Convolution-like Structures, Differential Operators and Diffusion Processes
Convolution-like Structures, Differential Operators and Diffusion Processes

Author: Rúben Sousa

Publisher: Springer Nature

Published: 2022-07-27

Total Pages: 269

ISBN-13: 303105296X

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T​his book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

Special Functions and Analysis of Differential Equations
Special Functions and Analysis of Differential Equations

Author: Praveen Agarwal

Publisher: CRC Press

Published: 2020-09-08

Total Pages: 349

ISBN-13: 1000078582

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Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

Modelling with Ordinary Differential Equations
Modelling with Ordinary Differential Equations

Author: Alfio Borzì

Publisher: CRC Press

Published: 2020-04-13

Total Pages: 405

ISBN-13: 1351190385

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Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Heat Kernels for Elliptic and Sub-elliptic Operators
Heat Kernels for Elliptic and Sub-elliptic Operators

Author: Ovidiu Calin

Publisher: Springer Science & Business Media

Published: 2010-10-10

Total Pages: 444

ISBN-13: 0817649956

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This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Computer Vision - ECCV 2008
Computer Vision - ECCV 2008

Author: David Forsyth

Publisher: Springer

Published: 2008-10-14

Total Pages: 869

ISBN-13: 3540886885

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The four-volume set comprising LNCS volumes 5302/5303/5304/5305 constitutes the refereed proceedings of the 10th European Conference on Computer Vision, ECCV 2008, held in Marseille, France, in October 2008. The 243 revised papers presented were carefully reviewed and selected from a total of 871 papers submitted. The four books cover the entire range of current issues in computer vision. The papers are organized in topical sections on recognition, stereo, people and face recognition, object tracking, matching, learning and features, MRFs, segmentation, computational photography and active reconstruction.

Practical Handbook on Image Processing for Scientific and Technical Applications
Practical Handbook on Image Processing for Scientific and Technical Applications

Author: Bernd Jahne

Publisher: CRC Press

Published: 2004-03-15

Total Pages: 624

ISBN-13: 0849390303

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Image processing is fast becoming a valuable tool for analyzing multidimensional data in all areas of natural science. Since the publication of the best-selling first edition of this handbook, the field of image processing has matured in many of its aspects from ad hoc, empirical approaches to a sound science based on established mathematical and p

Practical Asymptotics
Practical Asymptotics

Author: H.K. Kuiken

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 388

ISBN-13: 9401006989

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Practical Asymptotics is an effective tool for reducing the complexity of large-scale applied-mathematical models arising in engineering, physics, chemistry, and industry, without compromising their accuracy. It exploits the full potential of the dimensionless representation of these models by considering the special nature of the characteristic dimensionless quantities. It can be argued that these dimensionless quantities mostly assume extreme values, particularly for practical parameter settings. Thus, otherwise complicated models can be rendered far less complex and the numerical effort to solve them is greatly reduced. In this book the effectiveness of Practical Asymptotics is demonstrated by fifteen papers devoted to widely differing fields of applied science, such as glass-bottle production, semiconductors, surface-tension-driven flows, microwaving joining, heat generation in foodstuff production, chemical-clock reactions, low-Mach-number flows, to name a few. A strong plea is made for making asymptotics teaching an integral part of any numerics curriculum. Not only will asymptotics reduce the computational effort, it also provides a fuller understanding of the underlying problems.

Inverse Problems in Diffusion Processes
Inverse Problems in Diffusion Processes

Author: Heinz W. Engl

Publisher: SIAM

Published: 1995-01-01

Total Pages: 250

ISBN-13: 9780898713510

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This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.

Computational Data and Social Networks
Computational Data and Social Networks

Author: Xuemin Chen

Publisher: Springer

Published: 2018-12-11

Total Pages: 554

ISBN-13: 3030046486

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This book constitutes the refereed proceedings of the 7th International Conference on Computational Data and Social Networks, CSoNet 2018, held in Shanghai, China, in December 2018. The 44 revised full papers presented in this book toghether with 2 extended abstracts, were carefully reviewed and selected from 106 submissions. The topics cover the fundamental background, theoretical technology development, and real-world applications associated with complex and data network analysis, minimizing in uence of rumors on social networks, blockchain Markov modelling, fraud detection, data mining, internet of things (IoT), internet of vehicles (IoV), and others.