One Thousand Exercises in ProbabilityThird Edition
This 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. The text is intended to serve students as a companion for elementary, intermediate, and advanced courses in probability, random processes and operations research. It will also be useful for anyone needing a source for large numbers of problems and questions in these fields. In particular, this book acts as a companion to the authors' volume, Probability and Random Processes, fourth edition (OUP 2020).
Biomathematik
Auf der Basis von Differentialgleichungen, Spieltheorie und Wahrscheinlichkeitsrechnung behandelt der Autor mathematische Modelle zu Stoffwechselvorg瓣ngen, Abbauprozessen bei Medikamenten, Vererbung unter Selektionsdruck, Infektionsausbreitung sowie zur Virulenz von Bakterien, Parasiten und Viren. Hierbei werden die Formeln l羹ckenlos und leicht verst瓣ndlich hergeleitet, wobei zahlreiche Graphiken die Erl瓣uterungen veranschaulichen. Die ben繹tigten mathematischen Grundkenntnisse sind im Anhang zusammengestellt. Damit ist der Text f羹r Studierende der Biologie, Medizin oder Umweltwissenschaften ab den ersten Semestern geeignet. Ebenso ist er Mathematikern, Physikern und Ingenieuren zu empfehlen, die sich in die Modellierung biologischer Prozesse einarbeiten wollen.
Direct and Inverse Sturm-Liouville Problems
Introduction.- Preliminaries on Sturm-Liouville equations.- Finite interval.- Half-line.- Quantum scattering problem on the half-line.- Scattering problem on the line.- Inverse scattering transform method.- Main transmutation operators.- Series representations.- Series representations for the Jost solution.- Sturm-Liouville problems on finite intervals.- Spectral problems on infinite intervals.- The inverse problem on a finite interval.- Solving the inverse problem on a half-line.- Inverse quantum scattering on the half-line.- Inverse scattering on the line.
What Is Random?
We all know what randomness is. Or do we? Randomness turns out to be one of those concepts that works just fine on an everyday level, but becomes muddled upon close inspection. People familiar with quantum indeterminacy tell us that order is an illusion and that the world is fundamentally random. Yet these same people also say that randomness is an illusion: The appearance of randomness is only a sign of our ignorance and inability to detect the pattern. By applying mathematical thinking, mathematician Edward Beltrami removes much of the vagueness that encumbers the concept of randomness. You will discover how to quantify what would otherwise remain elusive. As the book progresses, you will see how mathematics provides a framework for unifying how chance is interpreted across diverse disciplines. Communication engineering, computer science, philosophy, physics, and psychology join mathematics in the discourse to illuminate different facets of the same idea. Thisbook will provoke, entertain, and inform by challenging your ideas about randomness, providing different interpretations of what this concept means, and showing how order and randomness are really two sides of the same mysterious coin. This second edition brings the question of randomness into the twenty-first century, adding compelling new topics such as quantum uncertainty, cognitive illusions caused by chance, Poisson processes, and Bayesian probability. An expanded technical notes section offers deeper explorations of a variety of mathematical concepts. On the first edition: I strongly recommend [What is Random?] to all who are interested in science and would like to see how the ideas of both theoretical mathematics and statistics have been observed and used in real life throughout history. The American Statistician
Numerische MethodenEin Lehr- Und ?bungsbuch
Die Mathematik ist in allen Bereichen der modernen Gesellschaft ein wichtiges Hilfsmittel, um bei der L繹sung der vielf瓣ltigen Probleme mit zu wirken, insbesondere in Technik, Naturwissenschaften und ?konomie. Die Mitwirkung mathematischer Methoden bei der L繹sung praktischer Aufgaben in diesen Bereichen vollzieht sich in folgenden Schritten: Pr瓣zise Formulierung des Problems: die Aufgabenstellung muss klar erkennbar werden. Es ist kenntlich zu machen, welche Schwerpunkte zu setzen sind. Erarbeitung eines mathematischen Modells des Problems: aus der technischen, 繹konomischen oder sonstigen Aufgabenstellung ist ein f羹r die mathematische Behandlung geeignetes Modell zu entwickeln und einer mathematischen Behandlung zug瓣nglich zu machen. Numerische Berechnung der L繹sung: es sind geeignete Algorithmen und die erforderlichen Rechenhilfsmittel auszuw瓣hlen. Es sind Anforderungen an den numerischen Algorithmus bez羹glich Rechenzeit und Rechengenauigkeit zu formulieren, sowie Absch瓣tzungen der zu erwartenden Rechenfehler durchzuf羹hren. Auswertung der erzielten Resultate: Es ist zu entscheiden, ob eine ausreichende L繹sung des praktischen Problems erzielt worden ist oder ob eine Verbesserung des mathematischen Modells erfolgen muss.
