This book is devoted to game theory and its applications to environmental problems, economics, and management. It collects contributions originating from the 12th International Conference on "Game Theory and Management" 2018 (GTM2018) held at Saint Petersburg State University, Russia, from 27 to 29 June 2018.

This edited volume aims at giving an overview of recent advances in the theory and applications of Partial Differential Equations and energy functionals related to the fractional Laplacian operator as well as to more general integro-differential operators with singular kernel of fractional differentiability. After being investigated firstly in Potential Theory and Harmonic Analysis, fractional operators defined via singular integral are nowadays riveting great attention in different research fields related to Partial Differential Equations with nonlocal terms, since they naturally arise in many different contexts, as for instance, dislocations in crystals, nonlocal minimal surfaces, the obstacle problem, the fractional Yamabe problem, and many others. Much progress has been made during the last years, and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Claudia Bucur, Zhen-Qing Chen, Francesca Da Lio, Donatella Danielli, Serena Dipierro, Rupert L. Frank, Maria del Mar Gonzalez, Moritz Kassmann, Tuomo Kuusi, Giuseppe Mingione, Giovanni Molica Bisci, Stefania Patrizi, Xavier Ros-Oton, Sandro Salsa, Yannick Sire, Enrico Valdinoci, Xicheng Zhang.

Sheldon Ross's classic bestseller, "Introduction to Probability Models," has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research.

The hallmark features of this renowned text remain in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data.
Updated data, and a list of commonly used notations and equations, instructor's solutions manualOffers new applications of probability models in biology and new material on Point Processes, including the Hawkes processIntroduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations researchCovers finite capacity queues, insurance risk models, and Markov chains Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new examsAppropriate for a full year course, this book is written under the assumption that students are familiar with calculus

This book reports on current challenges in bridge engineering faced by professionals around the globe, giving a special emphasis to recently developed techniques and methods for bridge design, construction and monitoring. Based on extended and revised papers selected from outstanding presentation at the Istanbul Bridge Conference 2018, held from November 5 - 6, 2018, in Istanbul, Turkey, and by highlighting major bridge studies, spanning from numerical and modeling studies to the applications of new construction techniques and monitoring systems, this book is intended to promote high standards in modern bridge engineering. It offers a timely reference to both academics and professionals in this field.

Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will be an excellent resource for undergraduate students in physics and a quick reference guide for more advanced students, as well as being appropriate for students in other physical sciences, such as astronomy, chemistry and earth sciences.

This book offers essential, systematic information on the assessment of the spatial association between two processes from a statistical standpoint. Divided into eight chapters, the book begins with preliminary concepts, mainly concerning spatial statistics. The following seven chapters focus on the methodologies needed to assess the correlation between two or more processes; from theory introduced 35 years ago, to techniques that have only recently been published. Furthermore, each chapter contains a section on R computations to explore how the methodology works with real data. References and a list of exercises are included at the end of each chapter. The assessment of the correlation between two spatial processes has been tackled from several different perspectives in a variety of applications fields. In particular, the problem of testing for the existence of spatial association between two georeferenced variables is relevant for posterior modeling and inference. One evident application in this context is the quantification of the spatial correlation between two images (processes defined on a rectangular grid in a two-dimensional space). From a statistical perspective, this problem can be handled via hypothesis testing, or by using extensions of the correlation coefficient. In an image-processing framework, these extensions can also be used to define similarity indices between images.

This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique-an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.

This book describes the variety of direct and indirect population size estimation (PSE) methods available along with their strengths and weaknesses. Direct estimation methods, such as enumeration and mapping, involve contact with members of hard-to-reach groups. Indirect methods have practical appeal because they require no contact with members of hard-to-reach groups. One indirect method in particular, network scale-up (NSU), has several strengths over other PSE methods: It can be applied at a province/country level, it can estimate size of several hard-to-reach population in a single study, and it is implemented with members of the general population rather than members of hard-to-reach groups. The book discusses methods to collect, analyze, and adjust results and presents methods to triangulate and finalize PSEs.

