Download or read book The Sub Laplacian Operators of Some Model Domains written by Der-Chen Chang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book studies sub-Laplacian operators on a family of model domains in C^{n+1}, which is a good point-wise model for a $CR$ manifold with non-degenerate Levi form. A considerable amount of study has been devoted to partial differential operators constructed from non-commuting vector fields, in which the non-commutativity plays an essential role in determining the regularity properties of the operators.
Download or read book The Sub Laplacian Operators of Some Model Domains written by Der-Chen Chang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-08-01 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker’s equations.
Download or read book Potentials and Partial Differential Equations written by Suzanne Lenhart and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-05-22 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Harmonic Analysis and Convexity written by Alexander Koldobsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-07-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the interaction between harmonic analysis and convex geometry has increased which has resulted in solutions to several long-standing problems. This collection is based on the topics discussed during the Research Semester on Harmonic Analysis and Convexity at the Institute for Computational and Experimental Research in Mathematics in Providence RI in Fall 2022. The volume brings together experts working in related fields to report on the status of major problems in the area including the isomorphic Busemann-Petty and slicing problems for arbitrary measures, extremal problems for Fourier extension and extremal problems for classical singular integrals of martingale type, among others.
Download or read book p Adic Analysis written by W. A. Zúñiga-Galindo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-12-02 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide a fast, interdisciplinary introduction to the basic results of p-adic analysis and its connections with mathematical physics and applications. The book revolves around three topics: (1) p-adic heat equations and ultradiffusion; (2) fundamental solutions and local zeta functions, Riesz kernels, and quadratic forms; (3) Sobolev-type spaces and pseudo-differential evolution equations. These topics are deeply connected with very relevant current research areas. The book includes numerous examples, exercises, and snapshots of several mathematical theories. This book arose from the need to quickly introduce mathematical audience the basic concepts and techniques to do research in p-adic analysis and its connections with mathematical physics and other areas. The book is addressed to a general mathematical audience, which includes computer scientists, theoretical physicists, and people interested in mathematical analysis, PDEs, etc.
Download or read book Geometric Potential Analysis written by Mario Milman and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-06-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
Download or read book Biology in Time and Space A Partial Differential Equation Modeling Approach written by James P. Keener and published by American Mathematical Soc.. This book was released on 2021-06-02 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do biological objects communicate, make structures, make measurements and decisions, search for food, i.e., do all the things necessary for survival? Designed for an advanced undergraduate audience, this book uses mathematics to begin to tell that story. It builds on a background in multivariable calculus, ordinary differential equations, and basic stochastic processes and uses partial differential equations as the framework within which to explore these questions.
Download or read book Three dimensional Finite element Time domain Modeling of the Marine Controlled source Electromagnetic Method written by Evan Schankee Um and published by Stanford University. This book was released on 2011 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: The survey design and data interpretation of the marine controlled-source electromagnetic (CSEM) method require modeling of complex and often subtle offshore geology with accuracy and efficiency. In this dissertation, I develop two efficient finite-element time-domain (FETD) algorithms for the simulation of three-dimensional (3D) electromagnetic (EM) diffusion phenomena. The two FETD algorithms are used to investigate the time-domain CSEM (TDCSEM) method in realistic shallow offshore environments and the effects of seafloor topography and seabed anisotropy on the TDCSEM method. The first FETD algorithm directly solves electric fields by applying the Galerkin method to the electric-field diffusion equation. The time derivatives of the magnetic fields are interpolated at receiver positions via Faraday's law only when the EM fields are output. Therefore, this approach minimizes the total number of unknowns to solve. To ensure both numerical stability and an efficient time-step, the system of FETD equations is discretized using an implicit backward Euler scheme. A sparse direct solver is employed to solve the system of equations. In the implementation of the FETD algorithm, I effectively mitigate the computational cost of solving the system of equations at every time step by reusing previous factorization results. Since the high frequency contents of the transient electric fields attenuate more rapidly in time, the transient electric fields diffuse increasingly slowly over