Quantitative Methods for Investigating Infectious Disease Outbreaks
This book provides a systematic treatment of the mathematical underpinnings of work in the theory of outbreak dynamics and their control, covering balanced perspectives between theory and practice including new material on contemporary topics in the field of infectious disease modelling. Specifically, it presents a unified mathematical framework linked to the distribution theory of non-negative random variables; the many examples used in the text, are introduced and discussed in light of theoretical perspectives. The book is organized into 9 chapters: The first motivates the presentation of the material on subsequent chapters; Chapter 2-3 provides a review of basic concepts of probability and statistical models for the distributions of continuous lifetime data and the distributions of random counts and counting processes, which are linked to phenomenological models. Chapters 4 focuses on dynamic behaviors of a disease outbreak during the initial phase while Chapters 5-6 broadly cover compartment models to investigate the consequences of epidemics as the outbreak moves beyond the initial phase. Chapter 7 provides a transition between mostly theoretical topics in earlier chapters and Chapters 8 and 9 where the focus is on the data generating processes and statistical issues of fitting models to data as well as specific mathematical epidemic modeling applications, respectively. This book is aimed at a wide audience ranging from graduate students to established scientists from quantitatively-oriented fields of epidemiology, mathematics and statistics. The numerous examples and illustrations make understanding of the mathematics of disease transmission and control accessible. Furthermore, the examples and exercises, make the book suitable for motivated students in applied mathematics, either through a lecture course, or through self-study. This text could be used in graduate schools or special summer schools covering research problems in mathematical biology.
Integral Inequalities on Time Scales
This book is devoted to recent developments of linear and nonlinear integral inequalities on time scales. The book is intended for the use in the field of dynamic calculus on time scales, dynamic equation and integral equations on time scales. It is also suitable for graduate courses in the above fields. The book is designed for those who have mathematical background on time scales calculus.
Modern Risk Quantification in Complex Projects
Project practitioners and decision makers complain that both parametric and Monte Carlo methods fail to produce accurate project duration and cost contingencies in the majority of cases. Apparently, these methods have unacceptably high systematic errors as they miss out critically important components of project risk exposure. In the case of complex projects, the components associated with structural and delivery complexity are often overlooked. Modern Risk Quantification in Complex Projects: Non-linear Monte Carlo and System Dynamics Methodologies zeroes in on the most crucial but systematically overlooked characteristics of complex projects. Any mismatches between two fundamental interacting subsystems - a project structure subsystem and a project delivery subsystem - result in non-linear interactions of project risks. Three kinds of the interactions are distinguished - internal risk amplifications stemming from long-term ('chronic') project system issues, knock-on interactions, and risk compounding. Affinities of interacting risks compose dynamic risk patterns supported by a project system. A new methodology to factor the patterns into Monte Carlo modelling referred to as "non-linear Monte Carlo schedule and cost risk analysis" (N-SCRA) is developed and demonstrated. It is capable of forecasting project outcomes with high accuracy even in the case of most complex and difficult projects, including notorious projects-outliers, and it has a much lower rate of systematic error. In this book, the power of project system dynamics is uncovered. It can be adopted as an accurate risk quantification methodology in complex projects, and the results produced by the system dynamics and the non-linear Monte Carlo methodologies are well-aligned. All built Monte Carlo and system dynamics models are available on the book's companion website.
