Exponential boundedness of solutions for impulsive delay differential equations

For an impulsive delay differential equation

exponent estimates of solutions have been obtained.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

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.     

Surface recombination in breakdown time delay experiments: Effect of different cathode materials

The late afterglow in nitrogen with iron electrode is studied by the breakdown time delay method, i.e., by measuring the breakdown time delay t_d as a function of the afterglow time . It is proposed that the cause of the secondary electrons initiating the breakdown is the energy of the surface recombination of nitrogen atoms on the iron electrode. The gas-phase and macrokinetic diffusive models are used to describe the experimental breakdown time delay data. By fitting the theoretical curve to the experimental data: (1) it has been confirmed that the recombination on the molybdenum glass is of the second order and the value of the surface recombination coefficient is determined at 4 mbar; (2) it has been shown that the surface recombination on the iron electrode is of the second order, and the effective recombination coefficients are determined; (3) the analytical form of the recombination coefficient as a function of the adsorption characteristics of surfaces and the pressure of the parent gas has been derived. In addition, the orders of surface recombination on the molybdenum-, aluminum-, and gold-plated electrode were determined by the same method.     

A theory of adsorption kinetics with time delay and its application to overshoot and oscillation in the surface tension of gelatin solution

A theory of adsorption kinetics with time delay [Ohshima et al. (1992) Colloid Polym. Sci. 270:707] is developed and applied to the surface tension of a polymer solution. It is found that the general appearance of the overshoot and oscillation in the time course of the surface tension of aqueous gelatin solution observed by Sato and Ueberreiter [(1979) Makromol. Chem. 180:829, 1107; (1979) Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 20:907) can be explained by the present theory.     

具无限时滞的非自治捕食者-食饵系统的持久性

本文采用新的方法研究了具无限时滞的非自治、非卷积的捕食者－食饵系统的持久性问题，得到了新的、有趣的结果。本文的结果包含已知的结果作为特例．     

Noether symmetry and conserved quantity for a Hamilton system with time delay

In this paper, the Noether symmetries and the conserved quantities for a Hamilton system with time delay are discussed. Firstly, the variational principles with time delay for the Hamilton system are given, and the Hamilton canonical equations with time delay are established. Secondly, according to the invariance of the function under the infinitesimal transformations of the group, the basic formulas for the variational of the Hamilton action with time delay are discussed,the definitions and the criteria of the Noether symmetric transformations and quasi-symmetric transformations with time delay are obtained, and the relationship between the Noether symmetry and the conserved quantity with time delay is studied. In addition, examples are given to illustrate the application of the results.     

考虑防御系统延迟使其预测误差最大的突防弹道设计

对中段多脉冲机动突防弹道的设计问题进行了研究。采用的原理与方法有别于成熟的航天器多脉冲变轨,而是基于路径规划的思想对弹道设计问题简化。考虑敌方防御系统延迟,改进多脉冲点火模型,并基于变射面的思想对关机点参数进行了设计及优化。然后,从使敌方预测误差最大的角度提出评价函数,并利用遗传算法进行优化。最后,给出了一种同时满足导弹机动突防与打击精度要求的多脉冲弹道设计方法。从模型的可行性,方法的有效性、灵活性、迭代效率及精度等方面进行了仿真验证分析。在PC机仿真中,20 s内就设计出一条保证打击精度的中段突防弹道。结果表明,建立的模型是可行的,提出的突防弹道设计方法是快速有效的。     

The research on temperature measurement based on polarization dependent loss

This paper analyzes the properties of reflected polarization dependent loss of apodized fiber Bragg gratings with temperature effective. We simulates reflected spectrum and polarization dependent loss of the apodized fiber Bragg gratings. The reflected spectrum and polarization dependent loss are measured under different temperatures. The analysis results show that reflected polarization dependent loss presents two peaks which shift an equal proportion to long wavelength with temperature increasing and have very good stability so we propose an idea that use polarization dependent loss as temperature sensor measurement parameters. The results show that the accuracy of measurement can be increased almost by one order of magnitude.