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers-Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg-Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdos-Renyi network model, strongly m-convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

This book takes the reader through real-world examples for how to characterize and measure the productivity and performance of NFPs and education institutions-that is, organisations that produce value for society, which cannot be measured accurately in financial KPIs. It focuses on how best to frame non-profit performance and productivity, and provides a suite of tools for measurement and benchmarking. It further challenges the reader to consider alternative and appropriate uses of quantitative measures, which are fit-for-purpose in individual contexts. It is true that the risk of misusing quantitative measures is ever-present. But does that risk outweigh the benefits of forming a more precise and shared understanding of what could generate better outcomes? There will always be concerns about policy and performance management. Goodheart's Law states that once a measure becomes a target, it is no longer a good measure. This book helps to strike a meaningful balance between what can be measured, what cannot, and how best to use quantitative information in sectors that are often averse to being held up to the light and put on a scale by outsiders.

The UK's most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson's own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Decision Mathematics 1 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 1 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel's interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well as supporting the large data set and calculators. They are packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises. There are full worked solutions to every question available free and online for quick and easy access. You will also have access to lots of free additional online content with GeoGebra interactives and Casio calculator tutorials. There are separate Pure and Applied textbooks for AS and A level Maths, and a textbook per option for AS and A level Further Maths. Practice books are also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions. Pearson's revision resources are the smart choice for those revising for Pearson Edexcel AS and A level Mathematics - there is a Revision Workbook for exam practice and a Revision Guide for classroom and independent study. Practice Papers Plus+ books contain additional full length practice papers, so you can practice answering questions by writing straight into the book and perfect your responses with targeted hints, guidance and support for every question, including fully worked solutions.

Applications of queueing network models have multiplied in the last generation, including scheduling of large manufacturing systems, control of patient flow in health systems, load balancing in cloud computing, and matching in ride sharing. These problems are too large and complex for exact solution, but their scale allows approximation. This book is the first comprehensive treatment of fluid scaling, diffusion scaling, and many-server scaling in a single text presented at a level suitable for graduate students. Fluid scaling is used to verify stability, in particular treating max weight policies, and to study optimal control of transient queueing networks. Diffusion scaling is used to control systems in balanced heavy traffic, by solving for optimal scheduling, admission control, and routing in Brownian networks. Many-server scaling is studied in the quality and efficiency driven Halfin-Whitt regime and applied to load balancing in the supermarket model and to bipartite matching in ride-sharing applications.

This book presents a survey of the aspects of economic complexity, with a focus on foundational, interdisciplinary ideas. The long-awaited follow up to his 2011 volume Complex Evolutionary Dynamics in Urban-Regional and Ecologic-Economic Systems: From Catastrophe to Chaos and Beyond, this volume draws together the threads of Rosser's earlier work on complexity theory and its wide applications in economics and an expanded list of related disciplines. The book begins with a full account of the broader categories of complexity in economics--dynamic, computational, hierarchical, and structural--before shifting to more detailed analysis. The next two chapters address problems associated with computational complexity, especially those of computability, and discuss the Godel Incompleteness Theorem with a focus on reflexivity. The middle chapters discuss the relationship between entropy, econophysics, evolution, and economic complexity, respectively, with applications in urban and regional dynamics, ecological economics, general equilibrium theory, as well as financial market dynamics. The final chapter works to bring together these themes into a broader framework and expose some of the limits concerning analysis of deeper foundational issues. With applications in all disciplines characterized by interconnected nonlinear adaptive systems, this book is appropriate for graduate students, professors and practitioners in economics and related disciplines such as regional science, mathematics, physics, biology, environmental sciences, philosophy, and psychology.

This book contains high-quality papers presented at the First International Forum on Financial Mathematics and Financial Technology. With the rapid development of FinTech, the in-depth integration between mathematics, finance and advanced technology is the general trend. This book focuses on selected aspects of the current and upcoming trends in FinTech. In detail, the included scientific papers focus on financial mathematics and FinTech, presenting the innovative mathematical models and state-of-the-art technologies such as deep learning, with the aim to improve our financial analysis and decision-making and enhance the quality of financial services and risk control. The variety of the papers delivers added value for both scholars and practitioners where they will find perfect integration of elegant mathematical models and up-to-date data mining technologies in financial market analysis.

