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.     

线弹性问题的一个四面体元分析

构造了一个新的locking-free非协调四面体元,研究了单元对三维纯位移弹性问题的一致收敛性,得到了最优的误差估计结果.     

3D Uranyl Organic Frameworks Supported by Rigid Octadentate Carboxylate Ligand: Synthesis,Structure Diversity,and Luminescence Properties

Seven three dimensional (3D) uranyl organic frameworks (UOFs), formulated as [NH₄][(UO₂)₃(HTTDS)(H₂O)] ( 1 ), [(UO₂)₄(HTTDS)₂](HIM)₆ ( 2 , IM=imidazole), [(UO₂)₄(TTDS)(H₂O)₂(Phen)₂] ( 3 , Phen=1,10-phenanthroline), [Zn(H₂O)₄]_0.5[(UO₂)₃(HTTDS)(H₂O)₄] ( 4 ), and {(UO₂)₂[Zn(H₂O)₃]₂(TTDS)} ( 5 ), {Zn(UO₂)₂(H₂O)(Dib)_0.5(HDib)(HTTDS)} ( 6 , Dib=1,4-di(1H-imidazol-1-yl)benzene) and [Na]{(UO₂)₄[Cu₃(u₃-OH)(H₂O)₇](TTDS)₂} ( 7 ) have been hydrothermally prepared using a rigid octadentate carboxylate ligand, tetrakis(3,5-dicarboxyphenyl)silicon(H₈TTDS). These UOFs have different 3D self-assembled structures as a function of co-ligands, structure-directing agents and transition metals. The structure of 1 has an infinite ribbon formed by the UO₇ pentagonal bipyramid bridged by carboxylate groups. With further introduction of auxiliary N-donor ligands, different structure of 2 and 3 are formed, in 2 the imidazole serves as space filler, while in 3 the Phen are bound to [UO₂]²⁺ units as co-ligands. The second metal centers were introduced in the syntheses of 4–7 , and in all cases, they are part of the final structures, either as a counterion ( 4 ) or as a component of framework ( 5 − 7 ). Interesting, in 7 , a rare polyoxometalate [Cu₃(μ₃-OH)O₇(O₂CR)₄] cluster was found in the structure. It acts as an inorganic building unit together with the dimer [(UO₂)₂(O₂CR)₄] unit. Those uranyl carboxylates were sufficiently determined by single crystal X-ray diffraction, and their topological structures and luminescence properties were analyzed in detail.     

Magnetization switching modes in nanopillar spin valve under the external field

The current-induced magnetic switching is studied in Co/Cu/Co nanopillar with an in-plane magnetization traversed under the perpendicular-to-plane external field.Magnetization switching is found to take place when the current density exceeds a threshold.By analyzing precessional trajectories,evolutions of domain walls and magnetization switching times under the perpendicular magnetic field,there are two different magnetization switching modes:nucleation and domain wall motion reversal;uniform magnetization ...     

Book review of spectral theory of linear operators and spectral systems in banach algebras,operator theory: advances and applications,Vladimir Müller,Birkhäuser Verlag,Basel-Boston-Berlin, 2003, Volume 139, 381 pages. ISBN 3-7643-6912-4

We explore how randomization can help asymptotic convergence properties of simple directional search-based optimization methods. Specifically, we develop a cheap, iterative randomized Hessian estimation scheme. We then apply this technique and analyse how it enhances a random directional search method. Then, we proceed to develop a conjugate-directional search method that incorporates estimated Hessian information without requiring the direct use of gradients.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.     

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.     

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.