Root determination by use of Padé approximants

In this paper we describe a new technique for generating iteration formulas — of arbitrary order — for determining a zero (assumed simple) of a functionf, assumed analytic in a region containing the zero. The 1/p Padé Approximant (p0) to the functiong(t)f(z) is formed wherez=w+t, using the Taylor series forf at the pointw, an approxination to the zero off. The value oft for which the 1/p Padé Approximant vanishes provides the basis of iteration formulas of orderp+2.Some known iteration formulas, e.g., Newton-Raphson's, Halley's and Kiss's of order of convergence two, three and four, are directly obtained by settingp=0,1 and 2, respectively.     

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.     

Kibble–Slepian formula and generating functions for 2D polynomials

We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given.     

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。     

Euler–MacLaurin formulas via differential operators

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.     

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.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.