Non-localization of eigenfunctions for Sturm–Liouville operators and applications

In this article, we investigate a non-localization property of the eigenfunctions of Sturm–Liouville operators $A_a=?{?}_{xx}+a(?)\mathrm{Id}$ with Dirichlet boundary conditions, where $a(?)$ runs over the bounded nonnegative potential functions on the interval $(0,L)$ with $L>0$. More precisely, we address the extremal spectral problem of minimizing the $L^2$-norm of a function $e(?)$ on a measurable subset ω of $(0,L)$, where $e(?)$ runs over all eigenfunctions of $A_a$, at the same time with respect to all subsets ω having a prescribed measure and all $L^{\infty }$ potential functions $a(?)$ having a prescribed essentially upper bound. We provide some existence and qualitative properties of the minimizers, as well as precise lower and upper estimates on the optimal value. Several consequences in control and stabilization theory are then highlighted.     

鱼类生长激素的研究概况

鱼类生长激素对鱼的生长发育有重要的作用.就生长激素在鱼类应用中的分离及活性鉴定方法、鱼类生长激素基因转移的研究、分泌季节性和药物影响进行简要概括.     

Pollution characteristics of atmospheric fine particles and their secondary components in the atmosphere of Shenzhen in summer and in winter

Two field measurements for atmospheric fine particles were conducted in Baoan district of Shenzhen during the summer and winter in 2004. Totally 30 sets of 24 h samples were collected, and then the mass concentrations and chemical compositions were determined. The seasonal varia- tions and secondary pollution characteristics of fine particles during the sampling periods were dis-cussed with meteorological factors. The results show that seasonal variations of atmospheric particles are significant in Shenzhen. The average mass concentrations of PM2.5 and PM10 in summer were 35 μg·m-3 and 57 μg·m-3, respectively, and those in winter were 99 μg·m-3 and 135 μg·m-3, respec-tively. The concentrations of both PM2.5 and PM10 in winter increased 184% and 137%, respectively, compared to those in summer. PM2.5 accounted for 61% and 75% of PM10 in summer and in winter, respectively, indicating severe fine particle pollution in Shenzhen. During the summer and winter sampling periods, the mean OC/EC ratios were 3.4 and 1.6, respectively. The estimated secondary organic carbon (SOC) averagely accounted for 56% and 6% of the total OC in summer and in winter, respectively, which implies a major contribution of SOC to OC in summer. During the continuous high temperature period in summer, both the concentrations and fractions of secondary aerosol compo-nents in PM2.5 were highly elevated, suggesting severe secondary pollution again. The prevailing wind was from South China Sea in summer, and the air quality was good. The prevailing wind in winter was from Mainland China to the north, and the polluted air mass led to poor air quality.     

工艺偏差下模拟电路模块行为级建模的稀疏网格随机配置法

为建立考虑工艺参数随机变化情况下的模拟电路模块的行为级模型,提出了基于稀疏网格的随机配置建模方法.首先,与传统的需要大量采点的蒙特卡罗方法相比,随机配置方法具有指数收敛的特性,大大降低了计算复杂度.其次,为了避免通常用于多维空间的直接张量积随机配置法所带来的采点数随空间维度指数增长的缺点,采用稀疏网格采点技术,在保证建模精度的同时大幅度减少了配置点数目,从而进一步降低了随机配置法的计算复杂度.     

Natural boundary conditions in the calculus of variations

We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end‐point. Copyright © 2010 John Wiley & Sons, Ltd.     

消费函数的季节性协整分析-北京数据的实证研究

本文对于１９８７－１９９６年的季度数据分别原数据和对数数据在３个频率处进行了季节性协整检验,分析了风险水平的特征,得出了季节性调整可能破坏协整性的结论     

一道竞赛题及其推广形式的另解

针对第67届（2006年）美国大学生数学竞赛题中的一道求最大值的问题及其推广形式,从泛函的视角,给出另一种解法．     

A maple® package for the calculus of variations based on jet manifolds

This contribution presents a computer algebra package for Lagrangian systems with p???1 independent and q???1 dependent variables. The Lagrangian may depend on the partial derivatives up to the order n???0 of the dependent variables with respect to the independent ones. In the case of one independent variable, p?=?1, the package derives the equations of motion in the form of a system of q ordinary differential equations of order 2n, for p?>?1 the result is a system of q partial differential equation up to the order 2n. In addition the package determines all the required boundary conditions in the case of p???3 and n???2. Since the presented method uses the concept of jet manifolds, a short introduction to the notation of jet theory is provided. Two examples — the Timoshenko beam and the Kirchhoff plate — demonstrate the main features of the presented computer algebra based approach.     

Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are proved. Several particular cases are considered illustrating the new results.     

基于两种契约下季节性产品的4级供应链协调研究

以季节性产品为研究对象,构建由供应商-制造商-零售商-消费者构成的4级供应链,研究多级收益共享契约和退货契约对季节性产品四级供应链的影响。通过数据对比分析4种供应链模型,发现在多级收益共享契约供应链模型中供应商和制造商利润增加,供应链总利润增加;加入退货契约后,产品的质量提高、销量增加,零售商利润增加,供应链总体利润增加;双重契约加入可以提高产品质量,供应商-制造商-零售商3方利润达到最优。结果表明,加入双重契约可以提高供应链的稳定性,增进产品质量,增加产品销量,降低季节性产品4级供应链的风险,实现供应链协调。