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
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
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
Dear Editor,This letter studies the problem of stealthy attacks targeting stochastic event-based estimation,alongside proposing measures for their mitigation.A general attack framework is introduced,and the correspond...Dear Editor,This letter studies the problem of stealthy attacks targeting stochastic event-based estimation,alongside proposing measures for their mitigation.A general attack framework is introduced,and the corresponding stealthiness condition is analyzed.To enhance system security,we advocate for a single-dimensional encryption method,showing that securing a singular data element is sufficient to shield the system from the perils of stealthy attacks.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
日负荷数据聚类是实现用户用电特性分析的重要方式。用于聚类的降维采样数据的指标权重会影响聚类结果,因此提出一种基于CRITIC赋权的奇异值分解(singular value decomposition,SVD)降维方法C-SVD与改进加权模糊C均值聚类(fuzzy C-means...日负荷数据聚类是实现用户用电特性分析的重要方式。用于聚类的降维采样数据的指标权重会影响聚类结果,因此提出一种基于CRITIC赋权的奇异值分解(singular value decomposition,SVD)降维方法C-SVD与改进加权模糊C均值聚类(fuzzy C-means,FCM)算法相结合的日负荷数据聚类方法,同时针对传统FCM易受初始聚类中心影响的问题,提出一种自适应确定初始聚类中心的密度‒距离中心点选择(density-distance centersr selection,DDCS)方法。首先,采用SVD对负荷数据进行降维处理;其次,使用CRITIC赋权法对降维指标进行权重配置;然后,使用DDCS法确定初始聚类中心;最后,使用加权FCM算法对负荷数据进行聚类。仿真算例表明,与传统方法相比,所提方法鲁棒性强,能够明显提升负荷数据聚类结果的准确性。展开更多
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)).
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.
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.
基金supported by the National Natural Science Foundation of China(62303353,62273030,62573320)。
文摘Dear Editor,This letter studies the problem of stealthy attacks targeting stochastic event-based estimation,alongside proposing measures for their mitigation.A general attack framework is introduced,and the corresponding stealthiness condition is analyzed.To enhance system security,we advocate for a single-dimensional encryption method,showing that securing a singular data element is sufficient to shield the system from the perils of stealthy attacks.
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.
