Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in ter...Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.展开更多
Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in da...Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.展开更多
为提高高光谱图像异常目标检测的精度,提出一种基于拉普拉斯矩阵图的异常目标检测方法(Laplacian Matrix Graph for Anomaly Detection,LGD)。通过构造全连接图和高斯核函数构造的近邻矩阵,将高光谱图像中异常目标的位置和光谱信息进行...为提高高光谱图像异常目标检测的精度,提出一种基于拉普拉斯矩阵图的异常目标检测方法(Laplacian Matrix Graph for Anomaly Detection,LGD)。通过构造全连接图和高斯核函数构造的近邻矩阵,将高光谱图像中异常目标的位置和光谱信息进行联合处理,实现了高光谱数据不同波段之间的信息融合;利用图的傅里叶变换和拉普拉斯矩阵性能,将图信号的总变差作为判断异常目标的评价函数,实现了异常目标像素点的准确检测,避免了常规检测算法中的矩阵求逆问题,降低了算法的复杂度。在异常检测常用的AVIRIS-I、AVIRIS-II、ABU-urban-2、ABU-urban-4和EI Segundo 5种高光谱数据集上,进行了算法性能验证。实验结果表明:该算法在5种数据集上异常目标检测的AUC值与ROC曲线均优于其他算法,在检测精度上具有明显优势。展开更多
In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors t...In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors translate the fourth-order impulsive differential equations with p-Laplacian (*) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (*) are obtained.展开更多
We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and...We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.展开更多
In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We ...In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].展开更多
基金National Natural Science Foundation of China(No.11371086)the Fund of Science and Technology Commission of Shanghai Municipality,China(No.13ZR1400100)
文摘Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
基金Supported by the National Natural Science Foundation of China (60973097)the Scientific Research Foundation of Liaocheng University(X0810029)~~
文摘Locality preserving projection （LPP） is a typical and popular dimensionality reduction （DR） method,and it can potentially find discriminative projection directions by preserving the local geometric structure in data. However,LPP is based on the neighborhood graph artificially constructed from the original data,and the performance of LPP relies on how well the nearest neighbor criterion work in the original space. To address this issue,a novel DR algorithm,called the self-dependent LPP （sdLPP） is proposed. And it is based on the fact that the nearest neighbor criterion usually achieves better performance in LPP transformed space than that in the original space. Firstly,LPP is performed based on the typical neighborhood graph; then,a new neighborhood graph is constructed in LPP transformed space and repeats LPP. Furthermore,a new criterion,called the improved Laplacian score,is developed as an empirical reference for the discriminative power and the iterative termination. Finally,the feasibility and the effectiveness of the method are verified by several publicly available UCI and face data sets with promising results.
文摘为提高高光谱图像异常目标检测的精度,提出一种基于拉普拉斯矩阵图的异常目标检测方法(Laplacian Matrix Graph for Anomaly Detection,LGD)。通过构造全连接图和高斯核函数构造的近邻矩阵,将高光谱图像中异常目标的位置和光谱信息进行联合处理,实现了高光谱数据不同波段之间的信息融合;利用图的傅里叶变换和拉普拉斯矩阵性能,将图信号的总变差作为判断异常目标的评价函数,实现了异常目标像素点的准确检测,避免了常规检测算法中的矩阵求逆问题,降低了算法的复杂度。在异常检测常用的AVIRIS-I、AVIRIS-II、ABU-urban-2、ABU-urban-4和EI Segundo 5种高光谱数据集上,进行了算法性能验证。实验结果表明:该算法在5种数据集上异常目标检测的AUC值与ROC曲线均优于其他算法,在检测精度上具有明显优势。
基金Supported by the National Natural Foundation of China (10371006)the Youth Teachers Science Projects of Central University for Nationalities (No.A08).
文摘In order to study three-point BVPs for fourth-order impulsive differential equation of the form with the following boundary conditions u'(0) = u(1) = 0. u'(0) == 0 = u'(1) -φq(α)u'(η). the authors translate the fourth-order impulsive differential equations with p-Laplacian (*) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (*) are obtained.
基金Supported by Doctor Special Foundation of Jiangsu Second Normal University(JSNU2015BZ07)
文摘We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.
基金Partially supported by NSFC(11571233)NSF DMS-1405175+1 种基金NSF of Shanghai16ZR1402100China Scholarship Council
文摘In this paper, we consider systems of fractional Laplacian equations in ]I^n with nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].
