This textbook is intended as a guide for undergraduate and graduate students in engineering, science and technology courses. Chapters of the book cover the numerical concepts of errors, approximations, differential equations and partial differential equations. The simple presentation of numerical concepts and illustrative examples helps students and general readers to understand the topics covered in the text.

This book presents a selection of the latest and representative developments in predictive analytics using big data technologies. It focuses on some critical aspects of big data and machine learning and provides studies for readers. The chapters address a comprehensive range of advanced data technologies used for statistical modeling towards predictive analytics. Topics included in this book include: - Categorized machine learning algorithms - Player monopoly in cricket teams. - Chain type estimators - Log type estimators - Bivariate survival data using shared inverse Gaussian frailty models - Weblog analysis - COVID-19 epidemiology This reference book will be of significant benefit to the predictive analytics community as a useful guide of the latest research in this emerging field.

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

Introduction: <p></p> Mathematicians and statisticians have made significant academic progress on the subject of distribution theory in the last two decades, and this area of study is becoming one of the main statistical tools for the analysis of lifetime (survival) data. In many ways, lifetime distributions are the common language of survival dialogue because the framework subsumes many statistical properties of interest, such as reliability, entropy and maximum likelihood. <p></p> Recent Advances in Lifetime and Reliability Models provides a comprehensive account of models and methods for lifetime models. Building from primary definitions such as density and hazard rate functions, this book presents readers a broad framework on distribution theory in survival analysis. This framework covers classical methods - such as the exponentiated distribution method – as well as recent models explaining lifetime distributions, such as the beta family and compounding models. Additionally, a detailed discussion of mathematical and statistical properties of each family, such as mixture representations, asymptotes, types of moments, order statistics, quantile functions, generating functions and estimation is presented in the book. <p></p> Key Features: <p></p> - presents information about classical and modern lifetime methods <p></p> - covers key properties of different models in detail <p></p> - explores regression models for the beta generalized family of distributions <p></p> - focuses information on both theoretical fundamentals and practical aspects of implementing different models <p></p> - features examples relevant to business engineering and biomedical sciences <p></p> Recent Advances in Lifetime and Reliability Models will equip students, researchers and working professionals with the information to make extensive use of observational data in a variety of fields to create inferential models that make sense of lifetime data.

Reliability Calculations with the Stochastic Finite Element presents different methods of reliability analysis for systems. Chapters explain methods used to analyze a number of systems such as single component maintenance system, repairable series system, rigid rotor balance, spring mechanics, gearbox design and optimization, and nonlinear vibration. The author proposes several established and new methods to solve reliability problems which are based on fuzzy systems, sensitivity analysis, Monte Carlo simulation, HL-RF methods, differential equations, and stochastic finite element processing, to name a few. This handbook is a useful update on reliability analysis for mechanical engineers and technical apprentices.

Probability and Statistics: Theory and Exercises is a textbook focused on practical examples of probability theory and statistics, with the goal of giving readers a thorough understanding of mathematical relationships in these subjects. The book is designed for basic courses in probability and statistics, and is aimed primarily at non-specialists and beginner level students. The book is divided into 2 sections, respectively. Probability: Includes a primer on set theory, basic probability theory definitions and calculations, combinatorial analysis, random variables and distribution laws Statistics: Covers basic concepts of descriptive statistics Key features - Simple, clear language for easy comprehension of key concepts - Carefully chosen exercises with solutions for self-learning - Over 40 Illustrations for clear explanations - References for further reading and tutorials.

This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and attractive way. Readers will easily identify problems/techniques/solutions without the frustration of long searches through previous notations, definitions and results. It begins with a sketch of axiomatic set theory and of the theory of categories. The fundamentals of the order relation are presented, including several properties equivalent to the axiom of choice, and culminating with well-ordered sets and transfinite numbers. This e-book also explains: (1) The complete existential theory of the various distinguished elements which a partially ordered set may possess, (2) The proof of the equivalence with the axiom of choice of 14 frequently used properties,(3) The fact that certain properties of ordinals are revealed as being just properties of well-ordered sets, and (4) The presentation of ordinals and cardinals both in axiomatic setting and following von Neumann&rsquo;s construction. Proofs are given in detail along with numerous examples and exercises illustrating the theory and demonstrating applications. Several classes of lattices, closure operators and Galois connections include tools which serve as prerequisites to universal algebra. Other topics include embeddings and topological duality for distributive lattices. The e-book serves both as a textbook for undergraduate and graduate students and as a reference book for mathematicians working in fields different from set theory or algebra, to whom it provides a quick access to basic facts from order theory.

Lately there is an increasing interest in partial difference equations demonstrated by the enormous amount of research papers devoted to them. The initial reason for this increasing interest was the development of computers and the area of numerical analysis, where partial difference equations arise naturally when discretizing a partial differential equation. The aim of this e-book is to provide some recent advances in the field of partial difference equations. Applications of partial difference equations in numerical analysis and systems theory are also presented. This e-book will be of use to high level undergraduate students, graduate students and researchers working in the area of partial difference equations.

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.

Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.