This book provides an insightful view of effective teaching practices in China from an international perspective by examining the grades 7-12 mathematics teacher preparation in the Shandong province of China. It is an excellent reference book for teacher educators, researchers, reformers, and teaching practitioners. A qualitative research approach, involving in-depth interviews with purposive sampling of ten grades 7-12 award-winning mathematics teachers, was chosen to conduct the study. The participants are from the Shandong province and have been awarded recognition for his/her achievements in teaching grades 7-12 mathematics by the different levels: school, district, city, province, or nation; and his/her students have achieved high average scores in college entrance exams or in high school entrance exams among the classes at the same grade level. Data analysis revealed the following findings: first, grades 7-12 mathematics teachers from the Shandong province of China were prepared to teach through pre-service training, in-service training, and informal learning. The pre-service training can be characterized as emphasizing formal mathematics training at advanced level. The in-service training is integrated with teacher collaboration and teaching research, and has the characteristics of diversity, continuity, and orientation toward teaching practice. The in-service training also stimulates teachers to conduct selfdirected learning. Second, the award-winning grades 7-12 mathematics teachers are identified by the following characteristics: they are passionate about mathematics and share their passion through teaching; they actively take part in teaching research through application of teaching research in the classroom, collaboration with peers, and systematic lesson preparation; they apply technology into teaching; and they take an active role in teaching research in order to expand their professional opportunities. Based on the findings of this study, the following conclusions were reached: pre-service training and in-service training are both necessary processes for mathematics teachers to build up their knowledge base for effective teaching. Pre-service training is just a starting point for the teaching profession. In-service training, integrated with teacher collaboration and teaching research should be a continuous activity that is a part of a teacher's everyday life.

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Goedel's classical completeness and incompleteness theorems. In particular, the book includes a full proof of Goedel's second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo's axioms, containing a presentation of Goedel's constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.

This book presents the stream-tube method (STM), a method offering computational means of dealing with the two- and three-dimensional properties of numerous incompressible materials in static and dynamic conditions. The authors show that the kinematics and stresses associated with the flow and deformation in such materials can be treated by breaking the system down into simple computational sub-domains in which streamlines are straight and parallel and using one or two mapping functions in steady-state and non-steady-state conditions. The STM is considered for various problems in non-Newtonian fluid mechanics with different geometries. The book makes use of examples and applications to illustrate the use of the STM. It explores the possibilities of computation on simple mapped rectangular domains and three-dimensional parallel-piped domains under different conditions. Complex materials with memory are considered simply without particle tracking problems. Readers, including researchers, engineers and graduate students, with a foundational knowledge of calculus, linear algebra, differential equations and fluid mechanics will benefit most greatly from this book.

Reliability is a fundamental criterium in engineering systems. This book shows innovative concepts and applications of mathematics in solving reliability problems. The contents address in particular the interaction between engineers and mathematicians, as well as the cross-fertilization in the advancement of science and technology. It bridges the gap between theory and practice to aid in practical problem-solving in various contexts.

This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.

This thesis is concerned with flows through cascades, i.e. periodic arrays of obstacles. Such geometries are relevant to a range of physical scenarios, chiefly the aerodynamics and aeroacoustics of turbomachinery flows. Despite the fact that turbomachinery is of paramount importance to a number of industries, many of the underlying mechanisms in cascade flows remain opaque. In order to clarify the function of different physical parameters, the author considers six separate problems. For example, he explores the significance of realistic blade geometries in predicting turbomachinery performance, and the possibility that porous blades can achieve noise reductions. In order to solve these challenging problems, the author deploys and indeed develops techniques from across the spectrum of complex analysis: the Wiener-Hopf method, Riemann-Hilbert problems, and the Schottky-Klein prime function all feature prominently. These sophisticated tools are then used to elucidate the underlying mathematical and physical structures present in cascade flows. The ensuing solutions greatly extend previous works and offer new avenues for future research. The results are not of simply academic value but are also useful for aircraft designers seeking to balance aeroacoustic and aerodynamic effects.

Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied to science - there are already many excellent books to choose from - rather, it tries to give an overview of the basic principles that physical scientists use to analyze their data and bring out the order of Nature from the fog of background noise.