A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

Carbon nanospheres with well‐controlled nano‐morphologies as support for palladium‐catalyzed Suzuki coupling reaction

Uniform carbon nanospheres (UCS) with well‐controlled nano‐morphologies were fabricated by hydrothermal carbonization of sucrose in the presence of kayexalate. Highly dispersed and ultrafine palladium nanoparticles were supported on the UCS through a facile co‐reduction process with NaBH₄ as reducing agent. The obtained Pd@UCS exhibited efficient catalytic activity for the Suzuki coupling reaction. Moreover, the as‐prepared catalyst could be recycled and reused at least five times without significant loss of its catalytic activity.     

中西部地区人口就近城镇化意愿的受教育程度差异研究

基于对中西部地区15个省市农业转移人口就近城镇化意愿的问卷调查数据,以社会认同度为研究视角,构建多群组结构方程模型分析中西部地区人口就近城镇化的受教育程度差异及其影响因素。研究结果表明:个人特征差异性对中西部地区不同受教育程度的农业转移人口的就近城镇化意愿影响显著;中西部地区不同受教育程度的农业转移人口的社会认同度与其就近城镇化意愿显著正相关,且社会认同度对中西部地区小学及以下学历的农业转移人口就近城镇化意愿的影响最显著,大专及以上学历的农业转移人口的就近城镇化意愿受社会认同度的影响最小。     

Optimal uniform approximation on angles by entire functions

The paper discusses the best or optimal uniform approximation problem by entire functions on a closed angle Δ. This problem has been studied by M.V. Keldysch in [4], under the assumption that the functions ? subject to approximation are holomorphic in a larger angle containing Δ and there is no restriction on the growth of ? at infinity. In [8], the problem was investigated for a wider class of functions ? continuously complex differentiable on Δ, with sharper estimates on the growth of approximating entire functions, linked with the growth of ? on Δ and the differential properties of ? on the boundary of Δ. In this paper, we improve some of the results on entire approximation on angles, using new approximation ideas partially presented in [9] and [10].     

第一性原理研究MgZn2相的电子结构及磁性质

运用密度泛函理论的第一性原理计算分析了MgZn₂相的电子结构及相关磁性质。能带结构和态密度分析表明Zn4s和Zn4p轨道、Mg3s和Mg3p轨道分别发生sp态杂化,然后杂化态之间相互作用而形成Zn-Mg键;Mulliken布居分布计算显示:Zn₁-Mg(Zn₁是处于晶格边缘的Zn原子)和Zn₂-Mg(Zn₂是处于晶格内部的Zn原子)电子云重叠布居数接近0,电子密度分析显示Zn-Mg之间电子密度分布具有明显的定域性。结合上述结果与Zn、Mg原子的电负性差异,确定Zn-Mg键为极性共价键。分态密度(PDOS)分析显示,Zn₁-Mg键和Zn₂-Mg键的差异主要表现在Zn₂4s轨道在-10~-6 eV区域对成键的贡献度高于Zn₁4s轨道,而Zn₁4s轨道在2~5 eV区域对成键的贡献度高于Zn₂4s轨道。进一步对MgZn₂的积分自旋态密度和磁矩计算表明:MgZn₂磁性质表现为顺磁性,其磁性主要来源于Zn₁-Mg键中的2个自旋相同的未配对电子;MgZn₂的顺磁性特性将使Al-Zn-Mg-Cu(7xxx系)高强铝合金产生磁致塑性效应。