基于门限面板模型的我国能源利用效率研究

根据三要素的柯布-道格拉斯生产函数,构建我国能源利用效率的门限面板模型,对2000~2014年我国30个省份(不含西藏)的样本数据,进行实证分析.研究表明:能源利用效率变量存在明显的三门限值,把我国30个省份分成四大类,不同类别的地区在能源效率和能源投入规模上存在显著差异.能源利用效率比较高的地区能源利用效率随能源投入增加而变大,而能源利用效率较低地区则相反.另外能源利用效率高的地区,能源投入规模大,能源产出弹性也大,说明在一定程度上对经济的贡献率也比较大,且未来继续靠能源拉动经济的可能性也比较大.     

The graph structure of a deterministic automaton chosen at random

An n‐state deterministic finite automaton over a k‐letter alphabet can be seen as a digraph with n vertices which all have k labeled out‐arcs. Grusho (Publ Math Inst Hungarian Acad Sci 5 (1960), 17–61). proved that whp in a random k‐out digraph there is a strongly connected component of linear size, i.e., a giant, and derived a central limit theorem. We show that whp the part outside the giant contains at most a few short cycles and mostly consists of tree‐like structures, and present a new proof of Grusho's theorem. Among other things, we pinpoint the phase transition for strong connectivity. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 428–458, 2017     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

On the computation of the optimal cost function for discrete time Markov models with partial observations

We consider several applications of two state, finite action, infinite horizon, discrete-time Markov decision processes with partial observations, for two special cases of observation quality, and show that in each of these cases the optimal cost function is piecewise linear. This in turn allows us to obtain either explicit formulas or simplified algorithms to compute the optimal cost function and the associated optimal control policy. Several examples are presented.Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-86-0029, in part by the National Science Foundation under Grant ECS-8617860, in part by the Advanced Technology Program of the State of Texas, and in part by the DoD Joint Services Electronics Program through the Air Force Office of Scientific Research (AFSC) Contract F49620-86-C-0045.     

用摄动法和有限条法分析矩形板的大挠度

本文将摄动法和有限条法结合起来进行矩形板的大挠度弯曲分析.用摄动的概念,将非线性微分方程组化为一系列线性微分方程组,然后用有限条法解这些线性微分方程组.     

奇异摄动偏微分方程的周期边界问题

本文讨论奇异摄动椭圆抛物型偏微分方程的周期边界问题.构造一个差分格式,利用分离解的奇性项的方法,结合问题的渐近展开,证明所构造的差分格式具有O(τ h~2)一致收敛阶.     

双曲-双曲奇异摄动问题的指数型拟合差分格式

本文讨论带有关于x的一阶导数项的双曲奇异摄动初边值问题,在较弱的相容性条件下构造了问题的渐近解并证明了解的一致有效性.然后我们对原问题构造一个指数型拟合差分格式并建立了离散能量不等式.最后我们证明差分问题的解一致收敛于原问题的精确解.     

非均匀Reissner板弯曲的精确元法

本文在阶梯折算法和精确解析法的基础上,提出构造有限元的新方法——精确元法.该方法不用变分原理,可适用于任意变系数正定和非正定偏微分方程.利用该方法,得到Reissuer板弯曲的一个非协调单元,它具有十五个自由度.由于节点位移参数仅含有挠度和转角,因此处理任意边界条件非常容易.文中给出证明,位移和内力均收敛于精确解.由精确元法所得到的单元不仅能用于厚板,也可用于薄板.文末给出四个算例.算例表明,利用本文的方法,可获得满意的结果,并有较高的数值精度.     

发展方程初边值问题的高阶差分-边界积分方程法及误差分析

本文结合差分方法与边界积分方程方法,提出并研究了一类新的求解发展型方程初边值问题的高阶差分与边界积分方程耦合数值方法.对于有界区域问题与无界区域问题给出了数值计算格式及其误差的先验估计.     

张力腿平台有限振幅运动的方程和数值解

论证了张力腿平台（TLP）在波浪作用下发生有限振幅运动时,所受惯性力、粘性力、浮力等载荷不仅与波浪场有关,还与瞬时响应有关,是响应的非线性函数;张力腿拉力也是各自由度位移的非线性函数．所以分析TLP受力时必须考虑平台的瞬时加速度、速度和位移,在瞬时位置建立运动方程．据此推导出TLP发生有限振幅运动时的外力计算公式,建立了TLP 6自由度有限振幅运动非线性控制方程．其中考虑了由6自由度有限位移引起的多种非线性因素,如各自由度之间的耦合、瞬时湿表面、瞬时位置等;还包括自由表面效应、粘性力等因素引起的非线性．用数值方法求解所得到的非线性运动方程．对典型平台ISSC TLP进行了数值分析,求得该平台在规则波作用下的6自由度运动响应．用退化到线性范围的解与已有解进行了对比,吻合良好．数值结果表明,综合考虑非线性因素后响应有明显改变．