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The Generalized Multipole Technique for Light Scattering: Recent Developments (Springer Series on Atomic, Optical, and Plasma Physics #99)
by Thomas Wriedt Yuri EreminThis book presents the Generalized Multipole Technique as a fast and powerful theoretical and computation tool to simulate light scattering by nonspherical particles. It also demonstrates the considerable potential of the method. In recent years, the concept has been applied in new fields, such as simulation of electron energy loss spectroscopy and has been used to extend other methods, like the null-field method, making it more widely applicable. The authors discuss particular implementations of the GMT methods, such as the Discrete Sources Method (DSM), Multiple Multipole Program (MMP), the Method of Auxiliary Sources (MAS), the Filamentary Current Method (FCM), the Method of Fictitious Sources (MFS) and the Null-Field Method with Discrete Sources (NFM-DS). The Generalized Multipole Technique is a surface-based method to find the solution of a boundary-value problem for a given differential equation by expanding the fields in terms of fundamental or other singular solutions of this equation. The amplitudes of these fundamental solutions are determined from the boundary condition at the particle surface. Electromagnetic and light scattering by particles or systems of particles has been the subject of intense research in various scientific and engineering fields, including astronomy, optics, meteorology, remote sensing, optical particle sizing and electromagnetics, which has led to the development of a large number of modelling methods based on the Generalized Multipole Technique for quantitative evaluation of electromagnetic scattering by particles of various shapes and compositions. The book describes these methods in detail.
Generalized Multiresolution Analyses (Applied and Numerical Harmonic Analysis)
by Kathy D. MerrillThis monograph presents the first unified exposition of generalized multiresolution analyses. Expanding on the author’s pioneering work in the field, these lecture notes provide the tools and framework for using GMRAs to extend results from classical wavelet analysis to a more general setting. Beginning with the basic properties of GMRAs, the book goes on to explore the multiplicity and dimension functions of GMRA, wavelet sets, and generalized filters. The author’s constructions of wavelet sets feature prominently, with figures to illustrate their remarkably simple geometric form. The last three chapters exhibit extensions of wavelet theory and GMRAs to other settings. These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L2(ℝn).This account of recent developments in wavelet theory will appeal to researchers and graduate students with an interest in multiscale analysis from a pure or applied perspective. Familiarity with harmonic analysis and operator theory will be helpful to the reader, though the only prerequisite is graduate level experience with real and functional analysis.
Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC (Forum for Interdisciplinary Mathematics)
by C. S. Lalitha Didier AusselThe book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.
Generalized Notions of Continued Fractions: Ergodicity and Number Theoretic Applications (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Juan Fernández Sánchez Jerónimo López-Salazar Codes Juan B. Seoane Sepúlveda Wolfgang TrutschnigAncient times witnessed the origins of the theory of continued fractions. Throughout time, mathematical geniuses such as Euclid, Aryabhata, Fibonacci, Bombelli, Wallis, Huygens, or Euler have made significant contributions to the development of this famous theory, and it continues to evolve today, especially as a means of linking different areas of mathematics.This book, whose primary audience is graduate students and senior researchers, is motivated by the fascinating interrelations between ergodic theory and number theory (as established since the 1950s). It examines several generalizations and extensions of classical continued fractions, including generalized Lehner, simple, and Hirzebruch-Jung continued fractions. After deriving invariant ergodic measures for each of the underlying transformations on [0,1] it is shown that any of the famous formulas, going back to Khintchine and Levy, carry over to more general settings. Complementing these results, the entropy of the transformations is calculated and the natural extensions of the dynamical systems to [0,1]2 are analyzed. Features Suitable for graduate students and senior researchers Written by international senior experts in number theory Contains the basic background, including some elementary results, that the reader may need to know before hand, making it a self-contained volume
Generalized Optimal Stopping Problems and Financial Markets (Chapman And Hall/crc Research Notes In Mathematics Ser. #358)
by Dennis WongProvides mathematicians and applied researchers with a well-developed framework in which option pricing can be formulated, and a natural transition from the theory of optimal stopping problems to the valuation of different kinds of options. With the introduction of generalized optimal stopping theory, a unifying approach to option pricing is presented.
Generalized Ordinary Differential Equations in Abstract Spaces and Applications
by Everaldo M. Bonotto Márcia Federson Jaqueline G. MesquitaGENERALIZED ORDINARY DIFFERENTIAL EQUATIONS IN ABSTRACT SPACES AND APPLICATIONS Explore a unified view of differential equations through the use of the generalized ODE from leading academics in mathematics Generalized Ordinary Differential Equations in Abstract Spaces and Applications delivers a comprehensive treatment of new results of the theory of Generalized ODEs in abstract spaces. The book covers applications to other types of differential equations, including Measure Functional Differential Equations (measure FDEs). It presents a uniform collection of qualitative results of Generalized ODEs and offers readers an introduction to several theories, including ordinary differential equations, impulsive differential equations, functional differential equations, dynamical equations on time scales, and more. Throughout the book, the focus is on qualitative theory and on corresponding results for other types of differential equations, as well as the connection between Generalized Ordinary Differential Equations and impulsive differential equations, functional differential equations, measure differential equations and dynamic equations on time scales. The book’s descriptions will be of use in many mathematical contexts, as well as in the social and natural sciences. Readers will also benefit from the inclusion of: A thorough introduction to regulated functions, including their basic properties, equiregulated sets, uniform convergence, and relatively compact sets An exploration of the Kurzweil integral, including its definitions and basic properties A discussion of measure functional differential equations, including impulsive measure FDEs The interrelationship between generalized ODEs and measure FDEs A treatment of the basic properties of generalized ODEs, including the existence and uniqueness of solutions, and prolongation and maximal solutions Perfect for researchers and graduate students in Differential Equations and Dynamical Systems, Generalized Ordinary Differential Equations in Abstract Spaces and Applications will also earn a place in the libraries of advanced undergraduate students taking courses in the subject and hoping to move onto graduate studies.
Generalized Principal Component Analysis
by René Vidal Yi Ma S. S. SastryThis book provides a comprehensive introduction to the latest advances in the mathematical theory and computational tools for modeling high-dimensional data drawn from one or multiple low-dimensional subspaces (or manifolds) and potentially corrupted by noise, gross errors, or outliers. This challenging task requires the development of new algebraic, geometric, statistical, and computational methods for efficient and robust estimation and segmentation of one or multiple subspaces. The book also presents interesting real-world applications of these new methods in image processing, image and video segmentation, face recognition and clustering, and hybrid system identification etc. This book is intended to serve as a textbook for graduate students and beginning researchers in data science, machine learning, computer vision, image and signal processing, and systems theory. It contains ample illustrations, examples, and exercises and is made largely self-contained with three Appendices which survey basic concepts and principles from statistics, optimization, and algebraic-geometry used in this book. René Vidal is a Professor of Biomedical Engineering and Director of the Vision Dynamics and Learning Lab at The Johns Hopkins University. Yi Ma is Executive Dean and Professor at the School of Information Science and Technology at ShanghaiTech University. S. Shankar Sastry is Dean of the College of Engineering, Professor of Electrical Engineering and Computer Science and Professor of Bioengineering at the University of California, Berkeley.
Generalized Rough Sets
by Anjan MukherjeeThe book introduces the concept of "generalized interval valued intuitionistic fuzzy soft sets". It presents the basic properties of these sets and also, investigates an application of generalized interval valued intuitionistic fuzzy soft sets in decision making with respect to interval of degree of preference. The concept of "interval valued intuitionistic fuzzy soft rough sets" is discussed and interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The book also details concept of interval valued intuitionistic fuzzy sets of type 2. It presents the basic properties of these sets. The book also introduces the concept of "interval valued intuitionistic fuzzy soft topological space (IVIFS topological space)" together with intuitionistic fuzzy soft open sets (IVIFS open sets) and intuitionistic fuzzy soft closed sets (IVIFS closed sets).
