对称蕴涵推理方法的鲁棒性分析北大核心CSCD

模糊推理方法已经被成功地应用于模糊控制器设计,模糊专家系统集成等诸多领域.作为对传统模糊推理方法的改进,我国学者提出了基于三Ⅰ方法的对称蕴涵推理方法.对于模糊推理方法性质的研究,尤其是对推理方法鲁棒性的研究是模糊逻辑领域的一个重要的研究方向.基于规范的Minkowski距离讨论对称蕴涵方法的鲁棒性,给出了针对不同蕴涵算子的四个算法的鲁棒性结论,为模糊推理方法的选择与应用提供科学依据.     

基于奇异摄动的柔性关节机械臂约束跟随控制研究北大核心CSCD

针对二连杆柔性关节机械臂,提出了一种基于奇异摄动理论和Udwadia-Kalaba(U-K)方法的控制方法.设计步骤主要分为两步:第一,基于奇异摄动法对系统进行降阶,把系统拆分为快、慢系统,不仅降低了求解系统的阶次,而且克服了系统柔性;第二,基于U-K方法设计了快、慢系统的状态反馈约束跟随控制律,能使快、慢系统约束跟随误差收敛到零,即使系统初始不满足约束条件,该方法不需要借助Lagrange乘子和伪广义速度等辅助变量,可以同时处理完整约束和非完整约束.将以上方法运用在二连杆柔性关节机械臂系统中,解决了二连杆柔性关节机械臂的柔性振荡和约束跟随的问题.使用MATLAB进行仿真,并且与传统PID控制进行了对比,验证了所提出的方法的有效性与优越性.     

两阶段可修串联系统的变点控制图与维修策略整合研究北大核心CSCD

针对两阶段串联可修系统,考虑系统的输出为多个质量特性且不同阶段均可能出现异常的情形,采用变点控制图监控系统,揭示系统的状态并据此进行相应的维护策略.首先,给出监控多阶段系统的变点控制图.其次,考虑两阶段过程均可能出现异常因素的情形,剖析过程演变可能的场景,进一步假设异常因素的发生服从一般分布,给出每个场景发生的概率;同时,分析维修行为发生的概率.再次,根据更新报酬理论构建变点控制图与维修策略整合的期望收益模型;采用具体实例来比较分析所提出的收益模型与单独的维修策略的收益模型,其结果表明构建的模型的明显优势;最后,运用分式析因设计对模型输入参数进行了敏感性分析.     

带方向信息的薄板样条插值函数及其应用北大核心CSCD

薄板样条(TPS)函数是一个很好的形变分析工具,常用于图像配准,传统的薄板样条函数只是利用特征点的坐标信息,而现实中很多特征点都带有方向信息,比如指纹细节点和sift特征点.为了在薄板样条函数中利用方向信息,本文在传统薄板样条目标函数基础上增加了方向平行惩罚项及方向一致性惩罚项,根据变分法的结论,目标函数的求解转换为求解一个微分方程,用格林函数法求解这个微分方程,从而得到带方向信息的薄板样条函数新形式.本文得到的薄板样条函数适合于任意维度的点集,在指纹图像配准和人造点集插值上的实验表明,和传统薄板样条函数相比,本文提出的薄板样条函数对于带方向信息的图像配准和点集插值更加准确.     

复杂网络基于最小驱动节点的能控性优化（英文）北大核心CSCD

在这篇文章中讨论了两个核心问题,分别是最小输入问题和输入信号对节点的控制问题.利用图论和矩阵理论,找到了具有强控制集中性和强控制能力的最优的最小驱动节点集.首先,确定了驱动节点的最小数量.然后,通过两种方法确定了最优的最小驱动节点集,一种是分析节点i的控制集中性,另一种是查找控制信号u^+(t)和具有强控制能力的节点i之间有用的连接添加.最后,输入信号被施加到最优的最小驱动节点上以使得网络能控.同时,关于最优的最小驱动节点集的算法也被提出用于复杂网络能控性的研究.     

基于粒子进化的SD多功效流率函数及其应用北大核心CSCD

系统动力学(SD)模型的流率是动态仿真决策控制要素,但在SD方法中,仅给出定义式,解析范式缺失,实际应用常采用模糊确定的表函数.由于SD模型的流位演进流率与粒子群算法(PSO)的粒子进化速度属性类同,则在析解流率决策控制机制与粒子进化速度方程的基础上,依据粒子进化的结构原理,讨论流率函数结构,建立多功效流率函数解析式,提出系数估计策略,构造动态仿真算法.以区域生态经济系统动态仿真为例,将流率函数及其系数估计策略和动态仿真算法加以实际应用,以检验多功效流率函数的有效性和适用性.多功效流率函数物理意义明确,具有可比可控性、结构优化性和减少主观性等多重功效,可作为SD方法中流率函数的范式.     

