一种基于梯度下降算法的蜕变关系生成方法

针对当前蜕变关系构造多数依赖测试人员测试程序时所在领域知识, 存在局限性和高成本的问题, 提出一种新的蜕变关系生成方法. 该方法将蜕变关系的构建与梯度下降算法相结合, 通过分析大量测试用例及其输出之间的数值关系生成对应的蜕变关系. 对比实验结果表明, 该方法可有效降低测试人员对相关领域知识的依赖性.     

考虑道路坡度因素的低碳VRP问题模型与求解策略

经典车辆路径问题（vehicle routing problem，VRP）模型不考虑道路的坡度，通常以最小化车辆行驶总距离、总耗时或派送车辆数为目标函数. 在考虑道路坡度因素的基础上，提出了以配送车辆总能耗最小为目标的低碳车辆路径问题模型 （energy consumption minimizing low-carbon VRP，ECM-LCVRP）；然后，以带能力约束的车辆路径问题 （capacitated VRP，CVRP）为参照，分析了 ECM-LCVRP 的解空间大小及基本算法改进法则在ECM-LCVRP 中的执行复杂度，发现ECM-LCVRP较CVRP更加难以求解，并且分析了不同坡度下 ECM-LCVRP 和 CVRP 的区别与联系；另外，基于配送方案的能耗值与行驶距离正相关的规律，提出了求解不同道路坡度环境下 ECM-LCVRP 的双目标策略 （two objective strategy，TOS）；最后，设计了40个 ECM-LCVRP 算例，并采用综合了算法基本改进规则的混合局部搜索算法 （hybrid local search，HLS）和HLS+TOS 两种方式求解，求解结果表明：在不同的运算时间内，TOS 策略均能够有效地提高HLS的求解质量，且求解时间越短，TOS的效果越明显.     

Balance between facilitation and competition determines spatial patterns in a plant population

A considerable challenge in plant ecology is to understand how interactions,such as competition or facilitation,shape the spatial distribution of plants.The‘‘stress gradient hypothesis’’predicts that facilitation and competition will vary inversely across gradients of abiotic stress or consumer pressure.Surprisingly,few previous studies have explored how the balance between facilitation and competition affects spatial patterns along gradients of stress in a plant population based on field experiments.In order to investigate the effects of consumer pressure,facilitation,and competition on the spatial pattern of plant populations,we conducted a restoration succession series field experiment in the Inner Mongolian steppe in which sample sites of graded consumer pressure,specifically grazing stress,were established.We chose to examine the spatial patterns of Leymus chinensis,a dominant species in our experimental site.In order to test the‘‘stress gradient hypothesis,’’we applied the univariate O-ring statistic to analyze local neighborhood density at different spatial scales.We used the pair-correlation function to detect the characteristics of point patterns using complete spatial randomness,the Poisson cluster process,and the nested double-cluster process.We found that the local densities of L.chinensis were higher under high stress than lower stress environments.This demonstrated the‘‘stress gradient hypothesis’’in that facilitation and competition varied inversely across gradients of consumer pressure.However,we found nodifferences in the spatial patterns of L.chinensis based on complete spatial randomness when interactions shifted from facilitation to competition along gradients of consumer pressure.Furthermore,we detected the characteristics of point patterns using the Poisson cluster and nested doublecluster processes.The results showed the spatial patterns of L.chinensis to fit well with the nested double-cluster model under highly stressful conditions,while in lower stress environments they were best approximated by the Thomas process.Our results illustrate that a shift in interactions from facilitation to competition along gradients of consumer pressure can shape spatial patterns and that a combination of the Poisson cluster process and nested doublecluster process can detect spatial pattern characteristics which cannot be detected by complete spatial randomness.     

等离子活化烧结过程的温度分布研究

以导电性的石墨和绝缘性的氧化铝为测试对象,对等离子活化烧结过程中试样和模具所组成体系的温度分布进行了理论分析和实验研究.结果表明,在200～800℃的测量范围内,石墨-模具体系和氧化铝-模具体系内均存在径向温度梯度,试样的温度均高于模具外壁的温度,2种体系的径向温差随温度的升高成抛物线趋势增大.在同一温度下,石墨-模具体系的径向温度梯度大于氧化铝-模具体系的径向温度梯度,2种体系内测温点与试样中心点之间的温差均随两点之间距离的增大而成抛物线趋势增大,这与理论分析结果是相一致的.     

p维Lipschitz函数的广义梯度及p维Lipschitz多目标规划的充分条件

本文定义了ｐ维Ｌｉｐｓｃｈｉｔｚ向量函数及其广义梯度，并在此基础上给出了ｐ维Ｌｉｐｓｃｈｉｔｚ规划的充分条件．     

特形脉冲激发轮廓的快速测量

利用脉冲梯度场技术，可采用自旋回波或梯度加波方法在单次或数次实验中获得高分辨的反映相位特性的特形脉冲激发轮廓，实验测量的关键在于准确确定回波汇集时间，由于脉冲梯度场的不完善，实验测量中任何回波时间确定的偏差将造成激发轮廓的线性相位误差，该文利用相位预补偿方法对实验测量的细节进行了讨论。     

线性约束梯度投影法理论的改进

利用广义逆矩阵的特性，改进了线性约束梯度投影法的理论。     

多元函数微分法的一点注记

在有限维欧氏空间中的任何子集上定义了实值可微分两次的函数，其梯度的模和Ｌａｐｌａｃｅ 算法的取值都与空间的坐标变换无关．     

f-拉普拉斯算子正调和函数的梯度估计

设M是m维完备的黎曼流形.在∞-Bakry-Emery Ricci曲率和Ricci曲率都有下界的条件下,Chen得到了f-拉普拉斯算子正调和函数的一类梯度估计.仅在∞-Bakry-Emery Ricci曲率有下界的条件下,得到了与Chen类似的梯度估计.     

一种新的修正 Liu-Storey 共轭梯度法的全局收敛性（英）

在 Liu-Storey(LS)公式的基础上给出了一个修正的共轭梯度公式 beta _k^MLS. 证明了该新公式在 Wolfe-Powell 线搜索下, 甚至在强 Wolfe-Powell 线搜索下, 在满足sigma in bigg(0,textstyle1 over 2bigg) 的同时, 新算法具有充分下降性和全局收敛性. 数值结果展现了算法的可行性.