Corruption, Infrastructure Management and Public-Private Partnership
Public-Private Partnerships (PPP or 3Ps) allow the public sector to seek alternative funding and expertise from the private sector during procurement processes. Such partnerships, if executed with due diligence, often benefit the public immensely. Unfortunately, Public-Private Partnerships can be vulnerable to corruption. This book looks at what measures we can put in place to check corruption during procurement and what good governance strategies the public sector can adopt to improve the performance of 3Ps.The book applies mathematical models to analyze 3Ps. It uses game theory to study the interaction and dynamics between the stakeholders and suggests strategies to reduce corruption risks in various 3Ps stages. The authors explain through game theory-based simulation how governments can adopt a evaluating process at the start of each procurement to weed out undesirable private partners and why the government should take a more proactive approach.Using a methodological framework rooted in mathematical models to illustrate how we can combat institutional corruption, this book is a helpful reference for anyone interested in public policymaking and public infrastructure management.
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Statistical Testing with jamovi Health
FeaturesWorked examples from health settingsClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Applied Functional Analysis
This textbook offers a concise and thorough introduction to the topic of applied functional analysis. Targeted to graduate students of mathematics, it presents standard topics in a self-contained and accessible manner. Featuring approximately 300 problems sets to aid in understanding the content, this text serves as an ideal resource for independent study or as a textbook for classroom use. With its comprehensive coverage and reader-friendly approach, it is equally beneficial for both students and teachers seeking a detailed and in-depth understanding of the subject matter.
Near Extensions and Alignment of Data in R^n
Near Extensions and Alignment of Data in Rn Comprehensive resource illustrating the mathematical richness of Whitney Extension Problems, enabling readers to develop new insights, tools, and mathematical techniques Near Extensions and Alignment of Data in Rn demonstrates a range of hitherto unknown connections between current research problems in engineering, mathematics, and data science, exploring the mathematical richness of near Whitney Extension Problems, and presenting a new nexus of applied, pure and computational harmonic analysis, approximation theory, data science, and real algebraic geometry. For example, the book uncovers connections between near Whitney Extension Problems and the problem of alignment of data in Euclidean space, an area of considerable interest in computer vision. Written by a highly qualified author, Near Extensions and Alignment of Data in Rn includes information on: Areas of mathematics and statistics, such as harmonic analysis, functional analysis, and approximation theory, that have driven significant advances in the field Development of algorithms to enable the processing and analysis of huge amounts of data and data sets Why and how the mathematical underpinning of many current data science tools needs to be better developed to be useful New insights, potential tools, and mathematical techniques to solve problems in Whitney extensions, signal processing, shortest paths, clustering, computer vision, optimal transport, manifold learning, minimal energy, and equidistribution Providing comprehensive coverage of several subjects, Near Extensions and Alignment of Data in Rn is an essential resource for mathematicians, applied mathematicians, and engineers working on problems related to data science, signal processing, computer vision, manifold learning, and optimal transport.
Statistical Testing with jamovi Criminology
FeaturesWorked examples from CriminologyClearly written, without mathematical formulaeWell-structured, for beginners and intermediate readersComprehensive chapter on categorical analysis - not just 'Chi squared'Effect sizes and confidence intervalsClear explanation of factor analysisCovers MANOVA and logistic regressionCovers partial correlations, survival analysis and cluster analysisIntroduces Bayesian statisticsReproduces a well-received short chapter on making presentationsData sets and case studies on the website
Advanced Topics in Fractional Differential Equations
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers' understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts - Approaches the topic of fractional differential equations while employing fixed point theorems as tools - Presents novel results, which build upon previous literature and many years of research by the authors
Twisted Isospectrality, Homological Wideness, and Isometry
The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings).The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology.The main goal of the book is to present the construction of finitely many "twisted" Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds.The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and "class field theory" for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.
On the Synthesis of the Distribution amongst the Integers of the Prime Number Counting Function, pi(k), viewed as a Geometric Object
Academic Paper from the year 2023 in the subject Mathematics - Analysis, grade: 2.00, language: English, abstract: A method is devised in which the prime number counting function, pi(k) is viewed as having the properties of a staircase. The terminology appropriate to a staircase is used to describe the parts of the distribution amongst the integers. Strings of limited extent of consecutive numbers which may contain prime numbers are generated from an iterative equation which contains Gauss' prime number counting function. In honour of Gauss we call these strings of numbers, Gauss strings., and they are used in the construction of the staircase. Further, we show that the prime number counting function may be represented in number space by an infinite set of connected trapezia, the individual areas of which are numerically equal to the gap between the primes that are situated on two of the borders of any given trapezium.
