This book reports on advanced concepts in fuzzy graph theory, showing a set of tools that can be successfully applied to understanding and modeling illegal human trafficking. Building on the previous book on fuzzy graph by the same authors, which set the fundamentals for readers to understand this developing field of research, this second book gives a special emphasis to applications of the theory. For this, authors introduce new concepts, such as intuitionistic fuzzy graphs, the concept of independence and domination in fuzzy graphs, as well as directed fuzzy networks, incidence graphs and many more.

Congruences are ubiquitous in computer science, engineering, mathematics, and related areas. Developing techniques for finding (the number of) solutions of congruences is an important problem. But there are many scenarios in which we are interested in only a subset of the solutions; in other words, there are some restrictions. What do we know about these restricted congruences, their solutions, and applications? This book introduces the tools that are needed when working on restricted congruences and then systematically studies a variety of restricted congruences. Restricted Congruences in Computing defines several types of restricted congruence, obtains explicit formulae for the number of their solutions using a wide range of tools and techniques, and discusses their applications in cryptography, information security, information theory, coding theory, string theory, quantum field theory, parallel computing, artificial intelligence, computational biology, discrete mathematics, number theory, and more. This is the first book devoted to restricted congruences and their applications. It will be of interest to graduate students and researchers across computer science, electrical engineering, and mathematics.

This book provides an enduring response to modern economic problems and the consequent crises, dealing with the economic modelling of nations and the forecasting of economic growth. The main arguments embodied constitute the creation of jobs and the restoration of economic growth, using the implicit acceptance of analysis on differential models and neutral systems for controlling the wealth of nations.

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.

The starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on 1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of -logic and related matters.

This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems. In the current interdisciplinary supercomputer-oriented research environment, semi-infinite fractional programming is among the most rapidly expanding research areas in terms of its multi-facet applications empowerment for real-world problems, which may stem from many control problems in robotics, outer approximation in geometry, and portfolio problems in economics, that can be transformed into semi-infinite problems as well as handled by transforming them into semi-infinite fractional programming problems. As a matter of fact, in mathematical optimisation programs, a fractional programming (or program) is a generalisation to linear fractional programming. These problems lay the theoretical foundation that enables us to fully investigate the second-order optimality and duality aspects of our principal fractional programming problem as well as its semi-infinite counterpart.

The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning.Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications.Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.

Linear and Nonlinear Programming is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. The new co-author, Yinyu Ye, has written chapters and chapter material on a number of these areas including Interior Point Methods.

Handbook of the Shapley Value contains 24 chapters and a foreword written by Alvin E. Roth, who was awarded the Nobel Memorial Prize in Economic Sciences jointly with Lloyd Shapley in 2012. The purpose of the book is to highlight a range of relevant insights into the Shapley value. Every chapter has been written to honor Lloyd Shapley, who introduced this fascinating value in 1953. The first chapter, by William Thomson, places the Shapley value in the broader context of the theory of cooperative games, and briefly introduces each of the individual contributions to the volume. This is followed by a further contribution from the editors of the volume, which serves to introduce the more significant features of the Shapley value. The rest of the chapters in the book deal with different theoretical or applied aspects inspired by this interesting value and have been contributed specifically for this volume by leading experts in the area of Game Theory. Chapters 3 through to 10 are more focused on theoretical aspects of the Shapley value, Chapters 11 to 15 are related to both theoretical and applied areas. Finally, from Chapter 16 to Chapter 24, more attention is paid to applications of the Shapley value to different problems encountered across a diverse range of fields. As expressed by William Thomson in the Introduction to the book, "The chapters contribute to the subject in several dimensions: Mathematical foundations; axiomatic foundations; computations; applications to special classes of games; power indices; applications to enriched classes of games; applications to concretely specified allocation problems: an ever-widening range, mapping allocation problems into games or implementation." Nowadays, the Shapley value continues to be as appealing as when it was first introduced in 1953, or perhaps even more so now that its potential is supported by the quantity and quality of the available results. This volume collects a large amount of work that definitively demonstrates that the Shapley value provides answers and solutions to a wide variety of problems.

Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business.

