变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

一个R2上含双曲函数核的Hilbert型不等式

通过引入参数,构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开,建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用,通过赋予参数不同的值,建立了一些有意义的特殊结果。     

运用Poincaré-Miranda定理数值验证变分不等式解的存在性

本文运用Poincaré-Miranda定理数值验证变分不等式问题解的存在性.证明这一新方法相对于已有的方法更具有普遍性,并通过数值例子说明本方法的高效性.     

Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach

Recent simulation results imply the lowering of the ground-state correlation energy per counterion at a charged planar wall, compared with that of the 2D and 3D one-component plasma systems. Our aim is to correctly evaluate the ground-state energy of strongly-coupled counterion systems by considering a quasi-2D bound state where bound counterions are confined to a layer of molecular thickness. We use a variational approach based on the Gibbs-Bogoliubov inequality for the lower-bound free energy so that the liquid-state theory can be incorporated into the formulations. The soft mean spherical approximation demonstrates that the lowered ground-state energy can be reproduced by the obtained analytical form of a quasi-2D bound state.     

Exploiting the Massey Gap

In this paper, we find new refinements to the Massey inequality, which relates the Shannon and guessing entropies, introducing a new concept: the Massey gap. By shrinking the Massey gap, we improve all previous work without introducing any new parameters, providing closed-form strict refinements, as well as a numerical procedure improving them even further.     

一个具最佳常数的复合核积分不等式

引入Γ-函数等特殊函数,利用权函数方法和实分析技巧,建立一个具最佳常数的复合核积分不等式.考虑了它的等价式,证明了它们的常数因子是最佳的,并通过取特殊的参数值,得到一些有意义的结果.     

关于有消失矩的函数的Hilbert变换的加权范数不等式

为刻划一类权函数W,使具有N阶消失矩的函数f的Hilbert变换f满足带权L~P强型不等式Adams给出了一个充要条件。利用A_P权的性质,本文进一步完善了这个结果。     

问题变分不等式的一类各向异性Crouzeix-Raviart型有限元逼近

本文研究了Signorini变分不等式问题的一类各向异性Crouzeix-Raviart型非协调有限元逼近。通过一些新的技巧,得到了相应的最优误差估计。     

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x, Du)+ F(u)) ■ f in Ω, where f ∈ L1 Ω. A vector field a(·,·) is a Carath′eodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．