相关论文: On the instability of eigenvalues

The Steklov eigenvalue problem, first introduced over 125 years ago, has seen a surge of interest in the past few decades. This article is a tour of some of the recent developments linking the Steklov eigenvalues and eigenfunctions of…

This paper investigates structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only…

This is the introduction and bibliography for lecture notes of a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September…

A matrix is well separated if all its Gershgorin circles are away from the unit circle and they are separated from each other. In this article, the region of relative errors in the eigenvalues is obtained as a quadratic oval for non…

We discuss the problems arising when computing eigenvalues of self-adjoint operators which lie in a gap between two parts of the essential spectrum. Spectral pollution, i.e. the apparent existence of eigenvalues in numerical computations,…

In his proof of Fermat's Last Theorem, Wiles deployed a commutative algebra technique, namely a numerical criterion for detecting isomorphisms of rings. In our recent work we pick up on Wiles' work and generalize the numerical criterion to…

We investigate the eigenvalue problem $-\text{div}(\sigma \nabla u) = \lambda u\ (\mathscr{P})$ in a 2D domain $\Omega$ divided into two regions $\Omega_{\pm}$. We are interested in situations where $\sigma$ takes positive values on…

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction…

We explore the effect of fluctuations for $T \geq T_c$ in the 2-D negative Hubbard model within the framework of the selfconsistent T-matrix formalism, which goes beyond the BCS approximation and includes pair fluctuations. We enter the…

We investigate eigenvalues of the zero-divisor graph $\Gamma(R)$ of finite commutative rings $R$ and study the interplay between these eigenvalues, the ring-theoretic properties of $R$ and the graph-theoretic properties of $\Gamma(R)$. The…

We prove some eigenvalue inequalities for positive semidefinite matrices partitioned into four blocks. The inradius of the numerical range of the off-diagonal block contributes to these estimates. Some related norm inequalities are given…

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

Tensor-valued and matrix-valued measurements of different physical properties are increasingly available in material sciences and medical imaging applications. The eigenvalues and eigenvectors of such multivariate data provide novel and…

We prove quadratic eigenvalue perturbation bounds for generalized Hermitian eigenvalue problems. The bounds are proportional to the square of the norm of the perturbation matrices divided by the gap between the spectrums. Using the results…

The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the transmission eigenvalue problem for…

We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…

The thermodynamics of Dirac fields under the influence of external electromagnetic fields is studied. For perturbations which act only for finite time, the influence of the perturbation can be described by an automorphism which can be…

We propose a new approach to the Kondo lattice in order to describe simultaneously the Kondo effect and the local magnetism. This approach relies on an original representation of the $S=1/2$ impurity spin in which the different degrees of…

Consider a bound state (an eigenfunction) $\psi$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $\gamma$ and of the one-particle kinetic energy density matrix $\tau$ associated with $\psi$. The paper…

Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of an operator where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several…