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.     

The inventory models under conditional trade credit in a supply chain system

In several recent investigations dealing with the economic order quantity with permissible delay in payments, the following assumptions are made:     

Uniform persistence for population interaction models with time delay

In this paper uniform persistence is establised for kolmogorov type Prey‐Predator and competion models with per capitals ent growth rates that are dependent on time‐lagged population densities.     

Optimal feedback gains of a delayed proportional-derivative (PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a con-trolled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a sys-tematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost charac-teristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial val-ues around the origin are fixed. The main results are checked by numerical simulation.     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

A Novel Approach to All-Optical Generation of Ultra-Wideband Signals

Abstract

The generation of ultra-wideband signals in the optical domain is highly desirable for ultra-wideband-over-fiber systems, which has recently become a topic of interest. In this article, a novel and simple approach to achieve all-optical generation of ultra-wideband signals is proposed, which is based on delaying and superimposing optical Gaussian pulses with opposite polarities. The proposed system is capable of generating both ultra-wideband monocycle and doublet pulses, and the polarity of the generated ultra-wideband monocycle pulses can be fast-switched to implement pulse polarity modulation with the required bit pattern. A model to describe the proposed system is developed, and the generation of ultra-wideband signals is demonstrated with simulations and a proof-of-concept experiment.     

On the solution of stochastic ordinary differential equations via small delays

dx(t)=g(x{t))dW(t) is proved using an approximating sequence of stochastic delay equationsGeneralizations of the approximation scheme are indicated for the Stratonovich case and when the Brownian motion W is replaced by a continuous semi-martingale.