用于周期有限带Dirac谱问题非线性化的迹公式

本文研究具有周期有限带位势的Dirac算子,利用Dirac算子与单值算子的交换性,定义Bloch函数和乘子曲线,获得Dubrovin-Novikov型公式;进而通过复球面上的留数计算及规范变换,分别得到相应于谱带左端点、右端点以及双侧端点的特征函数的迹公式.作为应用,将Dirac谱问题非线性化得到在Liouville意义下完全可积的Hamilton系统.     

On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function

We study the remainder RN(x) in an asymptotic expansion due to S.N.M. Ruijsenaars, for the logarithm of the double gamma function. We show that for any even number N the function is completely monotonic on (0,∞). This proves a recent conjecture of H.L. Pedersen. In addition, we give an estimate for the remainder RN(x) for N even.     

Transport Coefficients Of Ar—Kr Mixtures by Molecular Dynamics Computer Simulation

Abstract

Equilibrium molecular dynamics computer simulations have been used to determine the transport coefficients of model Ar—Kr mixtures, which are represented by Lennard-Jones pair potentials with Lorentz—Berthelot rules for the cross-species interactions. The component self-diffusion and mutual-diffusion coefficients are calculated from time correlation functions and mean square displacements. Time correlation functions are used to evaluate the shear and bulk viscosity, thermal conductivity and the thermal diffusion coefficient (Soret/Dufour coefficient). In the case of the thermal transport coefficients, the partial enthalpy of the two species is required at each state point to define the heat flux rigorously. We obtain this and the partial volume (and species resolved chemical potential) using particle-exchange (and particle insertion) techniques implemented in separate [NPT] simulations at the same state point.

The viscoelasticity of the fluids is characterised by the relaxation times for bulk and shear stress relaxation. The results are for dense liquids close to the triple point temperature and density. Agreement with experiment and previous simulation is particularly good for the density of the mixtures, the shear modulus, shear viscosity, shear stress relaxation time and thermal conductivity. As for the single component noble gas fluids (simulated and experiment) there is a significant qualitative difference in the temperature and, for mixtures, composition dependence of the bulk viscosity.     

数值积分的双侧逼近及应用

通过分析基本数值求积公式的双侧逼近现象,利用加权平均的方法构造出了比原来求积公式至少高二次代数精度新的混合型求积公式,使得积分近似值精度得到大幅度提高,并给出应用它们求数值积分的具体实例.     

基于阈上小色差的色差公式权重函数研究

利用心理物理实验的恒常刺激法,测得了在CIELAB颜色空间中a*b*平面上16个颜色中心的阈上小色差(约3ΔE*ab单位)色度椭圆.基于本实验和RIT-Dupont各16个非中性色颜色中心的彩度差和色调差数据分别拟合得到相应的彩度权重函数SC_ZJU07和色调权重函数SH_ZJU07.应用获得的视觉实验数据对六个基于CIELAB的典型色差公式的彩度和色调权重函数以及SC_ZJU07和SH_ZJU07的色差预测性能进行评价,结果表明所提出的SC_ZJU07和SH_ZJU07的预测性能均为最佳.对于彩度差数据,六个色差公式彩度权重函数的预测性能表现不佳;而对于色调差数据,CIEDE2000色调权重函数的预测性能明显优于其他公式.