Grundz羹ge Der Parametrischen Optimierung
Dieses Lehrbuch gibt eine verst瓣ndliche Einf羹hrung in die parametrische Optimierung, die mathematische Sachverhalte einerseits stringent behandelt, sie aber andererseits auch sehr ausf羹hrlich motiviert und mit vielen Abbildungen illustriert. Die vorwiegend geometrische Herleitung von zentralen Stabilit瓣tsresultaten setzt dabei einen neuen Akzent, der den Bestand der bisherigen Lehrb羹cher zur parametrischen Optimierung bereichert. Die Stabilit瓣ts- und Sensitivit瓣tsergebnisse werden nicht nur mit speziellen 繹konomischen Fragestellungen illustriert, sondern auch auf gr繹?ere Problemklassen wie Nash-Spiele und die semi-infinite Optimierung angewendet, die in den Ingenieur- und Wirtschaftswissenschaften wichtige eine Rolle spielen. Das Buch richtet sich daher nicht nur an Mathematiker, sondern auch an Natur-, Ingenieur- und Wirtschaftswissenschaftler, die mathematisch fundierte Verfahren in ihrem Gebiet verstehen und anwenden m繹chten. F羹r Dozenten stellt das Buch gen羹gend Auswahlm繹glichkeiten zur Verf羹gung, um es als Grundlage f羹r unterschiedlich angelegte Vorlesungen zur parametrischen Optimierung zu verwenden.
Wahrscheinlichkeitsrechnung Und Statistik
Dieses Lehrbuch f羹hrt in die zentralen Begriffe und Konzepte der Wahrscheinlichkeitsrechnung, der beschreibenden sowie der schlie?enden Statistik ein. Der Fokus liegt dabei auf einem intuitiven Verst瓣ndnis der grundlegenden Konzepte, Zusammenh瓣nge und Methoden. Trotzdem wird der Stoff mathematisch pr瓣zise pr瓣sentiert. Innerhalb jedes Kapitels finden Sie verschiedene didaktische Elemente, die Ihnen den Zugang und das Verst瓣ndnis, aber auch die Orientierung deutlich erleichtern: Kurz羹bersicht der wichtigsten Begriffe am KapitelanfangAnschauliche Erkl瓣rungen und BeispieleZentrale Sachverhalte und DefinitionenWarnungen vor h瓣ufigen Missverst瓣ndnissenSeparate Textabschnitte zur IntuitionGrafische oder tabellarische ?bersichten am KapitelendeAm Ende der meisten Abschnitte finden Sie kurze Lernkontrollen - hier k繹nnen Sie Ihr Wissen 羹berpr羹fen, indem Sie verschiedene Aussagen alswahr oder falsch einordnen. Die L繹sungen finden Sie im Anhang, je nach Schwierigkeitsgrad mit kurzem L繹sungsweg. Am Ende der Kapitel finden Sie au?erdem Verst瓣ndnisfragen, die noch einmal die wichtigsten Inhalte abfragen und so Ihren Lernfortschritt zeigen.
Global Solution for Sudoku
The present book aims to provide systematic and reliable techniques, called the global solution, for Sudoku puzzles. Any proper Sudoku puzzle, which has one and only one solution of Sudoku, can be solved by anyone following the techniques provided in this book. Specific symbols are introduced to express the 6 basic rules of the Sudoku global solution, as the results, those Sudoku solving techniques are presented similar to the annotations in chess. Finnish mathematician Arto Inkala proposed "the most difficult Sudoku puzzle" in 2007. Then, he designed another difficult Sudoku puzzle in 2012, named "the thing Everest". In the present book the solving process of those two difficult Sudoku puzzles are illustrated reliably by the specific symbols of the global solution step by step.
Stochastic Processes
This is the third edition of a popular UK textbook on stochastic processes. It has been updated with a new chapter on diffusion processes and Brownian motion, has extended material on birth and death processes and epidemics, plus new references throughout. The examples and exercises have all been expanded and improved.
Spectral and Scattering Theory for Ordinary Differential Equations
This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm-Liouville equations.Sturm-Liouville theory has applications in partial differential equations and mathematical physics. Examples include classical PDEs such as the heat and wave equations. Written by leading experts, this book provides a modern, systematic treatment of the theory. The main topics are the spectral theory and eigenfunction expansions for Sturm-Liouville equations, as well as scattering theory and inverse spectral theory. It is the first book offering a complete account of the left-definite theory for Sturm-Liouville equations.The modest prerequisites for this book are basic one-variable real analysis, linear algebra, as well as an introductory course in complex analysis. More advanced background required in some parts of the book is completely covered in the appendices. With exercises in each chapter, the book is suitable for advancedundergraduate and graduate courses, either as an introduction to spectral theory in Hilbert space, or to the spectral theory of ordinary differential equations. Advanced topics such as the left-definite theory and the Camassa-Holm equation, as well as bibliographical notes, make the book a valuable reference for experts.
