Qualitative estimation of the dependence of the number of energetic compounds on their oxygen coefficient

The ratio between the numbers of structural formulas of C,H,N,O-containing energetic compounds belonging to the classes of fuels (low values of the oxygen coefficientA), explosives (mediumA), and oxidants (highA values) was studied by a computer generation procedure. The number of the theoretically possible structural formulas was found to decrease rapidly on going from fuels to explosives and then to oxidants; this observation agrees with the data on the numbers of various energetic compounds currently used and proposed. The strategy of the search for new compounds with the specified properties is described in brief, and its applicability to the search for explosives and oxidants with a small (up to 12) number of atoms in a molecule is evaluated. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1304–1310, July, 1998.     

双质谱测定地卟啉取代基组成的解析方法及其应用

根据卟啉标样的双质谱特征，建立一种计算卟啉环上取代基组成的方法。卟啉的平均分子结构简式衡量其取代基的组成，尤其对地质体中相同碳数的卟啉“混合物”大环外取代基的构成十分有效。     

结构相角二阶代数式的应用：Ⅱ.正交空间群二阶式及其应用

以作者在前文中提出的单相角二阶代数式的推导方法为依据,在完成三斜、单斜空间群推导结果的基础上,进而又完成了正交晶系59个空间群二阶式的推导,从而提供了低级晶系(三斜、单斜和正交)全部74个空间群的简明、完备的二阶代数式运算用表。对三个晶体结构进行了相角估算,结果较好。文中提出了代数法应用的新特点,即“一种类型相角可用多种二阶式求得,多种类型相角也可用一种二阶式求算”。     

On the Integration by Parts and Characterization of a Fractional Diffusion Process北大核心CSCD

本文研究分数扩散过程和其分部积分公式的关系.首先利用Bismut方法给出拉回公式,进而得到分数扩散过程的分部积分公式。反过来,证明了分数扩散过程可由其分部积分公式唯一刻画.     

一类带扰动的随机脉冲泛函微分方程解的渐近性北大核心CSCD

该文讨论了一类带扰动的随机脉冲泛函微分方程解的渐近性.通过比较扰动方程的解和原方程的解,得到了两者逼近的充分条件.首先,两者在有限的时间区间上相互逼近;其次,当扰动趋于零时,区间长度趋于无穷大,在这个区间上两个解仍然是相互逼近的.最后,举例说明了结果的有效性.     

Hopf bifurcation of a tumor immune model with time delay

In this paper, a tumor immune model with time delay is studied. First, the stability of nonnegative equilibria is analyzed. Then the time delay τ is selected as a bifurcation parameter and the existence of Hopf bifurcation is proved. Finally, by using the canonical method and the central manifold theory, the criteria for judging the direction and stability of Hopf bifurcation are given.     

Set controllability of Markov jump switching Boolean control networks and its applications

In this article, a novel method is proposed for investigating the set controllability of Markov jump switching Boolean control networks (MJSBCNs). Specifically, the switching signal is described as a discrete-time homogeneous Markov chain. By resorting to the expectation and switching indicator function, an expectation system is constructed. Based on the expectation system, a novel verifiable condition is established for solving the set reachability of MJSBCNs. With the newly obtained results on set reachability, a necessary and sufficient condition is further derived for the set controllability of MJSBCNs. The obtained results are applied to Boolean control networks with Markov jump time delays. Examples are demonstrated to justify the theoretical results.     

Convolution semigroups and central limit theorem associated with a dual convolution structure

We consider hypergroups associated with Jacobi functions ⁽⁾ (x), (–1/2). We prove the existence of a dual convolution structure on [0,+[i(]0,s ₀]{{) =++1,s ₀=min(,–+1). Next we establish a Lévy-Khintchine type formula which permits to characterize the semigroup and the infinitely divisible probabilities associated with this dual convolution, finally we prove a central limit theorem.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.