This interdisciplinary thesis involves the design and analysis of coordination algorithms on networks, identification of dynamic networks and estimation on networks with random geometries with implications for networks that support the operation of dynamic systems, e.g., formations of robotic vehicles, distributed estimation via sensor networks. The results have ramifications for fault detection and isolation of large-scale networked systems and optimization models and algorithms for next generation aircraft power systems. The author finds novel applications of the methodology in energy systems, such as residential and industrial smart energy management systems.

Many questions dealing with solvability, stability and solution methods for va- ational inequalities or equilibrium, optimization and complementarity problems lead to the analysis of certain (perturbed) equations. This often requires a - formulation of the initial model being under consideration. Due to the specific of the original problem, the resulting equation is usually either not differ- tiable (even if the data of the original model are smooth), or it does not satisfy the assumptions of the classical implicit function theorem. This phenomenon is the main reason why a considerable analytical inst- ment dealing with generalized equations (i.e., with finding zeros of multivalued mappings) and nonsmooth equations (i.e., the defining functions are not c- tinuously differentiable) has been developed during the last 20 years, and that under very different viewpoints and assumptions. In this theory, the classical hypotheses of convex analysis, in particular, monotonicity and convexity, have been weakened or dropped, and the scope of possible applications seems to be quite large. Briefly, this discipline is often called nonsmooth analysis, sometimes also variational analysis. Our book fits into this discipline, however, our main intention is to develop the analytical theory in close connection with the needs of applications in optimization and related subjects. Main Topics of the Book 1. Extended analysis of Lipschitz functions and their generalized derivatives, including "Newton maps" and regularity of multivalued mappings. 2. Principle of successive approximation under metric regularity and its - plication to implicit functions.

The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

This volume of High Performance Computing in Science and Engineering is fully dedicated to the final report of KONWIHR, the Bavarian Competence Network for Technical and Scientific High Performance Computing. It includes the transactions of the final KONWIHR workshop, that was held at Technische Universitat Munchen, October 14-15, 2004, as well as additional reports of KONWIHR research groups. KONWIHR was established by the Bavarian State Government in order to support the broad application of high performance computing in science and technology throughout the country. KONWIHR is a supporting action to the installation of the German supercomputer Hitachi SR 8000 in the Leibniz Computing Center of the Bavarian Academy of Sciences. The report covers projects from basic research in computer science to develop tools for high performance computing as well as applications from biology, chemistry, electrical engineering, geology, mathematics, physics, computational fluid dynamics, materials science and computer science."

A best-seller in its French edition, the construction of this book is original and its success in the French market demonstrates its appeal. It is based on three principles: 1. An organization of the chapters by families of algorithms : exhaustive search, divide and conquer, etc. At the contrary, there is no chapter only devoted to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. 2. For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. 3. For its most part, the book details 150 problems, spanning on seven families of algorithms. For each problem, a precise and progressive statement is given. More important, a complete solution is detailed, with respect to the design principles that have been presented ; often, some classical errors are pointed at. Roughly speaking, two thirds of the book are devoted to the detailed rational construction of the solutions.

This is a textbook for a course (or self-instruction) in cryptography with emphasis on algebraic methods. The first half of the book is a self-contained informal introduction to areas of algebra, number theory, and computer science that are used in cryptography. Most of the material in the second half - "hidden monomial" systems, combinatorial-algebraic systems, and hyperelliptic systems - has not previously appeared in monograph form. The Appendix by Menezes, Wu, and Zuccherato gives an elementary treatment of hyperelliptic curves. This book is intended for graduate students, advanced undergraduates, and scientists working in various fields of data security.

This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.

The 1980s and 1990s have been a period of exciting new developments in the modelling of decision-making under risk and uncertainty. Extensions of the theory of expected utility and alternative theories of non-expected utility' have been devised to explain many puzzles and paradoxes of individual and collective choice behaviour. This volume presents some of the best recent work on the modelling of risk and uncertainty, with applications to problems in environmental policy, public health, economics and finance. Eighteen papers by distinguished economists, management scientists, and statisticians shed new light on phenomena such as the Allais and St. Petersburg paradoxes, the equity premium puzzle, the demand for insurance, the valuation of public health and safety, and environmental goods. Audience: This work will be of interest to economists, management scientists, risk and policy analysts, and others who study risky decision-making in economic and environmental contexts.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

With collective behaviors playing a fundamental role in many scientific and technical disciplines, the book, after an overview on the background to systemics, introduces the concept of COLLECTIVE BEING as a Multiple System established by processes of emergence and self-organization of the same agents simultaneously or dynamically interacting in different ways. The general principles underlying this approach are grounded on the theoretical role of the observer. This extended view allows to model in a more suitable way complex systems, such as in physics, biology and economics. The Dynamical Usage of Models (DYSAM) is the related modelling methodology. This innovating approach is applied to artificial and natural systems equipped with cognitive systems, such as autonomous robots and social systems. The authors discuss in two different chapters both traditional (i.e. based on dynamical systems and dissipative structures) and non-traditional (i.e. based on theory of phase transitions, Synergetics and connectionistic models) models of emergence. The book also introduces an innovative methodology for detecting the establishment of processes of emergence based on changes of ergodicity.

