一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.     

Asymptotic tail probability of randomly weighted sums of dependent random variables with dominated variation

This paper investigates the asymptotic behavior of tail probability of randomly weighted sums of dependent and real-valued random variables with dominated variation, where the weights form another sequence of nonnegative random variables. The result we obtain extends the corresponding result of Wang and Tang[7].     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

(α,β)混合序列的强稳定性

研究一类被随机控制的(α,β)混合序列,并得到了关于其强稳定性的若干结论.     

具有主导晶面的BiOIO3/BiOCl异质结制备与光催化性能

分别以乙二醇/去离子水为溶剂,通过溶剂热/水热法分别制备了具有不同主导晶面的BiOIO₃/{110}BiOCl和BiOIO₃/{001}BiOCl异质结。采用X射线衍射、扫描电子显微镜、能量色散谱和紫外可见漫反射光谱对制备的BiOIO₃/BiOCl光催化剂进行了表征。在可见光照射下,通过对罗丹明 B和苯酚水溶液的光催化降解,考察了 BiOIO₃/BiOCl异质结的光催化活性。结果显示25% BiOIO₃/{110}BiOCl异质结具有最高的光催化效率。BiOIO₃/{110}BiOCl较好的光催化性能是由于其在可见光区较强的光吸收,以及异质结结构和BiOCl所具有的(110)主导晶面有利于光生载流子的分离。超氧自由基(·O₂^-)和空穴(h⁺)是光催化过程中的主要活性物质。此外,根据实验结果探讨了光催化性能增强的机理。     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Dominated splitting versus small angles

In this paper, we give a partial answer to the problem proposed by Lan Wen. Roughly speaking, we prove that for a fixed i, f has C^1 persistently no small angles if and only if f has a dominated splitting of index i on the C^1 i-preperiodic set P＊^1（f）. To prove this, we mainly use some important conceptions and techniques developed by Christian Bonatti. In the last section, we also give a characterization of the finest dominated splitting for linear cocvcles.     

R^2上带奇异性的非线性多重调和方程的正整解

该文以Schauder-Tychonoff不动点定理为工具，建立了一类平面上带奇异性的非线性 多重调和方程的正的径向对称整体解的存在性定理，并给出了解的有关性质，所得的结果丰 富和发展文[1][4]的结果。     

线性对流占优Sobolev方程的流线扩散有限元方法

Abastract. In this paper,a streamline-diffusion F. E. M. for linear Sobolev equations with con-vection-dominated term is given. According to the range of space-time F. E mesh parameter h,two choices for artifical diffusion parameter are presented,and for the corresponding computa-tion schemes the stability and error estimates in suitable norms are estabilished.