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| multidimensional integration by parts: Introduction to Stochastic Calculus with Applications Fima C. Klebaner, 2005 This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author. |
| multidimensional integration by parts: Advanced Methods in the Fractional Calculus of Variations Agnieszka B. Malinowska, Tatiana Odzijewicz, Delfim F.M. Torres, 2015-02-05 This brief presents a general unifying perspective on the fractional calculus. It brings together results of several recent approaches in generalizing the least action principle and the Euler–Lagrange equations to include fractional derivatives. The dependence of Lagrangians on generalized fractional operators as well as on classical derivatives is considered along with still more general problems in which integer-order integrals are replaced by fractional integrals. General theorems are obtained for several types of variational problems for which recent results developed in the literature can be obtained as special cases. In particular, the authors offer necessary optimality conditions of Euler–Lagrange type for the fundamental and isoperimetric problems, transversality conditions, and Noether symmetry theorems. The existence of solutions is demonstrated under Tonelli type conditions. The results are used to prove the existence of eigenvalues and corresponding orthogonal eigenfunctions of fractional Sturm–Liouville problems. Advanced Methods in the Fractional Calculus of Variations is a self-contained text which will be useful for graduate students wishing to learn about fractional-order systems. The detailed explanations will interest researchers with backgrounds in applied mathematics, control and optimization as well as in certain areas of physics and engineering. |
| multidimensional integration by parts: Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion N. Bleistein, J.K. Cohen, John W. Jr. Stockwell, 2013-11-22 In the last 40 years geophysicists have found that it is possible to construct images and even determine important physical characteristics of rocks that can yield information about oil and gas bearing structures in the earth. To make these images and extract this information requires the application of an advanced understanding of the mathematical physics of wave propagation. The oil and gas industry labels a major collection of the necessary seismic data processing methods by the name seismic migration. This text ist the first to treat many kinds of migration in a unified mahtematical way. The audience is mathematically oriented geophysicists or applied mathematicians working in the field of inverse scattering imaging. The text can serve as a bridge between the applied math and geophysics community by presenting geophysicists with a practical introduction to advanced engineering mathematics, while presenting mathematicians with a window into the world of the mathematically sophistiated geophysicist. |
| multidimensional integration by parts: Tractability of Multivariate Problems: Standard information for functionals Erich Novak, H. Woźniakowski, 2008 This is the second volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. The second volume deals with algorithms using standard information consisting of function values for the approximation of linear and selected nonlinear functionals. An important example is numerical multivariate integration. The proof techniques used in volumes I and II are quite different. It is especially hard to establish meaningful lower error bounds for the approximation of functionals by using finitely many function values. Here, the concept of decomposable reproducing kernels is helpful, allowing it to find matching lower and upper error bounds for some linear functionals. It is then possible to conclude tractability results from such error bounds. Tractability results, even for linear functionals, are very rich in variety. There are infinite-dimensional Hilbert spaces for which the approximation with an arbitrarily small error of all linear functionals requires only one function value. There are Hilbert spaces for which all nontrivial linear functionals suffer from the curse of dimensionality. This holds for unweighted spaces, where the role of all variables and groups of variables is the same. For weighted spaces one can monitor the role of all variables and groups of variables. Necessary and sufficient conditions on the decay of the weights are given to obtain various notions of tractability. The text contains extensive chapters on discrepancy and integration, decomposable kernels and lower bounds, the Smolyak/sparse grid algorithms, lattice rules and the CBC (component-by-component) algorithms. This is done in various settings. Path integration and quantum computation are also discussed. This volume is of interest to researchers working in computational mathematics, especially in approximation of high-dimensional problems. It is also well suited for graduate courses and seminars. There are 61 open problems listed to stimulate future research in tractability. |
