导弹武器系统费用的模糊估算模型研究

利用模糊数学的基本原理,基于模糊贴近度的概念和择近原则,在同一条件下,研究和对比在研导弹武器系统与已有导弹武器系统的相似程度,在导弹武器系统费用历史资料的基础上,根据指数平滑法的理论,建立了在早期设计阶段导弹武器系统费用的模糊预测模型。仿真实例验证了该方法的适用性和结果的可靠性。     

二维非饱和土壤水分运动方程的径向基配点差分法

针对二维非饱和土壤水分运动方程,将径向基配点法结合差分法构造了一种新的数值算法.该算法先采用差分法处理非线性项,再利用径向基函数配点法的隐格式求解方程,避免了因非线性项的存在导致不能直接使用配点法的现象,并且证明了该算法解的存在唯一性.通过对非饱和土壤水分运动的数值模拟,并采用试验数据对新算法进行了验证,模拟结果与试验结果非常吻合,表明该算法实用、有效.同时,比较分析了不同径向基函数以及不同算法的模拟精度,结果表明,与MQ函数和Guass函数相比,新的径向基函数具有更好的模拟精度,且相对于有限差分法和有限元法,本文提出的方法具有一定的优越性.     

径向基函数在非线性PDE形状优化中的应用

提出了一种求解非线性偏微分方程形状优化问题的径向基函数方法.灵敏度分析结果采用的共轭方法;形状的演化通过最优性准则方法得到;控制方程和共轭方程的求解用的是径向基函数方法.由于径向基函数方法是真正的无网格方法,比网格依赖方法有更好的适应性.提供的数值算例说明了所提算法的稳定性和有效性.此外,所得方法可以灵活地与其他优化算法相结合,从而可以解决更复杂的非线性偏微分方程中的最优形状设计问题.     

求解Bratu型方程的径向基函数逼近法

基于径向基函数可以逼近几乎所有函数的强大逼近功能,借鉴弹塑性静力学的处理方法,提出位移、速度、加速度联合插值的径向基函数表达式,结合MATLAB数值软件进行计算机编程,成功求解了Bratu型强非线性方程,并给出相应的相对误差.通过分析几种典型的算例,并将计算结果与一些现有的数值分析法得到的数值解进行对比,表明了该方法的可行性和精确性,为求解强非线性Bratu型方程提供了一种新思路.     

基于Gauss全局径向基函数的近岸浅水变形波高数值计算新方法

应用Gauss全局径向基函数来模拟波浪浅水变形波高变化方程中的未知函数,经实例分析探讨得到了一种可用于求解该方程数值解的新方法,并将其计算结果与常用数值分析方法得到的数值解相互对比印证,证明了基于Gauss全局径向基函数法计算结果的正确性.经验证,Gauss径向基函数法的平均计算误差相比其他方法均要小,表明该方法拥有更高的计算精度.同时,根据Gauss全局径向基函数的逼近结果,得出了浅水变形波高变化微分方程数值解的拟合函数,在实际工程中,可以利用该拟合函数来代替原方程的解析解,研究成果可为求解近岸浅水区域波浪运动提供一种新思路.     

求解扩散方程的非对称径向基函数配点法

本文针对扩散方程,借助于Halton节点,基于径向基函数和迭代法提出一种新的无网格方法.该方法在时间层上采用全隐离散,在空间层上构造了θ-型迭代格式,然后利用径向基函数去逼近未知函数.由于本文采用紧支集径向基函数,因而导出的离散系统矩阵是稀疏的,且有较好的条件数.最后通过数值实验验证新方法的有效性.     

用径向基函数插值解自共轭椭圆型方程

本文讨论用MQ作为插值的径向基函数,对自共轭椭圆型方程进行插值,证明了插值系数的唯一性,并用投影法证明了用径向基函数解自共轭椭圆型方程的收敛性.     

基于FOA-RBF神经网络的外贸出口预测

应用果蝇优化算法对径向基神经网络扩展参数的优化方法进行研究,给出了一种以标准误差计算公式为味道判定函数,以此确定最优的径向基函数的扩展参数值的方法,并建立了相应的预测模型.应用该预测模型对黑龙江省外贸出口额进行预测,结果表明:预测模型的预测精度优于径向基神经网络,从而证明了方法的有效性.     

导弹武器系统生存能力研究

为了合理评估导弹武器系统的生存能力,分析了导弹武器系统所面临的威胁环境,提出了影响其生存能力的主要因素,建立了导弹武器系统的伪装能力模型、反应能力模型、防护能力模型、维修保障能力模型,以及生存能力的通用模型.最后讨论了各种因素在作战运用中的实际影响.     

