Related papers: A Small Note About Lower Bound of Eigenvalues

One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function…

We prove various estimates for the first eigenvalue of the magnetic Dirichlet Laplacian on a bounded domain in two dimensions. When the magnetic field is constant, we give lower and upper bounds in terms of geometric quantities of the…

If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian H = - Delta + f(r), where f(r)=sum_{i = 1}^{k}a_ir^{q_i}, 2\leq q_i < q_{i+1}, a_i \geq 0$, then the eigenvalues E = E_{n\ell}^{(d)}(\lambda) are given…

This work concerns the global minimization of a prescribed eigenvalue or a weighted sum of prescribed eigenvalues of a Hermitian matrix-valued function depending on its parameters analytically in a box. We describe how the analytical…

This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results…

A type of adaptive finite element method for the eigenvalue problems is proposed based on the multilevel correction scheme. In this method, adaptive finite element method to solve eigenvalue problems involves solving associated boundary…

We consider a Schr\"odinger operator H with a non-vanishing radial magnetic field B=dA and Dirichlet boundary conditions on the unit disk. We assume growth conditions on B near the boundary which guarantee in particular the compactness of…

Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…

In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable…

We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.

This is Part 1 of two papers where we develop the basic potential theory of elliptic operators on posssibly singular almost minimzers using their hyperbolic unfoldings. We can establish surprisingly robust boundary Harnack inequalities…

This work introduces the minimax Laplace transform method, a modification of the cumulant-based matrix Laplace transform method developed in "User-friendly tail bounds for sums of random matrices" (arXiv:1004.4389v6) that yields both upper…

Learning processes are useful methodologies able to improve knowledge of real phenomena. These are often dependent on hyperparameters, variables set before the training process and regulating the learning procedure. Hyperparameters…

A method for computing lower bounds to eigenvalues of sums of lower semibounded self-adjoint operators is presented. We apply the method to one-electron Hamiltonians. To improve the lower bounds we consider symmetry of molecules and use…

This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric…

We establish an explicit lower bound of the first eigenvalue of the Laplacian on K\"ahler manifolds based off the comparison results of Li and Wang. The lower bound will depend on the diameter, dimension, holomorphic sectional curvature and…

This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…

Given all moments of the marginals of a measure on Rn, one provides (a) explicit bounds on its support and (b), a numerical scheme to compute the smallest box that contains the support. It consists of solving a hierarchy of generalized…

This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…

In this paper, we propose a method for computing eigenvalues of elliptic problems using Deep Learning techniques. A key feature of our approach is that it is independent of the space dimension and can compute arbitrary eigenvalues without…