Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

Weighted approximation of functions on the real line by Bernstein polynomials

The authors give error estimates, a Voronovskaya-type relation, strong converse results and saturation for the weighted approximation of functions on the real line with Freud weights by Bernstein-type operators.     

Evaluation of quadrature schemes for the discrete ordinates method

After reviewing the presently available quadrature schemes for the discrete ordinates method, the accuracy of different schemes is analyzed and evaluated. It is shown from a comprehensive error analysis that the moment conditions have to satisfied not only for the principal coordinates directions, as it is mostly carried out, but for any arbitrary test direction. Among the schemes with approximately 50 discrete ordinates the DCT-020-2468 quadrature was found to give the best accuracy. The highest accuracy among all schemes is achieved by the LC-11 quadrature which requires 96 discrete ordinates. This scheme is rarely used up to date and deserves more attention for high accuracy predictions.     

Synthesis of poly(arylene disulfide)-vermiculite nanocomposites via in situ ring-opening reaction of cyclic oligomers

An exfoliated poly(4,4^′-oxybis(benzene)disulfide) (POBDS)/vermiculite (VMT) nanocomposite was prepared by using cyclo(4,4^′-oxybis(benzene)disulfide) (COBDS) oligomers and cetyltrimethyl ammonium bromide exchanged VMT. The POBDS/VMT nanocomposites were fabricated in two steps. First, the COBDS oligomers were used to swell and exfoliate organo VMT to afford COBDS-VMT nanocomposite precursor. Subsequently, the exfoliated POBDS-VMT nanocomposite can be made via in situ and instant melt ring-opening polymerization of the COBDS-VMT nanocomposite precursor. High molecular weight POBDS polymer can be formed in a few minutes. The nano scale dispersion of VMT layers within POBDS polymer was confirmed by both the X-ray diffraction patterns and TEM examinations. This methodology provides a potential approach to synthesize high performance polymer nanocomposite.     

第二类变型Bessel函数的Chebyshev逼近

第二类变型Bessel函数Kn(z)在自变量趋于无穷时就是指数变小的，使用多项式逼近的方法求解往往误差很大．采用指数变换和J．P．Boyd的有理Chebyshev多项式计算第二类变型Bessel函数，得到了令人满意的在较大范围内有效的解．     

Absorption measurement of strained SiGe nanostructures deposited by UHV-CVD

In order to obtain a low band gap photocell based on the widely spread silicon technology, e.g. for thermophotovoltaics, SiGe nanostructures can be introduced into a monocrystalline silicon photocell. Beforehand, it is necessary to know the absorption coefficient of the SiGe quantum wells. On a silicon (1 0 0) substrate multiple Si/SiGe quantum well structures were grown by UHV-CVD. The Ge concentration and the well width were used as growth parameters. To obtain significant absorption, the experiment was set up to allow for 200 internal reflections.The total reflection of the light results in a standing electromagnetic wave. The absorption coefficient was obtained from the experimental data taking the geometry and the electric field distribution in the absorbing layer into account. The influence of well width and germanium content on the absorption was investigated with the goal of maximizing the absorption for photons with energies below the band gap energy of silicon. The measurement results are compared with a theoretical model, which takes the band structure of strained SiGe including confinement effects into account.     

质子入射散裂产物理论研究方法探讨

简要介绍了几种关于中高能质子入射引起散裂反应产物理论计算的方法,以及这些方法的最新发展.比较了这些方法在理论计算中的特点,指出经典外推方法有局限性,量子分子动力学方法和改进后的M C方法的计算结果与实验数据有较好的符合,但是计算量大,而且量子分子动力学方法在与宏观输运理论连接上存在不少的困难.半经验计算方法已经取得了初步的成果,需要根据新的实验结果来对其进行发展. The analysis on spallation product of proton-induced reaction with intermediate energy has important applications, such as astrophysics, biophysics, spallation neutron source, and accelerator-driven system (ADS) etc. In recent year, some theoretical models have been developed to investigate this reaction processes. At present work, we introduce the extrapolated classic theory, the quantum molecule dynamic (QMD) plus statistical decay and fission models, the method of Mento-Carlo and Smiempirical method for...     

On the number of curves of genus 2 over a finite field

In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in , the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in .     

强爆轰参数的理论估算

用两相的排平物态方程对硝基甲烷的强爆轰参数进行了理论估算 ,理论值与拟稳态强爆轰的实验值(爆速、爆压和爆温 )符合得很好 .这既检验了这种理论估算方法 ,也再次检验了爆轰的ZND理论和两相的排平物态方程 ,也是对实验方法的一种支持 .常k形物态方程的强爆轰参数理论估算方法也得到了有条件的肯定     

Determination of contact stresses in problems on bending of a package of transversely isotropic bars

A mechanomathematical model for bending of packages of transversely isotropic bars of rectangular cross section is proposed. Adhesion, slippage, and separation zones between the bars are considered. The resolving equations for deflections and tangential displacements are supplemented with a system of linear differential equations for determining the normal and tangential contact stresses, and boundary conditions are formulated. A scheme for analytical solution of two contact problems—a package under the action of a distributed load and a round stamp—is considered. For these packages, a transition is performed from the initial system of differential equations for determining the contact stresses, where the unknown functions are interrelated by recurrent relationships, to one linear differential equation of fourth order and then to a system of linear algebraic equations. This transition allows us to integrate the initial system and get expressions for the contact stresses.Translated from Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 761–778, November–December, 2004.