time. Therefore, the FETD algorithm adaptively doubles a time-step size, speeding up simulations. Although the first FETD algorithm has the minimum number of unknowns, it still requires a large amount of memory because of its use of a direct solver. To mitigate this problem, the second FETD algorithm is derived from a vector-and-scalar potential equation that can be solved with an iterative method. The time derivative of the Lorenz gauge condition is used to split the ungauged vector-and-scalar potential equation into a diffusion equation for the vector potential and Poisson's equation for the scalar potential. The diffusion equation for the time derivative of the magnetic vector potentials is the primary equation that is solved at every time step. Poisson's equation is considered a secondary equation and is evaluated only at the time steps where the electric fields are output. A major advantage of this formulation is that the system of equations resulting from the diffusion equation not only has the minimum number of unknowns but also can be solved stably with an iterative solver in the static limit. The developed FETD algorithms are used to simulate the TDCSEM method in shallow offshore models that are derived from SEG salt model. In the offshore models, horizontal and vertical electric-dipole-source configurations are investigated and compared with each other. FETD simulation and visualization play important roles in analyzing the EM diffusion of the TDCSEM configurations. The partially-'guided' diffusion of transient electric fields through a thin reservoir is identified on the cross-section of the seabed models. The modeling studies show that the TDCSEM method effectively senses the localized reservoir close to the large-scale salt structure in the shallow offshore environment. Since the reservoir is close to the salt, the non-linear interaction of the electric fields between the reservoir and the salt is observed. Regardless of whether a horizontal or vertical electric-dipole source is used in the shallow offshore models, inline vertical electric fields at intermediate-to-long offsets are approximately an order of magnitude smaller than horizontal counterparts due to the effect of the air-seawater interface. Consequently, the vertical electric-field measurements become vulnerable to the receiver tilt that results from the irregular seafloor topography. The 3D modeling studies also illustrate that the short-offset VED-Ex configuration is very sensitive to a subtle change of the seafloor topography around the VED source. Therefore, the VED-Ex configuration is vulnerable to measurements and modeling errors at short offsets. In contrast, the VED-Ez configuration is relatively robust to these problems and is considered a practical short-offset configuration. It is demonstrated that the short-offset configuration can be used to estimate the lateral extent and depth of the reservoir. Vertical anisotropy in background also significantly affects the pattern in electric field diffusion by elongating and strengthening the electric field in the horizontal direction. As the degree of vertical anisotropy increases, the vertical resistivity contrast across the reservoir interface decreases. As a result, the week reservoir response is increasingly masked by the elongated and strengthened background response. Consequently, the TDCSEM method loses its sensitivity to the reservoir.
Download or read book 3D Seismic Imaging written by Biondo Biondi and published by SEG Books. This book was released on 2006 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM includes PDF slides for teaching the material in the book and the C3-narrow-azimuth classic data set.
Download or read book Fractional and Fractal Derivative Models for Anomalous Sediment Transport written by HongGuang Sun and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-12-02 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book will introduce new physical approaches (include fractional derivative models, continuous time random walk methods and Hausdorff derivative models) to accurately characterize anomalous sediment transport in turbulent flow. This book will systematically investigate anomalous sediment transport inexperiments, physical analysis, stochastic model and field applications.
Download or read book Advances in Complex Data Modeling and Computational Methods in Statistics written by Anna Maria Paganoni and published by Springer. This book was released on 2014-11-04 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is addressed to statisticians working at the forefront of the statistical analysis of complex and high dimensional data and offers a wide variety of statistical models, computer intensive methods and applications: network inference from the analysis of high dimensional data; new developments for bootstrapping complex data; regression analysis for measuring the downsize reputational risk; statistical methods for research on the human genome dynamics; inference in non-euclidean settings and for shape data; Bayesian methods for reliability and the analysis of complex data; methodological issues in using administrative data for clinical and epidemiological research; regression models with differential regularization; geostatistical methods for mobility analysis through mobile phone data exploration. This volume is the result of a careful selection among the contributions presented at the conference "S.Co.2013: Complex data modeling and computationally intensive methods for estimation and prediction" held at the Politecnico di Milano, 2013. All the papers published here have been rigorously peer-reviewed.
