The Sub Laplacian Operators Of Some Model Domains

Author : Der-Chen Chang
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110642999
Total Pages : 266 pages
Book Rating : 4.95/5 ( download)

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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.

Author : Mario Milman
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311074189X
Total Pages : 272 pages
Book Rating : 4.96/5 ( download)

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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.

Author : Praveen Agarwal
Publisher : Springer Nature
ISBN 13 : 981150430X
Total Pages : 251 pages
Book Rating : 4.03/5 ( download)

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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.

Author : Steve Zelditch
Publisher : American Mathematical Soc.
ISBN 13 : 1470410370
Total Pages : 394 pages
Book Rating : 4.77/5 ( download)

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Download or read book Eigenfunctions of the Laplacian on a Riemannian Manifold written by Steve Zelditch and published by American Mathematical Soc.. This book was released on 2017-12-12 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Author : Ravi P. Agarwal
Publisher : Springer Nature
ISBN 13 : 3030690296
Total Pages : 607 pages
Book Rating : 4.98/5 ( download)

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Download or read book Lyapunov Inequalities and Applications written by Ravi P. Agarwal and published by Springer Nature. This book was released on 2021-04-12 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive survey on Lyapunov-type inequalities. It summarizes and puts order into a vast literature available on the subject, and sketches recent developments in this topic. In an elegant and didactic way, this work presents the concepts underlying Lyapunov-type inequalities, covering how they developed and what kind of problems they address. This survey starts by introducing basic applications of Lyapunov’s inequalities. It then advances towards even-order, odd-order, and higher-order boundary value problems; Lyapunov and Hartman-type inequalities; systems of linear, nonlinear, and quasi-linear differential equations; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, half-linear, and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamic systems. Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations. Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.

Author : Russ B Altman
Publisher : World Scientific
ISBN 13 : 9811215642
Total Pages : 764 pages
Book Rating : 4.43/5 ( download)

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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.

Author : Panayotis G. Kevrekidis
Publisher : Springer Nature
ISBN 13 : 3031549783
Total Pages : 337 pages
Book Rating : 4.86/5 ( download)

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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:

Author : Evan Schankee Um
Publisher : Stanford University
ISBN 13 :
Total Pages : 207 pages
Book Rating : 4.62/5 ( download)

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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.

Author : Jan Janas
Publisher : Springer Science & Business Media
ISBN 13 : 3764387556
Total Pages : 437 pages
Book Rating : 4.56/5 ( download)

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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.

Author : Robert Osserman
Publisher : American Mathematical Soc.
ISBN 13 : 0821814397
Total Pages : 333 pages
Book Rating : 4.90/5 ( download)

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Download or read book Geometry of the Laplace Operator written by Robert Osserman and published by American Mathematical Soc.. This book was released on 1980 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: