函数矩阵的增减性及中值定理

通过对函数矩阵A（x）的研究，给出函数矩阵的增减性定义，并得出函数矩阵的中值定理等一系列结论。     

Krasnoselskii不动点定理的一个应用

不动点理论是研究方程解的存在性的一种强有力的工具.本文主要考虑了一类特殊的积分方程,并应用Krasnoselskii不动点定理得到了该类积分方程解的存在性.     

一类半线性积分方程的Stepanov型μ-伪概自守解

通过运用Stepanov型μ-伪概自守函数的概念,研究半线性积分方程在Banach空间中关于有界解的一些新的存在性结果。首先建立了这类函数的新的组合定理,并且通过这类函数的遍历性和组合定理,结合积分预解族的定义和性质,利用不动点定理和压缩原理得到半线性积分方程的μ-伪概自守解的存在唯一结果的主要结论。     

Lyapunov-based design of locally collocated controllers for semi-linear parabolic PDE systems

The design problem of collocated feedback controllers is addressed in this paper for a class of semi-linear distributed parameter systems described by parabolic partial differential equation (PDE), where a finite number of local actuators and sensors are intermittently distributed in space. A Lyapunov direct method for the exponential stability analysis of the resulting closed-loop system is first presented for the system, in which the first mean value theorem for integration and the Wirtinger's inequality are employed. The corresponding stabilization condition is then derived through the analysis result. Finally, the proposed design method is implemented on the feedback control of a fisher equation and its effectiveness is evaluated through simulation results.     

Information resources estimation for accurate distribution-based concept drift detection

Machine learning applications must continually utilize label information from the data stream to detect concept drift and adapt to the dynamic behavior. Due to the computational expensiveness of label information, it is impractical to assume that the data stream is fully labeled. Therefore, much research focusing on semi-supervised concept drift detection has been proposed. Despite the large research effort in the literature, there is a lack of analysis on the information resources required with the achievable concept drift detection accuracy. Hence, this paper aims to answer the unexplored research question of “How many labeled samples are required to detect concept drift accurately?” by proposing an analytical framework to analyze and estimate the information resources required to detect concept drift accurately. Specifically, this paper disintegrates the distribution-based concept drift detection task into a learning task and a dissimilarity measurement task for independent analyses. The analyses results are then correlated to estimate the required number of labels within a set of data samples to detect concept drift accurately. The proximity of the information resources estimation is evaluated empirically, where the results suggest that the estimation is accurate with high amount of information resources provided. Additionally, estimation results of a state-of-the-art method and a benchmark data set are reported to show the applicability of the estimation by proposed analytical framework within benchmarked environments. In general, the estimation from the proposed analytical framework can serve as guidance in designing systems with limited information resources. This paper also hopes to assist in identifying research gaps and inspiring new research ideas regarding the analysis of the amount of information resources required for accurate concept drift detection.     

基于FCM-PFS与PSO-RF的隐性知识外显案例适配研究

对隐性知识外显案例实施有效适配,于知识应用乃至创新、实现乃至增值知识资源的价值,具有重要意义。本文深入研究了隐性知识外显案例适配机理。首先,采用毕达哥拉斯模糊集对知识属性值进行处理,建立知识表达系统;接着,运用K-Means算法对FCM聚类算法进行改进,压缩匹配空间、提升案例匹配效率;而后,基于PFS相关系数求解知识供需间的视图相似度,从而获得适配案例集。在此基础上,构建随机森林适配模型,并采用粒子群算法对其优化,以确保适配效果。与传统算法的对比实验验证了本文算法的比较优势。     

无穷大开簇上构型出现次数的强大数律和中心极限定理(英文)

考虑定义在整点格网Ld上的参数为p的上临界Bernoulli渗流,研究无穷大开簇上构型的发生情况.用Λn表示一个给定的构型P在限制于框B(n)=[-n,n]d中的无穷大开簇上发生的次数,得到了关于Λn的强大数律和中心极限定理.     

以频率估计概率的误差估计及其应用

阐述了以频率估计概率的误差估计公式，并举例说明公式在实际问题中的有关应用。     

关于用等价无穷小量代换定理求极限的一个推广命题

对用等价无穷小量代换定理求极限进行了推广。     

两类多元函数条件极值的判定

对于用拉格朗日乘数法求出多元函数条件极值问题的可疑极值点,利用隐函数存在定理,给出了两类多元函数的条件极值问题的一些适用范围比较广的判定定理,并举例验证该判定定理的有效性.