两种细菌的毛细管电泳分离及其与药物相互作用的研究

通过对大肠杆菌与金黄色葡萄球菌的毛细管电泳行为的研究,包括对细菌样品预处理、缓冲液、检测波长以及聚合物添加剂对分离度的改进等的考察,在优化的实验条件下,实现了大肠杆菌与金黄色葡萄球菌的快速分离,从而建立一种新的细菌辅助识别与定性的补充方法。将抗菌药物阿奇霉素与金黄色葡萄球菌混合培育,发现由于阿奇霉素抑制细菌表面蛋白合成,造成与金黄色葡萄球菌作用后,细菌表面电荷密度降低,表现为阿奇霉素对金黄色葡萄球菌的电泳淌度的影响,而且培育时间与金黄色葡萄球菌的淌度线性相关。     

An optimal order multigrid method for biharmonic,C 1 finite element equations

Summary In this paper, we study a special multigrid method for solving large linear systems which arise from discretizing biharmonic problems by the Hsieh-Clough-Tocher,C ¹ macro finite elements or several otherC ¹ finite elements. Since the multipleC ¹ finite element spaces considered are not nested, the nodal interpolation operator is used to transfer functions between consecutive levels in the multigrid method. This method converges with the optimal computational order.     

A CANONICAL CONSTRUCTION OF $H^m$-NONCONFORMING TRIANGULAR FINITE ELEMENTS

We design a family of 2D H^m-nonconforming finite elements using the full P_2m-3 degree polynomial space, for solving $2m$th elliptic partial differential equations. The consistent error is estimated and the optimal order of convergence is proved. Numerical tests on the new elements for solving tri-harmonic, 4-harmonic, 5-harmonic and 6-harmonic equations are presented, to verify the theory.     

An iterative method based on equation decomposition for the fourth‐order singular perturbation problem

In this article, we propose an iterative method based on the equation decomposition technique ( 1 ) for the numerical solution of a singular perturbation problem of fourth‐order elliptic equation. At each step of the given method, we only need to solve a boundary value problem of second‐order elliptic equation and a second‐order singular perturbation problem. We prove that our approximate solution converges to the exact solution when the domain is a disc. Our numerical examples show the efficiency and accuracy of our method. Our iterative method works very well for singular perturbation problems, that is, the case of 0 < ε ? 1, and the convergence rate is very fast. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

A weak Galerkin-mixed finite element method for the Stokes-Darcy problem

In this paper, we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition. We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation. A discrete inf-sup condition is proved and the optimal error estimates are also derived. Numerical experiments validate the theoretical analysis.     

ON THE OPTIMAL CONVERGENCE RATE OF A ROBIN-ROBIN DOMAIN DECOMPOSITION METHOD

In this work, we solve a long-standing open problem： Is it true that the convergence rate of the Lions＇ Robin-Robin nonoverlapping domain decomposition （DD） method can be constant, independent of the mesh size h？ We closed this old problem with a positive answer. Our theory is also verified by numerical tests.     

New error estimates of nonconforming mixed finite element methods for the Stokes problem

In this paper, we revisit the classical error estimates of nonconforming Crouzeix–Raviart type finite elements for the Stokes equations. By introducing some quasi‐interpolation operators and using the special properties of these nonconforming elements, it is proved that their consistency errors can be bounded by their approximation errors together with a high‐order term, especially which can be of arbitrary order provided that f in the right‐hand side is piecewise smooth enough. Furthermore, we show an interesting result that both in the energy norm and L² norm the consistency errors are dominated by the approximation errors of their finite element spaces. As byproducts, we derive the error estimates in both energy and L² norms under the regularity assumption ( u ,p) ∈ H ^{1 + s}(Ω) × H^s(Ω) with any s ∈ (0,1], which fills the gap in the a priori error estimate of these nonconforming elements with low regularity . Furthermore, a robust convergence is proved with minimal regularity assumption s = 0. These results seem to be missing in the literature. Numerical tests are provided, confirming the analysis, especially the new results on the L² convergence. Copyright © 2013 John Wiley & Sons, Ltd.     

二层凸规划的基本性质

本文研究了一类抛述二层决策问题的二层数学规划模型，在一定条件下讨论了下层极值函数和上层复合目标函数的凸性和连续性，给出了二层决策问题优决策的存在条件。     

Stability and approximability of the 𝒫1–𝒫0 element for Stokes equations

In this paper we study the stability and approximability of the ??₁–??₀ element (continuous piecewise linear for the velocity and piecewise constant for the pressure on triangles) for Stokes equations. Although this element is unstable for all meshes, it provides optimal approximations for the velocity and the pressure in many cases. We establish a relation between the stabilities of the ??₁–??₀ element (bilinear/constant on quadrilaterals) and the ??₁–??₀ element. We apply many stability results on the ??₁–??₀ element to the analysis of the ??₁–??₀ element. We prove that the element has the optimal order of approximations for the velocity and the pressure on a variety of mesh families. As a byproduct, we also obtain a basis of divergence‐free piecewise linear functions on a mesh family on squares. Numerical tests are provided to support the theory and to show the efficiency of the newly discovered, truly divergence‐free, ??₁ finite element spaces in computation. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of a DG method for singularly perturbed convection-diffusion problems

In this article, we studied a discontinuous Galerkin finite element method for convection-diffusion-reaction problems with singular perturbation. Our approach is highly flexible by allowing the use of discontinuous approximating function on polytopal mesh without imposing extra conditions on the convection coefficient. A priori error estimate is devised in a suitable energy norm on general polytopal mesh. Numerical examples are provided.