Periodic solution of a chemostat model with variable yield and impulsive state feedback control

In this paper, a chemostat model with variable yield and impulsive state feedback control is considered. We obtain sufficient conditions of the globally asymptotical stability of the system without impulsive state feedback control. We also obtain that the system with impulsive state feedback control has periodic solution of order one. Sufficient conditions for existence and stability of periodic solution of order one are given. In some cases, it is possible that the system exists periodic solution of order two. Our results show that the control measure is effective and reliable.     

Stability Relationships Among the Gibbs Sampler and its Subchains

The use of Gibbs samplers driven by improper posteriors has been a controversial issue in the statistics literature over the last few years. It has recently been demonstrated that it is possible to make valid statistical inferences through such Gibbs samplers. Furthermore, theoretical and empirical evidence has been given to support the idea that there are actually computational advantages to using these nonpositive recurrent Markov chains rather than more standard positive recurrent chains. These results provide motivation for a general study of the behavior of the Gibbs Markov chain when it is not positive recurrent. This article concerns stability relationships among the two-variable Gibbs sampler and its subchains. We show that these three Markov chains always share the same stability; that is, they are either all positive recurrent, all null recurrent, or all transient. In addition, we establish general results concerning the ways in which positive recurrent Markov chains can arise from null recurrent and transient Gibbs chains. Six examples of varying complexity are used to illustrate the results.     

激光器机理及激光功率表达式的实验验证

运用光反馈的原理和技术演示并验证激光功率表达式，说明激光介质和光学谐振腔的性质和作用。     

Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study

State tomography on qubit pairs is routinely carried out by measuring the two qubits separately, while one expects a higher efficiency from tomography with highly symmetric joint measurements of both qubits. Our numerical study of simulated experiments does not support such expectations.     

Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method

We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large Courant–Friedrichs–Lewy number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback forcing scheme of the virtual boundary method with Peskin's regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta functions. The stability regime of the 4‐point regularized delta function was much wider than that of the 2‐point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite‐difference and fractional‐step context. The proposed method was tested on several flow problems, including the flow past a stationary cylinder, inline oscillation of a cylinder in a quiescent fluid, and transverse oscillation of a circular cylinder in a free‐stream. The findings were in excellent agreement with previous numerical and experimental results. Copyright © 2008 John Wiley & Sons, Ltd.     

PERMANENCE OF GENERAL NONAUTONOMOUS SINGLE-SPECIES KOLMOGOROV TYPE SYSTEM WITH DELAY AND FEEDBACK CONTROLS

In this paper, we consider the general nonautonomous single-species Kolmogorov type system with delay and feedback controls. Sufficient conditions for the permanence of species are established. Our results generalize some known results.     

A theorem on upper-lower solutions for nonlinear elliptic systems and its applications

We report on a result of upper-lower solutions for nonlinear elliptic systems without the assumption of quasi-monotonicity. An application is described involving the existence of positive steady states of a certain interaction system arising in biology and medical sciences.     

Photoreactions of a polyamic acid containing 2,2-dinitrodiphenylmethane segments at symmetrical positions in the main chain

A polyamic acid containing 2,2^′-dinitrodiphenylmethane segments in the main chain was synthesized from 4,4^′-diamino-2,2^′-dinitrodiphenylmethane and pyrromellitic dianhydride. Irradiation of the polyamic acid was done in solution (in a protic solvent, isopropanol, in isopropanol in the presence of a triplet exciter, benzophenone and in acidified isopropanol) and as thin film. The irradiations were done in an immersion type photoreactor using a 125 W high-pressure mercury vapour lamp. The average molecular weights of the polymers were determined by gel permeation chromatography. The polydispersity index of the polyamic acid and the photoproduct showed the absence of photodegradation. The photoproducts were identified by comparing the spectra of polymer photoproducts with that of low molecular weight 2,2^′-dinitrodiphenylmethane derivatives under identical conditions. A possible mechanism for the phototransformations is suggested. Evaluation of photoresist behaviour of the polyamic acid was also done.     

带有Bernoulli反馈的多级适应性休假的Geo/G/1排队系统分析

考虑带有Bernoulli反馈的多级适应性休假的Geo/G/1离散时间排队系统.通过引入服务员忙期和使用一种简洁的分解方法,讨论了队长的瞬时分布,得到了在任意时刻n队长为j的概率关于时刻n的z-变换的递推式,及队长平稳分布的递推式,且证明了稳态队长的随机分解性质.最后,给出了在特殊情形下相应的一些结果和数值计算实例.     

On finite unions of ideals and cosets

Abstract

Although it is well known that the growth of Thompson's group F is exponential, the exact growth function is still unknown. Elements of its submonoid of positive words can be described using a binary rooted tree, whose norm can be computed assigning weights to each caret. Combining this fact with a combinatorial argument, the growth function of the submonoid is computed and thus providing a first step in the computation of the growth function of the group, as well as a lower bound for the growth rate for the group.