两种群竞争模型的奇摄动群

本文应用多重尺度法构造出非线性微分方程组的解的渐近展开式。并用微分不等式的技巧，证明原问题的解的存在性，且给出解的一致有效渐近估计．     

伴有边界摄动的三阶拟线性向量微分方程边值问题的奇摄动

本文研究伴有边界摄动的三阶拟线性向量微分方程边值问题的奇摄动,在适当的假设下,利用对角化技巧和不动点原理证明了摄动问题解的存在唯一性并给出解的任意阶的一致有效的渐近展开式和余项的估计。     

From dilute to dense self-avoiding walks on hypercubic lattices

A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd ^–1 can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf1–(2d)^–1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).     

Defect of the five-thirds law using the Wiener-Hermite expansion

Application of the refined Wiener-Hermite expansion with moderate to high Reynolds numbers Re to homogeneous, isotropic turbulence is presented. The results show a defect to Kolmogorov's five-thirds law, increase in the absolute value of the exponent comparable with many theoretical predictions. Midrange spectra up to fluctuation Reynolds numbers of 10⁸ show little, if any, dependence of the defect on Re, as long as the initial spectra do not deviate too far from their equilibrium states. The renormalization scheme has also been proven to have no effect on the final shape of the spectrum.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.     

Studies on the Structure and Properties of Cordierite Synthesized by Talc-Magnesite

Homogeneous cordierite has been synthesized at low cost by talc-magnesite and coal gangue as the main raw materials. The mechanism of synthesizing cordierite under such a com- posing system of raw materials, and the effect of temperature on the crystal cell parameters and microstructure and thermal expansion coefficient of cordierite crystal have been studied via testing methods of XRD, SEM, etc. The result shows that the homogeneous cordierite can be synthesized by the systematic composing materials of “talc-magnesite—coal gangue—talc” with heat pre- servation at 1350 ℃ for 1 h; as the keeping time is prolonged, Al3+ and Mg2+ in cordierite crystal are replaced by a few impurity ions such as Fe3+, Fe2+, etc., and the crystal cell parameters of cordierite present an increase trend; as the high-temperature heat preservation is prolonged, the content of glassy phase in the sample is increased, its density is improved, and its thermal expansion coeffi- cient presents an increase trend.     

Thermal coefficient of linear expansion of non-crystalline chalcogenides in the As-S-Se-Te-I system

The object of the paper is an investigation of the glasses of the (As₂S₃)_x(AsSe_0.5Te_0.5I)_100-x. type for 65≤;x≤;95, using methods of thermomechanical analysis. Values of the thermal coefficients of linear expansion in solid and visco-plastic phase were determined. it was shown that introducing arsenic-sulfide in glass-matrix AsChI, i.e. (AsSe_0.5Te_0.5I), leads to an increasing stability of these glasses. The characteristic temperatures of softening Tg and the temperature of the beginning of deformation t_w increase by increasing content of As₂S₃. The analytical forms of dependence of four significant physical values α_g, α_l, Tg, Tw, as a function of As₂S₃ content in the structure of glasses were fitted. This revised version was published online in July 2006 with corrections to the Cover Date.     

液固流化床内床层动态特性的CFD模拟

在对液固流化床内流动特性进行理论分析的基础上，采用多相流CFD方法模拟了二维矩形流化床内水和玻璃球体系的流体动力学特性。实验结果表明，流体速度突变后，液固流化床从一个平衡状态向另一个平衡状态过渡。当液体速度减小时，床层表面及分隔界面的变化与理论模型预测一致；由于重力不稳定性的影响，当液体速度增大时，床层表面稳定上升但与时间不呈线性关系，且分隔界面难以分辨。进而膨胀后停留时间的长短对收缩过程的影响也可以忽略。尽管床层收缩时间明显小于实际膨胀时间，但是与预报的理想膨胀时间比较接近。模拟结果与前人的实验研究和理论分析相吻合，表明多相流CFD模拟可以很好地预测液固流化床的床层动态行为。     

Thermal analysis and thermal expansion studies on high density YBa2−xLaxCu3O7−δ, 0x0.2

The compositions in the YBa_2−xLa_xCu₃O_7−δ (0x0.2) system were prepared by the solid state reaction, employing a novel high-temperature oxygen sintering route. The modified sintering route yields dense slab like microstructures with large grains. The decomposition (incongruent melting) temperature of the YBa₂Cu₃O_7−δ (Y-123) phase was found to shift to higher temperatures with increasing oxygen partial pressure and lanthanum content. Structure remained orthorhombic up to x=0.2 with a decrease in the orthorhombic strain ((b−a)/b). Iodometric titration indicated a systematic increase in the oxygen content with increasing lanthanum content. Thermo-gravimetric studies in various oxygen partial pressures revealed that the oxygen diffusion in to the YBa₂Cu₃O_7−δ (δ>0.5) lattice is an exothermic event and takes place at temperatures not less than 573 K. High-temperature thermal-expansion measurements in air indicated that the nonlinearity in thermal expansion behaviour was reduced by the substitution of lanthanum.