p-Laplace方程正解的存在性和多重性

这篇文章讨论边值问题-(| u′|p-2u′)′=λf(t ,u) ,t∈(0,1) ,p >1,u(0) =u(1) =0,其中f(t ,u)≥-M( M是正常数) ,对(t ,u)∈0,1×0,∞) .我们利用度理论和锥上的不动点定理得到方程存在两个正解.     

Resistance distance and Laplacian spectrum

The resistance distance r _ij between two vertices v _i and v _j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r _ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r _ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.     

The Physical Basis of the VSEPR Model

The VSEPR model is a consequence of the correlation of same-spin electrons resulting from the operation of the Pauli exclusion principle. Although the VSEPR rules can be interpreted in terms of an orbital model they do not provide the physical basis for the model.     

基于多维行为分析的窃电高风险客户精准定位方法

窃电行为对国家电力系统及供电公司造成了极大的损失,故反窃电技术是电力行业的重要研究方向之一。传统的窃电用户定位方法存在定位不准确、查处效率低等问题,为了解决上述问题,提出基于多维行为分析的窃电高风险客户精准定位方法。首先通过相关矩阵R及特征值谱熵正则化完成用户数据去噪,其次在UFS-MI模型内提取用户数据特征,分析用户用电的多维行为,最后根据逻辑回归算法完成窃电高风险客户的精确定位。实验结果表明,所提方法的窃电高风险客户定位精准度较高,误判率较低,整体定位效果较好。     

k圈图的最大Laplace分离度

设$ G $是一个$ n $阶$ k $圈图, $ k $圈图为边数等于顶点数加$ k-1 $的简单连通图。$ \mu_{1}(G) $、$ \mu_{2}(G) $分别记为图$ G $的Laplace矩阵的最大特征值和次大特征值, 图$ G $的Laplace分离度定义为$ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $。本文研究了给定阶数的$ k $圈图的最大Laplace分离度, 并刻画了相应的极图, 其结果推广了已有当$ k=1, 2, 3 $时的结论。     

Regularity of Viscosity Solutions of the Biased Infinity Laplacian Equation

In this paper, we are interested in the regularity estimates of the nonnegative viscosity super solution of the $β$−biased infinity Laplacian equation $$∆^β_∞u = 0,$$ where $β ∈ \mathbb{R}$ is a fixed constant and $∆^β_∞u := ∆^N_∞u + β|Du|,$ which arises from the random game named biased tug-of-war. By studying directly the $β$−biased infinity Laplacian equation, we construct the appropriate exponential cones as barrier functions to establish a key estimate. Based on this estimate, we obtain the Harnack inequality, Hopf boundary point lemma, Lipschitz estimate and the Liouville property etc.     

空间听觉与虚拟听觉空间的计算机仿真

一些科学工作者对人类以及动物听觉的自由声场至耳膜的传递函数进行了测量,他们发现在宽带信号激励的情况下,不同频率分量之间的幅度差异是与声源的方向有关的,这一发现已被用于展现“真实”的三维听觉,称作虚拟听觉空间仿真。     

雷达辐射源信号双谱二次特征提取方法

现有的双谱特征提取方法可以满足信号分类识别，但是出现了交叉项、平凡双谱以及特征维数过高等一些问题。针对以上问题，提出一种双谱二次特征提取方法，将双谱转化为灰度图像，以灰度值表示双谱幅度；再利用图像处理技术提取双谱二次特征，提取出能够表征辐射源信号双谱图像纹理信息的灰度共生矩阵特征集；将该特征集与Hu-不变矩特征集进行对比实验。仿真结果表明：该方法具有更好的分类识别性能，对于CW、LFM和NLFM信号的平均识别率均达90%以上。     

改进的SIFT特征匹配算法

针对SIFT特征匹配算法在特征空间中进行历遍搜索,匹配速度慢的问题,提出一种金字塔层间匹配算法。首先,根据特征点所处金字塔层不同将特征点划分为不同的集合,其次,选择待配准图像金字塔中某一层集合,在基准图像金字塔中寻找相似层,并确定待配准图像金字塔与基准图像金字塔层之间的相似关系,最后,在相似层之间寻找匹配点。待配准图像中的选择层集合由金字塔底层到顶层,寻找相似层所用时间依次缩短。与原算法相比,该算法具有相同的旋转稳定性。将该算法与原算法分别应用实际图像配准中,结果表明:可见光图像配准中,匹配速度提高了3.2倍,正确匹配率提高了10.3％,红外图像配准中,匹配速度提高1.4倍,正确匹配率达到100％。     

Curvature invariants, differential operators and local homogeneity

We first prove that a Riemannian manifold with globally constant additive Weyl invariants is locally homogeneous. Then we use this result to show that a manifold whose Laplacian commutes with all invariant differential operators is a locally homogeneous space.