| multidimensional integration by parts: Classical Analysis of Real-Valued Functions V.S. Serov, 2023-09-11 Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first part of Classical Analysis of Real-Valued Functions covers the theorems of existence of supremum and infimum of bounded sets on the real line and the Lagrange formula for differentiable functions. Applications of these results are crucial for classical mathematical analysis, and many are threaded through the text. In the second part of the book, the implicit function theorem plays a central role, while the Gauss–Ostrogradskii formula, surface integration, Heine–Borel lemma, the Ascoli–Arzelà theorem, and the one-dimensional indefinite Lebesgue integral are also covered. This book is intended for first and second year students majoring in mathematics although students of engineering disciplines will also gain important and helpful insights. It is appropriate for courses in mathematical analysis, functional analysis, real analysis, and calculus and can be used for self-study as well. |
| multidimensional integration by parts: Characteristics Finite Element Methods in Computational Fluid Dynamics Joe Iannelli, 2006-09-24 This book details a systematic characteristics-based finite element procedure to investigate incompressible, free-surface and compressible flows. Several sections derive the Fluid Dynamics equations from first thermo-mechanics principles and develop this multi-dimensional and infinite-directional upstream procedure by combining a finite element discretization with an implicit non-linearly stable Runge-Kutta time integration for the numerical solution of the Euler and Navier Stokes equations. |
| multidimensional integration by parts: Monte Carlo and Quasi-Monte Carlo Methods 2000 Kai-Tai Fang, Fred J. Hickernell, Harald Niederreiter, 2011-06-28 This book represents the refereed proceedings of the Fourth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at Hong Kong Baptist University in 2000. An important feature are invited surveys of the state-of-the-art in key areas such as multidimensional numerical integration, low-discrepancy point sets, random number generation, and applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings include also carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active field. |
| multidimensional integration by parts: An Introduction to Partial Differential Equations with MATLAB, Second Edition Matthew P. Coleman, 2013-06-26 An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website. |
| multidimensional integration by parts: Random Number Generation and Quasi-Monte Carlo Methods Harald Niederreiter, 1992-01-01 This volume contains recent work in uniform pseudorandom number generation and quasi-Monte Carlo methods, and stresses the interplay between them. |
| multidimensional integration by parts: Computation of Multivariate Normal and t Probabilities Alan Genz, Frank Bretz, 2009-07-09 Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications. |
| multidimensional integration by parts: Applied Number Theory Harald Niederreiter, Arne Winterhof, 2015-09-01 This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource. |
| multidimensional integration by parts: Differential and Difference Equations with Applications Sandra Pinelas, Tomás Caraballo, Peter Kloeden, John R. Graef, 2018-05-08 This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications. |
| multidimensional integration by parts: Uniform Distribution of Sequences L. Kuipers, H. Niederreiter, 2012-05-24 The theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles. A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text. |
| multidimensional integration by parts: Mathematical Methods for Financial Markets Monique Jeanblanc, Marc Yor, Marc Chesney, 2009-10-13 Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice. |
| multidimensional integration by parts: A Nodal Method for Multigroup, Multidimensional Nuclear Reactor Dynamics with Thermal-hydraulics Feedback Thuy Trong Le, 1990 |
| multidimensional integration by parts: Partial Differential Equations: Modeling, Analysis and Numerical Approximation Hervé Le Dret, Brigitte Lucquin, 2016-02-11 This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems. |
| multidimensional integration by parts: Handbook of Computational and Numerical Methods in Finance Svetlozar T. Rachev, 2011-06-28 Numerical Methods in Finance have recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. They bridge the gap between financial theory and computational practice and provide solutions to problems where analytical methods are often non-applicable. Numerical methods are more and more used in several topics of financial analy sis: computation of complex derivatives; market, credit and operational risk assess ment, asset liability management, optimal portfolio theory, financial econometrics and others. Although numerical methods in finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research focusing on various numerical methods in finance. The contributions cover methodological issues. Genetic Algorithms, Neural Net works, Monte-Carlo methods, Finite Difference Methods, Stochastic Portfolio Opti mization as well as the application of other numerical methods in finance and risk management. As editor, I am grateful to the contributors for their fruitful collaboration. I would particularly like to thankStefan Trueck and Carlo Marinelli for the excellent editorial assistance received over the progress of this project. Thomas Plum did a splendid word-processingjob in preparing the manuscript. lowe much to George Anastassiou (ConsultantEditor, Birkhauser) and Ann Kostant Executive Editor, Mathematics and Physics, Birkhauser for their help and encouragement. |
| multidimensional integration by parts: Applied Analysis and Differential Equations Ovidiu Carja, Ioan I. Vrabie, 2007 This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics. |