The Projected Subgradient Algorithm in Convex Optimization
This focused monograph presents a study of subgradient algorithms for constrained minimization problems in a Hilbert space. The book is of interest for experts in applications of optimization to engineering and economics. The goal is to obtain a good approximate solution of the problem in the presence of computational errors. The discussion takes into consideration the fact that for every algorithm its iteration consists of several steps and that computational errors for different steps are different, in general. The book is especially useful for the reader because it contains solutions to a number of difficult and interesting problems in the numerical optimization. The subgradient projection algorithm is one of the most important tools in optimization theory and its applications. An optimization problem is described by an objective function and a set of feasible points. For this algorithm each iteration consists of two steps. The first step requires a calculation of a subgradient of the objective function; the second requires a calculation of a projection on the feasible set. The computational errors in each of these two steps are different. This book shows that the algorithm discussed, generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. Moreover, if computational errors for the two steps of the algorithm are known, one discovers an approximate solution and how many iterations one needs for this. In addition to their mathematical interest, the generalizations considered in this book have a significant practical meaning.
Capture-Recapture: Parameter Estimation for Open Animal Populations
This comprehensive book, rich with applications, offers a quantitative framework for the analysis of the various capture-recapture models for open animal populations, while also addressing associated computational methods. The state of our wildlife populations provides a litmus test for the state of our environment, especially in light of global warming and the increasing pollution of our land, seas, and air. In addition to monitoring our food resources such as fisheries, we need to protect endangered species from the effects of human activities (e.g. rhinos, whales, or encroachments on the habitat of orangutans). Pests must be be controlled, whether insects or viruses, and we need to cope with growing feral populations such as opossums, rabbits, and pigs. Accordingly, we need to obtain information about a given population's dynamics, concerning e.g. mortality, birth, growth, breeding, sex, and migration, and determine whether the respective population is increasing, static, or declining. There are many methods for obtaining population information, but the most useful (and most work-intensive) is generically known as "capture-recapture," where we mark or tag a representative sample of individuals from the population and follow that sample over time using recaptures, resightings, or dead recoveries. Marks can be natural, such as stripes, fin profiles, and even DNA; or artificial, such as spots on insects. Attached tags can, for example, be simple bands or streamers, or more sophisticated variants such as radio and sonic transmitters. To estimate population parameters, sophisticated and complex mathematical models have been devised on the basis of recapture information and computer packages. This book addresses the analysis of such models. It is primarily intended for ecologists and wildlife managers who wish to apply the methods to the types of problems discussed above, though it will also benefit researchers and graduate students in ecology. Familiarity with basic statistical concepts is essential.
Linear Models and Regression with R: An Integrated Approach
Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features: Applications with data sets, and their implementation in R, Comprehensive coverage of regression diagnostics and model building, Coverage of other special topics such as collinearity, stochastic and inequality constraints, misspecified models, etc., Use of simple statistical ideas and interpretations to explain advanced concepts, and simpler proofs of many known results, Discussion of models covering mixed-effects/variance components, spatial, and time series data with partially unknown dispersion matrix, Thorough treatment of the singular linear model, including the case of multivariate response, Insight into updates in the linear model, and their connection with diagnostics, design, variable selection, Kalman filter, etc., Extensive discussion of the foundations of linear inference, along with linear alternatives to least squares.
Type-2 Fuzzy Decision-Making Theories, Methodologies and Applications
This book integrates the type-2 fuzzy sets and multiple criteria decision making analysis in recent years and offers an authoritative treatise on the essential topics, both at the theoretical and applied end. In this book, some basic theory, type-2 fuzzy sets, methodology, algorithms, are introduced and then some compelling case studies in decision problems are covered in depth. The authors offer an authoritative treatise on the essential topics, both at the theoretical and applied end; In a systematic and logically organized way, the book exposes the reader to the essentials of the theory of type-2 fuzzy sets, methodology, algorithms, and their applications. Numerous techniques of decision making are carefully generalized by bringing the ideas of type-2 fuzzy sets; this concerns well-known methods including TOPSIS, Analytical Network Process, TODIM, and VIKOR. This book exposes the readers to the essentials of the theory of type-2 fuzzy sets, methodology, algorithms, and their applications.
