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991.
Let μ be a probability measure on [0,2π]. In this paper we shall be concerned with the estimation of integrals of the form

For this purpose we will construct quadrature formulae which are exact in a certain linear subspace of Laurent polynomials. The zeros of Szegö polynomials are chosen as nodes of the corresponding quadratures. We will study this quadrature formula in terms of error expressions and convergence, as well as, its relation with certain two-point Padé approximants for the Herglotz–Riesz transform of μ. Furthermore, a comparison with the so-called Szegö quadrature formulae is presented through some illustrative numerical examples.  相似文献   
992.
By means of a new technique of integral representations in C n given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in C n , which is different from the well-known Leray formula. This new formula eliminates the term that contains the parameter A from the classical Leray formula, and especially on some domains the uniform estimates for the are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in C n , which are different from the classical ones, when we properly select the vector function W.  相似文献   
993.
For each fixed n a radial weight function on is given in closed form which admits minimal cubature formulae of both even and odd degree. The connection between the cubature formula and the polynomial interpolation is discussed in detail. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   
994.
A characterization of round spheres   总被引:2,自引:0,他引:2  
A new characterization of geodesic spheres in the simply connected space forms in terms of higher order mean curvatures is given: An immersion of an dimensional compact oriented manifold without boundary into dimensional Euclidean space, hyperbolic space or the open half sphere is a totally umbilic immersion if, for some the -th mean curvature does not vanish and the ratio is constant.

  相似文献   

995.
Ballistic electron waveguides are open quantum systems that can be formed at very low temperatures at a GaAs/AlGaAs interface. Dissipation due to electron–phonon and electron–electron interactions in these systems is negligible. Although the electrons only interact with the walls of the waveguide, they can have a complicated spectrum including both positive energy bound states and quasibound states which appear as complex energy poles of the scattering S-matrix or energy Green's function. The quasibound states can give rise to zeros in the waveguide conductance as the energy of the electrons is varied. The width of the conduction zeros is determined by the lifetimes of the quasibound states. The complex energy spectrum associated with the quasibound states also governs the survival probability of electrons placed in the waveguide cavities.  相似文献   
996.
The mean-field density matrix of a changed plasma of quantum particles with Maxwell-Boltzmann statistics in a confining external potential is obtained as a limit of theN-body canonical states for suitably scaled charges. Also, it is shown that the density profile of the quantum mean-field theory converges to the solution of the classical mean-field equation when the Planck's constant tends to zero.  相似文献   
997.
 We propose a methodology to locate stationary points on a quantum mechanical/molecular mechanical potential-energy surface. This algorithm is based on a suitable approximation of an initial full Hessian matrix, either a modified Broyden–Fletcher–Goldfarg–Shanno or a Powell update formula for the location of, respectively, a minimum or a transition state, and the so-called rational function optimization. The latter avoids the Hessian matrix inversion required by a quasi-Newton–Raphson method. Some examples are presented and analyzed. Received: 16 July 2001 / Accepted: 9 October 2001 / Published online: 9 January 2002  相似文献   
998.
In the “Lost” note book, Ramanujan had stated a large number of results regarding evaluation of his continued fraction for certain values of τ. It is shown that all these results and many more have their source in the Kronecker limit formula.  相似文献   
999.
Experimental data are analysed to show that the activation enthalpy and the structural entropy appear to follow empirical relations for structural relaxation of polymeric systems. The relations indicate that melting temperature, glass transition temperature, relaxation time, coefficient of thermal expansion of free volume are interrelated in polymers. The parameters of structural relaxations, measured by mechanical and dielectric spectroscopies, are reviewed for polyethylene, poly(4-methyl-1-pentene) and a liquid-crystalline polynorbornene derivative. The thermodynamic parameters obtained from calorimetric measurements, are reported for zero heating rate extrapolation and they are used in the empirical relation, which combines the Arrhenius and the Vogel-Fulcher formulae.  相似文献   
1000.
 对基于J.C.Martin经验公式的多层长渡越时间轴向绝缘堆的闪络概率分析方法进行了分析与总结。在对比各种类似分析方法优劣的基础上,提出了一种较为成熟的针对多层长渡越时间轴向绝缘堆的闪络概率分析方法,为类似绝缘堆结构的设计提供了理论依据。同时,对其中的不确定因素和存在的问题也进行了较为详细的分析和讨论,为闪络概率分析方法的进一步完善奠定了基础。  相似文献   
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