A Note on the Spectral Collocation Approximation of Some Differential Equations with Singular Source Terms

The solution of differential equations with singular source terms contains the local jump discontinuity in general and its spectral approximation is oscillatory due to the Gibbs phenomenon. To minimize the Gibbs oscillations near the local jump discontinuity and improve convergence, the regularization of the approximation is needed. In this note, a simple derivative of the discrete Heaviside function H _c (x) on the collocation points is used for the approximation of singular source terms δ(x−c) or δ ⁽ⁿ⁾(x−c) without any regularization. The direct projection of H _c (x) yields highly oscillatory approximations of δ(x−c) and δ ⁽ⁿ⁾(x−c). In this note, however, it is shown that the direct projection approach can yield a non-oscillatory approximation of the solution and the error can also decay uniformly for certain types of differential equations. For some differential equations, spectral accuracy is also recovered. This method is limited to certain types of equations but can be applied when the given equation has some nice properties. Numerical examples for elliptic and hyperbolic equations are provided. The current address: Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA.     

基于亲缘选择的遗传算法

针对传统遗传算法容易陷入局部最优解的缺陷,借鉴生物中亲缘选择的思想,提出基于亲缘选择的遗传算法。该算法构造新选择算子,通过按亲缘关系放弃一个解而获得另一个解来保证算法在最优解的领域内的有效搜索,提高遗传算法对全局最优解的搜索能力和收敛速度。仿真结果表明,该算法正确有效,性能优于现有的传统算法。     

基于熵测度的自适应遗传算法

针对基本遗传算法SGA在搜索过程中易陷入局部最优解的问题,提出了基于熵测度的自适应遗传算法,并分析了熵测度下种群个体被选概率的极限行为。理论分析和对比实验表明,基于熵测度的自适应选择策略能根据种群性状来动态地调整选择压力,从而调整算法的开采和探索能力的平衡,提高算法的全局优化性能。     

英语动物习语的隐喻认知分析

隐喻是一种特殊的语言现象,其本质在于通过某种事物或概念来理解、感悟另一种事物和概念．本文以英语动物习语为研究语料,从隐喻认知角度研究了英语动物习语的认知理据及其解读过程．结果表明,隐喻认知理论对于英语动物习语的分析具有较强解释力,这为英语习语的研究奠定了基础并为其开拓了广阔前景．     

从品德形成的心理过程看品德形成滞后现象

针对德育工作中存在的品德形成滞后现象,从品德形成的心理过程分析了产生品德形成滞后的原因,提出了合理缩短品德形成滞后期的对策。     

Oxidation kinetics and high temperature in-situ observation of the oxidation behaviour of NbSi_2 at 1023 K

Pest oxidation has been known for a long time in refractory transition-metal disilicides such as NbSi2 and MoSi2[1―4]. However, the origin of pesting reaction of these materials is still under debate. Although the pesting phenomenon in NbSi2 has been reported in several works[5―7], a direct study of the mechanism is scarce at the moment. Compared to NbSi2, pesting in MoSi2 has received relatively extensive attention. Mckamey et al.[8] showed fragmentation near 773K occurred easily in as…     

压浆材料及施工技术的研究

根据高速公路路面实际情况对路面板脱空现象进行压浆处理。路面板脱空位置是通过弯沉法和雷达观测法确定的，并结合路面唧泥情况钻孔法进行压浆，最终取得了较好的压浆效果。     

遗传算法的一个调节算子研究

虽然遗传算法在许多领域获得了成功应用，但它本身存在不成熟的过早收敛问题是影响其发展的中的课题，本文通过对遗传算法要理的分析和认识，给出了遗传算法早熟现象产生的原因是模式缺少，并提出了一个在遗传算法中在于模式抽取和模式补偿的调节算子以解决早期现象，最后给出了运算实例证明该算子是有效的。     

论语言词汇中的借用与社会因素

分析了语言相互借用现象、借用方法及社会因素，旨在更好地发挥语言在经济发展中的中间作用。     

OPGW允许的最高温度

当电力系统发生短路故障时,流过OPGW的短路电流会使OPGW发热升温。当温度超过200℃时,不但会影响OPGW的性能(光纤的着色层变硬、退色,能量损耗增大),而且易造成OPGW发生鸟笼现象、断股现象。短路电流容量是衡量OPGW温度特征的尺码,文章介绍了有关标准,对各种典型结构的OPGW进行了短路电流容量和温升关系的分析,从而说明设计和选用OPGW时,遵循OPGW标准规定的重要意义。