Calculus for Scientists and Engineers
Discusses basic topics of calculus and its application to real-world problemsProvides special emphasis on applications without compromising rigorous analysis Features plenty of solved examples in order to clarify various techniques Uses MATLAB for solving many problems in calculus
Testing and Inspection Using Acceptance Sampling Plans
1 Introduction and genesis1.1 Introduction1.2 History1.3 Background: acceptance sampling1.4 Background: reliability theory1.5 Censorship and truncation1.6 Selecting a life distribution1.7 Applications2 Some life distributions2.1 Introduction2.2 Birnbaum-Saunders distribution2.3 Burr type XII distribution2.4 Gamma distribution2.5 Generalized Birnbaum-Saunders distribution2.6 Generalized exponential distribution2.7 Generalized Rayleigh distribution2.8 Inverse Gaussian distribution2.9 Inverse Rayleigh2.10 Log-logistic distribution2.11 Pareto distribution2.12 Lognormal distribution3 Acceptance sampling from truncated life tests3.1 Introduction3.2 Plans based on one point of the OC curve3.2.1 Simple acceptance sampling plans3.2.2 Double acceptance sampling plans3.2.3 Acceptance sampling plans by groups3.2.4 Reliable economical acceptance sampling plans3.3 Plans based on two points of the OC curve3.3.1 Simple acceptance sampling plans3.3.2 Double acceptance sampling plans3.3.3 Two stage acceptance sampling plans using groups3.3.4 Acceptance sampling plans by groups3.3.5 Reliable economical acceptance sampling plans3.3.6 Reliable economical group acceptance sampling plans4 Acceptance sampling based on life tests from some specific distributions4.1 Introduction4.2 Birnbaum-Saunders distribution4.3 Burr type XII distribution4.4 Gamma distribution34.5 Generalized Birnbaum-Saunders distribution4.6 Generalized exponential distribution4.7 Generalized Rayleigh distribution4.8 Inverse Gaussian distribution4.9 Inverse Rayleigh4.10 Log-logistic distribution4.11 Pareto distribution4.12 Lognormal distribution5 Some group acceptance sampling based on life tests from specific distributions5.1 Introduction5.2 Birnbaum-Saunders distribution5.3 Burr type XII distribution5.4 Gamma distribution5.5 Generalized Birnbaum-Saunders distribution5.6 Generalized exponential distribution5.7 Generalized Rayleigh distribution5.8 Inverse Gaussian distribution5.9 Inverse Rayleigh5.10 Log-logistic distribution5.11 Pareto distribution5.12 Lognormal distribution6 Skip Sampling Plans6.1 Introduction6.2 Skip-V plans6.3 Skip-R Plans6.4 Design of Skip-R Plans6.5 Economic Skip-R Plans6.6 Skip plan using reference plans7 Sampling Plans using Process Capability index (PCI)7.1 Introduction7.2 Repetitive sampling using PCI7.3 Resubmitted sampling PCI7.4 Mixed plan using PCI8 Miscellaneous acceptance sampling plans8.1 Bayesian Sampling plan8.2 sampling plan using loss function8.3 Sampling Plans using EWMA8.4 Hybrid Plan9 Sampling plan for Big Data9.1 Introduction of Big Data9.2 Application of Big Data in quality control9.3 Inspection for Big Data49.4 Sampling plans for Big Data9.5 Application of sampling plan for Big Data
Towards Mathematics, Computers and Environment: A Disasters Perspective
With relevant, timely topics, this book gathers carefully selected, peer-reviewed scientific works and offers a glimpse of the state-of-the-art in disaster prevention research, with an emphasis on challenges in Latin America. Topics include studies on surface frost, an extreme meteorological event that occasionally affects parts of Argentina, Bolivia, Peru, and southern Brazil, with serious impacts on local economies; near-ground pollution concentration, which affects many industrial, overpopulated cities within Latin America; disaster risk reduction and management, which are represented by mathematical models designed to assess the potential impact of failures in complex networks; and the intricate dynamics of international armed conflicts, which can be modeled with the help of stochastic theory. The book offers a valuable resource for professors, researchers, and students from both mathematical and environmental sciences, civil defense coordinators, policymakers, and stakeholders.