A Topology of Mind
This volume covers many diverse topics related in varying degrees to mathematics in mind including the mathematical and topological structures of thought and communication. It examines mathematics in mind from the perspective of the spiral, cyclic and hyperlinked structures of the human mind in terms of its language, its thoughts and its various modes of communication in science, philosophy, literature and the arts including a chapter devoted to the spiral structure of the thought of Marshall McLuhan. In it, the authors examine the topological structures of hypertext, hyperlinking, and hypermedia made possible by the Internet and the hyperlinked structures that existed before its emergence. It also explores the cognitive origins of mathematical thinking of the human mind and its relation to the emergence of spoken language, and studies the emergence of mathematical notation and its impact on education. Topics addressed include: -The historical context of any topic that involves how mathematical thinking emerged, focusing on archaeological and philological evidence. - Connection between math cognition and symbolism, annotation and other semiotic processes. - Interrelationships between mathematical discovery and cultural processes, including technological systems that guide the thrust of cognitive and social evolution. - Whether mathematics is an innate faculty or forged in cultural-historical context- What, if any, structures are shared between mathematics and language
Roc Analysis for Classification and Prediction in Practice
This book will present a unified and up-to date introduction to ROC methodologies, covering both diagnosis (classification) and prediction. The book will emphasize the practical implementation of these methods using standard statistical software such as R and STATA.
Sparse Polynomial Optimization
Many applications, including computer vision, computer arithmetic, deep learning, entanglement in quantum information, graph theory and energy networks, can be successfully tackled within the framework of polynomial optimization, an emerging field with growing research efforts in the last two decades. One key advantage of these techniques is their ability to model a wide range of problems using optimization formulations. Polynomial optimization heavily relies on the moment-sums of squares (moment-SOS) approach proposed by Lasserre, which provides certificates for positive polynomials. On the practical side, however, there is 'no free lunch' and such optimization methods usually encompass severe scalability issues. Fortunately, for many applications, including the ones formerly mentioned, we can look at the problem in the eyes and exploit the inherent data structure arising from the cost and constraints describing the problem.This book presents several research efforts to resolve this scientific challenge with important computational implications. It provides the development of alternative optimization schemes that scale well in terms of computational complexity, at least in some identified class of problems. It also features a unified modeling framework to handle a wide range of applications involving both commutative and noncommutative variables, and to solve concretely large-scale instances. Readers will find a practical section dedicated to the use of available open-source software libraries.This interdisciplinary monograph is essential reading for students, researchers and professionals interested in solving optimization problems with polynomial input data.
Learning Pandas 2.0
Mastering Data Wrangling and Analysis for Modern Data Science"Learning Pandas 2.0" is an essential guide for anyone looking to harness the power of Python's premier data manipulation library. With this comprehensive resource, you will not only master core Pandas 2.0 concepts but also learn how to employ its advanced features to perform efficient data manipulation and analysis.Throughout the book, you will acquire a deep understanding of Pandas 2.0's data structures, indexing, and selection techniques. Gain expertise in loading, storing, and cleaning data from various file formats and sources, ensuring data integrity and consistency. As you progress, you will delve into advanced data transformation, merging, and aggregation methods to extract meaningful insights and generate insightful reports."Learning Pandas 2.0" also covers specialized data processing needs like time series data, DateTime operations, and geospatial analysis. Furthermore, this book demonstrates how to integrate Pandas 2.0 with machine learning libraries like Scikit-learn, TensorFlow, and PyTorch for predictive analytics. This will empower you to build powerful data-driven models to solve complex problems and enhance your decision-making capabilities.What sets "Learning Pandas 2.0" apart from other books is its focus on numerous practical examples, allowing you to apply your newly acquired skills to tricky scenarios. By the end of this book, you will have the confidence and knowledge needed to perform efficient and robust data analysis using Pandas 2.0, setting you on the path to becoming a data analysis powerhouse.Key LearningsMaster core Pandas 2.0 concepts, including data structures, indexing, and selection for efficient data manipulation.Load, store, and clean data from various file formats and sources, ensuring data integrity and consistency.Perform advanced data transformation, merging, and aggregation techniques for insightful analysis and reporting.Harness time series data, DateTime operations, and geospatial analysis for specialized data processing needs.Visualize data effectively using Seaborn, Plotly, and advanced geospatial visualization tools.Integrate Pandas 2.0 with machine learning libraries like Scikit-learn, TensorFlow, and PyTorch for predictive analytics.Table of ContentIntroduction to Pandas 2.0Data Read, Storage, and File FormatsIndexing and Selecting DataData Manipulation and TransformationTime Series and DateTime OperationsPerformance Optimization and ScalingMachine Learning with Pandas 2.0Text Data and Natural Language ProcessingGeospatial Data AnalysisAudienceWhether you're a seasoned data professional or just starting your journey in data science, "Learning Pandas 2.0" is the perfect resource to help you harness the power of this cutting-edge library. This book is an absolute resource for implementing Pandas 2.0 in every possible data manipulation and analysis project.