| multidimensional integration by parts: Sequences, Discrepancies and Applications Michael Drmota, Robert F. Tichy, 2006-11-14 The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory. |
| multidimensional integration by parts: Tractability of Multivariate Problems: Linear information Erich Novak, H. Woźniakowski, 2008 Multivariate problems occur in many applications. These problems are defined on spaces of $d$-variate functions and $d$ can be huge--in the hundreds or even in the thousands. Some high-dimensional problems can be solved efficiently to within $\varepsilon$, i.e., the cost increases polynomially in $\varepsilon^{-1}$ and $d$. However, there are many multivariate problems for which even the minimal cost increases exponentially in $d$. This exponential dependence on $d$ is called intractability or the curse of dimensionality. This is the first volume of a three-volume set comprising a comprehensive study of the tractability of multivariate problems. It is devoted to tractability in the case of algorithms using linear information and develops the theory for multivariate problems in various settings: worst case, average case, randomized and probabilistic. A problem is tractable if its minimal cost is not exponential in $\varepsilon^{-1}$ and $d$. There are various notions of tractability, depending on how we measure the lack of exponential dependence. For example, a problem is polynomially tractable if its minimal cost is polynomial in $\varepsilon^{-1}$ and $d$. The study of tractability was initiated about 15 years ago. This is the first and only research monograph on this subject. Many multivariate problems suffer from the curse of dimensionality when they are defined over classical (unweighted) spaces. In this case, all variables and groups of variables play the same role, which causes the minimal cost to be exponential in $d$. But many practically important problems are solved today for huge $d$ in a reasonable time. One of the most intriguing challenges of the theory is to understand why this is possible. Multivariate problems may become weakly tractable, polynomially tractable or even strongly polynomially tractable if they are defined over weighted spaces with properly decaying weights. One of the main purposes of this book is to study weighted spaces and obtain necessary and sufficient conditions on weights for various notions of tractability. The book is of interest for researchers working in computational mathematics, especially in approximation of high-dimensional problems. It may be also suitable for graduate courses and seminars. The text concludes with a list of thirty open problems that can be good candidates for future tractability research. |
| multidimensional integration by parts: Applied Stochastic Differential Equations Simo Särkkä, Arno Solin, 2019-05-02 Stochastic differential equations are differential equations whose solutions are stochastic processes. They exhibit appealing mathematical properties that are useful in modeling uncertainties and noisy phenomena in many disciplines. This book is motivated by applications of stochastic differential equations in target tracking and medical technology and, in particular, their use in methodologies such as filtering, smoothing, parameter estimation, and machine learning. It builds an intuitive hands-on understanding of what stochastic differential equations are all about, but also covers the essentials of Itô calculus, the central theorems in the field, and such approximation schemes as stochastic Runge–Kutta. Greater emphasis is given to solution methods than to analysis of theoretical properties of the equations. The book's practical approach assumes only prior understanding of ordinary differential equations. The numerous worked examples and end-of-chapter exercises include application-driven derivations and computational assignments. MATLAB/Octave source code is available for download, promoting hands-on work with the methods. |
| multidimensional integration by parts: Monte Carlo and Quasi-Monte Carlo Methods 2012 Josef Dick, Frances Y. Kuo, Gareth W. Peters, Ian H. Sloan, 2013-12-05 This book represents the refereed proceedings of the Tenth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of New South Wales (Australia) in February 2012. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance, statistics and computer graphics. |
| multidimensional integration by parts: A Panorama of Discrepancy Theory William Chen, Anand Srivastav, Giancarlo Travaglini, 2014-10-07 This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research. |
| multidimensional integration by parts: Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2 , 2019-10-15 Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. |
| multidimensional integration by parts: Analysis and Modelling of Advanced Structures and Smart Systems Holm Altenbach, Erasmo Carrera, Gennady Kulikov, 2017-11-27 This book presents selected papers presented at the 8th International Conference Design, Modeling and Experiments of Advanced Structures and Systems (DeMEASS VIII, held in Moscow, Russia in May 2017) and reflects the modern state of sciences in this field. The contributions contain topics like Piezoelectric, Ferroelectric, Ferroelastic and Magnetostrictive Materials, Shape Memory Alloys and Active Polymers, Functionally Graded Materials, Multi-Functional Smart Materials and Structures, Coupled Multi-Field Problems, Design and Modeling of Sensors and Actuators, Adaptive Structures. |