球面上径向基函数最小范数插值逼近的误差估计

研究了球面径向基插值对球面函数的逼近问题,给出了一致逼近的上界估计式．文中结果说明,球面径向基插值的逼近阶会随函数光滑性的提高而增加．     

因子分析法在企业经济效益的综合分析与评价中的应用

企业经济效益评价往往涉及众多指标 ,利用多指标评价企业经济效益 ,使评价问题变得复杂。本文采用多元统计中的因子分析法来解决这一问题 ,介绍了分析、评价过程     

Graphs of maps between manifolds in trace spaces and with vanishing mean oscillation

We give a positive answer to a question raised by Alberti in connection with a recent result by Brezis and Nguyen. We show the existence of currents associated with graphs of maps in trace spaces that have vanishing mean oscillation. The degree of such maps may be written in terms of these currents, of which we give some structure properties. We also deal with relevant examples.     

Uniqueness and decay estimates for a class of parabolic partial differential equations with hysteresis and convection

We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators.     

RBF-PU方法求解二维非局部扩散问题和近场动力学问题

采用单位分解径向基函数(radial basis function partition of unity,RBF-PU)方法,数值求解了二维非局部扩散问题和近场动力学问题。主要思想是对求解区域进行局部划分,在局部子区域上分别进行函数逼近,然后加权得到未知函数的全局逼近。这种基于方程强形式的径向基函数方法在求解非局部问题时,不需要处理网格与球形邻域求交的问题,避免了额外的一层积分计算,实施简便,计算量小。数值实验显示计算结果与解析解吻合较好,RBF-PU方法可以准确有效地求解非局部扩散方程和近场动力学方程。     

关于型的L′Hospital法则的一个改进

本文对现行的数学分析、微积分及其高等数学的教材中的 ∞∞ 型的 L′Hospital法则进行了一个改进 ,论证了该法则在无须考虑分子是否趋于∞的条件时 ,仍旧成立 ,利用了这个减弱了的 ∞∞ 型的 L′Hospital法则给出了一大类的极限问题的简单解法     

Parallel radial basis function methods for the global optimization of expensive functions

We introduce a master–worker framework for parallel global optimization of computationally expensive functions using response surface models. In particular, we parallelize two radial basis function (RBF) methods for global optimization, namely, the RBF method by Gutmann [Gutmann, H.M., 2001a. A radial basis function method for global optimization. Journal of Global Optimization 19(3), 201–227] (Gutmann-RBF) and the RBF method by Regis and Shoemaker [Regis, R.G., Shoemaker, C.A., 2005. Constrained global optimization of expensive black box functions using radial basis functions, Journal of Global Optimization 31, 153–171] (CORS-RBF). We modify these algorithms so that they can generate multiple points for simultaneous evaluation in parallel. We compare the performance of the two parallel RBF methods with a parallel multistart derivative-based algorithm, a parallel multistart derivative-free trust-region algorithm, and a parallel evolutionary algorithm on eleven test problems and on a 6-dimensional groundwater bioremediation application. The results indicate that the two parallel RBF algorithms are generally better than the other three alternatives on most of the test problems. Moreover, the two parallel RBF algorithms have comparable performances on the test problems considered. Finally, we report good speedups for both parallel RBF algorithms when using a small number of processors.     

Dynamic analysis of plane elasticity with new complex Fourier radial basis functions in the dual reciprocity boundary element method

In this paper, dual reciprocity (DR) boundary element method (BEM) is reformulated using new radial basis function (RBF) to approximate the inhomogeneous term of Navier’s differential equation (i.e., inertia term). This new RBF, which is in the form of exp(iωr), is called complex Fourier RBF hereafter. The present RBF has simultaneously collected the properties of Gaussian and real Fourier RBF reported in literature together. Consequently, this promising feature has provided more robustness and potency of the proposed method. The required kernels for displacement and traction particular solutions are derived by employing the method of variation of parameters. As some terms of these kernels are singular, a new simple smoothing trick is employed to resolve the singularity problem. Moreover, the limiting values of relevant kernels are evaluated. The validity, accuracy, and strength of the present formulation are illustrated throughout several numerical examples. The numerical results show that the proposed complex Fourier RBF represents more accurate solutions, using less degree of freedom compared to other RBFs available in the literature.     

Improved radial basis function methods for multi-dimensional option pricing

In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black–Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is second-order accurate in time and spectrally accurate in space for constant shape parameter. For other non-optimal choices of shape parameter values, the resulting convergence rate is algebraic. We propose an adapted node point placement that improves the accuracy compared with a uniform distribution. Compared with an adaptive finite difference method, the RBF method is 20–40 times faster in one and two space dimensions and has approximately the same memory requirements.     

NUMERICAL APPROXIMATION OF THE SMOLUCHOWSKI EQUATION USING RADIAL BASIS FUNCTIONS

The goal of this paper is to present a numerical method for the Smoluchowski equation,a drift-diffusion equation on the sphere,arising in the modelling of particle dynamics.The numerical method uses radial basis functions(RBF).This is a relatively new approach,which has recently mainly been used for geophysical applications.For a simplified model problem we compare the RBF approach with a spectral method,i.e.the standard approach used in related physical applications.This comparison as well as our other accuracy studies show that RBF methods are an attractive alternative for these kind of models.