Counterexamples in Operator Theory
This text is the first of its kind exclusively devoted to counterexamples in operator theory and includes over 500 problems on bounded and unbounded linear operators in Hilbert spaces. This volume is geared towards graduate students studying operator theory, and the author has designated the difficulty level for each counterexample, indicating which ones are also suitable for advanced undergraduate students.The first half of the book focuses on bounded linear operators, including counterexamples in the areas of operator topologies, matrices of bounded operators, square roots, the spectrum, operator exponentials, and non-normal operators. The second part of the book is devoted to unbounded linear operators in areas such as closedness and closability, self-adjointness, normality, commutativity, and the spectrum, concluding with a chapter that features some open problems. Chapters begin with a brief "Basics" section for the readers' reference, and many of the counterexamples included are the author's original work. Counterexamples in Operator Theory can be used by students in graduate courses on operator theory and advanced matrix theory. Previous coursework in advanced linear algebra, operator theory, and functional analysis is assumed. Researchers, quantum physicists, and undergraduate students studying functional analysis and operator theory will also find this book to be a useful reference.
Applied Probability
This textbook presents the basics of probability and statistical estimation, with a view to applications. The didactic presentation follows a path of increasing complexity with a constant concern for pedagogy, from the most classical formulas of probability theory to the asymptotics of independent random sequences and an introduction to inferential statistics. The necessary basics on measure theory are included to ensure the book is self-contained. Illustrations are provided from many applied fields, including information theory and reliability theory. Numerous examples and exercises in each chapter, all with solutions, add to the main content of the book.Written in an accessible yet rigorous style, the book is addressed to advanced undergraduate students in mathematics and graduate students in applied mathematics and statistics. It will also appeal to students and researchers in other disciplines, including computer science, engineering, biology, physics and economics, who are interested in a pragmatic introduction to the probability modeling of random phenomena.
Spatial Data Science
Spatial Data Science introduces fundamental aspects of spatial data that every data scientist should know before they start working with spatial data. These aspects include how geometries are represented, coordinate reference systems (projections, datums), the fact that the Earth is round and its consequences for analysis, and how attributes of geometries can relate to geometries. In the second part of the book, these concepts are illustrated with data science examples using the R language. In the third part, statistical modelling approaches are demonstrated using real world data examples. After reading this book, the reader will be well equipped to avoid a number of major spatial data analysis errors.The book gives a detailed explanation of the core spatial software packages for R: sf for simple feature access, and stars for raster and vector data cubes - array data with spatial and temporal dimensions. It also shows how geometrical operations change when going from a flat space to the surface of a sphere, which is what sf and stars use when coordinates are not projected (degrees longitude/latitude). Separate chapters detail a variety of plotting approaches for spatial maps using R, and different ways of handling very large vector or raster (imagery) datasets, locally, in databases, or in the cloud. The data used and all code examples are freely available online from https: //r-spatial.org/book/. The solutions to the exercises can be found here: https: //edzer.github.io/sdsr_exercises/.
