人工脑的三维模型及应用

将二维人工脑模型推广到三维，并给出了一个实际应用算例，还将二、三维模型的计算结果进行了对比，发现三维模型的计算效果明显优于二维模型。     

带权的 p-Laplacian 非线性特征值问题解的存在性

文利用变分方法讨论了方程-△p^u=λ a(x)(u^{+})^q-1-μ a(x)(u^-)^q-1+f(x,u), u∈W₀^1,p(Ω), 当 p≠q时的可解性. 其中Ω是 R^N(N≥ 3)中的有界光滑区域,权重函数a(x)∈ L^r(Ω), (r≥Np/Np-Nq+pq)且a(x)>0, a.e.于Ω, f满足某些条件.     

Isotonicity of the metric projection with applications to variational inequalities and fixed point theory in Banach spaces

In this paper, we discuss isotonicity characterizations of the metric projection operator, including its necessary and sufficient conditions for isotonicity onto sublattices in Banach spaces. Then, we demonstrate their applications to variational inequalities and fixed point theory in Banach spaces. Our work generalizes many existing results obtained in earlier work.     

Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces

Through solving the problem step by step and by applying the method of a C₀ semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright © 2017 John Wiley & Sons, Ltd.     

基于Cayley变换的紧支撑二元正交小波滤波器组的构造

构造正交滤波器组,在多相域里就等价于构造仿酉矩阵,而仿酉矩阵的构造涉及到非线性方程组的求解.通过对Cayley变换的研究,把仿酉矩阵的构造转换为更易构造的仿斜厄米特矩阵,基于这种变换构造了二元紧支撑正交小波滤波器组,并给出了算例.     

Convergence and stability of the finite difference scheme for nonlinear parabolic systems with time delay

In this article, a class of nonlinear evolution equations – reaction–diffusion equations with time delay – is studied. By combining the domain decomposition technique and the finite difference method, the results for the existence, convergence and the stability of the numerical solution are obtained in the case of subdomain overlap and when the time-space is completely discretized. This revised version was published online in June 2006 with corrections to the Cover Date.     

一类n-阶m-点奇异边值问题的正解

研究n-阶m-点奇异边值问题其中h(t)允许在t=0,t=1处奇异,f(t,v_0,v_1,…,v_(n-2))允许在v_i=0(i=0,1,…,n-2)处奇异.利用锥拉伸与压缩不动点定理得到了上述奇异边值问题正解的存在性.     

无穷区间上两类抽象无界函数族相对紧的判定及其应用

给出了无穷区间上抽象无界连续函数族和抽象无界可微函数族相对紧性判定的充要条件,并应用它获得了无穷区间上二阶微分方程两点边值问题无界解的存在性.     

A combined ONIOM quantum chemical-molecular dynamics study of zinc-uracil bond breaking in yeast cytosine deaminase

A QM/MM method that combines ONIOM quantum chemistry and molecular dynamics is developed and applied to a step in the deamination of cytosine to uracil in yeast cytosine deaminase (yCD). A two-layer ONIOM calculation is used for the reaction complex, with an inner part treated at a high level for the chemical reaction (bond breaking) and a middle part treated at a lower level for relevant protein residues that are frozen in the quantum optimization. An outer layer (protein and solvent) is treated using MD. Configurations for the entire system are generated using MD and optimized with ONIOM. The method permits the use of high-level quantum calculations along with sufficient configurational sampling to approximate the potential of mean force for certain bond-breaking reactions. A previously proposed reaction mechanism for deamination (Sklenak, S.; Yao, L. S.; Cukier, R. I.; Yan, H. G. J. Am. Chem. Soc. 2004, 126, 14879) requires breaking the bond between a catalytic zinc and the O4 of uracil in order to permit product release. Using an ONIOM approach, direct bond cleavage was found to be energetically unfavorable. In the work presented here, the combined ONIOM MD method is used to show that the barrier for bond cleavage is small, approximately 3 kcal/mol, and, consequently, should not be the rate-limiting step in the reaction.     

Random approximations and random fixed point theorems for random 1-setn-contractive non-self-maps in abstract cones

In this paper, we will prove that the random version of Fan's Theorem [6, Theorem 2] is true for a random hemicompact 1-set-contractive map defined on a closed ball, a sphere and an annulus in cones. This class of random 1-set-contractive map includes random condensing maps, random continuous semicontractive maps, random LANE maps, random nonexpansive maps and others. As applications of our theorems, some random fixed point theorems of non-self-maps are proved under various well-known boundary conditions. Our results are generalizations, improvements or stochastic versions of the recent results obtained by many authors