Isbn: 9781333297213 - Zero Crossings and the Heat Equation (classic Reprint) (3 results)

PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000.

PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000.

Paperback. Condition: New. 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. print-on-demand item.…