Wavelet Analysis
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master's or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.). Features: Offers a self-contained discussion of wavelet theory Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists Provides researchers with detailed proofs Provides guides for readers to help them understand and practice wavelet analysis in different areas
Introduction to the Basics of Real Analysis
This book presents an introduction to the key topics in Real Analysis and makes the subject easily understood by the learners. The book is primarily useful for students of mathematics and engineering studying the subject of Real Analysis. It includes many examples and exercises at the end of chapters. This book is very authentic for students, instructors, as well as those doing research in areas demanding a basic knowledge of Real Analysis. It describes several useful topics in Real Analysis such as sets and functions, completeness, ordered field, neighborhoods, limit points of a set, open sets, closed sets, countable and uncountable sets, sequences of real numbers, limit, continuity and differentiability of real functions, uniform continuity, point-wise and uniform convergence of sequences and series of real functions, Riemann integration, improper integrals and metric spaces.
Problem Solving Methods and Strategies in High School Mathematical Competitions
This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking.It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools.The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu.The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results.
Problem Solving Methods and Strategies in High School Mathematical Competitions
This book not only introduces important methods and strategies for solving problems in mathematics competition, but also discusses the basic principles behind them and the mathematical way of thinking.It may be used as a valuable textbook for a mathematics competition course or a mathematics education course at undergraduate and graduate level. It can also serve as a reference book for students and teachers in primary and secondary schools.The materials of this book come from a book series of Mathematical Olympiad Competition. It is a collection of problems and solutions of the major mathematical competitions in China. The translation is done by Yongming Liu.The authors are mathematical competition teachers and researchers, many China's national team coaches and national team leaders. Many techniques and approaches in the book come directly from their own research results.
Statistics with Rust
Are you an experienced statistician or data professional looking for a powerful, efficient, and versatile programming language to turbocharge your data analysis and machine learning projects? Look no further! "Statistics with Rust" is your comprehensive resource to unlock Rust's true potential in modern statistical methods.This book is tailored specifically for statisticians and data professionals who are already familiar with the fundamentals of statistics and want to leverage the speed and reliability of Rust in their projects. Over 11 in-depth chapters, you will discover how Rust outperforms Python in various aspects of data analysis and machine learning and learn to implement popular statistical methods using Rust's unique features and libraries."Statistics with Rust" begins by introducing you to Rust's programming environment and essential libraries for data professionals. You'll then dive into data handling, preprocessing, and visualization techniques that form the backbone of any statistical analysis. As you progress through the book, you'll explore descriptive and inferential statistics, probability distributions, regression analysis, time series analysis, Bayesian statistics, multivariate statistical methods, and nonlinear models. Additionally, the book covers essential machine-learning techniques, model evaluation and validation, natural language processing, and advanced techniques in emerging topics.To ensure you get the most out of this book, each chapter includes hands-on examples and exercises to reinforce your understanding of the concepts presented. You'll also learn to optimize your Rust code and select the best tools and libraries for each task, maximizing your productivity and efficiency.Key LearningsDiscover Rust's unique advantages for statistical analysis and machine learning projects.Learn to efficiently handle, preprocess, and visualize data using Rust libraries.Implement descriptive and inferential statistics with Rust for powerful data insights.Master probability distributions and random variables in Rust for robust simulations.Perform advanced regression analysis with Rust's capabilities.Explore Bayesian statistics and Markov Chain Monte Carlo methods in Rust.Uncover multivariate techniques, including PCA and Factor Analysis, using Rust libraries.Implement cutting-edge machine learning algorithms and model evaluation techniques in Rust.Delve into text analysis, natural language processing, and network analysis with Rust.
Closure Properties for Heavy-Tailed and Related Distributions
A Toolbox of Averaging Theorems
This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε.Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs).In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
Heat Kernel on Lie Groups and Maximally Symmetric Spaces
This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form - and derives them - for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics - such as global analysis, spectral geometry, stochastic processes, and financial mathematics - as well in areas of mathematical and theoretical physics - including quantum field theory, quantum gravity, string theory, and statistical physics.
Stochastic Analysis, Filtering, and Stochastic Optimization
This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.