After a theoretical introduction of the concepts, the authors discuss the application to social systems and cognitive systems. Applications to social systems deal with issues such as representing and distinguishing growth and development, sustainable development, ethics and its crucial role to induce and maintain emergence of social systems, virtual systems, knowledge management and organizational learning. Applications to cognitive systems deal with approaches going beyond computationalism, theories ofconsciousness and embodied cognition.

Two conclusive appendices on (1) Some systemic properties and (2) Some questions and answers about Systemics, help the reader to have a synthesized view of the book.

The conference Operator Theory, Analysis and Mathematical Physics - OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics. The current volume presents articles written by participants, mostly invited speakers, and is devoted to problems at the forefront of modern mathematical physics such as spectral properties of CMV matrices and inverse problems for the non-classical Schroedinger equation. Other contributions deal with equations from mathematical physics and study their properties using methods of spectral analysis. The volume explores several new directions of research and may serve as a source of new ideas and problems for all scientists interested in modern mathematical physics.

This book is the result of my doctoral dissertation research at the Department of Econometrics of the University of Geneva, Switzerland. This research was also partially financed by the Swiss National Science Foundation (grants 12- 31072.91 and 12-40300.94). First and foremost, I wish to express my deepest gratitude to Professor Manfred Gilli, my thesis supervisor, for his constant support and help. I would also like to thank the president of my jury, Professor Fabrizio Carlevaro, as well as the other members of the jury, Professor Andrew Hughes Hallett, Professor Jean-Philippe Vial and Professor Gerhard Wanner. I am grateful to my colleagues and friends of the Departement of Econometrics, especially David Miceli who provided constant help and kind understanding during all the stages of my research. I would also like to thank Pascale Mignon for proofreading my text and im proving my English. Finally, I am greatly indebted to my parents for their kindness and encourage ments without which I could never have achieved my goals. Giorgio Pauletto Department of Econometrics, University of Geneva, Geneva, Switzerland Chapter 1 Introduction The purpose of this book is to present the available methodologies for the solution of large-scale macroeconometric models. This work reviews classical solution methods and introduces more recent techniques, such as parallel com puting and nonstationary iterative algorithms."

This book addresses several mathematical models from the most relevant class of kp-Schroedinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used with upscaling methods to deliver parameters needed in semi-classical models for semiconductor devices, such as quantum well lasers. This book covers in detail all these three aspects using a variety of illustrative examples. Readers will gain detailed insights into the status of the multiband effective mass method for semiconductor nano structures. Both users of the kp method as well as advanced researchers who want to advance the kp method further will find helpful information on how to best work with this method and use it as a tool for characterizing the physical properties of semiconductor nano structures. The book is primarily intended for graduate and Ph.D. students in applied mathematics, mathematical physics and theoretical physics, as well as all those working in quantum mechanical research or the semiconductor / opto-electronic industry who are interested in new mathematical aspects.

This volume will define the direction of eddy-current technology in nondestructive evaluation (NDE) in the twenty-first century. It describes the natural marriage of the computer to eddy-current NDE, and its publication was encouraged by favorable responses from workers in the nuclear-power and aerospace industries. It will be used by advanced students and practitioners in the fields of computational electromagnetics, electromagnetic inverse-scattering theory, nondestructive evaluation, materials evaluation and biomedical imaging, among others, and will be based on our experience in applying the subject of computational electromagnetics to these areas, as manifested by our recent research and publications. Finally, it will be a reference to future monographs on advanced NDE that are being contemplated by our colleagues and others. Its importance lies in the fact that it will be the first book to show that advanced computational methods can be used to solve practical, but difficult, problems in eddy-current NDE. In fact, in many cases these methods are the only things available for solving the problems. The book will cover the topic of computational electromagnetics in eddy-current nondestructive evaluation (NDE) by emphasizing three distinct topics: (a) fundamental mathematical principles of volume-integral equations as a subset of computational electromagnetics, (b) mathematical algorithms applied to signal-processing and inverse scattering problems, and (c) applications of these two topics to problems in which real and model data are used. This will make the book more than an academic exercise; we expect it to be valuable to users of eddy-current NDE technology in industries as varied as nuclear power, aerospace, materials characterization and biomedical imaging. We know of no other book on the market that covers this material in the manner in which we will present it, nor are there any books, to our knowledge, that apply this material to actual test situations that are of importance to the industries cited. It will be the first book to actually define the modern technology of eddy-current NDE, by showing how mathematics and the computer will solve problems more effectively than current analog practice.