| multidimensional integration by parts: Monte Carlo and Quasi-Monte Carlo Methods 2004 Harald Niederreiter, Denis Talay, 2006-02-08 This book represents the refereed proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. These conferences were held jointly at Juan-les-Pins (France) in June 2004. The proceedings include carefully selected papers on many aspects of Monte Carlo methods, quasi-Monte Carlo methods, and the numerical solution of partial differential equations. The reader will be informed about current research in these very active areas. |
| multidimensional integration by parts: Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing Harald Niederreiter, Peter J. Shiue, 2012-12-06 Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving. |
| multidimensional integration by parts: The Wave-Particle Dualism S. Diner, D. Fargue, G. Lochak, F. Selleri, 2012-12-06 The Louis de Broglie Foundation (which was created in 1973, for the fiftieth anniversary of the discovery of wave mechanics) and the University of Perugia, have offered an international symposium to Louis de Broglie on his 90th birthday. This publication re presents the Proceedings of this conference which was held in Perugia on April 22-30, 1982. It was an opportunity for the developing of physical conceptions of all origins, which may serve to throw light on the mysterious power of the quantum theory. Quantum Mechanics has reached matu rity in its formalism and although no experiment yet has come to challenge its predictions, one may question the limits of its va lidity. In fact the true meaning of this vision of the microphysi cal world remains the subject of endless debating, at the heart of which lies the foundational myth of wave-particle dualism. Albert Einstein and Louis de Broglie are the two discoverers of this fundamental duality, which they always considered as a deep physical reality rather than a phenomenological artifice. During the conference a survey has been given of the essential recent experimental results in corpuscular and quantum optics and the most up-to-date theoretical aspects of the specificity of mi crophysical phenomena : various interpretations of quantum mecha nics, al ternati ve theories and hidden parameters theories, pro· babilistic and axiomatic questions and tentative crucial experi ments. The conference took place in the magnificent atmosphere of the villa Colombella lent to us by the Universita per Stranieri di Perugia |
| multidimensional integration by parts: Monte Carlo and Quasi-Monte Carlo Methods 2002 Harald Niederreiter, 2011-06-28 This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area. |
| multidimensional integration by parts: Mathematical and Physical Modeling of Materials Processing Operations Olusegun Johnso Ilegbusi, Manabu Iguchi, Walter E. Wahnsiedler, 1999-07-29 The past few decades have brought significant advances in the computational methods and in the experimental techniques used to study transport phenomena in materials processing operations. However, the advances have been made independently and with competition between the two approaches. Mathematical models are easier and less costly to implement, but experiments are essential for verifying theoretical models. In Mathematical and Physical Modeling of Materials Processing Operations, the authors bridge the gap between mathematical modelers and experimentalists. They combine mathematical and physical modeling principles for materials processing operations simulation and use numerous examples to compare theoretical and experimental results. The modeling of transport processes is multi-disciplinary, involving concepts and principles not all of which can be associated with just one field of study. Therefore, the authors have taken care to ensure that the text is self-sustaining through the variety and breadth of topics covered. Beyond the usual topics associated with transport phenomena, the authors also include detailed discussion of numerical methods and implementation of process models, software and hardware selection and application, and representation of auxiliary relationships, including turbulence modeling, chemical kinetics, magnetohydrodynamics, and multi-phase flow. They also provide several correlations for representing the boundary conditions of fluid flow, heat transfer, and mass transfer phenomena. Mathematical and Physical Modeling of Materials Processing Operations is ideal for introducing these tools to materials engineers and researchers. Although the book emphasizes materials, some of the topics will prove interesting and useful to researchers in other fields of chemical and mechanical engineering. |
| multidimensional integration by parts: Convex Duality and Financial Mathematics Peter Carr, Qiji Jim Zhu, 2018-07-18 This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims |
| multidimensional integration by parts: HCI International 2021 - Posters Constantine Stephanidis, Margherita Antona, Stavroula Ntoa, 2021-07-03 The three-volume set CCIS 1419, CCIS 1420, and CCIS 1421 contains the extended abstracts of the posters presented during the 23rd International Conference on Human-Computer Interaction, HCII 2021, which was held virtually in July 2021. The total of 1276 papers and 241 posters included in the 39 HCII 2021 proceedings volumes was carefully reviewed and selected from 5222 submissions. The posters presented in these three volumes are organized in topical sections as follows: Part I: HCI theory and methods; perceptual, cognitive and psychophisiological aspects of interaction; designing for children; designing for older people; design case studies; dimensions of user experience; information, language, culture and media. Part II: interaction methods and techniques; eye-tracking and facial expressions recognition; human-robot interaction; virtual, augmented and mixed reality; security and privacy issues in HCI; AI and machine learning in HCI. Part III: interacting and learning; interacting and playing; interacting and driving; digital wellbeing, eHealth and mHealth; interacting and shopping; HCI, safety and sustainability; HCI in the time of pandemic. |
