Ekeland变分原理及其应用

本文将Ekeland变分原理作了推广，并将理论结果应用到正则约束最优化问题上．     

Extracting multiple layers from data having graph structures

Much data such as geometric image data and drawings have graph structures. Such data are called graph structured data. In order to manage efficiently such graph structured data, we need to analyze and abstract graph structures of such data. The purpose of this paper is to find knowledge representations which indicate plural abstractions of graph structured data. Firstly, we introduce a term graph as a graph pattern having structural variables, and a substitution over term graphs which is graph rewriting system. Next, for a graph G, we define a multiple layer (g, (θ1,…,θk)) of G as a pair of a term graph g and a list of k substitutions θ1,…,θk such that G can be obtained from g by applying substitutions θ1…,θk to g. In the same way, for a set S of graphs, we also define a multiple layer for S as a pair (D,Θ) of a set D of term graphs and a list Θ of substitutions. Secondly, for a graph G and a set S of graphs, we present effective algorithms for extracting minimal multiple layers of G and S which give us stratifying abstractions of G and S, respectively. Finally, we report experimental results obtained by applying our algorithms to both artificial data and drawings of power plants which are real world data.     

BCK—代数的两种扩张

给出了BCK-代数的两种扩张的方法。     

A Theorem on Surface with Parallel Nondegenerate Minimal Section

本文给出了空间形式中具平行极小截面曲面的一个定理,从而将文献中相应结果推广到一般的m维空间形式中。     

复合限制

限制是一种基于极小化模型的非单调逻辑,本文首先提出一种相对限制形式——基于极大化模型的限制,继而给出结合极小与极大化模型的复合限制形式,并进一步讨论它们在形式化机器学习中归纳推理的应用.     

关于亏格大子零的紧致黎曼曲面上的割迹

S.B.Myors证明了对亏格为零的紧致黎曼曲面的割迹C(p)上任一点q,在作为有限单纯复形的C(p)中从9点出发的一维胞腔的数目等于从p到q的极小测地线的数目。[2]用新的方法改进了其证明。本文证明了对亏格大于零的情形,相应的结论仍然成立。     

对《高等代数》中一个定理证明的商榷

指出[1]的一处疏漏,并给出证明。     

用于壁板结构多模态振动主动控制的改进最小控制合成(MCS)算法

针对压电壁板结构,引入具有良好非线性控制性能的最小控制合成(minimal controller synthesis,MCS)算法来抑制其振动.鉴于标准的MCS算法在快速扰动下缺乏稳定性,为进一步提高其控制效果,构造了一种新的自适应补偿因子,形成了改进MCS算法-IMCS算法,并通过波波夫准则验证了该控制系统的稳定性.选取LQR(linear quadratic regulator)控制作为参考模型,分别施加宽频随机扰动和前2阶正弦混合脉冲激励,分析比较了IMCS算法和标准MCS算法的控制效果、自适应增益因子和跟踪误差.仿真结果表明,IMCS算法具有更快的收敛速度和更小的跟踪误差;多模态扰动实验结果表明,当存在外部非线性扰动时,IMCS算法具有更好的控制效果和鲁棒性.     

基于神经网络的模糊关系方程极小解求解算法

利用神经网络求解有限论域上模糊关系方程的极小解,将未知的模糊关系作为神经网络的权重参数进行学习,并设计了相应的网络训练算法Ⅰ.证明了该训练算法将收敛到模糊关系方程的极小解,并通过2个数值实例来验证算法的有效性.     

Extracting multiple layers from data having graph structures

Much data such as geometric image data and drawings have graph structures. Such data are called graph structured data. In order to manage efficiently such graph structured data, we need to analyze and abstract graph structures of such data. The purpose of this paper is to find knowledge representations which indicate plural abstractions of graph structured data. Firstly, we introduce a term graph as a graph pattern having structural variables,and a substitution over term graphs which is graph rewriting system. Next,for a graph G,we define a multiple layer (g,（θ1, …,θk)) of G as a pair of a term graph g and a list of 4 substitutionsθ1, …,θk such that G can be obtained from g by applying substitutions θ1, …,θk to g. In the same way,for a set S of graphs, we also define a multiple layer for Sas a pair (D,@) of a set 5 of term graphs and a list 6 of substitutions. Secondly,for a graph G and a set S of graphs,we present effective algorithms for extracting minimal multiple layers of G and S which give us stratifying abstractions of G and S,respectively. Finally,we report experimental results obtained by applying our algorithms to both artificial data and drawings of power plants which are real world data.