时滞型脉冲神经网络的全局指数稳定性(英文)

对一类含时滞的脉冲神经网络平衡点的存在性和稳定性进行了研究.在不假定激励函数有界、单调或可微而仅假定激励函数Lipschitz连续的条件下,利用压缩映像原理证明了系统平衡点的存在性,利用右上Dini导数的性质并通过构造适当的Lyapunov函数得到了平衡点全局指数稳定的充分条件.文末通过实例说明了所获结论的有效性.     

具有时滞的一般型脉冲神经网络的指数稳定性

讨论具有时滞的一般性脉冲神经网络的稳定性.在不假定激励函数有界或可导的前提下,利用非光滑分析和Lyapunov泛函,得到了这类神经网络系统平衡点的存在唯一性和全局指数稳定性判别准则.作为特例,得到了Hopfield神经网络,时滞细胞神经网络,双向联想记忆神经网络的平衡点的存在唯一性和全局指数稳定性判定定理.     

时滞Hopfield神经网络模型渐进稳定性的新准则

在不考虑激励函数有界,可微和单调的情况下,利用Lyapunov泛函方法,得到了时滞Hopfield神经网络模型的平衡点存在性和全局渐近稳定性的新准则.研究结果改进和推广了以前相关文献的结果.     

具有变时滞脉冲效应的Hopfield神经网络的全局指数稳定性

研究了一类新的具有脉冲的时滞Hopfield神经网络系统模型,引入了新的脉冲条件,在不假设激励函数的可微性、单调性的条件下,得到了系统平衡点的存在性、唯一性及全局指数稳定性的充分条件和指数收敛速率,且所得结果改进了一些已知文献的结论.     

具有无穷时滞的细胞神经网络的全局稳定性分析

对具有无穷时滞的细胞神经网络平衡点的存在性、唯一性和全局渐近稳定性进行了分析．在放弃了激活函数的有界性、单调性和可微性假设的情况下,得到了系统的平衡点的存在性条件．利用向量Liapunov函数法的思想,构造适当的含有变时滞和无穷时滞的微分-积分不等式,通过对微分-积分不等式的稳定性分析,得到了神经网络系统的全局渐近稳定的充分条件．     

一类变时滞复数Cohen-Grossberg神经网络的动态行为分析

研究了一类具有变时滞的复数域Cohen-Grossberg神经网络平衡点的动态行为.在假定激活函数满足Lipschitz条件并且放大函数只满足具有下界的情况下, 利用M矩阵和同胚映射原理, 得到了确保该系统平衡点的存在性和唯一性的充分条件.基于矢量Lyapunov函数法和不等式技术, 得到了确保该系统平衡点的模指数稳定性的判据.该判据形式简单, 在实际应用时便于检验.该文所取得的研究成果推广了现有结论.最后通过给出一个数值算例和仿真结果验证了所得结论的正确性和可行性.     

向量对策理想-Nash平衡点的存在性

本文采用向量优化问题中理想解的概念,定义向量对策理想-Nash平衡点,并证明这一平衡点的存在性．这一结果一方面体现了向量对策Pareto-Nash平衡点和弱Pareto-Nash平衡点的存在性,同时,还给出了特殊的Pareto-Nash平衡点的存在性．     

具有扩散影响的Hopfield型神经网络的全局渐近稳定性

对具有扩散影响的Hopfield型神经网络平衡点的存在唯一性和全局渐近稳定性进行了研究．在激活函数单调非减、可微且关联矩阵和Liapunov对角稳定矩阵有关时,利用拓扑度理论得到了系统平衡点存在的充分条件．通过构造适当的平均Liapunov函数,分析了系统平衡点的全局渐近稳定性．所得结论表明系统的平衡点(如果存在)是全局渐近稳定的而且也蕴含着系统的平衡点的唯一性．     

二阶Hopfield神经网络周期解的存在性

本文讨论了一类带有时滞的二阶Hopfield神经网络周期解的存在性问题。首先利用Brouwer不动点定理证明了平衡点的存在性,通过平衡点和拉格朗日中值定理,将高阶神经网络模型转换为一阶模型,然后利用重合度理论给出了周期解存在的充分条件。     

时间标度上时滞脉冲复值神经网络的全局稳定性

研究了时间标度上具有时滞和脉冲影响的复值神经网络的全局稳定性问题.利用时间标度上的微积分理论,将连续时间型复值神经网络和离散时间型复值神经网络统一在同一个框架下进行研究.在不要求激励函数有界的条件下,运用同胚映射原理,建立了确保时滞复值神经网络平衡点存在性和唯一性的判定条件.通过构造合适的Lyapunov-Krasovskii泛函,并使用自由权矩阵方法和矩阵不等式技巧,获得了时间标度上具有时滞和脉冲影响的复值神经网络平衡点全局稳定性的充分条件.给出的判据是由复值线性矩阵表示的,易于MATLAB软件的YALMIP Toolbox实现.数值仿真实例验证了获得结果的有效性.     

