In this paper, we prove the local well-posedness of the viscous surface wave equation in low regularity Sobolev spaces. The key points are to establish several new Stokes estimates depending only on the optimal bounda...In this paper, we prove the local well-posedness of the viscous surface wave equation in low regularity Sobolev spaces. The key points are to establish several new Stokes estimates depending only on the optimal boundary regularity and to construct a new iteration scheme on a known moving domain. Our method could be applied to some other fluid models with free boundaries.展开更多
The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data i...The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s（R）（s 〉 -3/4）. For k = 2, local result for data in H^S（R）（s 〉1/4） is obtained. For k = 3, local result for data in H^S（R）（s 〉 -1/6） is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.展开更多
In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suita...In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.展开更多
In this paper,we study Ricci flow on compact manifolds with a continuous initial metric.It was known from Simon(2002)that the Ricci flow exists for a short time.We prove that the scalar curvature lower bound is preser...In this paper,we study Ricci flow on compact manifolds with a continuous initial metric.It was known from Simon(2002)that the Ricci flow exists for a short time.We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in the distributional sense provided that the initial metric is W^(1,p) for some n<p∞.As an application,we use this result to study the relation between the Yamabe invariant and Ricci flat metrics.We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in the distributional sense,then the manifold is isometric to a Ricci flat manifold.展开更多
目的现实中采集到的人脸图像通常受到光照、遮挡等环境因素的影响,使得同一类的人脸图像具有不同程度的差异性,不同类的人脸图像又具有不同程度的相似性,这极大地影响了人脸识别的准确性。为了解决上述问题对人脸识别造成的影响,在低秩...目的现实中采集到的人脸图像通常受到光照、遮挡等环境因素的影响,使得同一类的人脸图像具有不同程度的差异性,不同类的人脸图像又具有不同程度的相似性,这极大地影响了人脸识别的准确性。为了解决上述问题对人脸识别造成的影响,在低秩矩阵恢复理论的基础上提出了具有识别力的结构化低秩字典学习的人脸识别算法。方法该算法基于训练样本的标签信息将低秩正则化以及结构化稀疏同时引入到学习的具有识别力的字典上。在字典学习过程中,首先利用样本的重建误差约束样本与字典之间的关系;其次将Fisher准则应用到稀疏编码过程中,使其编码系数具有识别能力;由于训练样本中的噪声信息会影响字典的识别力,所以在低秩矩阵恢复理论的基础上将低秩正则化应用到字典学习过程中;接着,在字典学习过程中加入了结构化稀疏使其不丢失结构信息以保证对样本进行最优分类;最后再利用误差重构法对测试样本进行分类识别。结果本文算法在AR以及ORL人脸数据库上分别进行了实验仿真。在AR人脸数据库中,为了分析样本不同维数对实验结果造成的影响,选取了第一时期拍摄的每人6幅图像,包括1幅围巾遮挡,2幅墨镜遮挡以及3幅脸部表情变化以及光照变化(未被遮挡)的图像作为训练样本,同时选取相同组合的样本图像作为测试样本,无论哪种方法,图像的维度越高识别率越高。对比SRC(sparse representation based on classification)算法与DKSVD(discriminative K-means singular value decomposition)算法的识别率可知,DKSVD算法通过字典学习减缓了训练样本中的不确定因素对识别结果的影响;对比DLRD_SR(discriminative low-rank dictionary learning for sparse representation)算法与FDDL(Fisher discriminative dictionary learning)算法的识别率可知,当图像有遮挡等噪声信息存在时,字典低秩化可以提高至少5.8%的识展开更多
基金supported by National Postdoctoral Program for Innovative Talents of China(Grants No.BX201700039)supported by National Natural Science Foundation of China(Grant Nos.11571063 and 11771045)supported by National Natural Science Foundation of China(Grant No.11425103)
文摘In this paper, we prove the local well-posedness of the viscous surface wave equation in low regularity Sobolev spaces. The key points are to establish several new Stokes estimates depending only on the optimal boundary regularity and to construct a new iteration scheme on a known moving domain. Our method could be applied to some other fluid models with free boundaries.
文摘The Cauchy problem of the generalized Korteweg-de Vries-Benjamin-Ono equation is considered, and low regularity and limit behavior of the solutions are obtained. For k = 1, local well- posedness is obtained for data in H^s（R）（s 〉 -3/4）. For k = 2, local result for data in H^S（R）（s 〉1/4） is obtained. For k = 3, local result for data in H^S（R）（s 〉 -1/6） is obtained. Moreover, the solutions of generalized Korteweg-de Vries-Benjamin-Ono equation converge to the solutions of KdV equation if the term of Benjamin-Ono equation tends to zero.
基金supported by the NSFC(11901120)supported by the NSFC(12171356)the Science and Technology Program of Guangzhou,China(2024A04J4027)。
文摘In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.
基金supported by National Natural Science Foundation of China (Grant Nos.12125105 and 12071425)the Fundamental Research Funds for the Central Universities+1 种基金supported by National Natural Science Foundation of China (Grant Nos.11971424 and 12031017)supported by National Natural Science Foundation of China (Grant No.11971424)。
文摘In this paper,we study Ricci flow on compact manifolds with a continuous initial metric.It was known from Simon(2002)that the Ricci flow exists for a short time.We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in the distributional sense provided that the initial metric is W^(1,p) for some n<p∞.As an application,we use this result to study the relation between the Yamabe invariant and Ricci flat metrics.We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in the distributional sense,then the manifold is isometric to a Ricci flat manifold.
文摘目的现实中采集到的人脸图像通常受到光照、遮挡等环境因素的影响,使得同一类的人脸图像具有不同程度的差异性,不同类的人脸图像又具有不同程度的相似性,这极大地影响了人脸识别的准确性。为了解决上述问题对人脸识别造成的影响,在低秩矩阵恢复理论的基础上提出了具有识别力的结构化低秩字典学习的人脸识别算法。方法该算法基于训练样本的标签信息将低秩正则化以及结构化稀疏同时引入到学习的具有识别力的字典上。在字典学习过程中,首先利用样本的重建误差约束样本与字典之间的关系;其次将Fisher准则应用到稀疏编码过程中,使其编码系数具有识别能力;由于训练样本中的噪声信息会影响字典的识别力,所以在低秩矩阵恢复理论的基础上将低秩正则化应用到字典学习过程中;接着,在字典学习过程中加入了结构化稀疏使其不丢失结构信息以保证对样本进行最优分类;最后再利用误差重构法对测试样本进行分类识别。结果本文算法在AR以及ORL人脸数据库上分别进行了实验仿真。在AR人脸数据库中,为了分析样本不同维数对实验结果造成的影响,选取了第一时期拍摄的每人6幅图像,包括1幅围巾遮挡,2幅墨镜遮挡以及3幅脸部表情变化以及光照变化(未被遮挡)的图像作为训练样本,同时选取相同组合的样本图像作为测试样本,无论哪种方法,图像的维度越高识别率越高。对比SRC(sparse representation based on classification)算法与DKSVD(discriminative K-means singular value decomposition)算法的识别率可知,DKSVD算法通过字典学习减缓了训练样本中的不确定因素对识别结果的影响;对比DLRD_SR(discriminative low-rank dictionary learning for sparse representation)算法与FDDL(Fisher discriminative dictionary learning)算法的识别率可知,当图像有遮挡等噪声信息存在时,字典低秩化可以提高至少5.8%的识