一类耦合算子矩阵的极大Tseng逆及其在椭圆方程中的应用北大核心CSCD

作者给出了单边耦合算子矩阵的极大Tseng逆具有Banachiewicz-Schur形式的充要条件.作为应用,刻画了具有动态边界条件的椭圆方程{△u=h,在Ω中,-β■u/■v+q△■Ωu-γu=h,在■Ω上的最小范数解,其中Ω■R^(n)是具有光滑边界■Ω的有界域,Δ和Δ■Ω分别是在Ω和■Ω上定义的Laplace(Beltrami)算子,v(x)是在x处的单位外法向量,q,β,γ∈R且q≠0.     

基于简化的应变梯度理论下Kirchhoff板模型边值问题的提法及其应用北大核心CSCD

考虑应变梯度和速度梯度的影响,建立薄板控制微分方程及给出其边值问题的提法,修正了前人给出的薄板角点条件.采用Levy法,给出受分布力作用下简支板的挠度及自由振动频率的解析解.通过与文献中分子动力学数据对比,验证了该文模型的有效性并提出校核材料参数的一种方法.研究结果表明,增大弹性地基和应变梯度参数可以有效提高板的等效刚度,而速度梯度参数则相反.该文提出的板的边值问题为研究薄板在复杂支撑边界及外荷载等条件提供了理论依据.同时,有望为其有限元法、有限差分法和基于能量原理的Galerkin法等数值方法提供理论依据.     

The Effect of Carbon Fibers Modification on the Mechanical Properties of Polyamide Composites for Automobile Applications

Mechanics of Composite Materials - Carbon fiber (CF)/ polyamide (PA6) composites are one of the most promising thermoplastic materials for automobile applications. However, the interfacial...     

关于单形的几个不等式及其应用

Using theory of distance geometry and analytic method, the problem on relations about the volumes of some simplices is studied, and some new inequalities for the volumes of simplices are established. As special cases, an inequality for the volume of the pedal simplex of a simplex and other inequalities for simplices are gotten.     

Adaptation and Enhancement of Generalized Polynomial Chaos for Industrial Applications

This contribution presents ideas, how to adapt stochastic elements to industrial applications and reduce the number of simulations in comparison to Monte Carlo. Especially when the mathematical model equations are not known and just an input/output interface is given. For this so called black box model which can be generated by many simulation tools the generalized polynomial chaos based on the idea of Wiener [1], and extended by Xiu and Karniadakis [2] is a suitable technique. One main advantage of this concept can be seen in the ability to produce functional representations of stochastic variability. This yields in a reduction of the simulation number compared to classical methods and can intensified by using a sparse grids approach [3]. Looking at industrial applications the concept can be applied to a huge amount of systems. For example, components including electronic drives, fuel injection valves, and mechanical parts. As an example of use, a simplified model of a DC drive with six uncertain parameters is taken into account. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

T-Spaces and Their Applications

The paper is a review of recent results on T-spaces and their applications. It is proved that T-spaces over a field of zero characteristic from a large class are finitely based; this implies the positive solution of the local Specht problem. If the characteristic of the base field is positive, then similar assertions do not hold. The negative solution of Maltsev's problem on the existence of a finite basis of all identities of an associative ring is given. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 18, Algebra, 2004.     

多元函数的最值定理及其应用

给出多元函数最值存在的两个定理,然后通过一些实例说明它们在有界开集或无界闭集上的极值问题中的运用.     

Nonlocal Symmetries for Bilinear Equations and Their Applications

In this paper, nonlocal symmetries for the bilinear KP and bilinear BKP equations are re-studied. Two arbitrary parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under the transformation     . By expanding these nonlocal symmetries in power series of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP (NKP) and BKP hierarchies may be derived from the same nonlocal symmetries for the KP and BKP equations. Besides, as two concrete examples, we have derived bilinear Bäcklund transformations for   t ₋₂  -flow of the NKP hierarchy and   t ₋₁  -flow of the NBKP hierarchy. All these results have made it clear that more nice integrable properties would be found for these obtained NKP hierarchies and NBKP hierarchies. Because KP and BKP hierarchies have played an essential role in soliton theory, we believe that the bilinear NKP and NBKP hierarchies will have their right place in this field.     

Liouville Theorems for F-Harmonic Maps and Their Applications

We prove several Liouville theorems for F-harmonic maps from some complete Riemannian manifolds by assuming some conditions on the Hessian of the distance function, the degrees of F(t) and the asymptotic behavior of the maps at infinity. In particular, the results can be applied to F-harmonic maps from some pinched manifolds, and can deduce a Bernstein type result for an entire minimal graph.     

矩阵初等变换的推广及其应用

矩阵的初等变换及矩阵的分块是矩阵理论中的两个重要方法。本文将初等变换推广到分块矩阵上去，在引进了准初等变换概念后，证明了它的某些性质。本文的目的在于简化某些矩阵运算，并希望本文建立的概念与结论得到更加广泛的应用。     

Grothendieck环及其应用

本文以Ｇｒｏｔｈｅｎｄｉｅｃｋ环为工具，利用相关环刻划了环的Ｇｒｏｔｈｅｎｄｉｅｃｋ群，得到了环的连通性、稳定自由性等性质的重要特征．最后给出了它们在群环的应用．