| multidimensional integration by parts: Introduction to Analysis Maxwell Rosenlicht, 1986-01-01 Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition. |
| multidimensional integration by parts: Fundamentals of Finite Element Analysis Ioannis Koutromanos, 2018-02-12 An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis. |
| multidimensional integration by parts: Henstock-kurzweil Integration On Euclidean Spaces Tuo Yeong Lee, 2011-03-16 The Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus. |
| multidimensional integration by parts: Efficient High-Order Discretizations for Computational Fluid Dynamics Martin Kronbichler, Per-Olof Persson, 2021-01-04 The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations. |
| multidimensional integration by parts: Probabilistic Inequalities George A. Anastassiou, 2010 1. Introduction -- 2. Basic stochastic Ostrowski inequalities -- 3. Multidimensional Montgomery identities and Ostrowski type inequalities -- 4. General probabilistic inequalities -- 5. About Grothendieck inequalities -- 6. Basic optimal estimation of Csiszar's f-divergence -- 7. Approximation via representations of Csiszar's f-divergence -- 8. Sharp high degree estimation of Csiszar's f-divergence -- 9. Csiszar's f-divergence as a measure of dependence --10. Optimal estimation of discrete Csiszar f-divergence -- 11. About a general discrete measure of dependence -- 12. Hölder-Like Csiszar's f-divergence inequalities -- 13. Csiszar's discrimination and Ostrowski inequalities via Euler-type and Fink identities -- 14. Taylor-Widder representations and Grüss, Means, Ostrowski and Csiszar's inequalities -- 15. Representations of functions and Csiszar's f-divergence -- 16. About general moment theory -- 17. Extreme bounds on the average of a rounded off observation under a moment condition -- 18. Moment theory of random rounding rules subject to one moment condition -- 19. Moment theory on random rounding rules using two moment conditions -- 20. Prokhorov radius around zero using three moment constraints -- 21. Precise rates of Prokhorov convergence using three moment conditions -- 22. On Prokhorov convergence or probability measures to the unit under three moments -- 23. Geometric moment methods applied to optimal portfolio -- 24. Discrepancies between general integral means -- 25. Grüss type inequalities using the Stieltjes integral -- 26. Chebyshev-Grüss type and difference of integral means inequalities using the Stieltjes integral -- 27. An expansion formula -- 28. Integration by parts on the multidimensional domain. |
| multidimensional integration by parts: Stochastic Methods in Asset Pricing Andrew Lyasoff, 2017-08-25 A comprehensive overview of the theory of stochastic processes and its connections to asset pricing, accompanied by some concrete applications. This book presents a self-contained, comprehensive, and yet concise and condensed overview of the theory and methods of probability, integration, stochastic processes, optimal control, and their connections to the principles of asset pricing. The book is broader in scope than other introductory-level graduate texts on the subject, requires fewer prerequisites, and covers the relevant material at greater depth, mainly without rigorous technical proofs. The book brings to an introductory level certain concepts and topics that are usually found in advanced research monographs on stochastic processes and asset pricing, and it attempts to establish greater clarity on the connections between these two fields. The book begins with measure-theoretic probability and integration, and then develops the classical tools of stochastic calculus, including stochastic calculus with jumps and Lévy processes. For asset pricing, the book begins with a brief overview of risk preferences and general equilibrium in incomplete finite endowment economies, followed by the classical asset pricing setup in continuous time. The goal is to present a coherent single overview. For example, the text introduces discrete-time martingales as a consequence of market equilibrium considerations and connects them to the stochastic discount factors before offering a general definition. It covers concrete option pricing models (including stochastic volatility, exchange options, and the exercise of American options), Merton's investment–consumption problem, and several other applications. The book includes more than 450 exercises (with detailed hints). Appendixes cover analysis and topology and computer code related to the practical applications discussed in the text. |
| multidimensional integration by parts: Boundary Element Fundamentals G. Steven Gipson, 1987 |
| multidimensional integration by parts: Analytic Number Theory W. W. L. Chen, 2009-02-19 A collection of papers inspired by the work of Britain's first Fields Medallist, Klaus Roth. |
MULTIDIMENSIONAL Definition & Meaning - Merriam-Webster
The meaning of MULTIDIMENSIONAL is having or relating to multiple dimensions or aspects. How to use multidimensional in a sentence.