Functorial Semiotics for Creativity in Music and Mathematics
This book presents a new semiotic theory based upon category theory and applying to a classification of creativity in music and mathematics. It is the first functorial approach to mathematical semiotics that can be applied to AI implementations for creativity by using topos theory and its applications to music theory.Of particular interest is the generalized Yoneda embedding in the bidual of the category of categories (Lawvere) - parametrizing semiotic units - enabling a Čech cohomology of manifolds of semiotic entities. It opens up a conceptual mathematics as initiated by Grothendieck and Galois and allows a precise description of musical and mathematical creativity, including a classification thereof in three types. This approach is new, as it connects topos theory, semiotics, creativity theory, and AI objectives for a missing link to HI (Human Intelligence). The reader can apply creativity research using our classification, cohomology theory, generalized Yoneda embedding, and Java implementation of the presented functorial display of semiotics, especially generalizing the Hjelmslev architecture. The intended audience are academic, industrial, and artistic researchers in creativity.
Mathematical Tools for Neuroscience
This book provides a brief but accessible introduction to a set of related, mathematical ideas that have proved useful in understanding the brain and behaviour. If you record the eye movements of a group of people watching a riverside scene then some will look at the river, some will look at the barge by the side of the river, some will look at the people on the bridge, and so on, but if a duck takes off then everybody will look at it. How come the brain is so adept at processing such biological objects? In this book it is shown that brains are especially suited to exploiting the geometric properties of such objects. Central to the geometric approach is the concept of a manifold, which extends the idea of a surface to many dimensions. The manifold can be specified by collections of n-dimensional data points or by the paths of a system through state space. Just as tangent planes can be used to analyse the local linear behaviour of points on a surface, so the extension to tangent spaces can be used to investigate the local linear behaviour of manifolds. The majority of the geometric techniques introduced are all about how to do things with tangent spaces.Examples of the geometric approach to neuroscience include the analysis of colour and spatial vision measurements and the control of eye and arm movements. Additional examples are used to extend the applications of the approach and to show that it leads to new techniques for investigating neural systems. An advantage of following a geometric approach is that it is often possible to illustrate the concepts visually and all the descriptions of the examples are complemented by comprehensively captioned diagrams.The book is intended for a reader with an interest in neuroscience who may have been introduced to calculus in the past but is not aware of the many insights obtained by a geometric approach to the brain. Appendices contain brief reviews of the required background knowledge in neuroscience and calculus.
Introductory Statistics
This textbook is a primer for students on statistics. It covers basic statistical operations, an introduction to probability, distributions and regression. The book is divided into a series of 10 chapters covering a basic introduction to common topics for beginners. The goal of the book is to provide sufficient understanding of how to organize and summarize datasets through descriptive and inferential statistics for good decision-making. A chapter on ethics also informs readers about best practices for using statistics in research and analysis. Topics covered: 1. Introduction to Statistics2. Summarizing and Graphing3. Basic Concepts of Probability4. Discrete Random Variables5. Continuous Random Variables6. Sampling Distributions7. Estimation8. Hypothesis Testing9. Correlation and Regression10. Ethics
The Generalized Riemann Hypothesis - Dirichlet L-functions
This book is the second of two books in a series by the author on the generalized Riemann hypothesis. The Euler-Maclaurin summation formula, the Borel integral summation method, the Euler reflection formula for the gamma function, and the result of the first book of this series are used to prove that all roots of Dirichlet L-functions with principal characters in the critical strip are identical to the roots of the Riemann zeta function, and therefore have real part equal to 1/2. Furthermore, the Euler-Maclaurin summation formula, the Borel integral summation method, bi-lateral integral transform representations of the partial sums of the Dirichlet L-functions with non-principal characters in the critical strip, and the generalized functional equation of the Dirichlet L-functions are used to prove that all roots of the Dirichlet L-functions with non-principal characters in the critical strip have real part equal to 1/2.
Scalar and Vector Risk in the General Framework of Portfolio Theory
This book is the culmination of the authors' industry-academic collaboration in the past several years. The investigation is largely motivated by bank balance sheet management problems. The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks. The related theoretical investigation leads to a significant extension of the scope of portfolio theories. The book combines practitioners' perspectives and mathematical rigor. For example, to guide the bank managers to trade off different Pareto efficient points, the topological structure of the Pareto efficient set is carefully analyzed. Moreover, on top of computing solutions, the authors focus the investigation on the qualitative properties of those solutions and their financial meanings. These relations, such as the role of duality, are most useful in helping bank managers to communicate their decisions to the different stakeholders. Finally, bank balance sheet management problems of varying levels of complexity are discussed to illustrate how to apply the central mathematical results. Although the primary motivation and application examples in this book are focused in the area of bank balance sheet management problems, the range of applications of the general portfolio theory is much wider. As a matter of fact, most financial problems involve multiple types of risks. Thus, the book is a good reference for financial practitioners in general and students who are interested in financial applications. This book can also serve as a nice example of a case study for applied mathematicians who are interested in engaging in industry-academic collaboration.
