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3 produkter
3 produkter
Del 25 - London Mathematical Society Lecture Note Series
Lie Groups and Compact Groups
Häftad, Engelska, 1977
784 kr
Skickas inom 7-10 vardagar
The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups.
536 kr
Skickas inom 10-15 vardagar
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua non of Fourier analysis and synthesis, has led to the routine use of the methods originating with Fourier in a great diversity of areas - astrophysics, computing, economics, electrical engineering, geophysics, information theory, medical engineering, optics, petroleum and mineral exploration, quan tum physics and spectroscopy, to name a few.
1 152 kr
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This book studies the actual financial phenomena underlying the evaluation of financial derivatives, which is today virtually identified with and even replaced by the study of the mathematical aspects of stochastic calculus as a model for such phenomena. It adopts the view that the study of financial phenomena is on the brink of a revolution similar to that of quantum physics in the 1920s. History has shown that virtually all the major revolutions in physics were made through recognizing the presence of an inherent symmetry in underlying phenomena.In this volume, a fundamental symmetry in a foreign exchange market that associates financially equivalent options on opposite sides of the market is introduced. This symmetry holds in a general foreign exchange market environment. In particular, it requires no assumptions to be made on the nature of a probability distribution for exchange rates — not even on the existence of such a distribution. The practical applications of the symmetry are significant and far reaching. They range from the detection of a new type of true arbitrage and a screen for consistency of option pricing models, to the reduction of the cost of software development. The symmetry introduced is not restricted to foreign exchange markets but is also valid for any financial markets.