Understanding the Schrödinger Equation: Some [Non]Linear Perspectives

"The book contains various approaches to the Schrödinger equation (SE) as a fundamental equation of quantum mechanics. In Chapter 1, a new pedagogical paradigm is proposed which allows one to understand quantum mechanics as an extension of probability theory; its purpose is providing alternative methods to understand the Schrödinger equation. Chapter 2 is devoted to the derivation of SE from the classical Hamiltonian by some procedure of second quantization. In Chapters 3–5, the authors consider the nonlinear SE with many applications: from nonlinear waves in deep water to formation of a cosmogonical body, surface gravity waves, superconductivity and nonlinear optics. The goal of Chapter 6 is to establish the connection of Schrödinger, Madelung and Gross-Pitaevskii equations. Chapter 7, “Paradigm of infinite dimensional phase space,” describes the deep connection between SE and the infinite chain of equations for distribution functions of high-order kinematical values (Vlasov chain). The authors formulate the principles which allow one to combine and treat in unified form the physics of classical, statistical and quantum mechanical phenomena. And in final Chapter 8 it is shown that SE can be mathematically derived from Hamilton’s equation if one uses the metaplectic representation of canonical transformations. All that makes the book interesting for a wide community of physicists." - E.E. Perepelkin, B.I. Sadovnikov (Lomonosov Moscow State University, Department of Quantum Statistics and Field Theory, Moscow, Russia), and N.G. Inozemtseva (Moscow Technical University of Communications and Informatics, Department of Physics, Moscow, Russia)

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An Introduction to Capstone in Applied Analysis: A Fundamental Guide for Students and Instructors

“This is an excellent reference for anyone interested in applied analysis, especially for students and teachers working on Science, Technology, Engineering and Mathematics (STEM) capstone projects. It is an easy to read textbook that will help build mathematical foundations needed for capstone projects with plethora of examples in wide range of applications.” - Sudhir Shrestha, Ph.D., Department of Engineering Science, Sonoma State University, Rohnert Park, California

“A surge in undergraduate and capstone research has been noticed in the past several years. This is due to the great explosion in the advancement of technology. The traditional class courses taken are not enough anymore. This book aims to facilitate students and instructors working in capstone and undergraduate research projects. The book is written well, carefully designed for undergraduate students in mathematics and applied sciences. We see that we are looking at a very analytic and easy to read map in the exciting area of capstone projects, written by an experienced mathematician. It is certainly a must-read book. We strongly and enthusiastically recommend it for usage in classroom or as a study guide for capstone projects." - Ioannis K. Argyros, Ph.D., Professor, Department of Mathematical Sciences, Cameron University, Lawton, Oklahoma

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Mathematical Modeling of Real World Problems: Interdisciplinary Studies in Applied Mathematics

“The book is a compilation of a number of scientific papers providing a view on how mathematics can be applied to model some real world problems. In depth analyses and discussions are given by researchers applying wavelet to environmental problems, to water management and in medical sciences. The book can be recommended as a reference ‘handbook’ for those working in applications of data processes and in engineering applications.” - Honorary Professor Donald Gabriels, Ghent University, Belgium with the UNESCO Chair on Eremology

“The proposed book looks very interesting and covers a variety of subjects like environment, water management and medicine. Such interdisciplinary topics could prove to be useful to many researchers working in these fields.” - Professor Dr. Pammy Manchanda, Guru Nanak Dev University, India

“This book serves as an up-front review of mathematical modeling of real world problems and interdisciplinary studies in applied mathematics that not only scientists, engineers, planners, social scientists but also everyone can read and understand the real world problems. The content ranges from environmental problems to medicine and their interaction to mathematical implementation. Thank all contributors who ensure such extended and comprehensive study.” - Professor Dr. Hasan Saygin, Istanbul Aydin University, Turkey

“This book covers a broad spectrum of applying mathematical tools to solve problems in the real world, mainly in the environmental and medical sciences. I am very interested in chapters about the application of wavelet to the time series analysis and the use of numerical models to the meteorological and environmental studies. I believe that this book will be a valuable reference for those who work on or are interested in data processing and data mining researches.” - Professor Dr. Lin Wang, Chinese Academy of Sciences, China

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An Essential Guide to Fuzzy Systems

“The book is original and interesting. The authors prove to be mastering the subject of fuzzy information processing and intelligent algorithms. Apart from the fuzzy sets theory it is also related to the following research areas: computational thinking systems, intelligent computing, recent trends of machine learning and Artificial Intelligence techniques.” READ MORE... - Professor Abdel-Badeeh M. Salem, Professor of Computer Science, Founder & Head of Artificial Intelligence and Knowledge Engineering Research Labs, Faculty of Computer and Information Sciences, Ain Shams University, Abbasia, Cairo, Egypt

