Computational finance is increasingly important in the financial industry, as a necessary instrument for applying theoretical models to real-world challenges. Indeed, many models used in practice involve complex mathematical problems, for which an exact or a closed-form solution is not available. Consequently, we need to rely on computational techniques and specific numerical algorithms. This book combines theoretical concepts with practical implementation. Furthermore, the numerical solution of models is exploited, both to enhance the understanding of some mathematical and statistical notions, and to acquire sound programming skills in MATLAB (R), which is useful for several other programming languages also. The material assumes the reader has a relatively limited knowledge of mathematics, probability, and statistics. Hence, the book contains a short description of the fundamental tools needed to address the two main fields of quantitative finance: portfolio selection and derivatives pricing. Both fields are developed here, with a particular emphasis on portfolio selection, where the author includes an overview of recent approaches. The book gradually takes the reader from a basic to medium level of expertise by using examples and exercises to simplify the understanding of complex models in finance, giving them the ability to place financial models in a computational setting. The book is ideal for courses focusing on quantitative finance, asset management, mathematical methods for economics and finance, investment banking, and corporate finance.

The finite element and the boundary element methods are the two most important developments in numerical mathematics to occur in this century. Many engineering and mathematics graduate curricula now include a course in boundary element methods. Such a course must cover numerical methods, basic methodology to real problems, and interactive computer usage. Both theory and applications, necessary for applied courses, are available in this new textbook. An Introduction to Boundary Element Methods is logically organized and easy to read. The topics are carefully selected and meticulously presented. Applications are described for use in identifying potential problems and for heat transfer, diffusion equations, linear elasticity, water waves, ocean acoustics, acoustic scattering, aerodynamics, porous media, and simple laminar flows. More than 20 computer subroutines help develop and explain the computational aspect of the subject. Hundreds of figures, exercises, and solved examples supplement text and help clarify important information. The computer programs have been tested on some benchmark problems. Even in single precision the results are more accurate and better than those obtained from available Fortran programs.

The concept of derivatives of non-integer order, known as fractional derivatives, first appeared in the letter between L'Hopital and Leibniz in which the question of a half-order derivative was posed. Since then, many formulations of fractional derivatives have appeared. Recently, a new definition of fractional derivative, called the "fractional conformable derivative," has been introduced. This new fractional derivative is compatible with the classical derivative and it has attracted attention in areas as diverse as mechanics, electronics, and anomalous diffusion. Conformable Dynamic Equations on Time Scales is devoted to the qualitative theory of conformable dynamic equations on time scales. This book summarizes the most recent contributions in this area, and vastly expands on them to conceive of a comprehensive theory developed exclusively for this book. Except for a few sections in Chapter 1, the results here are presented for the first time. As a result, the book is intended for researchers who work on dynamic calculus on time scales and its applications. Features Can be used as a textbook at the graduate level as well as a reference book for several disciplines Suitable for an audience of specialists such as mathematicians, physicists, engineers, and biologists Contains a new definition of fractional derivative About the Authors Douglas R. Anderson is professor and chair of the mathematics department at Concordia College, Moorhead. His research areas of interest include dynamic equations on time scales and Ulam-type stability of difference and dynamic equations. He is also active in investigating the existence of solutions for boundary value problems. Svetlin G. Georgiev is currently professor at Sorbonne University, Paris, France and works in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, dynamic calculus on time scales, and integral equations.

Localized Dynamics of Thin-Walled Shells focuses on localized vibrations and waves in thin-walled structures with variable geometrical and physical characteristics. It emphasizes novel asymptotic methods for solving boundary-value problems for dynamic equations in the shell theory, in the form of functions which are highly localized near both fixed and moving lines/points on the shell surface. Features First-of-its-kind work, synthesizing knowledge of the localization of vibrations and waves in thin-walled shells with a mathematical tool to study them Suitable for researchers working on the dynamics of thin shells and also as supplementary reading for undergraduates studying asymptotic methods Offers detailed analysis of wave processes in shells with varying geometric and physical parameters

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: * Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity * Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes * Permit meaningful interpretations which link abstract inequalities with the real world * Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure * Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.