Multimode Relativistic String: Classical Solutions and Quantization

We find all independent classical solutions for the three-mode Nambu–Goto string. We investigate the geometry of the closed curves obtained. Canonical quantization is performed for a part of the solutions obtained. We consider the spectrum of the quantum states obtained. It is consistent with the experimental masses and quantum numbers of mesons corresponding to glueballs. The leading Regge trajectory of the obtained states is consistent with the available data on the Pomeron trajectory.Deceased     

Optical solitons with time-dependent dispersion,nonlinearity and attenuation in a power-law media

This paper studies optical solitons in a power-law media with time-dependent coefficients of dispersion, nonlinearity and attenuation. The 1-soliton solution is obtained for the nonlinear Schrödinger’s equation with power-law nonlinearity. In addition, a relation between these coefficients is obtained for the solitons to exist. Finally, the velocity of the soliton is also obtained in terms of these coefficients.     

A remark on a standard and linear vector network equilibrium problem with capacity constraints

In this paper, (weak) vector equilibrium principle with capacity constraints is introduced. A necessary condition that a vector minimum cost flow is a vector equilibrium flow with capacity constraints is obtained. When the number of paths connecting with each pair of source and sink is less than or equal to 2, a sufficient condition for a vector minimum cost flow to be a vector equilibrium flow is also obtained. A generalized (weak) vector equilibrium principle is also introduced. Without any additional assumption, a necessary and sufficient condition for a (weak) vector minimum cost flow to be a generalized (weak) vector equilibrium flow is obtained.     

关于非完整力学系统相对部分变量的稳定性*

本文给出研究非完整系统相对部分变量稳定性的一种方法,并得到非完整系统相对部分变量的一些稳定性定理:同时,本文还得到一类非完整系统相对全部变量稳定性与相对部分变量稳定性的关系。     

The effect of redundancy on probability bounds

Lower bounds on the probability of a union obtained by applying optimal bounds to subsets of events can provide excellent bounds. Comparisons are made with bounds obtained by linear programming and in the cases considered, the best bound is obtained with a subset that contains no redundant events contributing to the union. It is shown that redundant events may increase or decrease the value of a lower bound but surprisingly even removal of a non-redundant event can increase the bound.     

Solution of the stationary problem of heat conduction of laminated anisotropic inhomogeneous plates by the method of initial functions

The problem of stationary heat conduction of laminated plates of constant and variable thickness is formulated in the three-dimensional statement. We reduce the three-dimensional problem to a twodimensional one by the method of initial functions. For plates with layers of variable thickness, a system of resolving equations with variable coefficients is obtained. The obtained two-dimensional boundary-value problems are analyzed. For plates with homogeneous layers of constant thickness, we construct a solution in an analytic form. It is shown that this solution coincides with a solution obtained by the method of separation of variables.     

高等数学的阅读能力培养初探

认识高等数学阅读能力的重要性、激发大学生对高数学阅读的兴趣、提供数学阅读的具体方法是培养高等数学阅读能力的措施.其中,数学阅读的具体方法有:带有问题阅读、督促学生作读书笔记、个别指导、组织课堂讨论和经验交流、及时小结、合理评价等.高等数学教师应该努力探寻提高大学生数学阅读能力的有效方法.     

Modelling the bending behaviour of a new hybrid glulam beam reinforced with FRP and ultra-high-performance concrete

The main objective of this research project to develop a new type of hybrid glulam beam that will increase the performance of a timber structural element by combining it with ultra-high-performance concrete with short fibre reinforcement (UHPC-SFR). The hybrid beam is obtained is a layered structures obtained by combining a glued-laminated (glulam) wood beam with UHPC-SFR lamellae that is bonded to its top and bottom faces. The obtained hybrid beam possesses a lower bending stiffness than a glulam beam of similar overall dimensions but has a higher ultimate load capacity. Two models that were developed to validate this concept are presented in this paper. The first is an analytical model based on hypotheses related to the usual strength of materials, and the second is a finite element model. The load–displacement and moment–curvature relationships from both models are compared to the experimental results obtained from the large-scale specimens. The results show good correlation between the analytical modelling and experimental results and illustrate the potential applications of such composite beam configurations for civil engineering structures.     

时滞依赖型中立系统的鲁棒稳定性分析

研究了一类不确定中立型系统的时滞依赖稳定性问题.利用基于LMI正定解的存在性,给出了一个新时滞依赖型稳定性判据,相比于已有文献本文具有低的保守性.最后通过数值算例验证了本文得到的结论的正确性和有效性.