Sinopsis
Excerpt from The Singularities of the Riemann Function: January 1, 1961
S; the factor of proportionality can be determined solelyfrom knowledge of the tangent plane to S.
At singular points of S, such as cusps, we are able to give complete results only if n 2. For larger values of n, our methods cover many interesting cases, and we conjecture that the following description is correct in all cases. Let be the radii of principal curva ture of S. Assume that vanish at the point under consideration, to orders respectively.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Reseña del editor
Excerpt from The Singularities of the Riemann Function: January 1, 1961
S; the factor of proportionality can be determined solelyfrom knowledge of the tangent plane to S.
At singular points of S, such as cusps, we are able to give complete results only if n 2. For larger values of n, our methods cover many interesting cases, and we conjecture that the following description is correct in all cases. Let be the radii of principal curva ture of S. Assume that vanish at the point under consideration, to orders respectively.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from The Singularities of the Riemann Function: January 1, 1961
We shall deal with the Cauchy problem for linear hyperbolic systems of the first order, with n+1 independent variables. Our central problem is the description of the singularities of the Riemann function. In addition to its own intrinsic interest, this problem provides a key to the mathematical theory of wave propagation, since any solution of the Cauchy problem can be represented in terms of the Riemann function. In a sense, the singularities of the Riemann function determine the structure of the dependence of a solution on its initial data.
The analysis of the singularities of the Riemann function also represents a step towards an extension of the method of Hadamard to general linear hyperbolic equations. This method would determine the Riemann function by substitution of a function of the proper form into the differential equation.
Our analysis also provides an approach to problems involving propagation of waves in media where the characteristics have variable multiplicity, including questions of existence and uniqueness. Such problems are frequently ignored in the mathematical literature, although they have great physical interest.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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The Singularities of the Riemann Function: January 1, 1961 (Classic Reprint)
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Paperback. Condición: New. Print on Demand. This book concerns the Riemann function of the Cauchy problem for linear hyperbolic systems of first-order equations with n independent variables. The study of these equations is significant since any solution to the Cauchy problem can be represented in terms of the Riemann function, giving key knowledge on how solutions in the present depend on their initial data. The author investigates the Riemann function's singularities to determine the structure of this dependence, deriving formulas for different types of equations and singularities. The author also provides geometrical interpretations of their results, relating them to the geometry of the normal surface and ray conoid, and deriving insights that help predict singularities of the Riemann function. The work advances an understanding of the Cauchy problem for linear hyperbolic systems and provides a foundation for developing more effective wave propagation models. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781330152270_0
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The Singularities of the Riemann Function January 1, 1961 Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330152270
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The Singularities of the Riemann Function January 1, 1961 Classic Reprint
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PAP. Condición: New. New Book. Shipped from UK. Established seller since 2000. Nº de ref. del artículo: LW-9781330152270
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