Probability and Analysis in Interacting Physical Systems
This Festschrift on the occasion of the 75th birthday of S.R.S. Varadhan, one of the most influential researchers in probability of the last fifty years, grew out of a workshop held at the Technical University of Berlin, 15-19 August, 2016. This volume contains ten research articles authored by several of Varadhan's former PhD students or close collaborators. The topics of the contributions are more or less closely linked with some of Varadhan's deepest interests over the decades: large deviations, Markov processes, interacting particle systems, motions in random media and homogenization, reaction-diffusion equations, and directed last-passage percolation. The articles present original research on some of the most discussed current questions at the boundary between analysis and probability, with an impact on understanding phenomena in physics. This collection will be of great value to researchers with an interest in models of probability-based statistical mechanics.
Quantum Correlations
Preliminaries.- The Resource Theory of Entanglement.- Generalized Quantum Correlations in Discrete Variable Systems.- Generalized Quantum Correlations in Continuous Variable Systems.- Conclusion and Outlook.
Applied Civil Engineering Risk Analysis
This updated edition retains its introduction to applied fundamental statistics, probability, reliability, and decision theory as these pertain to problems in Civil Engineering. The new edition adds an expanded treatment of systems reliability, Bayesian methods, and spatial variabililty, along with additional example problems throughout. The book provides readers with the tools needed to determine the probability of failure, and when multiplied by the consequences of failure, illustrates how to assess the risk of civil engineering problems. Presenting methods for quantifying uncertainty that exists in engineering analysis and design, with an emphasis on fostering more accurate analysis and design, the text is ideal for students and practitioners of a range of civil engineering disciplines. Expands on the class-tested pedagogy from the first edition with more material and more examples;Broadens understanding with simulations coded both in Matlab and inR; Features new chapters on spatial variability and Bayesian methods;Emphasizes techniques for estimating the influence of uncertainty on the probability of failure
Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics
The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.
Cure Models
The first book in the last 25 years that provides a comprehensive and systematic introduction to the basics of modern cure models, including estimation, inference, software. Statistical researchers, graduate students, and practitioners in other disciplines will have a thorough review of modern cure model methodology.
An Introduction to Bayesian Biostatistics
With a focus on incorporating sensible prior distributions and discussions on many recent developments in Bayesian methodologies, Bayesian Thinking in Biostatistics considers statistical issues in biomedical research.
Principles of Uncertainty
Like the De Groot winning first edition, the second edition of Principles of Uncertainty is an accessible, comprehensive guide to the theory of Bayesian Statistics written in an appealing, inviting style, and packed with interesting examples.
Analysis of Operators on Function SpacesThe Serguei Shimorin Memorial Volume
This book contains both expository articles and original research in the areas of function theory and operator theory. The contributions include extended versions of some of the lectures by invited speakers at the conference in honor of the memory of Serguei Shimorin at the Mittag-Leffler Institute in the summer of 2018. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables. The expository articles reflecting the current status of several well-established and very dynamical areas of research will be accessible and useful to advanced graduate students and young researchers in pure and applied mathematics, and also to engineers and physicists using complex analysis methods in their investigations.
Uncertain Renewal Processes
Probability Theory.- Stochastic Renewal Processes.- Uncertainty Theory.- Uncertain Renewal Processes.- Chance Theory.- Uncertain Random Renewal Processes.
Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the EnvironmentSelected Wo
This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; aspects of blood circulation modeling; multidimensional modeling approach via time-frequency analysis and Edge Based Compartmental Model; and more. This book builds upon the tradition of the previous BIOMAT volumes to foster interdisciplinary research in mathematical biology for students, researchers, and professionals.Held every year since 2001, the BIOMAT International Symposium gathers together, in a single conference, researchers from Mathematics, Physics, Biology, and affine fields to promote the interdisciplinary exchange of results, ideas and techniques, promotingtruly international cooperation for problem discussion. The 2019 edition of BIOMAT International Symposium received contributions by authors from 14 countries: Brazil, Cameroon, Canada, Colombia, Czech Republic, Finland, Hungary, India, Italy, Russia, Senegal, Serbia, United Kingdom and the USA. Selected papers presented at the 2017 and 2018 editions of this Symposium were also published by Springer, in the volumes "Trends in Biomathematics: Modeling, Optimization and Computational Problems" (978-3-319-91091-8) and "Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics" (978-3-030-23432-4).
