Sobolev-Hardy不等式与临界双重调和问题

该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ，这里Ω包含R^N是包含0的有界光滑区域，u∈H0^2(Ω），μ∈R是参数，0≤s≤2,△^2=△△表示双重拉普拉斯算子，当f(x,u)=u^p,p=2N/N-4时，上述问题就是一个临界双重调和问题，该文运用Sobolev-Hardy不等式和变分方法，得到它的解的存在性的一些结果。     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Effect of ion impinging on the microstructure and field emission of carbon nanotubes

Effects of ion impinging on the microstructure and field electron emission properties of screen-printed carbon nanotube films were investigated. We observed that the plasma treatment modified the microstructure of CNTs along with the remarkable increase of emission site density. With the prolongation of ion impinging time, the emission current falls down first, and then rises up to higher than that of the untreated films. It is proposed that the change of emission characteristics is due to the different emission mechanisms. After the treatment, electrons are emitted predominantly from the nano-nodes on the tube wall instead from the nanotube tips.     

Absorbing boundary conditions for reaction-diffusion equations

We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reaction–diffusion equations.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

线性泛函方程解的振动性的新结果

本文研究高阶泛函方程x(g(t))=P(t)x(t)+Q1(t)x(g2(t))+…+Qk(t)x(gk+1(t))解的振动性,得到了一些新的振动条件.改进和推广了已有结果.     

First law of thermodynamics and Friedmann-like equations in braneworld cosmology

We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann–Robertson–Walker universe in both Randall–Sundrum II gravity and Dvali–Gabadadze–Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.     

From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

   Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.