The mesa problem for Neumann boundary value problem

In this paper, we study the singular limit of the Porous Medium equation u_t=Δu^m+g(x,u), as m→∞, in a bounded domain with Neumann boundary condition.     

级数小于1的亚纯函数的Borel例外值

证明了当超越亚纯函数的级小于1时，其Norel例外值最多只有一个．由于存在任何级的整函数，因此一个例外值总可达到，故所得结果不能再改进。     

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.     

On Brennan's Conjecture for a Special Class of Functions

In this paper, we prove Brennan's conjecture for conformal mappings f of the disk {z : | z| < 1} assuming that the Taylor coefficients of the function log(zf′(z)/f(z)) at zero are nonnegative. We also obtain inequalities for the integral means over the circle |z| = r of the squared modulus of the function zf′(z)/f(z).     

商空间的基

通过引入一个熟知的线性空间作桥梁，揭示了商空闻R^n／S基与矩阵A之间的关系。     

On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

辐射传递蒙特卡洛法精度分析及数值试验

本文建立了蒙特卡洛法模拟散射参与性介质内辐射传递计算模型。对蒙特卡洛法的计算精度及运行时间进行了较为详细的分析,提出了几种判断计算精度的方法。同时,借助蒙特卡洛法模拟辐射传递过程,进行数值“辐射实验”。利用该“实验结果”进行了物性反问题研究。在已知光学厚度的前提下,得到散射反照率与后半球辐射热流之间的单值函数关系。     

A note on the unsteady boundary layers over a flat plate

The unsteady boundary layer over a semi-infinite flat plate was investigated in this paper. The flow involves the unsteady flow over a flat plate with leading edge accretion or ablation. The momentum boundary layer was further analyzed and it was shown that the leading edge ablation had a similar effect to the wall mass injection or upstream wall movement making the fluid blown away from the wall. The thermal boundary layer of the same flow was also studied. Results show that the leading edge accretion or ablation can greatly change the fluid motion and the heat transfer characteristics.     

绿洲-荒漠生态系统演化因素及其非线性探讨——以新疆为例

对立统一于干旱区的绿洲—荒漠生态系统在降水等自然因素和人类活动等人为因素的影响下不断进行着演化.从长期看,这一演化过程具有不可预测性,短期内却有细微可预见性.现如今在绿洲扩展同时,荒漠也在扩展,整体趋势仍是荒漠在扩展.为维持绿洲的稳定性,促使绿洲—荒漠系统处于一种稳定的发展趋势,本文从分析绿洲-荒漠这对对立统一的生态系统入手,在探讨引起这对生态系统演化的自然因素和人为因素的基础上,确定了自然因素中的降水和人为因素中的政府调控行为为演化的主导因素,初步探索了促使这对生态系统统演化的主导因素作用所具有的非线性关系,这对维持绿洲的稳定性,抑制荒漠扩展有一定的实际意义.