Diffusion in Random FieldsApplications to Transport in Groundwater
This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling.Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems.
Descriptive Topology and Functional Analysis IIIn Honour of Manuel L籀pez-Pellicer Mathematical Work, Elche, Spain, June 7-8, 2018
1 J. C. Ferrando, On the mathematical work of professor Manuel L籀pez-Pellicer.- 2 G. Acosta and M. Sanchis, A Note On Nonautonomous Discrete Dynamical Systems.- 3 A. A. Albanese et al., Linear operators on the (LB)-sequence spaces ces(p-),1
Solved Exercises in Fractional Calculus
This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.
Applied Spatial Statistics and Econometrics
This textbook is a comprehensive introduction to applied spatial data analysis, using R. Each chapter walks the reader through a different method, explaining how to interpret the results and what conclusions can be drawn.
Open Quantum SystemsA Mathematical Perspective
Introduction to Classical and Quantum Markov Semigroups.- Introduction to Non-Markovian Evolution of n-Level Quantum Systems.- Aspects of Micro-local Analysis and Geometry in the Study of L矇vy-type Generators.- Lectures on Entropy. I: Information-Theoretic Notions.
Curvature Measures of Singular Sets
- Background from Geometric Measure Theory. - Background from Convex Geometry. - Background from Differential Geometry and Topology. - Sets with Positive Reach. - Unions of Sets with Positive Reach. - Integral Geometric Formulae. - Approximation of Curvatures. - Characterization Theorems. - Extensions of Curvature Measures to Larger set Classes. - Fractal Versions of Curvatures.
Integral Methods in Science and EngineeringAnalytic Treatment and Numerical Approximations
This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysisBoundary-domain integral equationsViscoplastic fluid flowStationary wavesInterior Neumann shape optimizationSelf-configuring neural networksThis collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can inspire researchers from various areas of operator theory and PDEs to explore new research directions in their fields. This monograph is the natural continuation of the book: Spectral Theory on the S-Spectrum for Quaternionic Operators by Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey (Operator Theory: Advances and Applications, Vol. 270).
A Primer of Permutation Statistical Methods
The primary purpose of this textbook is to introduce the reader to a wide variety of elementary permutation statistical methods. Permutation methods are optimal for small data sets and non-random samples, and are free of distributional assumptions. The book follows the conventional structure of most introductory books on statistical methods, and features chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, one-way fully-randomized analysis of variance, one-way randomized-blocks analysis of variance, simple regression and correlation, and the analysis of contingency tables. In addition, it introduces and describes a comparatively new permutation-based, chance-corrected measure of effect size. Because permutation tests and measures are distribution-free, do not assume normality, and do not rely on squared deviations among sample values, they are currently being applied in a wide variety of disciplines. This book presents permutation alternatives to existing classical statistics, and is intended as a textbook for undergraduate statistics courses or graduate courses in the natural, social, and physical sciences, while assuming only an elementary grasp of statistics.
Linear Systems, Signal Processing and Hypercomplex Analysis
This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.
Systemics of Incompleteness and Quasi-Systems
Presents outstanding contributions from the Italian Systems Society's Seventh National Conference on Systems ScienceExplores cases and presents conceptual approaches for systemics of incompleteness and quasi-systemsEditors are established and well respected in the field of systems science
Yield Curves and Forward Curves for Diffusion Models of Short Rates
This book is dedicated to the study of the term structures of the yields of zero-coupon bonds. The methods it describes differ from those usually found in the literature in that the time variable is not the term to maturity but the interest rate duration, or another convenient non-linear transformation of terms. This makes it possible to consider yield curves not only for a limited interval of term values, but also for the entire positive semiaxis of terms. The main focus is the comparative analysis of yield curves and forward curves and the analytical study of their features. Generalizations of yield term structures are studied where the dimension of the state space of the financial market is increased. In cases where the analytical approach is too cumbersome, or impossible, numerical techniques are used. This book will be of interest to financial analysts, financial market researchers, graduate students and PhD students.
Models for Tropical Climate DynamicsWaves, Clouds, and Precipitation
This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.