Teoria Della Probabilit?
1. Misure e spazi di probabilit?.- 2. Variabili aleatorie.- 3. Successioni di variabili aleatorie.- 4. Probabilit? condizionata.- 5. Processi stocastici.- 6. Elementi di statistica.- Appendice A.- Appendice B: Temi d'esame risolti.- Appendice C: Tavole riassuntive delle principali distribuzioni.
Nichtlineare Funktionalanalysis
Dieses Lehrbuch enth瓣lt eine Einf羹hrung in die nichtlineare Funktionalanalysis. Die Themenauswahl vermittelt grundlegende Methoden und Techniken, die bei der Untersuchung von nichtlinearen elliptischen und parabolischen partiellen Differentialgleichungen Anwendung finden. Es geht insbesondere auf Fixpunkts瓣tze, Differentiation und Integration in Banachr瓣umen, die Theorie monotoner Operatoren und den Abbildungsgrad ein. Der Darstellung des Stoffes liegt die gegenseitige Beeinflussung von Theorie und Anwendungen zugrunde. Kurze Einf羹hrungen am Kapitelanfang, illustrative Beispiele sowie die detaillierte Herleitung von Ergebnissen erleichtern das Verst瓣ndnis. Eine Kurzzusammenfassung von wichtigen Resultaten aus der linearen Funktionalanalysis ist im Anhang zu finden und vervollst瓣ndigt den Inhalt. Das Buch richtet sich an Studierende mit abgeschlossener Grundausbildung in Analysis, linearer Algebra und linearer Funktionalanalysis und umfasst den Lehrstoff f羹r eine vierst羹ndige einsemestrige Vorlesung. F羹r die 2. Auflage wurde insbesondere das Hauptkapitel zu monotonen Operatoren wesentlich 羹berarbeitet. Es beinhaltet nun eine moderne Darstellung von Evolutionsproblemen mithilfe Bochner-pseudomonotoner Operatoren sowie eine in sich geschlossene Darstellung maximal monotoner Operatoren.
Schnelleinstieg Differentialgleichungen
Anwendungsorientierte und verst瓣ndliche Einf羹hrung in gew繹hnliche DGLenVerzichtet weitestgehend auf abstrakte Beweise Bietet eine Vielzahl an Beispielen aus verschiedensten Bereichen
Global Riemannian Geometry: Curvature and Topology
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the study of scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is intended for both graduate students and researchers. This second edition has been updated to include recent developments such as promising results concerning the geometry of exit time moment spectra and potential analysis in weighted Riemannian manifolds, as well as results pertaining to an early conjecture on the geometry of the scalar curvature and speculations on new geometric approaches to the Index Theorem.
Gro?e Abweichungen
Dies ist eine Einf羹hrung in die Theorie der (Wahrscheinlichkeiten der) gro?en Abweichungen, die mit Hilfe analytischer Methoden die exponentielle Abfallrate sehr kleiner Wahrscheinlichkeiten charakterisiert. Diese Theorie wurde in den 1960er und 1970er Jahren stark ausgeweitet und bis in die j羹ngste Vergangenheit kontinuierlich auf immer neue probabilistische Strukturen erweitert. Ihre Grundz羹ge geh繹ren mittlerweile zu den Standardwerkzeugen eines Wahrscheinlichkeitstheoretikers In der ersten H瓣lfte werden die grundlegenden Ideen, Konzepte und Werkzeuge der Theorie erl瓣utert, in der zweiten werden Anwendungsbeispiele aus diversen Forschungsgebieten diskutiert, in denen die Theorie entscheidende Ergebnisse erm繹glichte, wie Spektren zuf瓣lliger Matrizen, eindimensionale Polymerketten oder Bose-Einstein-Kondensation. Der Text richtet sich an Studierende, die mindestens zwei einf羹hrende Vorlesungen der Wahrscheinlichkeitstheorie genossen haben, sowie an Lehrende, die auf der Basis dieses Buches eine fortf羹hrende Vorlesung halten m繹chten. Der Anwendungsteil eignet sich gut f羹r ein studentisches Seminar als Folgeveranstaltung der zugeh繹rigen Vorlesung.