The COVID-19 pandemic is not only a threat to our health and economy, but also has strong implications for defence and security. Indeed, defence leaders have highlighted a second fight surrounding the spread of COVID-19, namely disinformation and preparing to face adversaries willing to exploit the public health crisis for nefarious purposes. The current pandemic is a breeding ground for the propagation of disinformation, as it represents the first major global health event in which large social media platforms have become the main distributor of information. This multi-national edited volume consists of contributions from Defence Science, academia and industry, including NATO Headquarters, United States, Netherlands, Singapore, United Kingdom and Norway. The content is aimed at a diverse audience, including NATO members, researchers from defence and security organizations, academics, and militaries including analysts and practitioners, as well as policy makers. This volume focuses on various aspects of COVID-19 disinformation, including identifying global dominant disinformation narratives and the methods used to spread disinformation, examining COVID-19 disinformation within the broader context of the cognitive domain, examining the psychological effects of COVID-19 disinformation and COVID-19 disinformation on instant messaging platforms, along with examining various countermeasures to disinformation.

This book describes the modelling and optimisation of vibration reduction systems in an integrated fashion using nonlinear equations of motion. It proposes an effective optimisation method for determining the basic characteristics of the non-linear visco-elastic elements used in passive vibration reduction systems. In the case of semi-active and active vibration isolators, a design process of the advanced control systems is proposed that makes possible to optimise the controller settings relatively to the selected vibro-isolation criteria. The approach developed here is subsequently tested by means of experimental investigations conducted on various sample vibration reduction systems: passive, semi-active and active. The book presents a biomechanical modelling approach that allows users to select the properties of vibro-isolation systems for different types of oscillation and different optimisation criteria - and can significantly reduce the harmful vibrations that can affect the human body in the process. Further, the book equips readers to evaluate the viscoelastic characteristics of passive systems and design control systems for semi-active and active systems. Modelling and Control Design of Vibration Reduction Systems offers a valuable guide for researchers and practitioners alike. It also provides students and academics with systematic information on the procedures to be followed in the design process for semi-active or active vibration reduction systems.

This book presents simple design paradigms related to lightweight design, that are derived from an in-depth and theoretically sound analysis based on Pareto theory. It uses numerous examples, including torsion and inflated tubes, to fully explain the theories discussed. Lightweight Construction Principles begins by defining terms in relation to engineering design and optimal design of complex mechanical systems. It then discusses the analytical derivation of the Pareto-optimal set, before applying analytical formulae to optimal design of bent beams. The book moves through numerous case studies of different beam and tube construction including beams subject to bending, thin walled tubes under torsion and truss structures. This book will be of interest to researchers and graduate students in the field of structural optimisation and multi-objective optimization, as well as to practitioners such as design engineers.

Focuses on the latest research in the field of differential equations in engineering applications Discusses the most recent research findings that are occurring across different institutions Identifies the gaps in the knowledge of differential equations Presents the most fruitful areas for further research in advanced processes Offers the most forthcoming studies in modeling and simulation along with real-world case studies

The detailed survey on constraint handling techniques specifically penalty function approach is presented in the book; presents the Cohort Intelligence (CI) algorithm incorporated with a novel self-adaptive penalty function (SAPF) approach which helped in avoiding preliminary trials of selecting penalty parameter. The approach is referred to as CI-SAPF; CI-SAPF is further hybridized with Colliding Bodies Optimization (CBO) algorithm to promote a parameter less metaheuristic algorithm; presents solutions to several problems from discrete truss structure domain, mixed variable design engineering domain, and linear & nonlinear domain validating the CI-SAPF and CI-SAPF-CBO; behavior of SAPF approach on pseudo objective function, constraint violations, penalty function and penalty parameter have been analyzed and discussed in very detail; presents the in-depth analysis and comparison of the CI-SAPF, CI-SAPF-CBO and CBO algorithms with other contemporary techniques; provides the solution to real-world manufacturing problems of optimizing multi pass milling and turning processes using CI-SPF, CI-SAPF and CI-SAPF-CBO approaches.

Offers fundamental theories and practical and more sophisticated applications of Evolutionary Computation in varied industries Provides insight into various platforms, paradigms, techniques, and tools used in Evolutionary Computation for diverse fields Presents an understanding related to optimization, performance tuning, virtualization, deployment models, and their applications Covers a variety of applications for social and essential models and is based on real life examples Useful for decision making based on optimized data through Evolutionary Computation in multi-dimensions

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

How to Divide When There Isn't Enough develops a rigorous yet accessible presentation of the state-of-the-art for the adjudication of conflicting claims and the theory of taxation. It covers all aspects one may wish to know about claims problems: the most important rules, the most important axioms, and how these two sets are related. More generally, it also serves as an introduction to the modern theory of economic design, which in the last twenty years has revolutionized many areas of economics, generating a wide range of applicable allocations rules that have improved people's lives in many ways. In developing the theory, the book employs a variety of techniques that will appeal to both experts and non-experts. Compiling decades of research into a single framework, William Thomson provides numerous applications that will open a large number of avenues for future research.