It is well-known that modern stochastic calculus has been exhaustively developed under usual conditions. Despite such a well-developed theory, there is evidence to suggest that these very convenient technical conditions cannot necessarily be fulfilled in real-world applications. Optional Processes: Theory and Applications seeks to delve into the existing theory, new developments and applications of optional processes on "unusual" probability spaces. The development of stochastic calculus of optional processes marks the beginning of a new and more general form of stochastic analysis. This book aims to provide an accessible, comprehensive and up-to-date exposition of optional processes and their numerous properties. Furthermore, the book presents not only current theory of optional processes, but it also contains a spectrum of applications to stochastic differential equations, filtering theory and mathematical finance. Features Suitable for graduate students and researchers in mathematical finance, actuarial science, applied mathematics and related areas Compiles almost all essential results on the calculus of optional processes in unusual probability spaces Contains many advanced analytical results for stochastic differential equations and statistics pertaining to the calculus of optional processes Develops new methods in finance based on optional processes such as a new portfolio theory, defaultable claim pricing mechanism, etc.

An up-to-date survey of mathematical models of carcinogenesis, providing the most recent findings of cancer biology as evidence of the models, as well as extensive bibliographies of cancer biology and in-depth mathematical analyses for each of the models. May be used as a reference for courses on st

Perturbation theory is a powerful tool for solving a wide variety of problems in applied mathematics, a tool particularly useful in quantum mechanics and chemistry. Although most books on these subjects include a section offering an overview of perturbation theory, few, if any, take a practical approach that addresses its actual implementation Introduction to Perturbation Theory in Quantum Mechanics does. It collects into a single source most of the techniques for applying the theory to the solution of particular problems. Concentrating on problems that allow exact analytical solutions of the perturbation equations, the book resorts to numerical results only when necessary to illustrate and complement important features of the theory. The author also compares different methods by applying them to the same models so that readers clearly understand why one technique may be preferred over another. Demonstrating the application of similar techniques in quantum and classical mechanics, Introduction to Perturbation Theory in Quantum Mechanics reveals the underlying mathematics in seemingly different problems. It includes many illustrative examples that facilitate the understanding of theoretical concepts, and provides a source of ideas for many original research projects.

An introduction to general theories of stochastic processes and modern martingale theory. The volume focuses on consistency, stability and contractivity under geometric invariance in numerical analysis, and discusses problems related to implementation, simulation, variable step size algorithms, and random number generation.

Advanced mathematics used in engineering is studied here in this text which examines the relationship between the principles in natural processes and those employed in engineered processes. The text covers principles, practices and the mathematics involved in the design and operation of environmental engineering works. It also presents engineering modelling tools and environmental algorithm examples. Major subjects covered in this book include:* modelling * algorithms * air and water pollution assessment and control calculations Providing concepts, definitions, descriptions, and derivations in an intuitive manner, it is both a textbook and reference tool for practitioners involved in the protection of air, water, and land resources.

Provides One Unified Formula That Gives Solutions to Several Types of GSEs Generalized Sylvester equations (GSEs) are applied in many fields, including applied mathematics, systems and control, and signal processing. Generalized Sylvester Equations: Unified Parametric Solutions presents a unified parametric approach for solving various types of GSEs. In an extremely neat and elegant matrix form, the book provides a single unified parametric solution formula for all the types of GSEs, which further reduces to a specific clear vector form when the parameter matrix F in the equations is a Jordan matrix. Particularly, when the parameter matrix F is diagonal, the reduced vector form becomes extremely simple. The first chapter introduces several types of GSEs and gives a brief overview of solutions to GSEs. The two subsequent chapters then show the importance of GSEs using four typical control design applications and discuss the F-coprimeness of a pair of polynomial matrices. The next several chapters deal with parametric solutions to GSEs. The final two chapters present analytical solutions to normal Sylvester equations (NSEs), including the well-known continuous- and discrete-time Lyapunov equations. An appendix provides the proofs of some theorems. The book can be used as a reference for graduate and senior undergraduate courses in applied mathematics and control systems analysis and design. It will also be useful to readers interested in research and applications based on Sylvester equations.

Computer simulation is an effective and popular universal tool that can be applied to almost all disciplines. Requiring only basic knowledge of programming, mathematics, and probability theory, Computer Simulation: A Foundational Approach Using Python takes a hands-on approach to programming to introduce the fundamentals of computer simulation. The main target of the book is computer science and engineering students who are interested mainly in directly applying the techniques to their research problems. The book will be of great interest to senior undergraduate and starting graduate students in the fields of computer science and engineering and industrial engineering.

This book examines engineering and mathematical models for documenting and approving mechanical and environmental discharges. The author emphasizes engineering design considerations as well as applications to waste water and atmospheric discharges. Chapters discuss: the fundamentals of turbulent jet mixing, dilution concepts, and mixing zone concepts diffuser configurations and head loss calculations different modeling techniques and accepted models - discussed in detail with theoretical background, restrictions, input, output, and examples Lagrangian and the EPA UM 2-dimensional diffuser model the PLUMES interface Eulerian integral methods, EPA UDKHG 3-dimensional diffuser model, and PDSG surface discharge model empirical techniques, RSB diffuser model, the CORMIX family of models for both diffusers and surface discharge numerical methods with a discussion of shelf commercial models Gaussian atmospheric plume models Fundamentals of Environmental Discharge Modeling includes numerous case studies and examples for each model and problem.