Discrete-Time Semi-Markov Random Evolutions and Their Applications
Numerical and Engineering Analysis
The book is designed for use in a graduate program in Numerical Analysis that includes a basic introductory course and subsequent more specialized courses. The latter is envisaged to cover numerical linear algebra, the numerical solution of ordinary and partial differential equations, and perhaps additional topics related to complex analysis, multidimensional analysis, in particular optimization, and functional analysis and related functional equations.Viewed in this context, the first four chapters of our book could serve as a text for the basic introductory course on the Python program, andthe remaining chapters could provide a text for an advanced course on the numerical solution of ordinary differential equations. Therefore, the book breaks with tradition in that it no longer attempts to deal with all major topics of numerical mathematics. Those dealing with linear algebra and partial differential equations have developed into major fields of study that have attained a degree of autonomy and identity that justifies their treatment in separate books and separate courses on the graduate level. The term "Numerical Analysis" as used in this book, therefore, is to be taken in the narrow sense of the numerical analog of Mathematical Analysis, comprising such topics as machine arithmetic, the approximation of functions, approximate differentiation and integration, and the approximate solution of nonlinear equations and ordinary differential equations.This book aims to provide a good understanding of Numerical engineering analysis and its applications and optimization. The book begins with studying the concept of Python fundamentals for scientific computing. It then presents their applications in the different configurations shown in lucid detail.For more details, please visit https: //centralwestpublishing.com
Spreadsheet Problem Solving and Programming for Engineers and Scientists
This book provides a targeted and comprehensive resource essential to a full understanding of modern spreadsheet skills needed for engineering and scientific computations. Building on the authors' decades of experience teaching spreadsheets and programming, it is the ideal companion for all engineering courses and professional self-study.
Local Limit Theorems for Inhomogeneous Markov Chains
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. The book develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains.The inclusion of appendices with background material, numerous examples, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, Markov chains in random environments, random dynamical systems and non-stationary systems.
Measure Theory and Integration
This textbook contains a detailed and thorough exposition of topics in measure theory and integration. With abundant solved examples and more than 200 problems, the book is written in a motivational and student-friendly manner. Targeted to senior undergraduate and graduate courses in mathematics, it provides a detailed and thorough explanation of all the concepts. Suitable for independent study, the book, the first of the three volumes, contains topics on measure theory, measurable functions, Lebesgue integration, Lebesgue spaces, and abstract measure theory.
A Comprehensive Textbook on Metric Spaces
This textbook provides a comprehensive course in metric spaces. Presenting a smooth takeoff from basic real analysis to metric spaces, every chapter of the book presents a single concept, which is further unfolded and elaborated through related sections and subsections. Apart from a unique new presentation and being a comprehensive textbook on metric spaces, it contains some special concepts and new proofs of old results, which are not available in any other book on metric spaces. It has individual chapters on homeomorphisms and the Cantor set. This book is almost self-contained and has an abundance of examples, exercises, references and remarks about the history of basic notions and results. Every chapter of this book includes brief hints and solutions to selected exercises. It is targeted to serve as a textbook for advanced undergraduate and beginning graduate students of mathematics.
Normal Forms and Stability of Hamiltonian Systems
This book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of stronglystable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Optimization of Pharmaceutical Processes
Optimization of Pharmaceutical Processes presents contributions from leading authorities in the fields of optimization and pharmaceutical manufacturing. Formulated within structured frameworks, practical examples and applications are given as guidance to apply optimization techniques to most aspects of pharmaceutical processes from design, to lab and pilot scale, and finally to manufacturing. The increasing demand for better quality, higher yield, more efficient-optimized and green pharmaceutical processes, indicates that optimal conditions for production must be applied to achieve simplicity, lower costs and superior yield. The application of such methods in the pharmaceutical industry is not trivial. Quality of the final product is of major importance to human health and the need for deep knowledge of the process parameters and the optimization of the processes are imperative. The volume, which includes new methods as well as review contributions will benefit awide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.
