Partial Differential Equations and Solitary Waves Theory


Book Description

"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.




Biological Clocks, Rhythms, and Oscillations


Book Description

An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.







Proceedings of the Third Conference on Reactions between Complex Nuclei


Book Description

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1963.







Passive Location Method Based on Phase Difference Measurement


Book Description

Passive Location Method Based on Phase Difference Measurement presents groundbreaking information about passive location methods used for developing positioning technologies. The author has put forward a series of innovative solutions from the perspective of applied theory in distance finding with the aim of improving our understanding of systems designed to detect moving objects in small spaces. The book starts with a theoretical study of the relationship between phase frequency functions on a two-dimensional plane. This is followed by explanations of detection methods using unambiguous phase parameters. The analysis demonstrates how difference change rates work with parameters for measuring phase difference and wavelength integers. In addition, there is a jump phenomenon between the difference term of phase difference and the difference value of the wavelength integer, that can be used to mathematically compute the distance between these parameters respectively. The results in this work have interesting implications for location measurement with a lack of phase ambiguity. The methods show a framework for converting signal processing models for passive location detection systems for unambiguous phase difference calculations. It also provides an effective solution to the problem of how to eliminate the influence of the measurement error of the wavelength integer difference on the positioning accuracy. Key Features: - Sequentially presents theoretical frameworks to build the reader’s knowledge for better understanding the topics - Presents a unique method for measuring the motion parameters on a moving platform based on unambiguous phase difference measurement parameters. - Summarizes phase difference location methods, including direction finding and ranging - Discusses passive methods of phase difference localization by means of virtual observation - Includes references for further reading This reference is a resource for scholars, engineers and technicians involved in radio positioning research and the improvement of radar, satellite navigation systems, unmanned systems and Internet of Things infrastructure.