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1.
This paper investigates the global periodicity of cellular neural network with impulses and constant delay. Several conditions guaranteeing the existence, uniqueness, and global exponential stability of periodic solution are derived by using the continuation theorem of coincidence degree theory and suitable degenerate Lyapuniv–Krasvovskii functional.  相似文献
2.
The Cartan–Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan–Hartogs domain \(\Omega ^{B^{d_0}}(\mu )\) endowed with the canonical metric \(g(\mu ),\) we obtain an explicit formula for the Bergman kernel of the weighted Hilbert space \(\mathcal {H}_{\alpha }\) of square integrable holomorphic functions on \(\left( \Omega ^{B^{d_0}}(\mu ), g(\mu )\right) \) with the weight \(\exp \{-\alpha \varphi \}\) (where \(\varphi \) is a globally defined Kähler potential for \(g(\mu )\) ) for \(\alpha >0\) , and, furthermore, we give an explicit expression of the Rawnsley’s \(\varepsilon \) -function expansion for \(\left( \Omega ^{B^{d_0}}(\mu ), g(\mu )\right) .\) Secondly, using the explicit expression of the Rawnsley’s \(\varepsilon \) -function expansion, we show that the coefficient \(a_2\) of the Rawnsley’s \(\varepsilon \) -function expansion for the Cartan–Hartogs domain \(\left( \Omega ^{B^{d_0}}(\mu ), g(\mu )\right) \) is constant on \(\Omega ^{B^{d_0}}(\mu )\) if and only if \(\left( \Omega ^{B^{d_0}}(\mu ), g(\mu )\right) \) is biholomorphically isometric to the complex hyperbolic space. So we give an affirmative answer to a conjecture raised by M. Zedda.  相似文献
3.
Let ?0,n be the real Clifford algebra generated by e1, e2,…, en satisfying eiej+ejei=−2δij, i, j=1,2,…, n. e0 is the unit element. Let Ω be an open set. A function f is called left generalized analytic in Ω if f satisfies the equation
equation(0.1)
Lf=0,Lf=0,
where
L=q0e0∂x0+ q1e1∂x1+…+qnenxn,L=q0e0x0+q1e1x1++qnenxn,
qi <0, i=0,1,…, n. In this article, we first give the kernel function for the generalized analytic function. Further, the Hilbert boundary value problem for generalized analytic functions in ?n+1+ will be investigated.  相似文献
4.
In this paper, a class of nonlinear stochastic neutral differential equations with delays is investigated. By using the properties of ${\mathcal{M}}$ -matrix, a differential-difference inequality is established. Basing on the differential-difference inequality, we develop a ${\mathcal{L}}$ -operator-difference inequality such that it is effective for stochastic neutral differential equations. By using the ${\mathcal{L}}$ -operator-difference inequality, we obtain the global attracting and invariant sets of nonlinear stochastic neutral differential equations with delays. In addition, we derive the sufficient condition ensuring the exponential p-stability of the zero solution of nonlinear stochastic neutral differential equations with delays. One example is presented to illustrate the effectiveness of our conclusion.  相似文献
5.
In this paper, we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients. Some moment estima- tes of the solutions are given by establishing new Ito operator inequalities based on the Razumikhin technique. These estimates improve, extend and unify some related results including exponential stability of Mao (1997) [20], decay stability of Wu et al. (2010,2011) [32,33], Pavlovic et al. (2012) [24], asymptotic behavior of Luo et al. (2011) [18] and Song et al. (2013) [26]. Moreover, stochastic version of Wintner theorem in continuous space is established by the comparison principle, which improve and extend the main results of Xu et al. (2008 [39], 2013 [36]). When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces, we extend the related results of Govindana et al. (2013) [7], Liu et al. (2007) [15], Vinod- kumar (2010) [29] and Xu et al. (2012) [35]. Two examples are provided to illustrate the effectiveness of our results.  相似文献
6.
讨论了可实现布尔矩阵的容度问题.将可实现布尔矩阵看成是无向图,我们证明了可实现布尔矩阵的容度等于其相应无向图的团覆盖数与孤立点数之和,并给出了通过计算容度来计算团覆盖数,以及通过计算团覆盖数来计算容度的算法框架.  相似文献
7.
讨论了完备主因子格的一些结构性质,得到了完备分配格有不可约并既分解及不可约完全并既分解和不可约连续并既分解的一些充要条件。  相似文献
8.
对于完备格L上给定的|I|×|I|的矩阵R,若存在|I|×|I|的L上的矩阵S满足S⊙S=R,则称S为R的平方根,其中I表示指标集|I|的基数,⊙在本文中指的是sup-T合成算子并且T是无限∨分配的保序的算子。本文给出了完备格上基于sup-T合成算子的矩阵平方根存在的充要条件以及相应的理论上的算法求解所有的平方根。  相似文献
9.
宋际平  刘云 《数学杂志》2015,35(5):1053-1067
本文研究了锥b-度量空间上四个自映射的公共不动点问题.利用序列逼近的方法,获得了锥b-度量空间上四个自映射的一些公共不动点结果,将锥度量空间中的几个相关结果推广到锥b-度量空间中,并且给出了一个例子以支撑我们的结果.  相似文献
10.
为了提高电子支付系统的安全性,在深入研究面向服务架构和Web服务安全技术的基础上,提出一种基于Web服务面向服务架构的松耦合电子支付安全系统模型.该模型利用服务监控和企业服务总线,把交易协议、安全认证、安全技术、加密技术、访问控制、网络扫描、防火墙、内容识别等安全服务有效的集成为一体,构建出电子支付的安全模型,同时对模型的关键安全服务技术进行深入研究.最后对模型的机密性、公平性、完整性、授权等进行了安全性分析,证明提出的系统模型具有良好的安全性.  相似文献
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