Calculation of electron wave functions and refractive index of Ne

The radial wave functions of inner electron shell and outer electron shell of a Ne atom were obtained by the approximate analytical method and tested by calculating the ground state energy of the Ne atom. The equivalent volume of electron cloud and the refractive index of Ne were calculated. The calculated refractive index agrees well with the experimental result. Relationship between the refractive index and the wave function of Ne was discovered. Supported by the New Star Program of Beijing Science and Technology, China (Grant No. 952870400), the Beijing Municipal Commission of Education, and the Excellent Young Teachers Program of Ministry of Education, China     

On pointwise convergence of Fourier series of radial functions in several variables

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.

     

Mode Distribution and Bandwidth Characteristic of Arbitrarily Trapezoidal-Groove Guide for Millimeter Waves

The modes TE and TM of arbitrarily trapezoidal-groove guide are analyzed by using the mode-matching method. The mode TE₁₁ is the dominant mode of the trapezoidal-groove guide under different conditions. The bandwidth characteristic and the operation condition for the single dominant mode are discussed. The obtained conclusions are of very important significance in theoretical study and practical application of trapeziodal-groove guides for millimeter waves.     

Neighboring extremals of dynamic optimization problems with path equality constraints

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique. This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC-2-106. The author is indebted to Professor A. E. Bryson, Jr., Department of Aeronautics and Astronautics, Stanford University, for many stimulating discussions.     

窄带光纤光栅的写入

改进相位掩模法写入光栅的装置,提高其机械稳定性和温度稳定性,不仅提高了光纤光栅的反射率,而且降低了带宽,特别是能在国产的光敏光纤上写出了大于99%反射率和小于02nm带宽的高质量的光纤光栅.这种光栅特别适用于光纤光栅传感方面的应用。     

Volume variation of nuclear Grüneisen parameter for equation of state studies

The method of first principle pseudopotential is used to simulate the volume variation of nuclear Grüneisen parameter. The elements Al and Be, for which Neal’s experimental data exist are investigated. The nuclear Grüneisen obtained from the details of phonon frequencies are in better agreement with the experimental data as compared to those obtained from approximate Slater and Dugdale-MacDonald methods, often used in shock wave studies.     

Collisions and Fracture: a 1-D Theory. How to Tear off a Chandelier from the Ceiling

When a plate falls on the ground, it breaks. We study this phenomenon at the macroscopic level. We restrict ourselves to 1-D problems and illustrate the theory with a chandelier to which a falling stone is tied. The collisions are assumed instantaneous. Percussions are introduced at the unknown fracture points. Equations of motion and constitutive laws give a set of differential equations, whose corresponding variational problem may be solved in SBV (special functions of bounded variation). The example shows how the theory applies and gives realistic results.     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

Degree of approximation to function of bounded variation by Bézier variant of MKZ operators

Guo (Approx. Theory Appl. 4 (1988) 9-18) introduced the integral modification of Meyer-Konig and Zeller operators and studied the rate of convergence for functions of bounded variation. In this paper we introduce the Bézier variant of these integrated MKZ operators and study the rate of convergence by means of the decomposition technique of functions of bounded variation together with some results of probability theory and the exact bound of MKZ basis functions. Recently, Zeng (J. Math. Anal. Appl. 219 (1998) 364-376) claimed to improve the results of Guo and Gupta (Approx. Theory Appl. 11 (1995) 106-107), but there is a major mistake in the paper of Zeng. For special case our main theorem gives the correct estimate on the rate of convergence, over the result of Zeng.     

On the invariance of classes under composition

The necessary and sufficient condition for to be in the class for every of that class whose range is in the domain of is that be in .