This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold (M,g,partial derivative M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsf...
详细信息
This work considers the Neumann eigenvalue problem for the weighted Laplacian on a Riemannian manifold (M,g,partial derivative M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(M,g,\partial M)$$\end{document} under a singular perturbation. This perturbation involves the imposition of vanishing Dirichlet boundary conditions on a small portion of the boundary. We derive an asymptotic expansion of the perturbed eigenvalues as the Dirichlet part shrinks to a point x & lowast;is an element of partial derivative M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x<^>*\in \partial M$$\end{document} in terms of the spectral parameters of the unperturbed system. This asymptotic expansion demonstrates the impact of the geometric properties of the manifold at a specific point x & lowast;\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x<^>*$$\end{document}. Furthermore, it becomes evident that the shape of the Dirichlet region holds significance as it impacts the first terms of the asymptotic expansion. A crucial part of this work is the construction of the singularity structure of the restricted Neumann Green's function which may be of independent interest. We employ a fusion of layer potential techniques and pseudo-differential operators during this work.
The article consists of observations regarding complete theories of countable signatures and their countable models. We provide a construction of a countable linearly ordered theory that has the same number of countab...
详细信息
The article consists of observations regarding complete theories of countable signatures and their countable models. We provide a construction of a countable linearly ordered theory that has the same number of countable non-isomorphic models as the given countable, not necessarily linearly ordered, theory.
The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The s...
详细信息
The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.(c) 2023 ISA. Published by Elsevier Ltd. All rights reserved.
We introduce the generalized Besov-type space B-p theta(phi)([0,1];H) over the Haar basis. We givethe two-sided estimate for the norm of functions of the space in terms of their Fourier-Haar ***, we establish a criter...
详细信息
We introduce the generalized Besov-type space B-p theta(phi)([0,1];H) over the Haar basis. We givethe two-sided estimate for the norm of functions of the space in terms of their Fourier-Haar ***, we establish a criterion for the embedding B-p theta(phi)([0,1];H)?-> L-q tau[0,1] and some two-sided estimatefor the approximation of B-p theta(phi)([0,1],H) in the metric of L-q tau[0,1], with 1 <= p < q <+infinity and 1 <=tau <+infinity.
In this paper, boundedness, noetherity and smoothness properties of multidimensional singular integral operators and solvability of the corresponding singular integral equations in Besov spaces are studied.
In this paper, boundedness, noetherity and smoothness properties of multidimensional singular integral operators and solvability of the corresponding singular integral equations in Besov spaces are studied.
In this paper, we investigate the spectrum of the Cesaro-Hardy operator in rearrangement invariant spaces over a finite interval and a half line, thereby extending Boyd's and Leibowitz's results for L-p(1 <...
详细信息
In this paper, we investigate the spectrum of the Cesaro-Hardy operator in rearrangement invariant spaces over a finite interval and a half line, thereby extending Boyd's and Leibowitz's results for L-p(1 < p <= 8) spaces. In particular, when our rearrangement invariant space is the Lorentz space L-p,L-q, a full description of the spectrum and fine spectra is presented.
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, givi...
详细信息
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation in the Fourier domain between measurements of the scattered wave and reconstructions of the scattering potential. With this theorem at hand, Fourier coverages for different experimental setups are investigated taking into account parameters such as object orientation, direction of incidence, and frequency of illumination. Allowing for simultaneous and discontinuous variation of these parameters, a general filtered backpropagation formula is derived resulting in an explicit approximation of the scattering potential for a large class of experimental setups.
This paper investigates the problem of exponential synchronization and anti-synchronization for uncertain discrete-time neural networks (NNs) having time-varying delays with H infinity performance in complex domain. A...
详细信息
This paper investigates the problem of exponential synchronization and anti-synchronization for uncertain discrete-time neural networks (NNs) having time-varying delays with H infinity performance in complex domain. An output-feedback controller is utilized not only to guarantee the synchronization criteria between the addressed discrete-time complex-valued neural networks (CVNNs) but also to reduce the effect of external disturbance. In order to assure the anti-synchronization criteria with H infinity performance for the proposed CVNNs, we have introduced the output-feedback controller by anti-synchronization error analysis. With the help of Lyapunov-Krasovskii functional (LKF), some linear matrix inequality (LMI) based sufficient conditions are derived for both synchronization and anti-synchronization criteria which can be validated through YALMIP toolbox in MATLAB software. At last, a numerical simulation result is provided to verify the correctness of the established theoretical results.(c) 2023 International Association for mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
In this paper, we study non-local in time evolution type equations generated by the Dunkl operator. Direct and inverse problems are investigated with the Caputo time-fractional heat equation with the parameter 0 < ...
详细信息
In this paper, we study non-local in time evolution type equations generated by the Dunkl operator. Direct and inverse problems are investigated with the Caputo time-fractional heat equation with the parameter 0 < gamma <= 1. In particular, well-posedness properties are established for the forward problem. To adopt techniques of the harmonic analysis, we solve the problems in the Sobolev type spaces associated with the Dunkl operator. Our special interest is an inverse source problem for the Caputo-Dunkl heat equation. As additional data, the final time measurement is taken. Since our inverse source problem is ill-posed, we also show the stability result. Moreover, as an advantage of our calculus used here, we derive explicit formulas for the solutions of the direct and inverse problems.
暂无评论