Related papers: Upper and lower bounds to the eigenvalues of an an…
Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. The main goal of this paper is to estimate the lower bound for…
This paper proposes hybrid high-order eigensolvers for the computation of guaranteed lower eigenvalue bounds. These bounds display higher order convergence rates and are accessible to adaptive mesh-refining algorithms. The involved…
We consider the torsional rigidity and the principal eigenvalue related to the $p$-Laplace operator. The goal is to find upper and lower bounds to products of suitable powers of the quantities above in various classes of domains. The limit…
We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the…
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical…
The aim of this article is to provide a simple and unified way to obtain the sharp upper bounds of nodal sets of eigenfunctions for different types of eigenvalue problems on real analytic domains. The examples include biharmonic Steklov…
In this paper, we prove some isoperimetric bounds for lower order eigenvalues of the Wentzell-Laplace operator on bounded domains of a Euclidean space or a Hadamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean space or…
In this paper, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two and three dimensions. The analysis relies on an identity for the errors of…
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…
The polynomial solution of the Schrodinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum $l$. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically…
In this paper, we consider eigenvalues of the Dirichlet biharmonic operator on a bounded domain in a hyperbolic space. We obtain universal bounds on the $(k+1)$th eigenvalue in terms of the first $k$th eigenvalue independent of the domains.
We provide analytical lower and upper bounds for entanglement of formation for bipartite systems, which give a direct relation between the bounds of entanglement of formation and concurrence, and improve the previous results. Detailed…
The problem of resonant excitation of a harmonic oscillator the energy levels of which are slightly shifted under the action of a random potential is solved. It is shown that, in this case, there exists a threshold magnitude of the exciting…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator is developed. Based upon the $\hbar$-expansions and suitable quantization conditions a new…
This paper studies eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We prove universal bounds for the $k$-th eigenvalue in terms of the lower ones independent of the domains. Our…
The explicit semiclassical treatment of the logarithmic perturbation theory for the bound-state problem for the spherical anharmonic oscillator and the screened Coulomb potential is developed. Based upon the $\hbar$-expansions and suitable…
In this paper, we give some lower bounds for several eigenvalues. Firstly, we investigate the eigenvalues $\lambda_i$ of the Laplace operator and prove a sharp lower bound. Moreover, we extent this estimate of the eigenvalues to general…
We consider application of the multiple time delayed feedback for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, the multiple one exhibits resonances between feedback and…
The eigenvalues of a pure quartic oscillator are computed, applying a canonical operator formulation, generalized from the harmonic oscillator. Solving a 10x10 secular equation produces eigenvalues in agreement, to at least 4 significant…
We derive upper and lower bounds on the determinant of an exponential matrix. They can be transformed into corresponding bounds for the determinant of a univariate Gaussian matrix.