Approximation and Optimization
This book focuses on the development of approximation-related algorithms and their relevant applications. Individual contributions are written by leading experts and reflect emerging directions and connections in data approximation and optimization. Chapters discuss state of the art topics with highly relevant applications throughout science, engineering, technology and social sciences. Academics, researchers, data science practitioners, business analysts, social sciences investigators and graduate students will find the number of illustrations, applications, and examples provided useful. This volume is based on the conference Approximation and Optimization: Algorithms, Complexity, and Applications, which was held in the National and Kapodistrian University of Athens, Greece, June 29-30, 2017. The mix of survey and research content includes topics in approximations to discrete noisy data; binary sequences; design of networks and energy systems; fuzzy control; large scale optimization; noisy data; data-dependent approximation; networked control systems; machine learning; optimal design; no free lunch theorem; non-linearly constrained optimization; spectroscopy.
Hermitian AnalysisFrom Fourier Series to Cauchy-Riemann Geometry
This textbook provides a coherent, integrated look at various topics from undergraduate analysis. It begins with Fourier series, continues with Hilbert spaces, discusses the Fourier transform on the real line, and then turns to the heart of the book, geometric considerations. This chapter includes complex differential forms, geometric inequalities from one and several complex variables, and includes some of the author's original results. The concept of orthogonality weaves the material into a coherent whole. This textbook will be a useful resource for upper-undergraduate students who intend to continue with mathematics, graduate students interested in analysis, and researchers interested in some basic aspects of Cauchy-Riemann (CR) geometry. The inclusion of several hundred exercises makes this book suitable for a capstone undergraduate Honors class.​This second edition contains a significant amount of new material, including a new chapter dedicated to the CR geometry of the unit sphere. This chapter builds upon the first edition by presenting recent results about groups associated with CR sphere maps. From reviews of the first edition: The present book developed from the teaching experiences of the author in several honors courses. .... All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a first-year graduate course on the subject. .... The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study. Fabio Nicola, Politecnico di Torino, Mathematical ReviewsD'Angelo has written an eminently readable book, including excellent explanations of pretty nasty stuff for even the more gifted upper division players .... It certainly succeeds in hooking the present browser: I like this booka great deal. Michael Berg, Loyola Marymount University, Mathematical Association of America
Many Agent Games in Socio-Economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security
There has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games. Exhibiting various real world problems involving major and minor agents, this book presents a systematic continuous-space approximation approach for mean-field interacting agents models and mean-field games models. After describing Markov-chain methodology and a modeling of mean-field interacting systems, the text presents various structural conditions on the chain to yield respective socio-economic models, focusing on migration models via binary interactions. The specific applications are wide-ranging - including inspection and corruption, cyber-security, counterterrorism, coalition building and network growth, minority games, and investment policies and optimal allocation - making this book relevant to a wide audience of applied mathematicians interested in operations research, computer science, national security, economics, and finance.
Post-flop Online PokerThe 4 Post-flop Fundamentals of Hand Reading, Continuation Bets, Poker Math and Exploiting Your Opponents
In this follow-up to Preflop Online Poker, Sky teaches you the fundamental post-flop skills you MUST learn to profit in online poker.The insanely useful strategies presented here are clear and concise and taught with many hand examples that demonstrate profitable poker play. Sky will quiz your understanding throughout the book, and he'll have you taking action on- and off-the-felt with 55 different actions steps.This isn't just a read-it-in-5-days-and-shelve-it poker book. This book is your new poker coach; teaching you strategies and expecting you to use them. Then when you're ready, repeating the process with the next valuable set of strategies.In Post-flop Online Poker, you will learn::: How to do the most important poker skill: Hand Reading. You'll then use this skill throughout the rest of the book to drive home each valuable strategy.:: How to make profitable bluff and value cbets utilizing all the information available to you.:: How to use poker math to make +EV decisions that rake your opponent's chips into your stack.:: How to defend against cbets profitably with check-raises, floats, probes and even donk bets.:: How to use crucial post-flop HUD statistics to exploit your database of hands on every opponent.:: Important mental game skills that you can develop as you work through the book and execute the profitable strategies within.Your next poker coach is right here in your hands. Post-flop Online Poker will help you build the necessary skills on your way to the ultimate destination of Poker Excellence.Don't wait.Get this book NOW and begin learning from your new poker