Download or read book Biocomputing 2020 Proceedings Of The Pacific Symposium written by Russ B Altman and published by World Scientific. This book was released on 2019-11-28 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Pacific Symposium on Biocomputing (PSB) 2020 is an international, multidisciplinary conference for the presentation and discussion of current research in the theory and application of computational methods in problems of biological significance. Presentations are rigorously peer reviewed and are published in an archival proceedings volume. PSB 2020 will be held on January 3 -7, 2020 in Kohala Coast, Hawaii. Tutorials and workshops will be offered prior to the start of the conference.PSB 2020 will bring together top researchers from the US, the Asian Pacific nations, and around the world to exchange research results and address open issues in all aspects of computational biology. It is a forum for the presentation of work in databases, algorithms, interfaces, visualization, modeling, and other computational methods, as applied to biological problems, with emphasis on applications in data-rich areas of molecular biology.The PSB has been designed to be responsive to the need for critical mass in sub-disciplines within biocomputing. For that reason, it is the only meeting whose sessions are defined dynamically each year in response to specific proposals. PSB sessions are organized by leaders of research in biocomputing's 'hot topics.' In this way, the meeting provides an early forum for serious examination of emerging methods and approaches in this rapidly changing field.
Download or read book Fractional Dispersive Models and Applications written by Panayotis G. Kevrekidis and published by Springer Nature. This book was released on with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fractional Calculus written by Praveen Agarwal and published by Springer Nature. This book was released on 2019-11-23 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects papers presented at the International Conference on Fractional Differentiation and its Applications (ICFDA), held at the University of Jordan, Amman, Jordan, on 16–18 July 2018. Organized into 13 chapters, the book discusses the latest trends in various fields of theoretical and applied fractional calculus. Besides an essential mathematical interest, its overall goal is a general improvement of the physical world models for the purpose of computer simulation, analysis, design and control in practical applications. It showcases the development of fractional calculus as an acceptable tool for a large number of diverse scientific communities due to more adequate modeling in various fields of mechanics, electricity, chemistry, biology, medicine, economics, control theory, as well as signal and image processing. The book will be a valuable resource for graduate students and researchers of mathematics and engineering.
Download or read book Fourth Summer School in Analysis and Mathematical Physics written by Carlos Villegas-Blas and published by American Mathematical Soc.. This book was released on 2008-12-02 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of three expository articles written by outstanding researchers in Mathematical Physics: Rafael Benguria, Peter Hislop, and Elliott Lieb. The articles are based on their lectures at the Fourth Summer School in Analysis and Mathematical Physics, held at the Institute of Mathematics, Universidad Nacional Autonoma de Mexico, Cuernavaca in May 2005. The main goal of the articles is to link the basic knowledge of a graduate student in Mathematics with three current research topics in Mathematical Physics: Isoperimetric inequalities for eigenvalues of the Laplace Operator, Random Schrodinger Operators, and Stability of Matter, respectively. These well written articles will guide and introduce the reader to current research topics and will also provide information on recent progress in some areas of Mathematical Physics.
Download or read book Methods of Spectral Analysis in Mathematical Physics written by Jan Janas and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.
Download or read book Functional Analysis in Interdisciplinary Applications written by Tynysbek Sh. Kalmenov and published by Springer. This book was released on 2017-12-12 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents current research in functional analysis and its applications to a variety of problems in mathematics and mathematical physics. The book contains over forty carefully refereed contributions to the conference “Functional Analysis in Interdisciplinary Applications” (Astana, Kazakhstan, October 2017). Topics covered include the theory of functions and functional spaces; differential equations and boundary value problems; the relationship between differential equations, integral operators and spectral theory; and mathematical methods in physical sciences. Presenting a wide range of topics and results, this book will appeal to anyone working in the subject area, including researchers and students interested to learn more about different aspects and applications of functional analysis.