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming. SIP problems include finitely many variables and, in contrast to finite optimization problems, infinitely many inequality constraints. Prob lems of this type naturally arise in approximation theory, optimal control, and at numerous engineering applications where the model contains at least one inequality constraint for each value of a parameter and the parameter, repre senting time, space, frequency etc., varies in a given domain. The treatment of such problems requires particular theoretical and numerical techniques. The theory in SIP as well as the number of numerical SIP methods and appli cations have expanded very fast during the last years. Therefore, the main goal of this monograph is to provide a collection of tutorial and survey type articles which represent a substantial part of the contemporary body of knowledge in SIP. We are glad that leading researchers have contributed to this volume and that their articles are covering a wide range of important topics in this subject. It is our hope that both experienced students and scientists will be well advised to consult this volume. We got the idea for this volume when we were organizing the semi-infinite pro gramming workshop which was held in Cottbus, Germany, in September 1996."

The pioneering research of Hirotugu Akaike has an international reputation for profoundly affecting how data and time series are analyzed and modelled and is highly regarded by the statistical and technological communities of Japan and the world. His 1974 paper "A new look at the statistical model identification" (IEEE Trans Automatic Control, AC-19, 716-723) is one of the most frequently cited papers in the area of engineering, technology, and applied sciences (according to a 1981 Citation Classic of the Institute of Scientific Information). It introduced the broad scientific community to model identification using the methods of Akaike's criterion AIC. The AIC method is cited and applied in almost every area of physical and social science. The best way to learn about the seminal ideas of pioneering researchers is to read their original papers. This book reprints 29 papers of Akaike's more than 140 papers. This book of papers by Akaike is a tribute to his outstanding career and a service to provide students and researchers with access to Akaike's innovative and influential ideas and applications. To provide a commentary on the career of Akaike, the motivations of his ideas, and his many remarkable honors and prizes, this book reprints "A Conversation with Hirotugu Akaike" by David F. Findley and Emanuel Parzen, published in 1995 in the journal Statistical Science. This survey of Akaike's career provides each of us with a role model for how to have an impact on society by stimulating applied researchers to implement new statistical methods.

Provides a comprehensive summary on the physical models and current theory of black hole accretion, growth and mergers, in both the supermassive and stellar-mass cases. This title reviews in-depth research on accretion on all scales, from galactic binaries to intermediate mass and supermassive black holes. Possible future directions of accretion are also discussed. The following main themes are covered: a historical perspective; physical models of accretion onto black holes of all masses; black hole fundamental parameters; and accretion, jets and outflows. An overview and outlook on the topic is also presented. This volume summarizes the status of the study of astrophysical black hole research and is aimed at astrophysicists and graduate students working in this field. Originally published in Space Science Reviews, Vol 183/1-4, 2014.

VII Preface In many fields of mathematics, geometry has established itself as a fruitful method and common language for describing basic phenomena and problems as well as suggesting ways of solutions. Especially in pure mathematics this is ob vious and well-known (examples are the much discussed interplay between lin ear algebra and analytical geometry and several problems in multidimensional analysis). On the other hand, many specialists from applied mathematics seem to prefer more formal analytical and numerical methods and representations. Nevertheless, very often the internal development of disciplines from applied mathematics led to geometric models, and occasionally breakthroughs were b ed on geometric insights. An excellent example is the Klee-Minty cube, solving a problem of linear programming by transforming it into a geomet ric problem. Also the development of convex programming in recent decades demonstrated the power of methods that evolved within the field of convex geometry. The present book focuses on three applied disciplines: control theory, location science and computational geometry. It is our aim to demonstrate how methods and topics from convex geometry in a wider sense (separation theory of convex cones, Minkowski geometry, convex partitionings, etc.) can help to solve various problems from these disciplines."

This volume presents five pedagogical articles spanning frontier developments in contemporary nuclear physics ranging from the physics of a single nucleon to nucleosynthesis in the Big Bang. Although the objectives of Advances in Nuclear Physics have been and will continue to be quite distinct from those of conventional conference proceedings, the articles in this volume are carefully edited and expanded manuscripts based on an outstanding series of lectures delivered at the VI J. A. Swieca Summer School in Brazil. Starting at the smallest scale, the first article by Dan Olof Riska addresses realistic chiral symmetric models of the nucleon. Since the analytic tools are not yet developed to solve nonperturbative QCD directly, significant effort has been devoted in recent years to the development of models which incorporate and are constrained by the approximate chiral symmetry manifested in QCD. This article provides a clear introduction to chiral symmetry and the Skyrme model, and discusses the Skyrme model's relation to the chiral bag model, its extensions, and its application to nucleons and hyperons.

