Abstract. We consider the square root of the Laplace operator (−∆)1/2 in a bounded domain. The square root of the Laplacian can be realized as the Dirichlet to Neumann operator of an extension problem posed on a semi-infinite cylinder. This extension problem involves a mixed boundary value problem, which we analyze in the framework of Sobolev spaces. For numerical approximation we propose a sui...

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can pro tably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with non-central vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Ahar...

In this paper, we consider the variations of eigenvalues and eigenfunctions for the Laplace operator with homogeneous Dirichlet boundary conditions under deformation of the underlying domain of definition. We derive recursive formulas for the Taylor coefficients of the eigenvalues as functions of the shape-perturbation parameter and we establish the existence of a set of eigenfunctions that is ...

In this paper we construct new operators of Bernstein type with a better approximation than the classical Bernstein operator for some classes of functions on the whole interval [0,1]. Convergence of these operators and their shape preserving properties are discussed. We determine the subintervals in [0,1] in which the approximation order of constructed operators is better than that of the Berns...

Mesh segmentation offers a desirable divide-and-conquer strategy for many graphics applications. In this paper, we present a novel, efficient, and intrinsic method to segment meshes following the minima rule. The eigenfunctions of the Laplace-Beltrami operator define locality and volume-shape preserving functions over a surface. Inspired on Manifold learning theory, we use these functions as th...

Ideally the character of an evolutionary search algorithm should be predicated on the shape of the underlying search landscape. Unfortunately, a number of operators used in evolutionary computation are very sensitive to rotation of the encoding space. The potential bias of the orientation of the encoding for these operators indicates that both the alignment of the encoding as well as the search...

The Compass tokamak, reinstalled at IPP Prague, will have a new digital plasma position and shape control system. Development of a communication protocol is necessary for the connection between the energetics devices 1 built by CKD company and the operator either human or computer together. The present work is focused on development of such communication protocol. Human operator can send a requ...

The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high di...

We investigate the dispersive properties of evolution equations on waveguides with a non flat shape. More precisely we consider an operator H = −∆x −∆y + V (x, y) with Dirichled boundary condition on an unbounded domain Ω, and we introduce the notion of a repulsive waveguide along the direction of the first group of variables x. If Ω is a repulsive waveguide, we prove a sharp estimate for the H...

Correlation functions (CFs) associated with the inverse background-error correlations (iBECs) represented by polynomials of the diffusion operator D are obtained analytically for the binomial approximations of the Gaussian BEC and in the general case of a quadratic polynomial of D. The respective analytical expressions for one-, twoand three-dimensional cases have two tuning parameters, which p...