Sources in the Development of Mathematics
Author: Ranjan Roy
Publisher: Cambridge University Press
Published: 2011-06-13
Total Pages: 1139
ISBN-13: 1139497758
DOWNLOAD EBOOKThe discovery of infinite products by Wallis and infinite series by Newton marked the beginning of the modern mathematical era. It allowed Newton to solve the problem of finding areas under curves defined by algebraic equations, an achievement beyond the scope of the earlier methods of Torricelli, Fermat and Pascal. While Newton and his contemporaries, including Leibniz and the Bernoullis, concentrated on mathematical analysis and physics, Euler's prodigious accomplishments demonstrated that series and products could also address problems in algebra, combinatorics and number theory. In this book, Ranjan Roy describes many facets of the discovery and use of infinite series and products as worked out by their originators, including mathematicians from Asia, Europe and America. The text provides context and motivation for these discoveries, with many detailed proofs, offering a valuable perspective on modern mathematics. Mathematicians, mathematics students, physicists and engineers will all read this book with benefit and enjoyment.
Boolean Valued Analysis
Author: A.G. Kusraev
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 345
ISBN-13: 9401144435
DOWNLOAD EBOOKBoolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
Structure of Algebras
Author: Abraham Adrian Albert
Publisher: American Mathematical Soc.
Published: 1939-12-31
Total Pages: 224
ISBN-13: 0821810243
DOWNLOAD EBOOKThe first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI consists of the study of the abelian group of cyclic systems which is applied in Chapter VII to yield the theory of the structure of direct products of cyclic algebras and the consequent properties of norms in cyclic fields. This chapter is closed with the theory of $p$-algebras. In Chapter VIII an exposition is given of the theory of the representations of algebras. The treatment is somewhat novel in that while the recent expositions have used representation theorems to obtain a number of results on algebras, here the theorems on algebras are themselves used in the derivation of results on representations. The presentation has its inspiration in the author's work on the theory of Riemann matrices and is concluded by the introduction to the generalization (by H. Weyl and the author) of that theory. The theory of involutorial simple algebras is derived in Chapter X both for algebras over general fields and over the rational field. The results are also applied in the determination of the structure of the multiplication algebras of all generalized Riemann matrices, a result which is seen in Chapter XI to imply a complete solution of the principal problem on Riemann matrices.