Global Solution for Sudoku
The present book aims to provide systematic and reliable techniques, called the global solution, for Sudoku puzzles. Any proper Sudoku puzzle, which has one and only one solution of Sudoku, can be solved by anyone following the techniques provided in this book. Specific symbols are introduced to express the 6 basic rules of the Sudoku global solution, as the results, those Sudoku solving techniques are presented similar to the annotations in chess. Finnish mathematician Arto Inkala proposed "the most difficult Sudoku puzzle" in 2007. Then, he designed another difficult Sudoku puzzle in 2012, named "the thing Everest". In the present book the solving process of those two difficult Sudoku puzzles are illustrated reliably by the specific symbols of the global solution step by step.
Analysis F羹r Wirtschaftswissenschaftler
Analysis (Calculus auf Englisch) hat einen sehr schlechten Ruf zwischen Studenten, Sch羹ler und Laien. Das liegt oft an der extremen Abstraktion von Konzepte wie Ableitung oder Integrale. Mit einer Kombination aus der Geschichte der Analysis und mathematische Entwicklung versuche ich Analysis positiv zu pr瓣sentieren, die Basics erkl瓣ren mit dem Ziel, dass wenn man ein Analysis Lehrbuch nimmt, sich nicht mehr f羹rchten muss. All die Erkl瓣rungen sind fokussiert an der Anwendung der Analysis f羹r Wirtschaftswissenschaften Leibniz und Newton, Eltern der modernen Analysis, und Euler, helfen uns bei dieser Einf羹hrung in die Analysis mit Geschichte.
Gut Gepackt - Kein Bit Zu Viel
Bei der heutigen Datenflut, die auf Speichermedien und im Internet kursiert, ist die Kompression digitaler Daten nach wie vor ein immens wichtiger Aspekt bei Daten羹bertragung und -speicherung. Dieses essential erl瓣utert ohne theoretischen ?berbau und mit elementaren mathematischen und informatischen Methoden die wichtigsten Kompressionsverfahren, so unter anderem die Entropiecodierungen von Shannon-Fano und von Huffman, sowie die W繹rterbuchcodierungen der Lempel-Ziv-Familie. Ausf羹hrlich eingegangen wird auch auf Irrelevanzreduktion und die Quantisierung bei optischen und akustischen Signalen, die die Unzul瓣nglichkeiten des menschlichen Auges und Ohres zur Datenkompression ausnutzen. Illustriert wird das Ganze anhand g瓣ngiger Praxisanwendungen aus dem allt瓣glichen Umfeld. Die Aufbereitung erlaubt den Einsatz beispielsweise in Arbeitsgruppen an MINT-Schulen, bei Einf羹hrungskursen an Hochschulen und ist auch f羹r interessierte Laien geeignet.
Optimum Methods for Dynamic analysis of Telecommunication Tower
Over the past 35 years, the growing demand for wireless and broadcast communication has spurred a dramatic increase in steel telecommunication tower construction and maintenance. Failure of such structures due to severe earthquakes is a major concern. The Indian code suggests the detailed static and dynamic analysis provisions that are to be followed for lumped mass systems like buildings. In case of continuous structures the code only suggests the static analysis provisions in details. Due to the lack of detailed Indian codal provisions for dynamic analysis of telecommunication tower, this book is intended to give an insight on the comparative study using Response Spectrum method which is being carried out to obtain the optimum number of elemental discretization along with the optimum method of modal combination.
Differenzialgleichungen in Elementarer Darstellung
Dieses Lehrbuch leitet von den klassischen Schulinhalten der Analysis direkt zu einer Kategorisierung und Analyse spezieller (insbesondere linearer) Differenzialgleichungen 羹ber. Es betrachtet somit die klassische Analysis aus einer ungewohnten Perspektive und vermittelt inhaltlich zwischen dem mathematischen Denken an Gymnasien einerseits und an Hochschulen/Universit瓣ten andererseits. Dabei werden Definitionen weniger formal, sondern vielmehr als Handlungsanweisung, also funktional betrachtet. Beim mathematischen Beweis geht es weniger darum, eine Wahrheit zu entdecken, als vielmehr darum, eine Einsicht zu vermitteln. Die verwendeten mathematischen Zeichen erheben keinen Absolutheitsanspruch, sondern sollen im Betrachter ein Bild erzeugen. Dieses Buch m繹chte so eine Weiterentwicklung in der Didaktik ansto?en; es richtet sich daher prim瓣r an Studierende und Dozenten im gymnasialen Lehramt der Mathematik, aber auch an Sch羹lerInnen der gymnasialen Kursstufe, welche ein mathematikaffines Studium ins Auge fassen und daher den ?bergang von der gymnasialen Kursstufe zum Studium der Mathematik oder eines mathematikaffinen Faches zu bew瓣ltigen haben. Es m繹chte sie dazu ermutigen, die Mathematik als einen gro?en Werkzeugkasten zu begreifen, mit dessen Hilfe sich auf unglaublich vielen Gebieten allt瓣gliche wie nicht allt瓣gliche Fragen l繹sen und Sachverhalte quantifizieren lassen.
