A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight

In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula

Elastic scattering of electrons from alanine

Differential cross sections (DCSs) for elastic scattering of electrons from alanine, have been measured using a crossed beam system for incident energies between 20 and 80 eV and scattering angles from 10° to 150°. The experimental data were placed upon an absolute scale by normalisation to calculated absolute integral cross sections obtained using the corrected independent-atom method incorporating an improved quasifree absorption model. The calculated data-set includes DCSs and integral elastic and inelastic cross sections in the incident energy range between 1 and 10,000 eV. These theoretical results are found to agree very well with the experimental data both in the shape and magnitude of DCSs except at the smallest scattering angles

Excitations of 1P levels of zinc by electron impact on the ground state

We present results of a joint theoretical and experimental investigation of electron scattering from the 4s2 1S ground state of zinc. The 4s4p 1Po and 4s5p 1Po differential cross sections were measured at scattering angles between 10° and 150° and electron-energies of 15, 20, 25, 40, and 60 eV. Corresponding convergent close-coupling calculations have been performed and are compared with experiment

Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions. ETNA - Electronic Transactions on Numerical Analysis

We consider the Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula for the Fourier-Chebyshev coefficients with the highest algebraic degree of precision. For analytic functions, the remainder term of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ∓1 and the sum of semi-axes ρ>1 for the mentioned quadrature formulas. We derive L∞-error bounds and L1-error bounds for these quadrature formulas. Finally, we obtain explicit bounds by expanding the remainder term. Numerical examples that compare these error bounds are included

Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results. ETNA - Electronic Transactions on Numerical Analysis

This paper presents a survey of recent results on error estimates of Gaussian-type quadrature formulas for analytic functions on confocal ellipses

VOLUME CORRECTION FACTOR IN ELECTRON-INDIUM ATOM SCATTERING EXPERIMENTS UDC 539.171

Abstract. In crossed electron beam- Indium atom beam scattering experiments the measured signal arises from a spatial region (the 'interaction volume') defined by the overlap of the electron and target atom beam and the view cone of the detector. The exchange of the interaction volume with the scattering angle, named a volume correction factor is discussed. The approach of R. T. Brinkmann and S. Trajmar (J. Phys. E 14, 245-254 (1981)) is adopted for our experimental conditions to determine the volume correction factor and accordingly to transfer angular distributions of scattered electrons to relative differential cross sections. Key words: Volume correction facto

Optical and Electron Spectrometry of Molecules of Biological Interest

Optical absorption and emission spectroscopy together with low energy electron interaction (elastic scattering, excitation, ionization, resonances) with biologically relevant molecules (nitrogen, oxygen, water, alcohols, tetrahydrofuran, tetrahydrofurfuril alcohol, 3-hydroxytetrahydrofuran, pyrimidine, glycine, alanine) are studied in order to understand radiation damage and to investigate the presence of pollutants in the atmosphere. Versatile high resolution electron spectrometers are used in the present study of electron-molecule interactions. Energy loss spectra were recorded for these molecules in order to identify electronic transitions from ground state to both allowed and optically forbidden states. Optical emission spectra have been recorded from gas discharge processes by low resolution optical spectrometer (Ocean Optics 2000). Also, electronic spectra were compared with high resolution synchrotron photoabsorption spectra where these spectra had been available. Experimental methods of absorption-based laser spectroscopy were reviewed being of the most widely used analytical tools for detection of a specific molecule and quantitative measurements, based on the Beer-Lambert absorption law