Book Reviews

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

This book was reviewed by the online bibliographic database created by the American Mathematical Society. To read the review, click here...

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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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High Order Boundary Value Problems: Existence, Localization and Multiplicity Results

"This very interesting book is devoted to the study of higher order boundary value problems. The main tool utilized throughout the volume is the method of upper and lower solutions. Of particular interest is the fact that in many cases the authors give an explicit construction of the upper and lower solution. The authors illustrate how this location tool can be utilized to gain qualitative information regarding the solutions: existence, multiplicity, monotonicity. Another nice feature of the book is that the methodology is applied also to real world phenomena: the London Millenium bridge and the periodic oscillations of the axis of a satellite. Overall the book is fairly easy to read and would be helpful for graduate students and young researchers willing to learn more on this method." - Gennaro Infante, Ph.D., Associate Professor, Department of Mathematics and Computer Science, University of Calabria, Italy

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Recent Advances in Fixed Point Theory and Applications

“This book is a nice collection of research papers on Fixed Point Theory and Applications. Researchers in this field will find this volume invaluable because of the impact it has on practical applications. This book has been very beneficial for me and I highly recommend it for anyone interested in learning more about the subject.” - Ravi P. Agarwal, Professor and Chair of the Department of Mathematics, Texas A&M University-Kingsville, Texas

"The book Recent Advances in Fixed Point Theory and Applications proposes several actual and important topics in nonlinear analysis. Fixed point problems, common fixed point problems, coincidence point problems, coupled coincidence problems are considered in various contexts and for different classes of single-valued and multi-valued operators. A consistent part is dedicated to the applications of the theoretical results. Different types of operator equations and applications to the mathematics of fractals are discussed. This book is an inspired choice of both the editors and the publishing house. The book will be useful to students and researchers in nonlinear analysis and related fields." - Adrian Petruşel, Professor, Faculty of Mathematics and Computer Science, Babeș-Bolyai University Cluj-Napoca , Romania

“This book in a comprehensive way presents interesting contributions by well-established as well as young authors to different aspects of fixed point theory and its applications. Self-contained and unified in presentation, the book touches upon a wide range of areas that include solutions of functional integral equations and fractals apart from the results which deal with the existence of coincidence and common fixed points of various classes of mappings in different settings. The book will serve as a reference book to researchers in fixed point theory and will be a valuable addition to any library.” - S. N. Mishra, Professor Emeritus, Department of Mathematics, Walter Sisulu University, South Africa

"The contributions in this book have significant, interesting and novel applications of the fixed point theory in various branches of mathematics, physics and engineering sciences. The emphasis is given to interdisciplinary research. All the articles in this volume are treated in a unified and self-contained manner, which can be viewed as innovative style. Presentation of the techniques, theory and applications make this book an invaluable references for researchers and other professional interested in pure and applied sciences. Some papers published in this volume will be useful for graduate students and researchers, who are interested in latest information. Applications of the fixed points theory in fractal geometry and other branches are novel one and will have important impact in the developments of fixed point theory. These developments may be regarded a stranding point for future research." - Muhammad Aslam Noor, Eminent Professor, Department of Mathematics, Islamabad Campus, COMSATS Institute of Information Technology, Islamabad, Pakistan

"Fixed Point Theory is the cornerstone of Topology, Functional Nonlinear Analysis and Applied Sciences. The crucial role of fixed point theory in quantitative sciences make it attractive in researchers. As a consequence of its charm, this theory has been improved so fast in the last decades and several nice results have been announced. Among them, the recent book of Umesh Chandra Gairola and Rajendra Pant, Recent Advances in Fixed Point Theory and Applications, has a special place due to expressing of the connections between the theory and practice with concrete examples of applications." - Erdal Karapinar, Professor of Mathematics, ATILIM University, Ankara, Turkey

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Advances in Linear Algebra Research