Excel 2019 for Marketing Statistics
This book shows the capabilities of Microsoft Excel in teaching marketing statistics effectively. It is a step-by-step, exercise-driven guide for students and practitioners who need to master Excel to solve practical marketing problems. If understanding statistics isn't your strongest suit, you are not especially mathematically inclined, or if you are wary of computers, this is the right book for you.Excel, a widely available computer program for students and managers, is also an effective teaching and learning tool for quantitative analyses in marketing courses. Its powerful computational ability and graphical functions make learning statistics much easier than in years past. Excel 2019 for Marketing Statistics: A Guide to Solving Practical Problems capitalizes on these improvements by teaching students and managers how to apply Excel to statistical techniques necessary in their courses and work.In this new edition, each chapter explains statistical formulas and directs the reader to use Excel commands to solve specific, easy-to-understand marketing problems. Practice problems are provided at the end of each chapter with their solutions in an appendix. Separately, there is a full practice test (with answers in an appendix) that allows readers to test what they have learned.
Neural Networks and Statistical Learning
This book provides a broad yet detailed introduction to neural networks and machine learning in a statistical framework. A single, comprehensive resource for study and further research, it explores the major popular neural network models and statistical learning approaches with examples and exercises and allows readers to gain a practical working understanding of the content. This updated new edition presents recently published results and includes six new chapters that correspond to the recent advances in computational learning theory, sparse coding, deep learning, big data and cloud computing.Each chapter features state-of-the-art descriptions and significant research findings. The topics covered include: - multilayer perceptron;- the Hopfield network;- associative memory models;- clustering models and algorithms;- t he radial basis function network;- recurrent neural networks;- nonnegative matrix factorization;- independent component analysis;-probabilistic and Bayesian networks; and- fuzzy sets and logic.Focusing on the prominent accomplishments and their practical aspects, this book provides academic and technical staff, as well as graduate students and researchers with a solid foundation and comprehensive reference on the fields of neural networks, pattern recognition, signal processing, and machine learning.
Nonuniformly Hyperbolic Attractors
This monograph offers a coherent, self-contained account of the theory of Sinai-Ruelle-Bowen measures and decay of correlations for nonuniformly hyperbolic dynamical systems. A central topic in the statistical theory of dynamical systems, the book in particular provides a detailed exposition of the theory developed by L.-S. Young for systems admitting induced maps with certain analytic and geometric properties. After a brief introduction and preliminary results, Chapters 3, 4, 6 and 7 provide essentially the same pattern of results in increasingly interesting and complicated settings. Each chapter builds on the previous one, apart from Chapter 5 which presents a general abstract framework to bridge the more classical expanding and hyperbolic systems explored in Chapters 3 and 4 with the nonuniformly expanding and partially hyperbolic systems described in Chapters 6 and 7. Throughout the book, the theory is illustrated with applications. A clear and detailed account of topicsof current research interest, this monograph will be of interest to researchers in dynamical systems and ergodic theory. In particular, beginning researchers and graduate students will appreciate the accessible, self-contained presentation.
