Towards a unified recurrent neural network theory: The uniformly pseudo-projection-anti-monotone net

In the past decades, various neural network models have been developed for modeling the behavior of human brain or performing problem-solving through simulating the behavior of human brain. The recurrent neural networks are the type of neural networks to model or simulate associative memory behavior of human being. A recurrent neural network (RNN) can be generally formalized as a dynamic system associated with two fundamental operators: one is the nonlinear activation operator deduced from the input-output properties of the involved neurons, and the other is the synaptic connections (a matrix) among the neurons. Through carefully examining properties of various activation functions used, we introduce a novel type of monotone operators, the uniformly pseudo-projectionanti-monotone (UPPAM) operators, to unify the various RNN models appeared in the literature. We develop a unified encoding and stability theory for the UPPAM network model when the time is discrete. The established model and theory not only unify but also jointly generalize the most known results of RNNs. The approach has lunched a visible step towards establishment of a unified mathematical theory of recurrent neural networks.     

局部凸空间的若干凸性及其相互关系

引进了局部完全K凸的概念,讨论了这种凸性与其它凸性间的关系,并给出了K非常凸,(弱)局部K一致凸的等价刻画.     

C[0,1]上完备的三角形正交函数系

基于W alsh函数,建立一个新的函数系T n n∈N.它是一个分段线性函数序列,在0,1的子区间上其函数图像呈现三角形。并且证明了它是C[0,1]上一个完备的正交函数系。在此函数系上展成的Fourier级数有许多与三角Fourier级数相似的性质,三角形Fourier级数的部分和在作为函数的逼近工具时确实要比三角Fourier级数优越一些。     

一类二阶非线性微分方程一致渐进稳定的概周期解的存在性

利用指数型二分性理论和Lyapunov函数法研究二阶非线性微分系统概周期解的存在性和稳定性,得到了该系统一致渐进稳定的概周期解的存在性的一个充分性条件.     

钢梁柱弱轴顶底角钢半刚性连接的抗弯特性

为了解顶底角钢半刚性连接的抗弯特性,利用简化的斜率-位移方程推导了半刚性连接初始刚度的计算公式,根据角钢的塑性特性计算了半刚性连接的极限弯矩,进行了两类柱弱轴顶底角钢半刚性连接的抗弯试验,并利用三参数幂函数模型模拟了所研究的半刚性连接的弯矩-转角曲线.结果表明,模拟结果与试验结果吻合很好,文中提出的新型连接形式具有很好的抗弯能力.     

也谈均匀带电细圆环的电场分布

用Mathematica研究均匀带电细圆环的电场的空间分布,准确地绘制出电场强度量值的分布图和电场方向的分布图,并纠正了最近文献中一幅场强量值分布图的失误.     

格林互易定理在求解均匀带电圆环的静电势分布中的应用

对于静电场,由普遍的格林互易定理得出特殊情形下的格林互易定理.应用该定理推导出均匀带电圆环的数种在形式上互不相同的静电势分布解式.     

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.     

3维chemotaxis-fluid方程弱解的整体存在性

针对具有非线性3维扩散chemotaxis-fluid模型,在其初边值问题基础上,提出了在m>7/6时该模型具有弱解整体存在性的论断。利用正则化问题的先验估计方法,给出了基于chemotaxis-fluid模型的5个引理并进行了证明,在此证明基础上,对所提论断进行了证明。     

具交叉感染的流行病模型的数学分析

In this paper,an initial boundary value problem with homogeneous Neumann boundary condition is studied for a reaction-diffusion system which models the spread of infectious diseases within two population groups by means of self and criss-cross infection mechanism. Existence,uniqueness and boundedness of the nonnegative global solution (u1,u2,u3,u4),existence of the limit of the solution as t→+∞,namely,(u1,u2,u3,u4)→(u*1,0,u*3,0),are proved.