Zero Crossings and the Heat Equation (Classic Reprint)
Language: English
Published by Forgotten Books, 2024
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 13.41
Quantity: Over 20 available
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Print on Demand. This book explores the mathematical structure of zero crossings in a solution to the heat equation, providing a theoretical basis for the analysis of signal and image data representations. It draws parallels between the investigation of zero crossings and human neural processing of visual data, suggesting the potential of this mathematical framework in artificial intelligence and representation theory. The author examines the unique properties of zero crossings, their evolution over time, and their significance in determining the initial data of a solution. Through a detailed analysis of parabolic initial value problems, the book establishes that zero crossings are never created as time increases and that they correspond to surfaces separating positive and negative regions of the solution. The author demonstrates that the knowledge of zero crossings together with gradient data at those crossings uniquely determines the initial data, providing an algorithm for reconstructing it via the backwards heat equation. This book offers essential insights into the behavior and utility of zero crossings, expanding our understanding of their role in data representation and analysis. 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.…
Seller Inventory # 9781333297213_0
- Title
- Zero Crossings and the Heat Equation (Classic Reprint)
- Author
- Robert A. Hummel, Basilis C. Gidas
- Publisher
- Forgotten Books
- Publication year
- 2024
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1333297211
- ISBN 13
- 9781333297213
- Seller catalogs
- Calculus
Thus a representation of the v(x,t) data provides an implicit representation of the f(x) and u(x,t) data. Since v(x,t) is a solution to the heat equation, we are henceforth concerned with representations of the data in a solution to the heat equation such that some form of the initial data can be reconstructed. In what follows, u(x,t) will stand for any generic solution to the heat equation, with f(x) as initial data, although in terms of the above notation, v(x,t) and g(x) are likely instances of the representation problem.
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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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
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.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
The digital edition of all books may be viewed before purchase if you request a sample.
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