Economy and Disability
Society has developed so that it accommodates the needs of intertwined people, but a question arises as to which people have been accommodated. Has everyone been taken care of in an equal manner? If not, who has fallen into the gap between the institutions that are supposed to accommodate them? This book is a study of these issues of economy and disability using game theory, which has provided a means of analyzing various social phenomena. Part I provides actual cases related to economy and disability, with the stories based on interviews by the author. Part II is geared toward a game theoretic analysis. This book explains disability-related issues by game theory and innovates that theory by deeply contemplating the issues.It is not common that first-rate theorists manage to make their research relevant and applicable to the most pressing problems our society faces these days. This is the remarkable achievement of this book. Akihiko Matsui, an internationally recognized leader in economic theory, succeeds in bringing profound game theoretical insights to the questions of disability, the social norms relating to it, and the ethical and economic problems they raise. The book is a tour de force, brilliantly combining economic and sociology, mathematics and philosophy, to provide us a fresh look at the way we run modern societies.Itzahk Gilboa, Professor, Eitan Berglas School of Economics, Tel-Aviv University and Professor of Economics and Decision Sciences, HEC, ParisThe present world faces a broad range of societal problems such as discrimination against minorities and conflicts between groups. The market mechanism may solve some of these dilemmas, but many others remain. This book targets various societal problems and provides game theoretical approaches to them, stressing the importance of social institutions including the market system and individual interactive attitudes to society. Aki Matsui's splendid Economy and Disability is indispensable for students and scholars interested in social science, particularly in economic theory, and gives a better understanding of these phenomena and their potential cures.Mamoru Kaneko, Professor, Faculty of Political Science and Economics, Waseda UniversityIn this book, Aki Matsui is revealed to be a fully-fledged humanist in the guise of a game theoretician. He beautifully presents game-theoretical ideas while at the same time suggesting how society should relate to the disabled. This unique combination makes Economy and Disability--apart from anything else--a truly moving book.Ariel Rubinstein, Professor of Economics, Eitan Berglas School of Economics, Tel-Aviv University and Professor of Economics, New York University
Interdisciplinary Perspectives on Math Cognition
This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding.This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Stochastic Calculus for Financial Modeling with Stochastic Volatility
I dedicate this work to my father that he rest in peace Mr. Amar Arbai. Index returns are subject of several sources of uncertainty. To better model market, searchers required a Levy process to master randomness. Through this book, we discuss some particular Levy process corresponding to different structure of financial series, to show whether the data are free or include diffusion component and whether the process contains finite or infinite variation. Then, we attempt to provide an alternative approach, Fourier transform, to pricing European option under SVJJ and CGMY models since their probability density functions are unknowns. For ending, we deal with necessary tools for understanding and implementing paths through Monte Carlo simulation and make use the efficient numerical pattern which serve to fulfill the closed-form analytical solution for European call option.
Nonlinear Expectations and Stochastic Calculus Under Uncertainty
This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author.This book is based on Shige Peng's lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes.With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter.Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
Satellite Dynamics and Space Missions
This book discusses the design of new space missions and their use for a better understanding of the dynamical behaviour of solar system bodies, which is an active field of astrodynamics. Space missions gather data and observations that enable new breakthroughs in our understanding of the origin, evolution and future of our solar system and Earth's place within it. Covering topics such as satellite and space mission dynamics, celestial mechanics, spacecraft navigation, space exploration applications, artificial satellites, space debris, minor bodies, and tidal evolution, the book presents a collection of contributions given by internationally respected scientists at the summer school "Satellite Dynamics and Space Missions: Theory and Applications of Celestial Mechanics", held in 2017 at San Martino al Cimino, Viterbo (Italy). This school aimed to teach the latest theories, tools and methods developed for satellite dynamics and space, and as such the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
Research Problems in Function Theory
In 1967 Walter K. Hayman published 'Research Problems in Function Theory', a list of 141 problems in seven areas of function theory. In the decades following, this list was extended to include two additional areas of complex analysis, updates on progress in solving existing problems, and over 520 research problems from mathematicians worldwide. It became known as 'Hayman's List'. This Fiftieth Anniversary Edition contains the complete 'Hayman's List' for the first time in book form, along with 31 new problems by leading international mathematicians. This list has directed complex analysis research for the last half-century, and the new edition will help guide future research in the subject. The book contains up-to-date information on each problem, gathered from the international mathematics community, and where possible suggests directions for further investigation. Aimed at both early career and established researchers, this book provides the key problems andresults needed to progress in the most important research questions in complex analysis, and documents the developments of the past 50 years.
Symplectic Difference Systems: Oscillation and Spectral Theory
This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.
Capacitated Vehicle Routing Problem
Cost of transportation of goods and services is an interesting topic in today's society. Capacitated vehicle routing problem is one of the variants of the vehicle routing problem. In this research we develop a machine learning technique to nd optimal paths from a depot to the set of customers while also considering the capacity of the vehicles, in order to reduce the cost of transportation of goods and services. Each vehicle originates from a depot, service the customers and return to the depot. We compare the machine learning model with an exact method; column generation. Our objective is to solve a large-size of vehicle routing problem to optimality.
Time Series Data Mining
The time series data mining (TSDM) framework is a fundamental contribution to the fields of time series and data mining. Methods based on the time series data mining framework are able to successfully characterize and predict complex, non-parametric, irregular and chaotic time series. The time series data mining methods overcome limitations (including stationarity and linearity requirements) of traditional time series analysis technique by adapting data mining concepts for analyzing time series.