Generalized Solutions of Operator Equations and Extreme Elements
by D. A. Nomirovskii D. A. Klyushin Vladimir Semenov Yu. I. Petunin S. I. LyashkoAbstract models for many problems in science and engineering take the form of an operator equation. The resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. "Generalized Solutions of Operator Equations and Extreme Elements" presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
Generalized Statistical Thermodynamics: Thermodynamics of Probability Distributions and Stochastic Processes (Understanding Complex Systems)
by Themis MatsoukasThis book gives the definitive mathematical answer to what thermodynamics really is: a variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble, the Author imagines the ensemble of all possible probability distributions and assigns probabilities to them by selection rules that are fairly general. The calculus of the most probable distribution in the ensemble produces the entire network of mathematical relationships we recognize as thermodynamics. The first part of the book develops the theory for discrete and continuous distributions while the second part applies this thermodynamic calculus to problems in population balance theory and shows how the emergence of a giant component in aggregation, and the shattering transition in fragmentation may be treated as formal phase transitions. While the book is intended as a research monograph, the material is self-contained and the style sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in such fields as physics, chemistry, and engineering.
Generalized Stochastic Processes: Modelling and Applications of Noise Processes (Compact Textbooks in Mathematics)
by Stefan SchäfflerThis textbook shall serve a double purpose: first of all, it is a book about generalized stochastic processes, a very important but highly neglected part of probability theory which plays an outstanding role in noise modelling. Secondly, this textbook is a guide to noise modelling for mathematicians and engineers to foster the interdisciplinary discussion between mathematicians (to provide effective noise models) and engineers (to be familiar with the mathematical backround of noise modelling in order to handle noise models in an optimal way).Two appendices on "A Short Course in Probability Theory" and "Spectral Theory of Stochastic Processes" plus a well-choosen set of problems and solutions round this compact textbook off.
Generalized Trigonometric and Hyperbolic Functions
by Ronald E. MickensGeneralized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies. Features Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences
Generalized Vectorization, Cross-Products, and Matrix Calculus
by Darrell A. TurkingtonThis book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators, and a Lagrangian multiplier test for endogeneity.
Generalized Wavelets and Hypergroups
by Khalifa TrimecheWavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now
Generalized Weibull Distributions
by Chin-Diew LaiThe Weibull distribution has been one of the most cited lifetime distributions in reliability engineering. Over the last decade, many generalizations and extensions of the Weibull have been proposed in order to provide more flexibility than the traditional version when it comes to modeling lifetime data in diverse fields. This book offers an update on these developments, presenting the essential properties of each model. Several plots of density and hazard rate functions are also included, and a brief outline of known application(s) for each model is also given.
Generalizing from Educational Research: Beyond Qualitative and Quantitative Polarization
by Kadriye Ercikan Wolff-Michael Roth"This book frames the major challenge facing educational researchers as one of going beyond the mindless qualitative-quantitative divide and addressing the overarching/fundamental challenge of enriching and enlarging educational inquiry. It is a signature contribution to the field." - Clifton F. Conrad, University of Wisconsin-Madison, USA Tackling one of the most critical issues in education research today - how research methods are related to value and meaningfulness - this frontline volume achieves two purposes. First, it presents an integrated approach to educational inquiry that works toward a continuum instead of a dichotomy of generalizability, and looks at how this continuum might be related to types of research questions asked and how these questions should determine modes of inquiry. Second, it discusses and demonstrates the contributions of different data types and modes of research to generalizability of research findings, and to limitations of research findings that utilize a single approach. International leaders in the field take the discussion of generalizing in education research to a level where claims are supported using multiple types of evidence. The volume pushes the field in a different direction, where the focus is on creating meaningful research findings that are not polarized by qualitative versus quantitative methodologies. The integrative approach allows readers to better understand possibilities and shortcomings of different types of research.
Generalizing the Regression Model: Techniques for Longitudinal and Contextual Analysis
by Blair Wheaton Marisa YoungThis comprehensive text introduces regression, the general linear model, structural equation modeling, the hierarchical linear model, growth curve models, panel data, and event history models, and includes discussion of published implementations of each technique showing how it was used to address substantive and interesting research questions. It takes a step-by-step approach in the presentation of each topic, using mathematical derivations where necessary, but primarily emphasizing how the methods involved can be implemented, are used in addressing representative substantive problems than span a number of disciplines, and can be interpreted in words. The book demonstrates the analyses in STATA and SAS. Generalizing the Regression Model provides students with a bridge from the classroom to actual research practice and application. A website for the book at https://edge.sagepub.com/wheaton1e (coming soon!) includes resources for instructors and students.