The authors examine topics in modern physics and offer a unitary and original treatment of the fundamental problems of the dynamics of physical systems, as well as a description of the nuclear matter within a framework of general relativity. They show that some physical phenomena studied at two different resolution scales (e.g. microscale, cosmological scale), apparently with no connection between them, become compatible by means of the operational procedures, acting either as some "hidden" symmetries, or harmonic-type mappings. The book is addressed to the students, researchers and university/high school teachers working in the fields of mathematics, physics, and chemistry.

Despite significant advances in technology and equipment for rolled steel, the computerization of production processes and the steady increase in production of sheet steel, recent scientific and technological achievements have not been compiled in the special literature and revealed to a wide range of specialists. This book details new approaches, computational techniques, and reliable calculation methods of leaf-rolling modes, forecasting and optimization of the technologies, increasing productivity of the mill and a radical improvement in the quality of steel products.

A Computational Approach to Statistical Learning gives a novel introduction to predictive modeling by focusing on the algorithmic and numeric motivations behind popular statistical methods. The text contains annotated code to over 80 original reference functions. These functions provide minimal working implementations of common statistical learning algorithms. Every chapter concludes with a fully worked out application that illustrates predictive modeling tasks using a real-world dataset. The text begins with a detailed analysis of linear models and ordinary least squares. Subsequent chapters explore extensions such as ridge regression, generalized linear models, and additive models. The second half focuses on the use of general-purpose algorithms for convex optimization and their application to tasks in statistical learning. Models covered include the elastic net, dense neural networks, convolutional neural networks (CNNs), and spectral clustering. A unifying theme throughout the text is the use of optimization theory in the description of predictive models, with a particular focus on the singular value decomposition (SVD). Through this theme, the computational approach motivates and clarifies the relationships between various predictive models. Taylor Arnold is an assistant professor of statistics at the University of Richmond. His work at the intersection of computer vision, natural language processing, and digital humanities has been supported by multiple grants from the National Endowment for the Humanities (NEH) and the American Council of Learned Societies (ACLS). His first book, Humanities Data in R, was published in 2015. Michael Kane is an assistant professor of biostatistics at Yale University. He is the recipient of grants from the National Institutes of Health (NIH), DARPA, and the Bill and Melinda Gates Foundation. His R package bigmemory won the Chamber's prize for statistical software in 2010. Bryan Lewis is an applied mathematician and author of many popular R packages, including irlba, doRedis, and threejs.

This book serves as a guide for discovering pathways to more efficient energy use. The first part of the book illustrates basic laws of energy conversion and principles of thermodynamics. Laws of energy conservation and direction of energy conversion are formulated in detail, and the types of thermodynamic processes are explained. Also included is the characterization of various types of real energy conversion. The second part of the book discusses types of energy conversion referred to as thermal-energy technologies. The advantages of the co-generation processes and devices operating within the Brayton direct cycle and their adaptively to household energetics are underlined.

The H control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H control, and studies more complex and practically useful mixed H2/H controller synthesis rather than the pure H control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H control theory, while practitioners can apply our efficient algorithms to address their practical problems.

When people or computers need to make a decision, typically multiple conflicting criteria need to be evaluated; for example, when we buy a car, we need to consider safety, cost and comfort. Multiple criteria decision making (MCDM) has been researched for decades. Now as the rising trend of big-data analytics in supporting decision making, MCDM can be more powerful when combined with state-of-the-art analytics and machine learning. In this book, the authors introduce a new framework of MCDM, which can lead to more accurate decision making. Several real-world cases will be included to illustrate the new hybrid approaches.

