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Explains how business-to-business marketers can create and use online content and communication strategies to keep prospects engaged and increase sales, and how to encourage their sales force to adopt the same techniques to create a unified ...
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.
Interpolation formulas Hitherto we have studied primarily interpolation and
approximation by polynomials in the complex variable 2. We shall now
commence the study of interpolation and approximation by more general rational
functions, ...
This work studies abelian branched coverings of smooth complex projective surfaces from the topological viewpoint. Geometric information about the coverings (such as the first Betti numbers of a smooth model or intersections of embedded curves) is related to topological and combinatorial information about the base space and branch locus. Special attention is given to examples in which the base space is the complex projective plane and the branch locus is a configuration of lines.
Since, in particular, Y is smooth at p, q must also be a smooth point of X. We will
now assume p is a point in B. Let U be a small ball around p isomorphic to a complex disk, so that, for any two distinct points q1 and q2 in p"(p), the connected
...
The mathematics of Bose-Fock spaces is built on the notion of a commutative algebra and this algebraic structure makes the theory appealing both to mathematicians with no background in physics and to theorectical and mathematical physicists who will at once recognize that the familiar set-up does not obscure the direct relevance to theoretical physics. The well-known complex and real wave representations appear here as natural consequences of the basic mathematical structure - a mathematician familiar with category theory will regard these representations as functors. Operators generated by creations and annihilations in a given Bose algebra are shown to give rise to a new Bose algebra of operators yielding the Weyl calculus of pseudo-differential operators. The book will be useful to mathematicians interested in analysis in infinitely many dimensions or in the mathematics of quantum fields and to theoretical physicists who can profit from the use of an effective and rigrous Bose formalism.
more or less obvious way: 1) the algebra of complex polynomials with scalar
product as in [1], 2) the algebra generated by Hermite polynomials (here the
operation of multiplication is rather obscure), 3) One can also attach a Bose
algebra in a ...
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Dr. Gloria Schrager has written a revealing memoir about her struggle to become a doctor at a time when women physicians were an anomaly. The era she has lived through has been incredibly eventful: she relates how the Great Depression, World War II, the McCarthy Unamerican Activities Committee, the overt bias and harassment that women in the professions had to face, all impacted on her life. But the memoir has a lighter side, recounting some of the adventures and mishaps of medical school, internship, maintaining a successful marriage and raising a family while engaged in the full-time practice of medicine. Both of her sons as well as a niece and grandniece have become physicians, and the book describes some the differences, both good and bad, between the practice of medicine today and how it was practiced over fifty years ago.
Understanding the mechanism of a socio-economic system requires more than an understanding of the individuals that comprise the system. It also requires understanding how individuals interact with each other, and how the agg- gated outcome can be more than the sum of individual behaviors. This book contains the papers fostering the formation of an active multi-disciplinary community on socio-economic systems with the exciting new ?elds of age- based modeling and econophysics. We especially intend to increase the awareness of researchers in many ?elds with sharing the common view many economic and social activities as collectives of a large-scale heterogeneous and interacting agents. Economists seek to understand not only how individuals behave but also how the interaction of many individuals leads to complex outcomes. Age- based modeling is a method for studying socio-economic systems exhibiting the following two properties: (1) the system is composed of interacting agents, and (2) the system exhibits emergent properties, that is, properties arising from the interactions of the agents that cannot be deduced simply by agg- gating the properties of the system’s components. When the interaction of the agents is contingent on past experience, and especially when the agents continually adapt to that experience, mathematical analysis is typically very limited in its ability to derive the outcome.
As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
... + l(s > 1) segments of equal length with a common endpoint at the origin and
forming equal angles of opening 27r/(2s + 1) in the complex plane. In this chapter
the main notations of Section 6.2 of Chapter 6 are frequently used without any ...