Boundary Value Problems, Weyl Functions, and Differential Operators
This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schr繹dinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory.Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Financial Models in Production
This book provides a hands-on guide to how financial models are actually implemented and used in practice, on a daily basis, for pricing and risk-management purposes. It shows how to put these models into use in production while minimizing the cost of implementation and maximizing robustness and control. Addressing some of the most important and cutting-edge issues, it describes how to build the necessary models in order to risk manage all the costs involved in options fabrication within the world of equity derivatives and hybrids. This is achieved by extending classical models and improving them in order to account for complex features. The book is primarily aimed at market practitioners (traders, risk managers, risk control, top managers), as well as Masters students in Quantitative/Mathematical Finance. It will also be useful for instructors hoping to enrich their courses with practical examples. The prerequisites are basic stochastic calculus and a general knowledge of financial markets and financial derivatives.
Theory of Probability
This treatise is written on an elementary level; in more difficult cases the final formulas are provided without proof. Nevertheless, it was impossible to leave out integrals and I also had to differentiate an integral with respect to a parameter. I include many examples taken from the history of probability and hope that my subject has thus become lively. I especially quote Karl Pearson's (1978, p. 1) repentant confession: I do feel how wrongful it was to work for so many years at statistics and neglect its history. In spite of a few mistakes, his book deserves serious attention. Thus, in 禮 4.1.1 I criticize his opinion about Jakob Bernoulli. I have devoted much attention to the notion of probability which fully conforms to Langevin's statement (1913/1914, p. 3): Dans toutes ces questions [in the kinetic theory] la difficult矇 principale est, comme nous le verrons, de donner une d矇finition correcte et claire de la probabilit矇. Note however that correct definition sounds strangely.
Statistical Analysis using SAS and SPSS Software
This book explains how both SAS and SPSS programs are working; and how the data should be input, process and analyse for each kind of analysis within each analysis subject. All procedures have been covered by examples that contained real numerical data and analysed step by step by using print screen function, in addition to explain and showing the outputs as numeric and curves; also the necessary equations and models have been reported for analysis methods in this book. Two reasons encouraged me to publish this book: First; the researchers and postgraduate students are needed such book to be analyzer and can efficiently analyse their experiment's data statistically. Second; to permit for the planners and statisticians discover more about analyzing the relationship between statistical variables via SAS and SPSS.
Hypothesis Testing
The world produces more data than ever. Are you ready for it?In today's data-driven world, you hear about making decisions based on data all the time. Hypothesis testing plays a crucial role in that process, whether you're in academia, business, or data science. Without hypothesis tests, you risk making bad decisions.Chances are high you'll need to understand these tests to analyze your data and evaluate the work of others.Build the knowledge for effective hypothesis testing! Know when to use each test, how to use them reliably, and how to interpret the results correctly!Understand why you need hypothesis tests and how they work.Effectively use significance levels, p-values, confidence intervals.Select the correct type of test to answer your question.Learn how to test means, medians, variances, proportions, distributions, counts, correlations for continuous and categorical data, and find outliers.One-Way ANOVA, Two-Way ANOVA, and interaction effects.Check assumptions to obtain reliable results.Manage the error rates for false positives and false negatives.Understand sampling distributions, the central limit theorem, and statistical power.Know how t-tests, F-tests, chi-squared, and post hoc tests work.Learn about differences between parametric, nonparametric, and bootstrapping methods.Examples of many hypothesis tests.Access free downloadable datasets so you can try it yourself.
Basic Structures in Mathematical Analysis
The purpose of this book is to make available to the student some fundamentals of mathematical analysis. Specifically, it is intended to make such fundamentals available in a form that meets their need in many applications, like real analysis, integration, measure theory, and representation theory. The principal point of view is to develop the basic structures of analysis, under which one can appropriately go on further in the domain of functional analysis. The book is intended to be essentially self contained and accessible to well-trained under graduated students. Its prerequisites are elementary standards from basic algebra. In writing this book, we care about doing things as little abstract as possible. So, to make easy the access to the main concepts, each section of each chapter is illustrated by simple examples and exercises, which are mostly applications to concrete problems.
Emerging Problems in the Homogenization of Partial Differential Equations
Nika, G. and Vernescu, B., Micro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids.- Jerez-Hanckes, C. et al., Multiscale analysis of myelinated axons.- P矇rez-Mart穩nez, M., Homogenization for alternating boundary conditions with large reaction terms concentrated in small regions.- G. Fulgencio, R. and Guib矇, O., Quasilinear Elliptic Problems in a Two-Component Domain with L^1 data.- Donato, P. et al., Homogenization of an eigenvalue problem in a two-component domain with interfacial jump.
