Theoretical analysis of collisional shift and broadening of antiprotonic helium spectral lines

Effect of medium density on shift and broadening of ( ) spectral lines is considered in the framework of binary-collision approximation with an effective ( )–He potential including the long-range attraction and short-range repulsion. Quantum calculations of the scattering phase shifts at reasonable values of the potential parameters allow to explain the main features of the observed density effect on the shape of ( ) spectral lines in low-temperature helium. This revised version was published online in August 2006 with corrections to the Cover Date.     

A fast algorithm for Gaussian type quadrature formulae with mixed boundary conditions and some lumped mass spectral approximations

After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.

     

Sharp Spectral Asymptotics and Weyl Formula for Elliptic Operators with Non-smooth Coefficients

The aim of this paper is to give the Weyl formula for eigenvalues of self-adjoint elliptic operators, assuming that first-order derivatives of the coefficients are Lipschitz continuous. The approach is based on the asymptotic formula of Hörmander"s type for the spectral function of pseudodifferential operators having Lipschitz continuous Hamiltonian flow and obtained via a regularization procedure of nonsmooth coefficients.     

一类新型的“三块板”式卟咻化合物的合成及光物理性质初探

在光合作用原初过程中,太阳能转化成电能的关键步骤为:在光引发下,电子从一个叶绿素给体 D 转移到泛醌受体 A,从而产生D~ 和 A~-。光合作用原初过程及其人工模拟是受到世界各国普遍重视的一个研究领域。特别是近年来。卟啉(D)-醌(A)类化合物引起了人们的广泛兴趣,其中三块板式化合物是目前最接近     

Single and Multi-Interval Legendre τ-Methods in Time for Parabolic Equations

In this paper, we take the parabolic equation with periodic boundary conditions as a model to present a spectral method with the Fourier approximation in spatial and single/multi-interval Legendre Petrov–Galerkin method in time. For the single interval spectral method in time, we obtain the optimal error estimate in L ²-norm. For the multi-interval spectral method in time, the L ²-optimal error estimate is valid in spatial. Numerical results show the efficiency of the methods.     

Remote spectrophotometry as applied to determination of the degree of mineralization of peat soils in polesie

Regression relations between the first main component, slope of the SBC curve towards the wavelength axis, and the degree of mineralization of peat soils are established from experimental data. Errors in determination of peat soil productivity are estimated using different spectral indices. For practical use it is recommended to measure the spectral brightness coefficients of peat soils in the 0.50–0.75 μm range. B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 1, pp. 102–106, January–February, 1998.     

Correlation Analysis of the Fluorescence Data of Some Benzaldehyde Derivatives by the Dual-Parameter Equation

Ithasbeenrecentlyestablishedthattherearefourcategoriesofpossiblecircumstancesforcorrelati0nanalyses0fradicalreactivitiesandspectralpropertiesbyEq.(l),Eq.(2)andEq.(3)."(I)Bothp0larandspin-del0calisationeffectsaretwortant,O.2l.O.(III)Thespin-delocalizationeffectspredominate,lpmdpJJ'I<0.2.(IV)Nocorrelationcanbeachieved.Wehavef0undthatthebehavi0roffluorescencespectraldataofsomestyrenes,'bycorrelati0nanalysiswiththedual-parameterEq.(…     

Pressure effects on 2p5 3p - 2p5 3d transitions in neon

The collisional broadening and shift of four spectral lines of neon (747.2, 748.8, 753.5, 754.4 nm) arising from 2p⁵ 3p - 2p⁵ 3d transitions, emitted from a low-pressure glow discharge in pure neon and neon-helium mixtures have been measured using a Fabry-Perot interferometer. The values of pressure broadening and shift coefficients are determined and analyzed in terms of the impact theory.     

一类Schrodinger方程的周期解和谱方法

本文利用半群理论讨论了一类非线性非自共轭Ｓｃｈｒｏｄｉｎｇｅｒ方程周期初边值解的存在唯一性，以及它的Ｆｏｕｒｉｅｒ谱方法的可解性，稳定性和收敛性     

Pressure dependence of the spectral lines of a high power, high pressure atomic fluorine laser pumped by a charge transfer from He2

Various transitions of a pressure tunable atomic fluorine laser have been observed over a rather wide spectral range, 634.8–755.2 nm, by exciting the atmospheric pressure of helium containing 0.2% F₂ in a preionized Blumlein discharge device with a charging voltage of 10–15 kV. The intensity of two quartet transitions, 739.9 and 755.2 nm, increases with pressure, whereas that of the other quartet and doublet lines, 634.8, 641.4, 712.8 and 731.1 nm, decreases with increasing atmospheric fill-pressure. The pumping mechanisms at high pressures appear to be different from those at relatively low pressures.