This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items,  generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

"Nonconvex Optimal Control and Variational Problems "is an important contribution to the existing literature in the field and is devoted to the presentation of progress made in the last 15 years of research in the area of optimal control and the calculus of variations. This volume contains a number of results concerning well-posedness of optimal control and variational problems, nonoccurrence of the Lavrentiev phenomenon for optimal control and variational problems, and turnpike properties of approximate solutions of variational problems.

Chapter 1 contains an introduction as well as examples of select topics. Chapters 2-5 consider the well-posedness condition using fine tools of general topology and porosity. Chapters 6-8 are devoted to the nonoccurrence of the Lavrentiev phenomenon and contain original results. Chapter 9 focuses on infinite-dimensional linear control problems, and Chapter 10 deals with good functions and explores new understandings on the questions of optimality and variational problems. Finally, Chapters 11-12 are centered around the turnpike property, a particular area of expertise for the author.

This volume is intended for mathematicians, engineers, and scientists interested in the calculus of variations, optimal control, optimization, and applied functional analysis, as well as both undergraduate and graduate students specializing in those areas. The text devoted to Turnpike properties may be of particular interest to the economics community."

In today's world, with an increase in the breadth and scope of real-world engineering optimization problems as well as with the advent of big data, improving the performance and efficiency of algorithms for solving such problems has become an indispensable need for specialists and researchers. In contrast to conventional books in the field that employ traditional single-stage computational, single-dimensional, and single-homogeneous optimization algorithms, this book addresses multiple newfound architectures for meta-heuristic music-inspired optimization algorithms. These proposed algorithms, with multi-stage computational, multi-dimensional, and multi-inhomogeneous structures, bring about a new direction in the architecture of meta-heuristic algorithms for solving complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data. The architectures of these new algorithms may also be appropriate for finding an optimal solution or a Pareto-optimal solution set with higher accuracy and speed in comparison to other optimization algorithms, when feasible regions of the solution space and/or dimensions of the optimization problem increase. This book, unlike conventional books on power systems problems that only consider simple and impractical models, deals with complicated, techno-economic, real-world, large-scale models of power systems operation and planning. Innovative applicable ideas in these models make this book a precious resource for specialists and researchers with a background in power systems operation and planning. Provides an understanding of the optimization problems and algorithms, particularly meta-heuristic optimization algorithms, found in fields such as engineering, economics, management, and operations research; Enhances existing architectures and develops innovative architectures for meta-heuristic music-inspired optimization algorithms in order to deal with complicated, real-world, large-scale, non-convex, non-smooth engineering optimization problems having a non-linear, mixed-integer nature with big data; Addresses innovative multi-level, techno-economic, real-world, large-scale, computational-logical frameworks for power systems operation and planning, and illustrates practical training on implementation of the frameworks using the meta-heuristic music-inspired optimization algorithms.

This book focuses on the design of efficient & dynamic methods to allocate divisible resources under various auction mechanisms, discussing their applications in power & microgrid systems and the V2G & EV charging coordination problems in smart grids. It describes the design of dynamic methods for single-sided and double-sided auction games and presents a number of simulation cases verifying the performances of the proposed algorithms in terms of efficiency, convergence and computational complexity. Further, it explores the performances of certain auction mechanisms in a hierarchical structure and with large-scale agents, as well as the auction mechanisms for the efficient allocation of multi-type resources. Lastly, it generalizes the main and demonstrates their application in smart grids. This book is a valuable resource for researchers, engineers, and graduate students in the fields of optimization, game theory, auction mechanisms and smart grids interested in designing dynamic auction mechanisms to implement optimal allocation of divisible resources, especially electricity and other types of energy in smart grids.

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 a wide readership including engineers in pharmaceuticals, chemical, biological, to name just a few.

The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model.

This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed.

The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options. "

This book provides several inventory models for making the right decision in inventory management under different environments. Basically, the optimal ordering policies are determined for situations with and without shortages in production-inventory systems. The chapters in the book include various features of inventory modeling i.e., inflation, deterioration, supply chain, learning, credit financing, carbon emission policy, stock-dependent demand, among others. The book is a useful resource for academicians, researchers, students, practitioners, and managers who can be benefited with the policies provided in the chapters of the book.