Pioneering Works on Distribution Theory
This book highlights the forefront of research on statistical distribution theory, with a focus on unconventional random quantities, and on phenomena such as random partitioning. The respective papers reflect the continuing appeal of distribution theory and the lively interest in this classic field, which owes much of its expansion since the 1960s to Professor Masaaki Sibuya, to whom this book is dedicated.The topics addressed include a test procedure for discriminating the (multivariate) Ewens distribution from the Pitman Sampling Formula, approximation to the length of the Ewens distribution by discrete distributions and the normal distribution, and the distribution of the number of levels in [s]-specified random permutations. Also included are distributions associated with orthogonal polynomials with a symmetric matrix argument and the characterization of the Jeffreys prior.
Lie Groups
Preface.- Introduction.- Part I: Topological Groups.- Topological Groups.- Haar Measure.- Representations of Compact Groups.- Part II: Lie Groups and Algebras.- Lie Groups and Lie Algebras.- Lie Subgroups.- Homomorphism and Coverings.- Series Expansions.- Part III: Lie Algebras and Simply Connected Groups.- The Affine Group and Semi-direct Products.- Solvable and Nilpotent Groups.- Compact Groups.- Noncompact Semi-simple Groups.- Part IV: Transformation Groups.- Lie Group Actions.- Invariant Geometry.- Appendices.
Fractals in Engineering: Theoretical Aspects and Numerical Approximations
C. Alberini and S. Finzi Vita, A numerical approach to a nonlinear diffusion model for self-organised criticality phenomena.- M. Cefalo et al., Approximation of 3D Stokes flows in fractal domains.- S. Fragapane, ∞-Laplacian obstacle problems in fractal domains.- M. Gabbard, Discretization of the Koch Snowflake Domain with Boundary and Interior Energies.- M.V. Marchi, On the dimension of the Sierpinski gasket in l2.- U. Mosco and M.A. Vivaldi, On the external approximation of Sobolev spaces by M-convergence.- A. Rozanova-Pierrat, Generalization of Rellich-Kondrachov theorem and trace compacteness for fractal boundaries.
Applications of Wavelet Multiresolution Analysis
Fabio, M. et al., Approximate Solutions to Fractional Boundary Value Problems by Wavelet Decomposition Methods.- Calder籀n, L., Wavelet B-splines bases on the interval for solving boundary value problems.- La Mura, G. et al, Kalman-Wavelet combined Filtering.- Arouxet, M. et al., Using the Wavelet Transform for Time Series Analysis.- Muszkats, J. et al., Application of Wavelet Transform to Damage Detection in Brittle Materials via Energy and Entropy Evaluation of Acoustic Emission Signals.
Current Trends in Mathematical Analysis and Its Interdisciplinary Applications
This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers' understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book's main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.
Human Population Genomics
This textbook provides a concise introduction and useful overview of the field of human population genomics, making the highly technical and contemporary aspects more accessible to students and researchers from various fields. Over the past decade, there has been a deluge of genetic variation data from the entire genome of individuals from many populations. These data have allowed an unprecedented look at human history and how natural selection has impacted humans during this journey. Simultaneously, there have been increased efforts to determine how genetic variation affects complex traits in humans. Due to technological and methodological advances, progress has been made at determining the architecture of complex traits. Split in three parts, the book starts with the basics, followed by more advanced and current research. The first part provides an introduction to essential concepts in population genetics, which are relevant for any organism. The second part covers the genetics of complex traits in humans. The third part focuses on applying these techniques and concepts to genetic variation data to learn about demographic history and natural selection in humans. This new textbook aims to serve as a gateway to modern human population genetics research for those new to the field. It provides an indispensable resource for students, researchers and practitioners from disparate areas of expertise.
Analysis of Multivariate Data with SPSS
The book introduces the most important statistical methods for analyzing multivariate data sets. After reading the book, the reader (female, male) is able to autonomously carry out comprehensive statistical analyzes of data. The steps for finding a solution with SPSS are shown in the book. The individual procedures are explained using easy-to-understand examples to ensure learning success. Previous knowledge of statistics is helpful for reading the book, but not essential. The procedures presented are plausible even without prior basic knowledge of statistics. This book was written over a period of twenty semesters and benefited from the questions raised by the listeners in my lecture.
Mathematical Modelling and Biomechanics of the Brain
1. Introduction.- 2. Brief Review of Continuum Mechanics Theories.- 3. Mechanics of Hydrocephalus.- 4. Modeling Traumatic Brain Injuries, Aneurysms, and Strokes.- 5. Models of Tumor Growth.- 6. Concluding Remarks.