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Hyperbolic Equations and General Relativity

"This is an excellent book that can be used to introduce the reader to the theory of hyperbolic equations and to the mathematical theory of gravitational waves and Einstein equations. Several basic concepts such as wavelike propagation, fundamental solution, Riemann kernel and its existence, world function and its role in the fundamental solution, characteristic conoid, are well presented. The reader is then offered the opportunity to learn in detail how Choquet-Bruhat proved existence and uniqueness of the solution of vacuum Einstein equations with non-analytic Cauchy data. Last, an introduction to some important aspects of high-speed black hole collisions, a masterpiece work of D'Eath and Payne, is presented. The appendices on Sobolev spaces and Kasner spacetime are also very useful, as well as the suggested literature at the end. The author should be congratulated for having written a book of high pedagogical value for future generations of research workers in general relativity." - Giampiero Esposito, INFN Sezione di Napoli, Naples, Italy

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Understanding Banach Spaces

"Banach spaces as well as their specializations such as Hilbert or Euclidean spaces to mention a few are of great interest in Pure as well as Applied Mathematics. In particular Dr. González is connecting Banach spaces to applications using iterative methods. Researchers and practitioners consider Banach spaces general enough for studying operator equations, since problems from diverse disciplines can be reduced to locating a zero of a Banach space valued operator. These zeros are needed in closed form but this is achieved in rare situations. That is why he has presented a plethora of alternative iterate methods generating a sequence approximating a zero under certain initial conditions about a zero (local convergence) or about in an initial point (semilocal convergence). These methods converge with linear, quadratic or higher order of convergence and under weak conditions. Researchers and practitioners will find this book very useful as a source book, utilize its methods and also use it as a classroom text for a senior undergraduate or graduate course. It is certainly an excellent must read book." - Ioannis K. Argyros, Cameron University, Department of Mathematics, Lawton, Oklahoma, USA

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New Trends in Fractional Programming

"The author in his six chapters of this book presents a very well thought of study of, in particular smooth and unified generalized programming problems. See for example Problem (P). Numerous study cases are presented involving convexity and non-convexity, specializations of which reduce to earlier results by the author or others. The material is very elegantly presented. It is highly recommended to researchers and practitioners who will find it very readable and useful for their research. Parts of this book can also be used in seminars for graduate students as well as senior undergraduate students with interests in this area of research. The bibliography is very informed and updated which makes the book also a great reference source." - Professor Dr. Ioannis K. Argyros, Cameron University, Department of, Mathematical Sciences, Lawton, OK, USA

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Variational Calculus on Time Scales

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Dynamic Shapley Value and Dynamic Nash Bargaining

"The book Dynamic Shapley Value and Dynamic Nash Bargaining of Professor Yeung and Professor Petrosyan provides a new evidence of their indisputable scientific authority in the field of Dynamic Games theory and applications." READ MORE... - Professor Vladimir Turetsky, Ort Braude College of Engineering, Karmiel, Israel.

"This book makes a significant contribution to the game theory applications and methodologies as it provides in depth theoretical and mathematical expansions of the seminal work of Shapley value and Nash bargaining to a dynamic framework. Though its analyses involve an advanced level of mathematics, the book is an excellent reference text for academics and economists interested in real-life cooperative studies like trade pact, environmental collaborations and joint technology development. The book also provides the fundamentals for dynamic cooperative analysis, and itself can be regarded as a front-running textbook on the dynamic cooperative game theory applications and methodologies, especially with the solution concept and technique of cooperative subgame consistency (that were originated by the authors). Also, the Nash-Petrosyan-Yeung dynamic bargaining solution and the Petrosyan-Yeung dynamic Shapley value imputation are sophisticated game theory solutions that serious economists in need to know in their research on real-life economic cooperation problems." - Professor Sardar M. N. Islam (Naz) Ph. D., CPA, LL.B., M.A., Professor, VU Research; Professor of Business, Economics and Finance (2007 to 2017); Victoria University, Melbourne, Australia

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Sequencing and Scheduling with Inaccurate Data

"Often the problem data of a scheduling instance such as the processing times, the setup times, the release dates or the due dates are not exactly known before a particular solution algorithm is applied. This observation may substantially restrict practical aspects of scheduling theory. Within the last 40 years, several approaches have been developed for scheduling problems with inaccurate data depending on whether the data are given as random numbers, fuzzy numbers or whether they are uncertain (which means that they can take values from a given interval). This edited book considers the four major approaches for dealing with such problems: a stochastic approach, a fuzzy approach, a robust approach and a stability approach." READ MORE... - Dr. Erwin Pesch, Faculty of Economics and Business Administration, University in Siegen

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