Get First-Hand Insight from a Contributor to the Standard Model of Particle Physics Written by an award-winning former director-general of CERN and one of the world's leading experts on particle physics, Electroweak Interactions explores the concepts that led to unification of the weak and electromagnetic interactions. It provides the fundamental elements of the theory of compact Lie groups and their representations, enabling a basic understanding of the role of flavor symmetry in particle physics. Understand Conceptual Elements of the Theory of Elementary Particles The book begins with the identification of the weak hadronic current with the isotopic spin current, Yang-Mills theory, and the first electroweak theory of Glashow. It discusses spontaneous breaking of a global symmetry and a local symmetry, covering the Goldstone theorem, Brout-Englert-Higgs mechanism, and the theory of Weinberg and Salam. The author then describes the theory of quarks, quark mixing, the Cabibbo angle, the Glashow-Iliopoulos-Maiani (GIM) mechanism, the theory of Kobayashi and Maskawa, six quark flavors, and CP violation. Delve into Experimental Tests and Unresolved Problems The author goes on to explore some phenomenological topics, such as neutral current interactions of neutrinos and CP violation in the neutral K-meson system. He also highlights how flavor-changing neutral current processes have emerged as probes to reveal the presence of new phenomena at energies not yet accessible with particle accelerators. The book concludes with an explanation of the expected properties of the Higgs boson and the methods adopted for its search. The predictions are also compared with relevant experimental results. View the author's first book in this collection: Relativistic Quantum Mechanics: An Introduction to Relativistic Quantum Fields.

'Lighting Engineering: Applied Calculations' describes the mathematical background to the calculation techniques used in lighting engineering and links them to the applications with which they are used. The fundamentals of flux and illuminance, colour, measurement and optical design are covered in detail. There are detailed discussions of specific applications, including interior lighting, road lighting, tunnel lighting, floodlighting and emergency lighting. The authors have used their years of experience to provide guidance for common mistakes and useful techniques including worked examples and case studies. The last decade has seen the universal application of personal computers to lighting engineering on a day-to-day basis. Many calculations that were previously impracticable are therefore now easily accessible to any engineer or designer who has access to an appropriate computer program. However, a grasp of the underlying calculation principles is still necessary in order to utilise these technologies to the full. Written by two of the leading authorities on this subject, 'Lighting Engineering' is essential reading for practising lighting engineers, designers and architects, and students in the field of lighting.

Image Processing and Acquisition using Python provides readers with a sound foundation in both image acquisition and image processing-one of the first books to integrate these topics together. By improving readers' knowledge of image acquisition techniques and corresponding image processing, the book will help them perform experiments more effectively and cost efficiently as well as analyze and measure more accurately. Long recognized as one of the easiest languages for non-programmers to learn, Python is used in a variety of practical examples. A refresher for more experienced readers, the first part of the book presents an introduction to Python, Python modules, reading and writing images using Python, and an introduction to images. The second part discusses the basics of image processing, including pre/post processing using filters, segmentation, morphological operations, and measurements. The second part describes image acquisition using various modalities, such as x-ray, CT, MRI, light microscopy, and electron microscopy. These modalities encompass most of the common image acquisition methods currently used by researchers in academia and industry. Features Covers both the physical methods of obtaining images and the analytical processing methods required to understand the science behind the images. Contains many examples, detailed derivations, and working Python examples of the techniques. Offers practical tips on image acquisition and processing. Includes numerous exercises to test the reader's skills in Python programming and image processing, with solutions to selected problems, example programs, and images available on the book's web page. New to this edition Machine learning has become an indispensable part of image processing and computer vision, so in this new edition two new chapters are included: one on neural networks and the other on convolutional neural networks. A new chapter on affine transform and many new algorithms. Updated Python code aligned to the latest version of modules.

Autowave Plasticity: Localization and Collective Modes discusses the nature of plastic flow in solids associated with the development of a localized plastic flow. Written by an authority in the field, the author demonstrates how patterns of localized plastic flow are associated with autowave modes that are generated in a deformable sample and delivers a complete work on the subject. Key Features An original work on the nature of plastic flows in solids, particularly metals and crystals Focuses on plastic flow as an autowave process Contains elements of theories, experimental considerations, and numerical modeling This reference will help readers with creating experimental methods to observe or localize plastic flow and with the modeling of plastic flows. It is a valuable reference for graduate students and research specialists working in material science.

This book provides a concise introduction to the mathematical aspects of the origin, structure and evolution of the universe. The book begins with a brief overview of observational and theoretical cosmology, along with a short introduction of general relativity. It then goes on to discuss Friedmann models, the Hubble constant and deceleration parameter, singularities, the early universe, inflation, quantum cosmology and the distant future of the universe. This new edition contains a rigorous derivation of the Robertson-Walker metric. It also discusses the limits to the parameter space through various theoretical and observational constraints, and presents a new inflationary solution for a sixth degree potential. This book is suitable as a textbook for advanced undergraduates and beginning graduate students. It will also be of interest to cosmologists, astrophysicists, applied mathematicians and mathematical physicists.

Impulsive differential equations have been the subject of intense investigation in the last 10-20 years, due to the wide possibilities for their application in numerous fields of science and technology. This new work presents a systematic exposition of the results solving all of the more important problems in this field.