非自治刚性随机微分方程正则EM分裂方法的收敛性和稳定性

本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂（CEMS）方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果.     

An explicit characterization of cubic symmetric bi-Cayley graphs on nonabelian simple groups

One of the remarkable contributions in the study of symmetric Cayley graphs on nonabelian simple groups is the complete classification of such graphs that are cubic and nonnormal. This naturally motivates the study of cubic (normal and nonnormal) symmetric bi-Cayley graphs on nonabelian simple groups. In this paper, the full automorphism groups of these graphs are determined, and necessary and sufficient conditions are given for a graph being a cubic normal symmetric Cayley or bi-Cayley graph on a nonabelian simple group (one may then find many examples). As an application, we also prove that cubic symmetric Cayley graphs on nonabelian simple groups are stable.     

Exponential stability of discrete-time systems with slowly time-varying delays

Slowly time-varying delays are seldom, but do need to be, considered in the context of discrete-time systems. This paper addresses the exponential stability issue of discrete-time systems with slowly time-varying delays. The basic idea is to transform, by utilizing the switching transformation approach, the original system with slowly time-varying delays into an equivalent switched system with special switching signal. Different types of delays correspond to different types of switching signals, and the stability issue of the original system is converted into that of a switched system. It is the first time that the method of switched homogeneous polynomial Lyapunov function is applied to general delayed systems. Some sufficient exponential stability conditions for the original system are proposed in several situations. It is numerically shown that the conservativeness of the proposed conditions reduces as the degree of the switched homogeneous polynomial Lyapunov function increases.     

Stability of multistage stochastic programming

In this paper, we study the stability of multistage stochastic programming with recourse in a way that is different from that used in studying stability of two-stage stochastic programs. Here, we transform the multistage programs into mathematical programs in the space ⁿ ×L _p with a simple objective function and multistage stochastic constraints. By investigating the continuity of the multistage multifunction defined by the multistage stochastic constraints and applying epi-convergence theory we obtain stability results for linear and linear-quadratic multistage stochastic programs.Project supported by the National Natural Science Foundation of China.     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

The stability of the exponential equation

We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .

     

聚苯胺尿酸酶电极性能的研究

依据pH对聚苯胺尿酸酶电极最大响应电流的影响, logim～pH图表明尿酸酶电极的催化活性只与其电离基团的碱性形式有关. 扫描电镜的结果表明, 聚苯胺尿酸酶电极的稳定性与其制备方法有关. 电化学法固定的尿酸酶电极具有高的稳定性.     

复合固体超强酸催化剂SO_4~(2-)_4-WO_3-ZrO_2的结构研究

已报导，经适当处理的SO42-ZrO2和WO3－ZrO2具有超强酸性［1］．在此基础上将SO42-和WO3同时负载于ZrO2表面，发现其表面酸性有明显增强，得到的固体超强酸504－W0s－Zro。在很宽的焙烧温度范围内（700七00“C）都具有HO三一16．04的酸强度，吸附毗院的红外光谱研究表明，其表面同时具有强的L酸性和B酸性问，140“C时，对正乙烷裂解及异构化的催化活性比SO4－－ZrO。和WO3－ZI02都高，表现出相当的协同效应同．本文用XRD，DTA－TG，比表面测定等技术研究催化剂的组成、结构形态及其随焙烧温度的变化．并与504－Zro：和WO。…     

N－乙酸基取代四氮杂大环及其镧系配合物的热力学研究

用ｐＨ电位滴定法分别在２５±０．１℃，４０±０．１℃和８０±０．１℃，０．５ｍｏｌ／ＬＫＮＯ３水溶液中测定了Ｈ_４Ｌ（５，７，１２，１４－四甲基－１，４，８，１１－四氮杂环十四烷－Ｎ＇，ｎ＂，Ｎ＂＇，Ｎ＂＂－四乙酸）的逐级质子化常数和焓值。又在４０±０．１℃和８０±０．１℃条件下测定了Ｈ４Ｌ与镧系金属离子（Ｌａ~（３＋），Ｎｄ~（３＋），ｐｒ~（３＋），Ｓｍ~（３＋），Ｅｕ~（３＋），Ｇｄ~（３＋），Ｄｙ~（３＋），Ｙｂ~（３＋））配合物的稳定常数。结果表明：配合物稳定性高。     

SAPO-34分子筛骨架稳定性的研究

利用差热分析，原位ＸＲＤ技术，高温条件下的焙烧和水蒸气处理并关联其催化性能变化，研究了ＳＡＰＯ－３４分子筛的热及水热稳定性，差热分析结果表明，ＳＡＰＯ－３４的骨架破坏温度高于１３００Ｋ，原位ＸＲＤ跟踪研究证实，ＳＡＰＯ－３４分子筛原粉在高温焙烧以除掉有机胺及随后的降温过程中无明显的骨架破坏；而焙烧型ＳＡＰＯ－３４在空气中放置一定时间后，水分子吸附微孔中明业降低样品的ＸＲＤ峰强度，且降低幅度随放置时