Lipschitz Continuous Solutions to the Cauchy Problem for Quasi-linear Hyperbolic Systems

Lipschitz continuous solutions to the Cauchy problem for 1-D first order quasilinear hyperbolic systems are considered. Based on the methods of approximation and integral equations,the author gives two...     

PbTe纳米晶高压热电性能的研究

 利用自建的400 t四柱双缸液压机,研究了PbTe纳米晶在0~0.8 GPa压力范围内热电性能随压力的变化。实验结果表明：PbTe纳米晶电导率随压力的增加而增加,而热电动势随压力的增加而减小,两者随压力的变化具有可逆性;PbTe纳米晶具有极高的热电动势,在常压下达到565 μV/K,在0.8 GPa压力下,材料的电导率为常压下的4倍,热电动势仅降低20%,功率因子则达到常压下的3倍。研究表明,高压能显著提高PbTe纳米晶的热电性能。利用第一性原理计算了0.4~4.0 GPa压力范围内材料的简约费米能级,计算结果与实验结果相吻合。     

第一原理研究铝锂金属间化合物

运用密度泛函理论系统地研究了二元铝锂金属间化合物Al₃Li、AlLi、Al₂Li₃和Al₄Li₉的结构、形成热、弹性和电子结构.通过计算四种金属间化合物的形成热,证明了金属间化合物中铝和锂之间具有强烈的化学作用. 在富锂金属间化合物中,随着锂的含量的增加,金属间化合物热力学稳定性呈线性减弱. 计算金属间化合物的单晶弹性常数可以得出四种金属间化合物都是机械稳定的. 运用Voigt-Reuss-Hil     

Barium Peroxide: a Simple Test Case for First‐Principles Investigations on the Temperature Dependence of Solid‐State Vibrational Frequencies

The vibrational properties of barium peroxide, BaO₂, were investigated by phonon calculations based on density‐functional theory and the ab initio force‐constant method. In order to reproduce the correct wavenumber of the peroxide vibration at finite temperatures, its volume dependence together with the calculated volume expansion was taken into account. Using this approximation we found a quantitative agreement of the calculated value with experimental data observed by Raman spectroscopy.     

Sharp bounds for the first eigenvalue of symmetric Markov processes and their applications

By adopting a nice auxiliary transform of Markov operators, we derive new bounds for the first eigenvalue of the generator corresponding to symmetric Markov processes. Our results not only extend the related topic in the literature, but also are efficiently used to study the first eigenvalue of birth-death processes with killing and that of elliptic operators with killing on half line. In particular, we obtain two approximation procedures for the first eigenvalue of birth-death processes with killing, and present qualitatively sharp upper and lower bounds for the first eigenvalue of elliptic operators with killing on half line.     

The stability of limit cycles in nonlinear systems

In this paper, a necessary condition is first presented for the existence of limit cycles in nonlinear systems, then four theorems are presented for the stability, instability, and semistabilities of limit cycles in second order nonlinear systems. Necessary and sufficient conditions are given in terms of the signs of first and second derivatives of a continuously differentiable positive function at the vicinity of the limit cycle. Two examples considering nonlinear systems with familiar limit cycles are presented to illustrate the theorems.     

巴比妥酸系列衍生物第一超级化率的理论研究及分子设计

在ＺＩＮＤＯ方法基础上,按完全态求和（ＳＯＳ）公式编制程序并计算了第一超极化率β,研究了巴比妥酸系列衍生物分子的结构,光谱和第一超级化率β（－２ω,ω,ω）,β（０,０,０）,考察了给体、桥和受体的变化、Ｄ－π－Ａ结构及Ｄ－Ａ－Ｄ结构和Ｄ－Ａ结构对β的影响,设计了一系列有实际应用价值的热稳定性好,具有优良非线性光学性质的分子。     

自治差分方程的稳定性

本文首先给出了文献[2]中关于一次近似系统不稳定性定理的一个反例,然后给出了关于自治差分方程利用其一次近似系统的不稳定性来判别原系统不稳定性的判别定理。     

Importance sampling for elasto-plastic systems using adapted process with deterministic control

A new importance sampling method is presented for computing the first passage probability of elasto-plastic systems under white noise excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an ‘adapted’ stochastic process whose future is determined based on information only up to the present. This causal property is responsible for maintaining the theoretical rigor of the resulting importance sampling procedure. It opens up great possibilities in the design of adapted process for variance reduction using importance sampling. In this work the adapted process is designed using concepts of deterministic optimal control. Numerical results show that the use of adapted process is particularly useful for hysteretic systems where hysteretic effects undermine the effectiveness of conventional importance sampling method based on fixed design points.     

利率相依的离散时间保险风险模型的破产问题

本文对利率具有一阶自回归的离散时间风险模型进行了研究,得到了破产前最大盈余的分布,破产前盈余、破产后赤字与破产前最大盈余的联合分布以及首达某一水平x的时间分布的递推公式.