Mark Alber, Bei Hu and Joachim Rosenthal . . . . . . . . . . . . . . . . . . . . . . vii Part I Some Remarks on Applied Mathematics Roger Brockett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Mathematics is a Profession Christopher 1. Byrnes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Comments on Applied Mathematics Avner Friedman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Towards an Applied Mathematics for Computer Science Jeremy Gunawardena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Infomercial for Applied Mathematics Darryl Holm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 On Research in Mathematical Economics M. Ali Khan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Applied Mathematics in the Computer and Communications Industry Brian Marcus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 'frends in Applied Mathematics Jerrold E. Marsden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Applied Mathematics as an Interdisciplinary Subject Clyde F. Martin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 vi Contents Panel Discussion on Future Directions in Applied Mathe matics Laurence R. Taylor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Part II Feedback Stabilization of Relative Equilibria for Mechanical Systems with Symmetry A. M. Bloch, J. E. Marsden and G. Sanchez . . . . . . . . . . . . . . . . . . . . . . . 43 Oscillatory Descent for Function Minimization R. Brockett . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 On the Well-Posedness of the Rational Covariance Extension Problem C. l. Byrnes, H. J. Landau and A. Lindquist . . . . . . . . . . . . . . . . . . . . . . 83 Singular Limits in Fluid Mechanics P. Constantin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Singularities and Defects in Patterns Far from Threshold N. M. Ercolani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Mathematical Modeling and Simulation for Applications of Fluid Flow in Porous Media R. E. Ewing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 On Loeb Measure Spaces and their Significance for N on Cooperative Game Theory M. A. Khan and Y. Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms J. E. Marsden and J. M. Wendlandt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Preface The applied sciences are faced with increasingly complex problems which call for sophisticated mathematical models."

Imperfections and Behavior in Economic Organizations analyzes the organization of economic decision making in a contemporary setting. The contributors focus on two important aspects of this analysis. First, they address the issue of imperfect or incomplete information and communication in economic organizations and consider imperfections arising from the interaction of the market organization with its environment. Second, the issue of cooperation in a competitive environment is thoroughly analyzed and alternative social trade organizations are designed to dissipate the allocation problems that arise in these situations.

About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods." 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A."

The Theory of the Top was originally presented by Felix Klein as an 1895 lecture at Goettingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. The Theory of the Top: Volume IV. Technical Applications of the Theory of the Top is the fourth and final installment in a series of self-contained English translations that provide insights into kinetic theory and kinematics.

Goal Programming Applications in Accounting 74 Goal Programming Applications in Agriculture 76 Goal Programming Applications in Economics 78 Goal Programming Applications in Engineering 79 Goal Programming Applications in Finance 80 Goal Programming Applications in Government 83 Goal Programming Applications in an International Context 88 Goal Programming Applications in Management 90 Goal Programming Applications in Marketing 97 Summary 98 CHAPTER 5. FUTURE TRENDS IN GOAL PROORAMMING 101 GP is Positioned for Growth 101 Shifting the Life Cycle of GP Research to Growth 103 Summary 107 Reference 108 APPENDIX A TEXTBOOKS, READINGS BOOKS AND MONOORAPHS ON GOAL PROORAMMING 109 APPENDIX B. JOURNAL RESEARCH PUBLICATIONS ON GOAL PROORAMMING 113 INDEX 213 viii LIST OF FIGURES Figure 1-1. Summary Relationship of GP with MS/OR and MCDM Figure 1-2. Frequency Distribution for GP Journal Publications Figure 1-3. Life Cycle ofGP Research Figure 2-1. Set of GP Efficient Solutions Figure 5-1. Life Cycle of GP Research ix LIST OF TABLES Table 1-1. MS/OR Topics and Their Related GP Topics Table 1-2. MCDM Subareas and Their Related GP Topics Table 1-3. Frequency Listing ofGP Journal Publications and Book Titles Table 2-1. Solutions for a Dominated GP Problem Table 2-2. Conversion ofLP Constraints to Goal Constraints Table 2-3. GP Citations on Dominance, Inferiority and Inefficiency Table 2-4. GP Citations on Relative Weighting, Prioritization and Incommensurability Table 2-5. MS/OR Topics and Their Related GP Topics Table 3-1. Citations on WeightedlPreemptive GP Methodology Table 3-2. Citations on Pure/Mixed Integer GP Methodology Table 3-3.

Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the 'fractional' perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag-Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB (R) codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.