"This book presents some recent theoretical and computational results on Linear Algebra and Applications. The investigations developed in each one of its ten chapters have been written by one or more experts. They analyze subjects as quadratic forms, homogeneous matrix polynomials, linear control systems, Hermitian matrix-valued functions, triangular matrices, linear matrix equations, simultaneous triangularization over principal ideal domains and matrix differential equations, among others. Matrix Analysis Theory and Generalized Inverses are two extreme usefulness tools used to solve several of the proposed problems. In addition, settings such as the complex field or an arbitrary field, a ring or a quaternion algebra are the structures to work with. This interesting book is written in a very readable style and it is a very good contribution to the Linear Algebra Community and other interested readers." - Nestor Thome, Professor, Department of Applied Mathematics of Polytechnical University of Valencia, Spain

"This is a worth-reading book about the recent developments in Linear Algebra and it includes contributions of fourteen authors from all over the world. The themes analyzed by the researchers in the ten chapters include quadratic optimization, matrix pencils, generalized inverses, matrix equations, maximal and minimal ranks and inertias, triangular matrices (tables) and their parafunctions, iterative methods, eigenvalues and eigenvectors, quasideterminants, regular rings and quaternions, among others. These developments have strong connections with other branches of mathematics like statistics, optimization, discrete mathematics and differential equations and they are related to important topics like fractals, graphs, power series, Markovian transitions and ODEs stability. Outside mathematics, potential applications to financial problems, electrical networks, filter design, chemical kinetics mechanisms and control theory, remark the importance of the topics considered. Finally, the inclusion of several open problems, numerical examples that clarify the theory and even a touch of humor in one of the footnotes, complete this interesting, enjoyable and easy readable book." - Victor Martinez-Luaces, Profesor, Universidad de la República, Uruguay

"This book is a very interesting overview of recent topics of Linear Algebra and matrix Analysis. It includes topics such as Quadratic optimization, generalized inverses, Matrix Polynomials, Matrix functions, Iterative methods for solving matrix equations, simultaneous triangularization over a principal ideal domain, matrix differential equations and other very important topics. The book is quite easy to read and is written for postgraduate and/or PhD students, and researchers in the field of Linear Algebra. It includes theoretical investigations and many clarifying examples to support them, as well as numerical experiments presented. It can be used as a strong reference for scientific publications. Open problems on these topics are also presented and discussed." - Dimitrios Pappas, Athens University of Economics and Business, Greece

"The book is devoted to advanced topics in Linear Algebra and its Application. It covers a broad range of topics. Some of them, for instance, paradeterminants and parapermanents, are not covered in the standard English books on the subject. Among the nice features of the book is the use of various tools of general algebra: fields, rings, quaternions, ... The book is interesting and should be useful for experts and Ph.D. students in such areas of mathematics as PDE, control systems, graph theory, combinatorics, as well as in theoretical physics. It can also be of interest to engineers and researches working on the border between mathematics and chemistry, biology, or medicine." - Professor Rostislav Grigorchuk, Mathematics Department of Texas A&M University

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Spectral Theory for Bounded Functions and Applications to Evolution Equations

“This monograph is devoted to the theory of spectra of bounded functions in abstractspaces. Spectral theory is very important as it gives important qualitative properties ofsolutions to evolution equations. It is particularly useful in the study of the asymptoticbehavior of mild solutions of evolution equations. The monograph is divided into fivechapters. Chapter 1 is about some basic defnitions and notations. Chapter 2 is devotedto the theory of almost periodic functions. These functions have important applicationsin celestial mechanics, control theory and other fields. In chapter 3, the author discussesthe concepts of almost automorphic functions and sequences, which are generalizationsof almost periodic functions and sequences. After these chapters, the author moves onto defining the spectrum of bounded functions, in chapter 4. The concepts of Carleman,Beurling, uniform and circular spectra are defined. The last chapter is devoted to thestudy of difference and first- and second-order differential equations.Overall, this monograph is useful for researchers working in the field of spectraltheory of bounded functions and the qualitative theory of differential equations inabstract spaces. The monograph is written for graduate students, and to read it oneneeds to first go through the basics of abstract spaces and functional analysis.” - Dr. Syed Abbas, Professor, Indian Institute of Technology Mandi, India

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