This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the F...This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.展开更多
It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets o...It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets or a countably infinite family of such sets. In particular, for a closed interval of the real line endowed with the usual topology, we see that we cannot partition it into a countably infinite number of disjoint, nonempty closed sets. On the positive side, however, one can certainly express such an interval as a union of c disjoint closed sets, where c is the cardinality of the real line. For example, a closed interval is surely the union of its points, each set consisting of a single point being closed. Surprisingly enough, except for a set of Lebesgue measure 0, these closed sets can be chosen to be perfect sets, i.e., closed sets every point of which is an accumulation point. They even turn out to be nowhere dense (containing no intervals). Such nowhere dense, perfect sets are sometimes called Cantor sets.展开更多
In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generali...In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generalized closed sets are given.展开更多
In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the ...In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.展开更多
Objective： To evaluate the efficiency of an implanted chip system for the control of heart rate （HR）. Methods： The HR was recorded in six conscious Sprague-Dawley （SD） rats. An implanted chip system was designed...Objective： To evaluate the efficiency of an implanted chip system for the control of heart rate （HR）. Methods： The HR was recorded in six conscious Sprague-Dawley （SD） rats. An implanted chip system was designed to regulate the HR by stimulating the right cervical vagus nerve according to the feedback of real time HR. Each rat was subjected to 30-min regulation and 30-min recovery. The change of HR during the regulation period was compared with the control. The ECG was recorded during the experiment for 24 h. Results： The ECG signals were successfully recorded during the experiment. The HR was significantly decreased during the period of regulation compared with control （-79.3 ± 34.5, P 〈 0.01, n = 6） and then recovered to normal after regulation. Conclusion： The described implanted chip system can regulate the HR to a designated set point.展开更多
Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar ...Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.展开更多
In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provid...In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.展开更多
针对某电厂发电机组3号机气泵速关电磁阀进行活动性试验,发现试验成功后,行程开关的“开”指示信号在分布式控制系统(Distributed Control System,DCS)画面无反馈,同时会出现行程开关脱开后不能回到开状态的情况,造成气泵遥控(自动)退出...针对某电厂发电机组3号机气泵速关电磁阀进行活动性试验,发现试验成功后,行程开关的“开”指示信号在分布式控制系统(Distributed Control System,DCS)画面无反馈,同时会出现行程开关脱开后不能回到开状态的情况,造成气泵遥控(自动)退出,导致不能正常投入使用,引起给水系统不稳定运行。经检查,发现行程开关安装位置不佳且摆臂转动死区太大是导致故障现象的主要原因。为此,实际测量现场位置,并改进安装位置,调整摆臂死区角度,设计一套优化方案。经试验验证,改进的方案切实可行,有效解决了问题。展开更多
基金supported by the Mathematical Tianyuan Foundation (No. 10826078)the National Natural Science Foundation of China (No. 60874006)
文摘This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.
文摘It has been shown by Sierpinski that a compact, Hausdorff, connected topological space (otherwise known as a continuum) cannot be decomposed into either a finite number of two or more disjoint, nonempty, closed sets or a countably infinite family of such sets. In particular, for a closed interval of the real line endowed with the usual topology, we see that we cannot partition it into a countably infinite number of disjoint, nonempty closed sets. On the positive side, however, one can certainly express such an interval as a union of c disjoint closed sets, where c is the cardinality of the real line. For example, a closed interval is surely the union of its points, each set consisting of a single point being closed. Surprisingly enough, except for a set of Lebesgue measure 0, these closed sets can be chosen to be perfect sets, i.e., closed sets every point of which is an accumulation point. They even turn out to be nowhere dense (containing no intervals). Such nowhere dense, perfect sets are sometimes called Cantor sets.
文摘In this paper, the authors introduce and study the concept of （1, 2）^＊-generalized closed sets with respect to an ideal in a bitopological space. Also, some characterizations and applications of（1, 2）^＊-generalized closed sets are given.
文摘In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.
基金supported by grant from National Nature Science Found (30670767)
文摘Objective： To evaluate the efficiency of an implanted chip system for the control of heart rate （HR）. Methods： The HR was recorded in six conscious Sprague-Dawley （SD） rats. An implanted chip system was designed to regulate the HR by stimulating the right cervical vagus nerve according to the feedback of real time HR. Each rat was subjected to 30-min regulation and 30-min recovery. The change of HR during the regulation period was compared with the control. The ECG was recorded during the experiment for 24 h. Results： The ECG signals were successfully recorded during the experiment. The HR was significantly decreased during the period of regulation compared with control （-79.3 ± 34.5, P 〈 0.01, n = 6） and then recovered to normal after regulation. Conclusion： The described implanted chip system can regulate the HR to a designated set point.
基金the Fujian Provincial Natural Science Foundation of China (Z0510492006J0391)
文摘Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree.
文摘In this article, under quite weaker conditions, theorems of Helly’s type for(not necessarily finite) family of partially closed half-spaces are presented in both analytic and geometric forms. Examples are also provided to show that these conditions cannot be omitted in general.
文摘针对某电厂发电机组3号机气泵速关电磁阀进行活动性试验,发现试验成功后,行程开关的“开”指示信号在分布式控制系统(Distributed Control System,DCS)画面无反馈,同时会出现行程开关脱开后不能回到开状态的情况,造成气泵遥控(自动)退出,导致不能正常投入使用,引起给水系统不稳定运行。经检查,发现行程开关安装位置不佳且摆臂转动死区太大是导致故障现象的主要原因。为此,实际测量现场位置,并改进安装位置,调整摆臂死区角度,设计一套优化方案。经试验验证,改进的方案切实可行,有效解决了问题。
