We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating s...We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.展开更多
In this paper, we will analyze the blow-up behaviors for solutions to the Laplacian equation with exponential Neumann boundary condition. In particular, the boundary value is with a kind of singular data. We show a Br...In this paper, we will analyze the blow-up behaviors for solutions to the Laplacian equation with exponential Neumann boundary condition. In particular, the boundary value is with a kind of singular data. We show a Brezis–Merle type concentration-compactness theorem, calculate the blow up value at the blow-up point, and give a point-wise estimate for the profile of the solution sequence at the blow-up point.展开更多
In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an ele...In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).展开更多
A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the p...A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.展开更多
为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理...为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理想解排序(technique for order preference by similarity to an ideal solution,TOPSIS)法对分解后的奇异值进行优选,在确保数据真实性的前提下用少量奇异值表征原始图像,进行图像压缩,降低数据大小,提高传输效率;提出多通道猫脸分割加密方法,分别对每个颜色通道的图像进行随机分割、随机加密和随机排序,解决了传统猫脸加密算法颜色通道线性相关度高,整体置乱度低的问题.结果表明:改进奇异值压缩技术在保证图像清晰的情况下仅利用15%的奇异值数据完成对图像的压缩,最大图像压缩比可达4.43,平均压缩后所占用的存储空间仅为原空间的26.29%,数据传输控制协议通信平均传输效率提高86.39%.在加密图像达到0相关的前提下,多通道猫脸分割加密算法加密图像在像素点处三通道颜色值完全不同,新方法颜色通道相关系数分别为0.20、0.22和0.25,对比传统猫脸加密方法,分别降低0.78、0.75和0.71.新方法加密效果好、难破解,可为石油行业数字化转型提供理论和技术支撑.展开更多
针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数...针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数据先验信息的问题,引入相空间重构算法将原始缺失数据映射到高维空间,利用数据间的关联性和结构特征,为后续数据恢复算法提供先验知识;结合对数与Sigmoid函数构建变步长基础函数,并利用等比项提高前期步长,构建自适应变步长SVT算法,克服传统SVT在大规模数据情况下计算效率低的问题.结合多项公用电力负荷数据集及多种常用电力负荷数据恢复算法进行对比实验分析,结果表明,改进SVT算法可获得更好的数据恢复效果,收敛速度、精度以及稳定性得到提升,具有较强的工程实用性.展开更多
文摘We study the existence problem for the equations of first order quasilinearequations in several inpendent variables with singular initial data Lp(P<∞). We the convergence of the Lp(P<∞) bounded approximating sequences generatedby the method of vanishing viscosity. The uniqueness of the generalized solutions whichcan be obtained by the method of vanishing viscosity is also obtained.
文摘In this paper, we will analyze the blow-up behaviors for solutions to the Laplacian equation with exponential Neumann boundary condition. In particular, the boundary value is with a kind of singular data. We show a Brezis–Merle type concentration-compactness theorem, calculate the blow up value at the blow-up point, and give a point-wise estimate for the profile of the solution sequence at the blow-up point.
文摘In this paper, it is considered that the global existence, uniqueness and regularity results for the Cauchy problem of the well-known Kuramoto-Sivashinsky equation [GRAPHICS] only under the condition u(0)(x) is an element of L-2(R-N, R-n). Where u(t, x) = (u(1)(t, x), ..., u(n)(t, x))(T) is the unknown vector-valued function. Results show that for N < 6,.u(0)(x) is an element of L-2(R-N, R-n), the above Cauchy problem admits a unique global solution u(t, x) which belongs to C-infinity,C-infinity(R-N x (0, infinity)).
基金the State Key Program for Basic Research of China(No.2007CB816003)the Open Item of the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics of China
文摘A novel interval quartering algorithm （IQA） is proposed to overcome insufficiency of the conventional singular spectrum analysis （SSA） iterative interpolation for selecting parameters including the number of the principal components and the embedding dimension. Based on the improved SSA iterative interpolation, interpolated test and comparative analysis are carried out to the outgoing longwave radiation daily data. The results show that IQA can find globally optimal parameters to the error curve with local oscillation, and has advantage of fast computing speed. The improved interpolation method is effective in the interpolation of missing data.
文摘为解决石油行业大数据高效安全传输难题,将图像转化为三通道矩阵数据并对矩阵进行奇异值分解,综合考虑Laplace算子、灰度方差函数、离散余弦变换系数、图像相关系数、熵函数、图像结构相似度和图像信噪比等7个评价因素,利用熵权逼近理想解排序(technique for order preference by similarity to an ideal solution,TOPSIS)法对分解后的奇异值进行优选,在确保数据真实性的前提下用少量奇异值表征原始图像,进行图像压缩,降低数据大小,提高传输效率;提出多通道猫脸分割加密方法,分别对每个颜色通道的图像进行随机分割、随机加密和随机排序,解决了传统猫脸加密算法颜色通道线性相关度高,整体置乱度低的问题.结果表明:改进奇异值压缩技术在保证图像清晰的情况下仅利用15%的奇异值数据完成对图像的压缩,最大图像压缩比可达4.43,平均压缩后所占用的存储空间仅为原空间的26.29%,数据传输控制协议通信平均传输效率提高86.39%.在加密图像达到0相关的前提下,多通道猫脸分割加密算法加密图像在像素点处三通道颜色值完全不同,新方法颜色通道相关系数分别为0.20、0.22和0.25,对比传统猫脸加密方法,分别降低0.78、0.75和0.71.新方法加密效果好、难破解,可为石油行业数字化转型提供理论和技术支撑.
文摘针对传统奇异值阈值(Singular Value Thresholding,SVT)数据恢复算法在对电力负荷数据恢复中忽视数据先验信息以及大规模数据计算效率低等问题,提出一种基于相空间重构与自适应变步长的改进SVT的数据恢复算法.为解决传统SVT容易忽视数据先验信息的问题,引入相空间重构算法将原始缺失数据映射到高维空间,利用数据间的关联性和结构特征,为后续数据恢复算法提供先验知识;结合对数与Sigmoid函数构建变步长基础函数,并利用等比项提高前期步长,构建自适应变步长SVT算法,克服传统SVT在大规模数据情况下计算效率低的问题.结合多项公用电力负荷数据集及多种常用电力负荷数据恢复算法进行对比实验分析,结果表明,改进SVT算法可获得更好的数据恢复效果,收敛速度、精度以及稳定性得到提升,具有较强的工程实用性.
