某类一阶非线性双曲型方程的Cauchy问题

本文考虑一类具实际物理背景的一阶非线性双曲型方程，证明了解的存在唯一及正则性。     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

Multipliers of convergence in norm of series with respect to multiplicative systems

We prove analogs of the Telyakovskii-Pochuev criteria for multipliers of uniform convergence and of convergence in the integral metric for multiplicative systems with bounded generating sequence.     

On sequential procedures for the point estimation of the mean of a normal population

The sequential procedures developed by Starr (1966, Ann. Math. Statist., 37, 1173–1185) for estimating the mean of a normal population are further analyzed. Asymptotic properties of the regret and first two moments of the stopping rules are studied and second-order approximations are derived.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

UO22＋•nH2O和PuO22＋•nH2O (n＝2, 4, 5, 6)密度泛函理论研究

首先用密度泛函理论(DFT)方法研究了铀酰和钚酰离子的几何与电子结构, 计算结果与实验基本符合, 表明DFT方法也能用于含铀和钚重原子的化合物计算. 然后对铀酰和钚酰水合离子的几何构型、Mulliken集居数分布以及铀酰(钚酰)与配体水分子的结合能进行计算, 计算结果表明UO₂^2＋•5H₂O和PuO₂^2＋•5H₂O分别为铀酰和钚酰系列水合离子中最稳定的配合物.     

氢部分选择性催化还原NO反应研究

在低钯含量活性非均布Pd/Al2O3催化剂上，实现了富氧条件下，氢部分选择性催化还原NO过程，低温、富氧条件下NO的转化率高达80％－100％。NO直接分解实验表明，600℃，NO分解转化率在无氧时为17．3％，有0．5％氧存在时接近于0。氢非选择性还原NO条件下，100℃以下，NO转化率为100％。根据实验结果及文献，推测了氢部分选择性还原NO过程中可能存在的反应，不同的反应温度下，NO脱除反应有所不同。在115℃以下，NO还原产物为NH3；115℃－155℃，NO还原产物为NH3、N2O和N2；155℃以上，NO还原产物中无NH3存在。NO还原反应与氢氧反应是平行的竞争反应。     

神经系统铅中毒

阐述了铅对人类尤其是胎儿、婴幼儿神经系统毒害的病因、发病机制、临床表现及治疗，并提出解决铅中毒的关键是易感人群的预防。     

不依赖于统计模型的手性毛细管电泳分离多指标同时优化

考虑到手性毛细管电泳分离机理的复杂性，提出了不依赖于统计模型的二进制编码遗传算法多目标优化策略。根据实验参数的多少及其重要性，采用均匀设计安排完成初步实验。并用Derringer功效函数作为多指标同时优化的评价指标，以取得较高的分离度和较快分离速度；通过对实验参数给予编码，转化为二进制字符串，根据得到的总功效函数值大小进行遗传算法操作，产生新的一组实验条件。重复上述过程直到得到最佳分离条件为止。此方法成功地应用于华法令对映体的毛细管电泳分离条件优化。