Probability and Random Processes with One Thousand Exercises in Probability
Probability and Random Processes begins with the basic ideas common to most undergraduate courses in mathematics, statistics, and science. It ends with material usually found at graduate level, for example, Markov processes, (including Markov chain Monte Carlo), martingales, queues, diffusions, (including stochastic calculus with It繫's formula), renewals, stationary processes (including the ergodic theorem), and option pricing in mathematical finance using the Black-Scholes formula. Further, in this new revised fourth edition, there are sections on coupling from the past, L矇vy processes, self-similarity and stability, time changes, and the holding-time/jump-chain construction of continuous-time Markov chains. Finally, the number of exercises and problems has been increased by around 300 to a total of about 1317, and many of the existing exercises have been refreshed by additional parts. The solutions to these exercises and problems can be found in the companion volume, One Thousand Exercises in Probability, third edition. One Thousand Exercises in Probability, third edition is a revised, updated, and greatly expanded version of previous edition of 2001. The 1300+ exercises contained within are not merely drill problems, but have been chosen to illustrate the concepts, illuminate the subject, and both inform and entertain the reader. A broad range of subjects is covered, including elementary aspects of probability and random variables, sampling, generating functions, Markov chains, convergence, stationary processes, renewals, queues, martingales, diffusions, L矇vy processes, stability and self-similarity, time changes, and stochastic calculus including option pricing via the Black-Scholes model of mathematical finance.
Active Particles, Volume 2
Kinetic and moment models for cell motion in fiber structures.- Kinetic models for pattern formation in animal aggregations: a symmetry and bifurcation approach.- Aggregation-diffusion equations: dynamics, asymptotics, and singular limits.- High-resolution positivity and asymptotic preserving Numerical methods for chemotaxis and related models.- Control strategies for the dynamics of large particle systems.- Kinetic equations and self-organized band formations.- Singular Cucker-Smale dynamics.- A stochastic-statistical residential burglary model with finite size effects.
Potential Theory on Sierpiński Carpets
- Introduction. - Harmonic Functions on Sierpiński Carpets. - Uniformization of Sierpiński Carpets by Square Carpets.
Topics in Uniform Approximation of Continuous Functions
This book presents the evolution of uniform approximations of continuous functions. Starting from the simple case of a real continuous function defined on a closed real interval, i.e., the Weierstrass approximation theorems, it proceeds up to the abstract case of approximation theorems in a locally convex lattice of (M) type. The most important generalizations of Weierstrass' theorems obtained by Korovkin, Bohman, Stone, Bishop, and Von Neumann are also included. In turn, the book presents the approximation of continuous functions defined on a locally compact space (the functions from a weighted space) and that of continuous differentiable functions defined on 癒n. In closing, it highlights selected approximation theorems in locally convex lattices of (M) type.The book is intended for advanced and graduate students of mathematics, and can also serve as a resource for researchers in the field of the theory of functions.
Determining Sample Size and Power in Research StudiesA Manual for Researchers
This book addresses sample size and power in the context of research, offering valuable insights for graduate and doctoral students as well as researchers in any discipline where data is generated to investigate research questions. It explains how to enhance the authenticity of research by estimating the sample size and reporting the power of the tests used. Further, it discusses the issue of sample size determination in survey studies as well as in hypothesis testing experiments so that readers can grasp the concept of statistical errors, minimum detectable difference, effect size, one-tail and two-tail tests and the power of the test. The book also highlights the importance of fixing these boundary conditions in enhancing the authenticity of research findings and improving the chances of research papers being accepted by respected journals. Further, it explores the significance of sample size by showing the power achieved in selected doctoral studies. Procedure has been discussed to fix power in the hypothesis testing experiment. One should usually have power at least 0.8 in the study because having power less than this will have the issue of practical significance of findings. If the power in any study is less than 0.5 then it would be better to test the hypothesis by tossing a coin instead of organizing the experiment. It also discusses determining sample size and power using the freeware G*Power software, based on twenty-one examples using different analyses, like t-test, parametric and non-parametric correlations, multivariate regression, logistic regression, independent and repeated measures ANOVA, mixed design, MANOVA and chi-square.
Primer for Data Analytics and Graduate Study in Statistics
This book is specially designed to refresh and elevate the level of understanding of the foundational background in probability and distributional theory required to be successful in a graduate-level statistics program. Advanced undergraduate students and introductory graduate students from a variety of quantitative backgrounds will benefit from the transitional bridge that this volume offers, from a more generalized study of undergraduate mathematics and statistics to the career-focused, applied education at the graduate level. In particular, it focuses on growing fields that will be of potential interest to future M.S. and Ph.D. students, as well as advanced undergraduates heading directly into the workplace: data analytics, statistics and biostatistics, and related areas.
