Approximate Approximations from scattered data

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe the application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators.Comment: 29 pages, 17 figure

Computation of volume potentials over bounded domains via approximate approximations

We obtain cubature formulas of volume potentials over bounded domains combining the basis functions introduced in the theory of approximate approximations with their integration over the tangential-halfspace. Then the computation is reduced to the quadrature of one dimensional integrals over the halfline. We conclude the paper providing numerical tests which show that these formulas give very accurate approximations and confirm the predicted order of convergence.Comment: 18 page

Approximate approximations from scattered data

AbstractThe aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe an application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators

Fast computation of elastic and hydrodynamic potentials using approximate approximations

We propose fast cubature formulas for the elastic and hydrodynamic potentials based on the approximate approximation of the densities with Gaussian and related functions. For densities with separated representation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures. We obtain high order approximations up to a small saturation error, which is negligible in computations. Results of numerical experiments which show approximation order O(h2M) , M= 1 , 2 , 3 , 4 , are provided

Application of advanced computational codes in the design of an experiment for a supersonic throughflow fan rotor

Increased emphasis on sustained supersonic or hypersonic cruise has revived interest in the supersonic throughflow fan as a possible component in advanced propulsion systems. Use of a fan that can operate with a supersonic inlet axial Mach number is attractive from the standpoint of reducing the inlet losses incurred in diffusing the flow from a supersonic flight Mach number to a subsonic one at the fan face. The design of the experiment using advanced computational codes to calculate the components required is described. The rotor was designed using existing turbomachinery design and analysis codes modified to handle fully supersonic axial flow through the rotor. A two-dimensional axisymmetric throughflow design code plus a blade element code were used to generate fan rotor velocity diagrams and blade shapes. A quasi-three-dimensional, thin shear layer Navier-Stokes code was used to assess the performance of the fan rotor blade shapes. The final design was stacked and checked for three-dimensional effects using a three-dimensional Euler code interactively coupled with a two-dimensional boundary layer code. The nozzle design in the expansion region was analyzed with a three-dimensional parabolized viscous code which corroborated the results from the Euler code. A translating supersonic diffuser was designed using these same codes

Interaction between Mn Ions and Free Carriers in Quantum Wells with Asymmetrical Semimagnetic Barriers

Investigations of photoluminescence (PL) in the magnetic field of quantum structures based on the ZnSe quantum well with asymmetrical ZnBeMnSe and ZnBeSe barriers reveal that the introduction of Be into semimagnetic ZnMnSe causes a decrease of the exchange integrals for conductive and valence bands as well as the forming of a complex based on Mn, degeneration of an energy level of which with the energy levels of the V band of ZnBeMnSe or ZnSe results in spin-flip electron transitions.Comment: Accepted to Europhys. Let

Infrared electron modes in light deformed clusters

Infrared quadrupole modes (IRQM) of the valence electrons in light deformed sodium clusters are studied by means of the time-dependent local-density approximation (TDLDA). IRQM are classified by angular momentum components $\lambda\mu =$20, 21 and 22 whose $\mu$ branches are separated by cluster deformation. In light clusters with a low spectral density, IRQM are unambiguously related to specific electron-hole excitations, thus giving access to the single-electron spectrum near the Fermi surface (HOMO-LUMO region). Most of IRQM are determined by cluster deformation and so can serve as a sensitive probe of the deformation effects in the mean field. The IRQM branch $\lambda\mu =$21 is coupled with the magnetic scissors mode, which gives a chance to detect the latter. We discuss two-photon processes, Raman scattering (RS), stimulated emission pumping (SEP), and stimulated adiabatic Raman passage (STIRAP), as the relevant tools to observe IRQM. A new method to detect the IRQM population in clusters is proposed.Comment: 22 pages, 6 figure

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde