Markov processes in single molecule fluorescence

This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the first-passage time (FPT) distributions out of those states must be describable by a simple exponential law. The observation of non-exponential FPT distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system.     

On-line analysis of polymer melt processes

Molten polymer process streams are difficult to analyze either in- or on-line because of sampling problems due to the high temperature and viscosity of the molten state. Real-time monitoring of chemical compositions in these processes can significantly improve safety and product quality and minimize process costs and waste. The information content of the mid-infrared spectrum combined with the recent development of rugged process Fourier transform (FT) IR spectrometers is stimulating the application of process FT-IR to industrial polymer melt processes. Sampling considerations for polymer melts are reviewed. Also, the use of FT-IR spectrometry for on-line measurements of the polymer composition for polymer blends and copolymers in the melt, and the question of how this information could be used to monitor and control the quality of the product given by the process are discussed.     

D072型树脂脱除过氧化氢中金属阳离子的工艺研究

实验考察D072型阳离子交换树脂在交换柱中脱除过氧化氢中微量金属阳离子的动态行为．通过改变料液流速、高径比、料液中交换离子浓度及料液组成等参数，绘制不同条件下的透过曲线，以此考察D072型树脂对过氧化氢中金属阳离子的动态交换性能，从而确定适宜的工艺条件，为工业化生产提供科学依据．     

Teaching of process analytical chemistry

In the teaching of analytical chemistry for chemical engineering students it is essential today to teach the chemical analysis of dynamic systems, not only in the process control of the modern technological systems, where the control of composition or structure of different material streams is necessary, but also in all other instances where analysis, decision and intervention follow each other, forming a closed cycle. Teaching can be made effective if students already have a knowledge of the basic disciplines (including analytical chemistry). The schedule of the teaching programme should include the mathematical statistical treatment of process signals, quality of the signals, signal-improvement methods, characteristics of instruments, calibration and an introduction to sensors, analysers suitable for continuous or periodical measurements and local area networks. As practical exercizes an apparatus for investigation of the dynamic properties of a thermoanalytical detector system, a computer program for simulating process variables and the control loop including the measuring system are presented.     

有限型的首次返回例外集的测度和维数北大核心CSCD

设M=(m_(ij))是一个b×b阶矩阵且m_(ij)∈{0,1},∑_(M)是矩阵M=(m_(ij))诱导产生的有限型,σ是其上左推移算子.本文主要研究的是有限型动力系统(∑_(M),σ)上的首次返回速度问题.令τ_(k)(x)是点x∈∑_(M)首次返回到包含x的k阶柱集时间,且E_(α,β)={x∈∑_(M):lim inf_(k→∞)(logτ_(k)(x))/k=α,lim sup_(k→∞)(logτ_(k)(x))/k=β}.我们证明了:当M是不可约矩阵时,对任意0≤α≤β≤+∞,集合E_(α,β)的Markov测度要么等于0要么等于1并且具有满的Hausdorff维数.     

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.     

The nearest neighbor random walk on subspaces of a vector space and rate of convergence

LetX be the collection ofk-dimensional subspaces of ann-dimensional vector spaceV _n overGF(q). A metric may be defined onX by letting

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.