相关论文: Localization of the interior transmission eigenval…
Let M be a closed Riemannian manifold. We consider the inner radius of a nodal domain for a large eigenvalue \lambda. We give upper and lower bounds on the inner radius of the type C/\lambda^k. Our proof is based on a local behavior of…
We prove an optimal stability estimate for Electrical Impedance Tomography with local data, in the case when the conductivity is precisely known on a neighborhood of the boundary. The main novelty here is that we provide a rather general…
A commutative ring $R$ is stable if every non-zero ideal $I$ of $R$ is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much…
We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the…
A reduction of the transmission eigenvalue problem for multiplicative sign-definite perturbations of elliptic operators with constant coefficients to an eigenvalue problem for a non-selfadjoint compact operator is given. Sufficient…
An eigenvalue problem relevant for non-linear sigma model with singular metric is considered. We prove the existence of a non-degenerate pure point spectrum for all finite values of the size R of the system. In the infrared (IR) regime…
Let $A = \pmatrix A_{11} & A_{12} \cr A_{21} & A_{22}\cr\pmatrix \in M_n$, where $A_{11} \in M_m$ with $m \le n/2$, be such that the numerical range of $A$ lies in the set $\{e^{i\varphi} z \in \IC: |\Im z| \le (\Re z) \tan \alpha\}$, for…
We study the asymptotic behavior of the principal eigenvector and eigenvalue of the random conductance Laplacian in a large domain of $\mathbb{Z}^d$ ($d\geq 2$) with zero Dirichlet condition. We assume that the conductances $w$ are positive…
We consider a random symmetric matrix ${\bf X} = [X_{jk}]_{j,k=1}^n$ with upper triangular entries being independent identically distributed random variables with mean zero and unit variance. We additionally suppose that $\mathbb E…
In this paper we extend Sylvester's approach via upper triangular compact operators to establish the discreteness of transmission eigenvalues for higher-order main terms and higher-order perturbations. The coefficients of the perturbations…
We obtain local estimates, also called propagation of smallness or Remez-type inequalities, for analytic functions in several variables. Using Carleman estimates, we obtain a three sphere-type inequality, where the outer two spheres can be…
We consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eingenvalue problem. In order to improve the stability of the plate, it seems…
In this note, we investigate the coboundaries of interval exchange transformations of 3 intervals (3-IETs). More precisely, we show that a differentiable function with absolutely continuous derivative with bounded variation, whose integral…
In this paper, we study the transmission eigenvalue problem for an anisotropic material with a conductive boundary. We prove that the transmission eigenvalues for this problem exist and are at most a discrete set. We also study the…
We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and…
In this addendum, we relax a restrictive assumption in [1] needed for the interior transmission eigenfunctions to hold the intrinsic geometric vanishing property in a corner. In addition we present in more detail another assumption which…
Pre-trained transformers exhibit the capability of adapting to new tasks through in-context learning (ICL), where they efficiently utilize a limited set of prompts without explicit model optimization. The canonical communication problem of…
We report on the electronic structure, density of states and transmission properties of the periodic one-dimensional Tight-Binding (TB) lattice with a single orbital per site and nearest-neighbor interactions, with a generic unit cell of…
Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…
In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.