Generalizing the Regression Model: Techniques for Longitudinal and Contextual Analysis
by Blair Wheaton Marisa YoungThis comprehensive text introduces regression, the general linear model, structural equation modeling, the hierarchical linear model, growth curve models, panel data, and event history models, and includes discussion of published implementations of each technique showing how it was used to address substantive and interesting research questions. It takes a step-by-step approach in the presentation of each topic, using mathematical derivations where necessary, but primarily emphasizing how the methods involved can be implemented, are used in addressing representative substantive problems than span a number of disciplines, and can be interpreted in words. The book demonstrates the analyses in STATA and SAS. Generalizing the Regression Model provides students with a bridge from the classroom to actual research practice and application. A website for the book at https://edge.sagepub.com/wheaton1e (coming soon!) includes resources for instructors and students.
Generated Dynamics of Markov and Quantum Processes
by Martin JanßenThis book presents Markov and quantum processes as twosides of a coin called generated stochastic processes. It deals withquantum processes as reversible stochastic processes generated byone-step unitary operators, while Markov processes are irreversible stochasticprocesses generated by one-step stochastic operators. The characteristicfeature of quantum processes are oscillations, interference, lots of stationarystates in bounded systems and possible asymptotic stationary scattering statesin open systems, while the characteristic feature of Markov processes arerelaxations to a single stationary state. Quantum processes apply to systemswhere all variables, that control reversibility, are taken as relevantvariables, while Markov processes emerge when some of those variables cannot befollowed and are thus irrelevant for the dynamic description. Their absencerenders the dynamic irreversible. Afurther aim is to demonstrate that almost any subdiscipline of theoretical physicscan conceptually be put into the context of generated stochastic processes. Classical mechanics and classical field theory are deterministic processeswhich emerge when fluctuations in relevant variables are negligible. Quantummechanics and quantum field theory consider genuine quantum processes. Equilibrium and non-equilibrium statistics apply to the regime where relaxingMarkov processes emerge from quantum processes by omission of a large number ofuncontrollable variables. Systems with many variables often self-organize insuch a way that only a few slow variables can serve as relevant variables. Symmetries and topological classes are essential in identifying such relevantvariables. Thethird aim of this book is to provide conceptually general methods of solutionswhich can serve as starting points to find relevant variables as to apply best-practice approximation methods. Such methods are available through generatingfunctionals. The potential reader is a graduate student whohas heard already a course in quantum theory and equilibrium statisticalphysics including the mathematics of spectral analysis (eigenvalues,eigenvectors, Fourier and Laplace transformation). The reader should be openfor a unifying look on several topics.
Generating Analog IC Layouts with LAYGEN II
by Nuno C. Lourenço Ricardo M. Martins Nuno C.G. HortaThis book presents an innovative methodology for the automatic generation of analog integrated circuits (ICs) layout, based on template descriptions and on evolutionary computational techniques. A design automation tool, LAYGEN II was implemented to validate the proposed approach giving special emphasis to reusability of expert design knowledge and to efficiency on retargeting operations.
Generation and Application of High Power Microwaves
by R A Cairns A D R Phelps P OsborneWritten at the graduate level, Generation and Application of High Power Microwaves discusses the basic physics of the generation of microwave and radiofrequency waves in the megawatt power range and the application of these ideas to a range of devices such as klystrons, gyrotrons, and free electron lasers. The book also contains chapters covering the transmission of the power through waveguides and the problems associated with mode conversion in transmission lines. The main application area covered is the heating and current drive in tokamaks and other devices for research into controlled nuclear fusion. Other applications of high power microwave technology are not neglected, and among those discussed are multiple charged ion and soft x-ray sources, electron spin resonance spectroscopy, advanced materials processing, millimeter wave radar, and supercolliders.
Generation Me - Revised and Updated: Why Today's Young Americans Are More Confident, Assertive, Entitled--and More Miserable Than Ever Before
by Ph.D. Jean M. TwengeThe Associated Press calls them "The Entitlement Generation," and they are storming into schools, colleges, and businesses all over the country. They are today's young people, a new generation with sky-high expectations and a need for constant praise and fulfillment. In this provocative new book, headline-making psychologist and social commentator Dr. Jean Twenge documents the self-focus of what she calls "Generation Me" -- people born in the 1970s, 1980s, and 1990s. Herself a member of Generation Me, Dr. Twenge explores why her generation is tolerant, confident, open-minded, and ambitious but also cynical, depressed, lonely, and anxious. Using findings from the largest intergenerational study ever conducted -- with data from 1.3 million respondents spanning six decades -- Dr. Twenge reveals how profoundly different today's young adults are -- and makes controversial predictions about what the future holds for them and society as a whole. But Dr. Twenge doesn't just talk statistics -- she highlights real-life people and stories and vividly brings to life the hopes and dreams, disappointments and challenges of Generation Me.With a good deal of irony, humor, and sympathy she demonstrates that today's young people have been raised to aim for the stars at a time when it is more difficult than ever to get into college, find a good job, and afford a house -- even with two incomes. GenMe's expectations have been raised just as the world is becoming more competitive, creating an enormous clash between expectations and reality. Dr. Twenge also presents the often-shocking truths about her generation's dramatically different sexual behavior and mores. GenMe has created a profound shift in the American character, changing what it means to be an individual in today's society. Engaging, controversial, prescriptive, and often funny, Generation Me will give Boomers new insight into their offspring, and help GenMe'ers in their teens, 20s, and 30s finally make sense of themselves and their goals and find their road to happiness.
The Generation Myth: Why When You're Born Matters Less Than You Think
by Bobby DuffyMillennials, Baby Boomers, Gen Z—we like to define people by when they were born, but an acclaimed social researcher explains why we shouldn't.Boomers are narcissists. Millennials are spoiled. Gen Zers are lazy. We assume people born around the same time have basically the same values. It makes for good headlines, but is it true?Bobby Duffy has spent years studying generational distinctions. In The Generation Myth, he argues that our generational identities are not fixed but fluid, reforming throughout our lives. Based on an analysis of what over three million people really think about homeownership, sex, well-being, and more, Duffy offers a new model for understanding how generations form, how they shape societies, and why generational differences aren&’t as sharp as we think.The Generation Myth is a vital rejoinder to alarmist worries about generational warfare and social decline. The kids are all right, it turns out. Their parents are too.
Generation, Ungleichheit, Technik: Technikkompetenz im höheren Lebensalter (Vechtaer Beiträge zur Gerontologie)
by Bill PottharstIn diesem Buch wird versucht, die Theorieansätze der Technikgenerationen mit jenen der sozialen Ungleichheit auf eine Weise zu verbinden, dass Rückschlüsse auf die Technikakzeptanz, die Technikkompetenz und die Techniknutzung im höheren Lebensalter abgeleitet werden können. Technikroutinen werden im höheren Lebensalter insbesondere durch Prägungen im Lebensverlauf und die soziale Lage in der aktuellen Lebenssituation bestimmt. Unerlässlich scheint, älteren Menschen Zugang zu neuen Technologien zu ermöglichen, ihnen jedoch ebenso genügend Freiraum dafür einzuräumen, auf den Einsatz ungewollter Technologien verzichten zu können.
Generation Z: A Century in the Making
by Corey Seemiller Meghan GraceNo other generation in history has received as much coverage as the Millennial generation. Books, Google searches, blogs, and news articles are everywhere about them. Yet, Generation Z is comprised of our youth and young adults today and has received very little attention comparatively. Those in Generation Z are among our youngest consumers, students, colleagues, constituents, voters, and neighbors. Being able to better understand who they are and how they see the world can be helpful in effectively working with, teaching, supervising, and leading them. Generation Z: A Century in the Making offers insight into nearly every aspect of the lives of those in Generation Z, including a focus on their career aspirations, religious beliefs and practices, entertainment and hobbies, social concerns, relationships with friends and family, health and wellness, money management, civic engagement, communication styles, political ideologies, technology use, and educational preferences. Drawing from an unprecedented number of studies with higher education research institutions, market research firms such as Pew and Census, other generational researchers and industry leaders, this is the authoritative defining work on Generation Z that market researchers, consumer behaviour specialists, and employers sorely need – and it is a fascinating read for anyone interested in the sociology of generations.