求解参数识别反问题的同伦正则化方法

提出了求解参数识别反问题的同伦正则化方法,给出了相应的收敛性定理.数值结果表明该方法是一种快速的大范围收敛方法.     

几类特定边界值条件下的常微分方程特征值问题

在文献[1]的基础上,借助于图形分析方法,讨论了几类特定边界值条件下的特征值问题.同时,本文对文献[1]中的错误结论作出了更正.本文给出的方法对讨论非线性边值问题的可解性提供了一种新的途径.     

对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理.作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理.     

Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems

In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices A_n. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix A_n. Thus if A_n is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix A_n has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥₂. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.     

开展化学教育硕士学位试点工作的实践和思考

本文结合近几年我们开展化学教育硕士学位试点工作的实践 ,介绍了一些成功的经验 ,同时对存在的问题也提出了一些建议和思考。     

Competition between fingers in Hele-Shaw flows

In experiments on the displacement of viscous fluids in a Hele-Shaw cell of channel type the catastrophic development of competition between fingers is sometimes observed: for a long time two fingers propagate almost side by side and then one of them suddenly suppresses the other. It is believed that this is a manifestation of the capillary forces on the phase interface [1]. Using the solution found in [2] for the problem in an idealized formulation, it is shown that this scenario is perfectly feasible without having to take capillary forces into account.     

Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects

In this paper, we study the existence, uniqueness and stability of traveling wave fronts in the following nonlocal reaction–diffusion equation with delay

How to predict viscous fingering in three component flow

In a WAG process (Water Alternate Gas), water and a miscible solvent (gas) are injected into a reservoir containing water and oil. The solvent will finger through the oil, leading to early breakthrough and poor recovery. Compared with a miscible flood, when only solvent is injected, fingering is supressed by the simultaneous injection of water, since this reduces the apparent mobility contrast between the injected and displaced fluids. The fingering in a miscible flood, with only hydrocarbon flowing, can be modelled successfully using a Todd and Longstaff fractional flow. In this paper, we demonstrate how to modify the effective Todd and Longstaff mobility ratio self-consistently to account for fingering in three component systems. The resultant empirical equations of flow are solved exactly in one dimension and are in excellent agreement with the averaged saturation and concentration profiles computed using two dimensional high resolution simulation, for a variety of injected water saturations, in both secondary and tertiary displacements.     

一类含P拉普拉斯算子的非线性椭圆边值问题解的存在性

利用非线性增生映射值域的扰动定理 ,研究了非线性椭圆边值问题 (@)在 Ls(Ω) ,p s<+∞中解的存在性 .(@) -△ pu +g(x,u) =f a.e.在Ω中-〈v,| u|p-2 u〉∈βx(u(x) ) a.e.在Γ上其中 f∈ Ls(Ω) ,p s<+∞给定 ,Ω RN为有界锥形区域 ,△ pu=div(| u|p-2 u)为 P拉普拉斯算子 ,max(N ,2 ) p<+∞ ,v为Γ的外法向导数 ,g∶Ω× R→ R满足 Caratheodory条件 ,对 x∈Γ ,βx 是正常、凸、下半连续函数 φx=φ(x,· )的次微分 ,其中 φ∶ Γ× R→ R.本文推广了魏利和何震所讨论的非线性问题的边值条件 .     

一类半线性积分微分方程初边值问题的爆破解和全局解

本文研究初边值问题的爆破解和全局解，证明了在ｆ的凸性假设和一定的增长性假定下解在有限时刻爆破，而在ｆ的其他假设下证明了全局解的存在性。