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.     

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。     

家用超声波儿童防坠楼监护系统

高层建筑是城市发展的必然产物,随之而来的是儿童意外坠楼安全事故频频发生,主要原因是儿童独自在家且缺少家长的监护,其中窗台是最易酿成坠楼事故的高危地带。对此,文章设计出一套家用儿童防坠楼监护系统。该系统运用超声波的渡越时间检测法和三球定位算法来实时检测儿童与窗台的位置,并设立两级预警机制。当二次警报触发时,即儿童离窗台太近时,激发执行机构及时封闭窗台。此外,从空气温度、湿度以及两者距离三个角度来分析超声波系统工作的误差并将之解决。     

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.     

罗尔中值定理在高等数学竞赛题中的运用

结合江苏省高等数学竞赛题探讨中值问题中等式的证明,从罗尔中值定理的结构分析、求导法则的熟练使用以及辅助函数构造的对比分析三个角度出发,分析了罗尔中值定理在微分中介值问题证明中的运用.     

新交通流模型对信号交叉路口通行能力的影响分析

合理准确的交通流模型不仅有利于理解车辆的行驶行为,而且对分析交通流状况,规划交通网络和实现交通优化控制策略都有重要的作用。车一车通信环境下多车型合作驾驶跟驰模型将车辆类型的差异化信息以及前方车辆的交通诱导信息包含其中。仿真结果表明,信号交叉路口的通行能力会随着参与合作驾驶的车辆数目的增多而得到显著增强,但其随着车辆密度的走势不会发生变化。     

点的存在性的证明方法的分析

本文主要讨论了在给定不同的条件下．证明点的存在性的一般分析方法。大体上分成三种情况：1）连续条件,利用连续函数的性质及其定理进行证明：2）可导或者积分,利用费马定理和中值定理证明;3）无连续或者可导条件时,通常需要用实数理论进行分析。