In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling fa...Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket （SG）. As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5 ：△=0 on SG ／ {q1, q2, q3}, and u（qi）=ai, i = 1, 2, 3, where qi, i=1, 2, 3, are boundary points of SG.展开更多
The Laplacian of a function measures the difference between the value of the function at a point and its average around that point. It is a differential operator appears in many differential equations describing many ...The Laplacian of a function measures the difference between the value of the function at a point and its average around that point. It is a differential operator appears in many differential equations describing many physical phenomena. We establish some inequalities involving the Laplacian of warping function for screen conformal lightlike warped product hypersurface in Lorentzian manifold of constant sectional curvature. The existence of such hypersurface is deduced in minimal case.展开更多
针对当前去雾算法效率不高、细节恢复较差等问题,提出一种改进多尺度AOD-Net(all in one dehazing network)的去雾算法。通过增加注意力机制、调整网络结构和改变损失函数这3方面的改进,增强网络的特征提取和恢复能力。模型的第1层增加...针对当前去雾算法效率不高、细节恢复较差等问题,提出一种改进多尺度AOD-Net(all in one dehazing network)的去雾算法。通过增加注意力机制、调整网络结构和改变损失函数这3方面的改进,增强网络的特征提取和恢复能力。模型的第1层增加空间金字塔注意力(spatial pyramid attention,SPA)机制,使网络在特征提取过程中避免冗余信息。将网络改成拉普拉斯金字塔型结构,使模型能够提取不同尺度的特征,保留特征图的高频信息。使用多尺度结构相似性(multi-scale structural similarity,MS-SSIM)+L1损失函数替换原有的损失函数,提高模型保留结构的能力。实验结果表明,本方法去雾效果更好,细节更丰富。在定性可视化评价方面,去雾图像效果优于原网络。在定量评估层面,与原网络相比PSNR值提升了2.55 dB,SSIM值提升了0.04,IE熵值增加了0.18,这些数值指标充分验证了本算法的出色去雾效果和稳定性。展开更多
文摘In this paper,the boundary value problems of p-Laplacian functional differential equation are studied.By using a fixed point theorem in cones,some criteria for the existence of positive solutions are given.
基金Supported by the National Natural Science Foundation of China(11271327)Zhejiang Provincial National Science Foundation of China(LR14A010001)
文摘Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket （SG）. As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5 ：△=0 on SG ／ {q1, q2, q3}, and u（qi）=ai, i = 1, 2, 3, where qi, i=1, 2, 3, are boundary points of SG.
文摘The Laplacian of a function measures the difference between the value of the function at a point and its average around that point. It is a differential operator appears in many differential equations describing many physical phenomena. We establish some inequalities involving the Laplacian of warping function for screen conformal lightlike warped product hypersurface in Lorentzian manifold of constant sectional curvature. The existence of such hypersurface is deduced in minimal case.
文摘针对当前去雾算法效率不高、细节恢复较差等问题,提出一种改进多尺度AOD-Net(all in one dehazing network)的去雾算法。通过增加注意力机制、调整网络结构和改变损失函数这3方面的改进,增强网络的特征提取和恢复能力。模型的第1层增加空间金字塔注意力(spatial pyramid attention,SPA)机制,使网络在特征提取过程中避免冗余信息。将网络改成拉普拉斯金字塔型结构,使模型能够提取不同尺度的特征,保留特征图的高频信息。使用多尺度结构相似性(multi-scale structural similarity,MS-SSIM)+L1损失函数替换原有的损失函数,提高模型保留结构的能力。实验结果表明,本方法去雾效果更好,细节更丰富。在定性可视化评价方面,去雾图像效果优于原网络。在定量评估层面,与原网络相比PSNR值提升了2.55 dB,SSIM值提升了0.04,IE熵值增加了0.18,这些数值指标充分验证了本算法的出色去雾效果和稳定性。