Introduction to Queueing Systems with Telecommunication Applications
The book is the extended and revised version of the 1st edition and is composed of two main parts: mathematical background and queueing systems with applications. The mathematical background is a self-containing introduction to the stochastic processes of the later studied queueing systems. It starts with a quick introduction to probability theory and stochastic processes and continues with chapters on Markov chains and regenerative processes. More recent advances of queueing systems are based on phase type distributions, Markov arrival processes and quasy birth death processes, which are introduced in the last chapter of the first part.The second part is devoted to queueing models and their applications. After the introduction of the basic Markovian (from M/M/1 to M/M/1//N) and non-Markovian (M/G/1, G/M/1) queueing systems, a chapter presents the analysis of queues with phase type distributions, Markov arrival processes (from PH/M/1 to MAP/PH/1/K). Thenext chapter presents the classical queueing network results and the rest of this part is devoted to the application examples. There are queueing models for bandwidth charing with different traffic classes, slotted multiplexers, media access protocols like Aloha and IEEE 802.11b, priority systems and retrial systems.An appendix supplements the technical content with Laplace and z transformation rules, Bessel functions and a list of notations. The book contains examples and exercises throughout and could be used for graduate students in engineering, mathematics and sciences.Reviews of first edition: "The organization of the book is such that queueing models are viewed as special cases of more general stochastic processes, such as birth-death or semi-Markov processes. ... this book is a valuable addition to the queuing literature and provides instructors with a viable alternative for a textbook to be used in a one- or two-semester course on queueing models, at the upper undergraduate or beginning graduate levels."Charles Knessl, SIAM Review, Vol. 56 (1), March, 2014
Einf羹hrung in Die Ergodentheorie
Dieses essential gibt eine kompakte Einf羹hrung in die Ergodentheorie, die Dynamische Systeme mit Methoden der Ma?theorie untersucht. Lesende lernen wundervolle Resultate von herausragenden Mathematikern des 20. Jahrhunderts kennen. Eine F羹lle von Beispielen Dynamischer Systeme mit invarianten und ergodischen Ma?en werden beschrieben. Zus瓣tzlich finden sich gro?artige Anwendungen der Ergodentheorie in der Zahlentheorie.
Introduction to Statistics
Learn statistics without fear! Build a solid foundation in data analysis. Be confident that you understand what your data are telling you and that you can explain the results to others! I'll help you intuitively understand statistics by using simple language and deemphasizing formulas.This guide starts with an overview of statistics and why it is so important. We proceed to essential statistical skills and knowledge about different types of data, relationships, and distributions. Then we move to using inferential statistics to expand human knowledge, how it fits into the scientific method, and how to design and critique experiments.Learn the fundamentals of statistics: Why is the field of statistics so vital in our data-driven society?Interpret graphs and summary statistics.Find relationships between different types of variables.Understand the properties of data distributions.Use measures of central tendency and variability.Interpret correlations and percentiles.Use probability distributions to calculate probabilities.Learn about the normal and binomial distributions in depth.Grasp the differences between descriptive and inferential statistics.Use data collection methodologies properly and understand sample size considerations.Design and critique scientific experiments-whether it's your own or another researcher's.Free access to downloadable datasets to follow along with the examples.
Analytical Methods in Statistics
Preface.- Y. G羹ney, J. Jurečkov獺 and O. Arslan, Averaged Autoregression Quantiles in Autoregressive Model.- J. Kalina and P. Vidnerov獺, Regression Neural Networks with a Highly Robust Loss Function.- H. L. Koul and P. Geng, Weighted Empirical Minimum Distance Estimators in Berkson Measurement Error Regression Models.- M. Maciak, M. Pesta and S. Vitali, Implied Volatility Surface Estimation via Quantile Regularization.- I. Mizera, A remark on the Grenander estimator.- U. Radojičic and K. Nordhausen, Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace.- P. Vidnerov獺, J. Kalina and Y. G羹ney, A Comparison of Robust Model Choice Criteria within a Metalearning Study.- S. Zwanzig and R. Ahmad, On Parameter Estimation for High Dimensional Errors-in-Variables Models.
