In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation e...In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.展开更多
This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical...This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].展开更多
We establish the global existence of small-amplitude solutions near a global Maxwellian to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system for non-cutoff soft potentials with weak angular singularity. This e...We establish the global existence of small-amplitude solutions near a global Maxwellian to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system for non-cutoff soft potentials with weak angular singularity. This extends the work of Duan et al.(2013), in which the case of strong angular singularity is considered, to the case of weak angular singularity.展开更多
针对密度峰值聚类算法CFSFDP(clustering by fast search and find of density peaks)计算密度时人为判断截断距离和人工截取簇类中心的缺陷,提出了一种基于非参数核密度估计的密度峰值聚类算法。首先,应用非参数核密度估计方法计算数...针对密度峰值聚类算法CFSFDP(clustering by fast search and find of density peaks)计算密度时人为判断截断距离和人工截取簇类中心的缺陷,提出了一种基于非参数核密度估计的密度峰值聚类算法。首先,应用非参数核密度估计方法计算数据点的局部密度;其次,根据排序图采用簇中心点自动选择策略确定潜在簇类中心点,将其余数据点归并到相应的簇类中心;最后,依据簇类间的合并准则对邻近相似子簇进行合并,并根据边界密度识别噪声点得到聚类结果。在人工测试数据集和UCI真实数据集上的实验表明,新算法较之原CFSFDP算法,不仅有效避免了人为判断截断距离和截取簇类中心的主观因素,而且可以取得更高的准确度。展开更多
基金supported by the NSFC(12101012)the PhD Scientific Research Start-up Foundation of Anhui Normal University.Zeng’s research was supported by the NSFC(11961160716,11871054,12131017).
文摘In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.
基金supported by the Fundamental Research Funds for the Central Universities
文摘This paper is concerned with the non-cutoff Boltzmann equation for full-range interactions with potential force in the whole space. We establish the global existence and optimal temporal convergence rates of classical solutions to the Cauchy problem when initial data is a small perturbation of the stationary solution. The analysis is based on the time-weighted energy method building also upon the recent studies of the non-cutoff Boltzmann equation in [1-3, 15] and the non-cutoff Vlasov-Poisson-Boltzmann system [6].
基金supported by the Fundamental Research Funds for the Central UniversitiesNational Natural Science Foundation of China(Grant Nos.11601169,11471142,11271160,11571063,11731008 and 11671309)
文摘We establish the global existence of small-amplitude solutions near a global Maxwellian to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system for non-cutoff soft potentials with weak angular singularity. This extends the work of Duan et al.(2013), in which the case of strong angular singularity is considered, to the case of weak angular singularity.
文摘针对密度峰值聚类算法CFSFDP(clustering by fast search and find of density peaks)计算密度时人为判断截断距离和人工截取簇类中心的缺陷,提出了一种基于非参数核密度估计的密度峰值聚类算法。首先,应用非参数核密度估计方法计算数据点的局部密度;其次,根据排序图采用簇中心点自动选择策略确定潜在簇类中心点,将其余数据点归并到相应的簇类中心;最后,依据簇类间的合并准则对邻近相似子簇进行合并,并根据边界密度识别噪声点得到聚类结果。在人工测试数据集和UCI真实数据集上的实验表明,新算法较之原CFSFDP算法,不仅有效避免了人为判断截断距离和截取簇类中心的主观因素,而且可以取得更高的准确度。