Stochastic Processes and Financial Mathematics
The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics. It is wide-ranging in content, while at the same time placing much emphasis on good readability, motivation, and explanation of the issues covered. Financial mathematical topics are first introduced in the context of discrete time processes and then transferred to continuous-time models. The basic construction of the stochastic integral and the associated martingale theory provide fundamental methods of the theory of stochastic processes for the construction of suitable stochastic models of financial mathematics, e.g. using stochastic differential equations. Central results of stochastic analysis such as the It繫 formula, Girsanov's theorem and martingale representation theorems are of fundamental importance in financial mathematics, e.g. for the risk-neutral valuation formula (Black-Scholes formula) or the question of the hedgeability of options and the completeness of market models. Chapters on the valuation of options in complete and incomplete markets and on the determination of optimal hedging strategies conclude the range of topics. Advanced knowledge of probability theory is assumed, in particular of discrete-time processes (martingales, Markov chains) and continuous-time processes (Brownian motion, L矇vy processes, processes with independent increments, Markov processes). The book is thus suitable for advanced students as a companion reading and for instructors as a basis for their own courses.This book is a translation of the original German 1st edition Stochastische Prozesse und Finanzmathematik by Ludger R羹schendorf, published by Springer-Verlag GmbH Germany, part of Springer Nature in 2020. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com) and in a subsequent editing, improved by the author. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Large Sample Techniques for Statistics
This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways.The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science.This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..
Durable-Strategies Dynamic Games
Durable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics."Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dusan M Stipanovic, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College "Durable-strategies Dynamic Games is trulya world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies." Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games
Statistical Modeling
Statistical Modeling provides an introduction to regression, survival analysis, and time series analysisfor students who have completed calculus-based coursesin probability and mathematical statistics.The book uses the R language to fit statistical models, conduct Monte Carlo simulation experiments, and generate graphics.Over 300 exercises at the end of the chapters make this an appropriate text for a class in statistical modeling.This book is an open educational resource.
On Generalized Growth rates of Integer Translated Entire and Meromorphic Functions
The theory of entire and meromorphic functions is a very important area of complex analysis. This monograph aims to expand the discussion about some growth properties of integer translated composite entire and meromorphic functions on the basis of their (p, q, t)L -order and (p, q, t)L -type. This book presents six chapters. Chapter 1 introduces the reader to the preliminary definitions and notations. Chapter 2 and Chapter 3 discuss some results related to (p; q; t) L-th order and (p; q; t)L-th lower order of composite entire and meromorphic functions on the basis of their integer translation. Chapter 4 establishes some relations of integer translated composite entire and meromorphic functions based on their (p; q; t) L-th type and (p; q; t) L-th weak type. Chapter 5 deals with some results about (p; q; t) L-th order and (p; q; t) L-th type of composite entire and meromorphic functions on the basis of their integer translation. Chapter 6 focuses on some results about (p; q; t) L-th order and (p; q; t) L-th type of composite entire and meromorphic functions on the basis of their integer translation. This monograph will be very helpful for postgraduates, researchers, and faculty members interested in value distribution theorems in complex mathematical analysis.
New Perspectives on the Theory of Inequalities for Integral and Sum
This book provides new contributions to the theory of inequalities for integral and sum, and includes four chapters. In the first chapter, linear inequalities via interpolation polynomials and green functions are discussed. New results related to Popoviciu type linear inequalities via extension of the Montgomery identity, the Taylor formula, Abel-Gontscharoff's interpolation polynomials, Hermite interpolation polynomials and the Fink identity with Green's functions, are presented. The second chapter is dedicated to Ostrowski's inequality and results with applications to numerical integration and probability theory. The third chapter deals with results involving functions with nondecreasing increments. Real life applications are discussed, as well as and connection of functions with nondecreasing increments together with many important concepts including arithmetic integral mean, wright convex functions, convex functions, nabla-convex functions, Jensen m-convex functions, m-convex functions, m-nabla-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator of order m. The fourth chapter is mainly based on Popoviciu and Cebysev-Popoviciu type identities and inequalities. In this last chapter, the authors present results by using delta and nabla operators of higher order.
