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

Approximation of Uncoupled Quasi-Static Thermoelasticity Solutions Based on Gaussians

A fast approximation method to three dimensional equations in quasi-static uncoupled thermoelasticity is proposed. We approximate the density via Gaussian approximating functions introduced in the method approximate approximations. In this way the action of the integral operators on such functions is presented in a simple analytical form. If the density has separated representation, the problem is reduced to the computation of one-dimensional integrals which admit efficient cubature procedures. The comparison of the numerical and exact solution shows that these formulas are accurate and provide the predicted approximation rate 2 , 4 , 6 and 8

Approximation of solutions to multidimensional parabolic equations by Approximate Approximations

Abstract. We propose a fast method for high order approximations of the solution of ndimensional parabolic problems over hyper-rectangular domains in the framework of the method of approximate approximations. This approach, combined with separated representations, make our method effective also in very high dimensions. We report on numerical results illustrating that our formulas are accurate and provide the predicted approximation rate 6 up to dimension 10 7

A high-efficiency spin-resolved phototemission spectrometer combining time-of-flight spectroscopy with exchange-scattering polarimetry

We describe a spin-resolved electron spectrometer capable of uniquely efficient and high energy resolution measurements. Spin analysis is obtained through polarimetry based on low-energy exchange scattering from a ferromagnetic thin-film target. This approach can achieve a similar analyzing power (Sherman function) as state-of-the-art Mott scattering polarimeters, but with as much as 100 times improved efficiency due to increased reflectivity. Performance is further enhanced by integrating the polarimeter into a time-of-flight (TOF) based energy analysis scheme with a precise and flexible electrostatic lens system. The parallel acquisition of a range of electron kinetic energies afforded by the TOF approach results in an order of magnitude (or more) increase in efficiency compared to hemispherical analyzers. The lens system additionally features a 90{\deg} bandpass filter, which by removing unwanted parts of the photoelectron distribution allows the TOF technique to be performed at low electron drift energy and high energy resolution within a wide range of experimental parameters. The spectrometer is ideally suited for high-resolution spin- and angle-resolved photoemission spectroscopy (spin-ARPES), and initial results are shown. The TOF approach makes the spectrometer especially ideal for time-resolved spin-ARPES experiments.Comment: 16 pages, 11 figure

Emotional intelligence in children with severe sleep-related breathing disorders

Background. Obstructive sleep apnea syndrome (OSAS) affects up to 4% of a pediatric population, with many comorbidities in the medium-long term. Functional alterations in the prefrontal cortex (PFC) may explain why OSAS impacts aspects such as executive functions, memory, motor control, attention, visual-spatial skills, learning, and mood regulation. Emotional intelligence (EI) is a complex neuropsychological function that could be impaired in many clinical conditions. Purpose. The aim of the study is to evaluate the difference in emotional intelligence skills among children with OSAS and healthy subjects (nOSAS). Methods. 129 children (72 males; mean age 7.64 ± 1.98 years) affected by OSAS were compared to 264 non-OSAS (nOSAS) children (138 males; mean age 7 98 ± 2.13) similar for gender, age, and socioeconomic status. In order to assess the emotional quotient, the Bar-On Emotional Quotient Inventory: Youth Version (EQ-i:YV) was used. Results. The comparison for means and standard deviation between OSAS children and nOSAS children for EQ-i:YV scores showed significant differences for Interpersonal, Adaptability, and Stress Management scales and EQ Total score. Conclusions. Our findings highlighted the role of intermittent hypoxia in the genesis of the effects of sleep-related respiratory disorders, which involves also aspects different from physical impairments

Disentangling the electronic and phononic glue in a high-Tc superconductor

Unveiling the nature of the bosonic excitations that mediate the formation of Cooper pairs is a key issue for understanding unconventional superconductivity. A fundamen- tal step toward this goal would be to identify the relative weight of the electronic and phononic contributions to the overall frequency (\Omega) dependent bosonic function, \Pi(\Omega). We perform optical spectroscopy on Bi2212 crystals with simultaneous time- and frequency-resolution; this technique allows us to disentangle the electronic and phononic contributions by their different temporal evolution. The strength of the interaction ({\lambda}~1.1) with the electronic excitations and their spectral distribution fully account for the high critical temperature of the superconducting phase transition.Comment: 9 pages, 4 figure

Charge fluctuations and electron-phonon interaction in the finite-UU Hubbard model

In this paper we employ a gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of $U$ and $n$. The suppression of large momentum scattering and the onset a small-${\bf q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole $U$-$n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.Comment: 4 pages, eps figures include