OU型Markov过程的不变测度及弱对偶性

本文研究ＯＵ型Ｍａｒｋｏｖ过程的不变测度、参考测度和弱对偶半群的存在性问题，并得出了不变测度的唯一性。     

Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

随机环境中双移民生灭过程的极限性质

引入了随机环境中双移民生灭过程的概念，定义了过程的模态指示函数，在此基础上研究了其转移矩阵的平稳分布，给出了平稳分布众数的位置与模态指示函数之间的关系．研究了平稳分布的众数与边界关系．     

Photoinitiated curing of mono‐ and bifunctional epoxides by combination of active chain end and activated monomer cationic polymerization methods

Photoinitiated cationic polymerization of mono‐ and bifunctional epoxy monomers, namely cyclohexeneoxide (CHO), 4‐epoxycyclohexylmethyl‐3′,4′‐epoxycyclohexanecarboxylate (EEC), respectively by using sulphonium salts in the presence of hydroxylbutyl vinyl ether (HBVE) was studied. The real‐time FTIR spectroscopic, gel content determination, and thermal characterization studies revealed that both hydroxyl and vinyl ether functionalities of HBVE take part in the polymerization. During the polymerization, HBVE has the ability to react via both active chain end (ACE) and activated monomer mechanisms through its hydroxyl and vinyl ether functionalities, respectively. Thus, more efficient curing was observed with the addition of HBVE into EEC‐containing formulations. It was also demonstrated that HBVE is effective in facilitating the photoinduced crosslinking of monofunctional epoxy monomer, CHO in the absence of a conventional crosslinker. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4914–4920, 2007     

Investigation of Scale Exponents of Complete and Incomplete Aggregation-Annihilation Processes

The complete and incomplete aggregation-annihilation processes are investigated with the method of generating function, and the scale exponents are obtained exactly. We find that the scale exponents of incomplete aggregation-annihilation process are different from the previous exponents obtained by different methods. The time dependence of the total number of clusters and the total mass of clusters are analytically obtained.     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.      

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

Approximating schedules for dynamic process graphs efficiently

A model for parallel and distributed programs, the dynamic process graph (DPG), is investigated under graph-theoretic and complexity aspects. Such graphs embed constructors for parallel programs, synchronization mechanisms as well as conditional branches. They are capable of representing all possible executions of a parallel or distributed program in a very compact way. The size of this representation can be as small as logarithmic with respect to the size of any execution of the program.

In a preceding paper [A. Jakoby, et al., Scheduling dynamic graphs, in: Proc. 16th Symposium on Theoretical Aspects in Computer Science STACS'99, LNCS, vol. 1563, Springer, 1999, pp. 383–392] we have analysed the expressive power of the general model and various variants of it. We have considered the scheduling problem for DPGs given enough parallelism taking into account communication delays between processors when exchanging data. Given a DPG the question arises whether it can be executed (that means whether the corresponding parallel program has been specified correctly), and what is its minimum schedule length.

In this paper we study a subclass of dynamic process graphs called -output DPGs, which are appropriate in many situations, and investigate their expressive power. In a previous paper we have shown that the problem to determine the minimum schedule length is still intractable for this subclass, namely this problem is -complete as is the general case. Here we will investigate structural properties of the executions of such graphs. A natural graph-theoretic conjecture that executions must always split into components that are isomorphic to subgraphs turns out to be wrong. We are able to prove a weaker property. This implies a quadratic upper bound on the schedule length that may be necessary in the worst case, in contrast to the general case, where the optimal schedule length may be exponential with respect to the size of the representing DPG. Making this bound constructive, we obtain an approximation to a -complete problem. Computing such a schedule and then executing the program can be done on a parallel machine in polynomial time in a highly distributive fashion.