Multidimensional - Definition, Meaning & Synonyms
The adjective multidimensional describes anything with many different parts or aspects. You might talk about your relationship with the next door neighbor as multidimensional if, say, he's also …
MULTIDIMENSIONAL | English meaning - Cambridge Dictionary
In general, physical systems expressed in probabilistic form will have multidimensional states associated with the moments of the probability distributions. The difficulty in settling these …
10 Synonyms & Antonyms for MULTIDIMENSIONAL
Find 10 different ways to say MULTIDIMENSIONAL, along with antonyms, related words, and example sentences at Thesaurus.com.
MULTIDIMENSIONAL definition and meaning | Collins English …
2 meanings: 1. having many aspects or facets 2. having many physical dimensions.... Click for more definitions.
multidimensional - The Free Dictionary
multidimensional - having or involving or marked by several dimensions or aspects; "multidimensional problems"; "a multidimensional proposition"; "a multidimensional personality"
multidimensional adjective - Definition, pictures, pronunciation …
having several dimensions (= measurements in space) Definition of multidimensional adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, …
multi-dimensional or multidimensional? - TextRanch
Mar 31, 2024 · Both 'multi-dimensional' and 'multidimensional' are correct, but 'multidimensional' is more commonly used in English. They have the same meaning and can be used …
What does Multidimensional mean? - Definitions.net
In mathematics and physics, it's often used to describe a space or phenomenon that is characterized by more than three dimensions. In psychology or sociology, a multidimensional …
multidimensional - Wiktionary, the free dictionary
Jan 2, 2025 · (mathematics) Having more than two dimensions. Crossing through or existing in multiple dimensions (spacial planes). The Cosmic Woman is an integrated, multidimensional …
MULTIDIMENSIONAL Definition & Meaning - Merriam-Webster
The meaning of MULTIDIMENSIONAL is having or relating to multiple dimensions or aspects. How to use multidimensional in a sentence.
Multidimensional - Definition, Meaning & Synonyms
The adjective multidimensional describes anything with many different parts or aspects. You might talk about your relationship with the next door neighbor as multidimensional if, say, he's also …
MULTIDIMENSIONAL | English meaning - Cambridge Dictionary
In general, physical systems expressed in probabilistic form will have multidimensional states associated with the moments of the probability distributions. The difficulty in settling these …
10 Synonyms & Antonyms for MULTIDIMENSIONAL
Find 10 different ways to say MULTIDIMENSIONAL, along with antonyms, related words, and example sentences at Thesaurus.com.
MULTIDIMENSIONAL definition and meaning | Collins English …
2 meanings: 1. having many aspects or facets 2. having many physical dimensions.... Click for more definitions.
multidimensional - The Free Dictionary
multidimensional - having or involving or marked by several dimensions or aspects; "multidimensional problems"; "a multidimensional proposition"; "a multidimensional personality"
multidimensional adjective - Definition, pictures, pronunciation …
having several dimensions (= measurements in space) Definition of multidimensional adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, …
multi-dimensional or multidimensional? - TextRanch
Mar 31, 2024 · Both 'multi-dimensional' and 'multidimensional' are correct, but 'multidimensional' is more commonly used in English. They have the same meaning and can be used …
What does Multidimensional mean? - Definitions.net
In mathematics and physics, it's often used to describe a space or phenomenon that is characterized by more than three dimensions. In psychology or sociology, a multidimensional …
multidimensional - Wiktionary, the free dictionary
Jan 2, 2025 · (mathematics) Having more than two dimensions. Crossing through or existing in multiple dimensions (spacial planes). The Cosmic Woman is an integrated, multidimensional …
