A note on rough set and non-measurable set

It is proved that rough set is equivalent to non-measurable set in measure theory. Hence, rough set is not a new concept in some sense. At the same time, we defined the measurable degree of a set by inner measure and outer measure. Its special case is the accuracy measure of rough set.     

Laser beams: knotted threads of darkness

Destructive interference may lead to complete cancellation when light waves travelling in different directions cross, and in three-dimensional space this occurs along lines that are vortices of electromagnetic energy flow. Here we confirm theoretical predictions by experimentally creating combinations of optical laser beams in which these dark threads form stable loops that are linked and knotted.     

不为框架集的正测Cantor集

修正了由Casazza给出的对任意a,b,{E_(mb)T_(na)g}都不是框架的例子,再构造了一个正测Cantor集,使得对于所有可数点列{x_n}和{y_m},集E均不是WH框架集,并且集E也不是小波框架集.     

一种泥页岩层系岩相划分方法

泥页岩层系中成分复杂,岩相划分方案不统一。通过岩心观察、显微镜下鉴定、全岩分析及有机地化数据分析,采用岩心宏观构造、有机质含量和岩石类型相结合的方法,以"四组分三端元"分类为原则,建立一种泥页岩层系岩相综合划分方案。结果表明:该分类方案引入有机质组分的含量,体现了泥页岩层系的构造特征、混积特征及其实用性,在苏北盆地阜二段泥页岩层系岩相划分研究中得以有效应用,可以为后续泥页岩储集空间研究、测井岩相识别和储层可改造性评价奠定基础。     

关于攀援集的一点注记

设 $(X,f)$ 是一个动力系统, 其中 $X$ 是一个紧致度量空间, $\\map{f}{X}{X}$ 是一个连续映射. 得到如下结果: (1) 如果 Borel 集 $D\\subset X$ 是 $f$ 的一个分布攀援集, 并且存在一个不变概率测度 $\\mu$ 使得 $\\mu(D)0$, 那么 $\\mu$ 是一个原子测度. (2) 强混合性不能蕴含分布攀援偶对的存在性.     

用VC++实现多线程方式下的串行通信

结合实际工程 ,在 VC 环境下通过采用创建事件对象来保持线程同步、利用两个监听函数提高数据接收效率和可靠性等措施实现了多线程串行通信 ,完成了工程前端数据采集器与后台计算机之间的数据传输。     

FD集归并依赖集的左部联合集

基于左部联合集,给出了归并依赖集的左右部冲突的概念。同时讨论了对无内部冲突的FD集,归并依赖集的左右部冲突与无α环、3NF数据库模式分解的关系。     

关于广义Jeans数集的一个性质

用初等简洁的方法给出了广义Jeans数集的一个性质,证明了Halbeisen和Hungerbh櫣ler提出的一个猜想.     

有关链极限集的一个Conley定理

讨论度量空间里流的Ω-极限集和子集序列的极限集.指出了文[8]错误地否定了一个Conley定理,同时加强了Conley的结论.     

一类三分集合及其性质

考虑闭区间[0，1]，构造一类三分集C3，得到它的一些实变性质，并计算了C3的Hausdorff维数。     

有关链极限集的一个Conley定理

讨论度量空间里流的Ω-极限集和子集序列的极限集 .指出了文 [8]错误地否定了一个 Conley定理 ,同时加强了 Conley的结论 .     

二维不可测集的一个注记

给出了一个二维不可测集。一维空间的不可测集的构造方法基本相同,本文通过将二维空间里的点其对应坐标为有理数的划分方法来确定亲和集,进而给出了一个二维的不可测集。     

A game-theoretic perspective on rough set analysis

Determining the correct threshold values for the probabilistic rough set approaches has been a heated issue among the community. Existing techniques offer no way in guaranteeing that the calculated values optimize the classification ability of the decision rules derived from this configuration. This article will formulate a game theoretic approach to calculating these thresholds to ensure correct approximation region size. Using payoff tables created from approximation measures and modified conditional risk strategies, we provide the user with tolerance levels for their loss functions. Using the tolerance values, new thresholds are calculated to provide correct classification regions. This will aid in determining a set of optimal region threshold values for decision making.     

A new minimal rough set axiom group

Rough set axiomatization is one aspect of rough set study, and the purpose is to characterize rough set theory using independahle and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. To characterize rough set theory, an axiom group named H consisting of 4 axioms, is proposed. That validity of the axiom group in characterizing rough set theory is reasonable, is proved. Simultaneously, the minimization of the axiom group, which requires that each axiom is an inequality and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.     

Limitations in the use of actomyosin threads as model contractile systems

Recent studies have suggested that actomyosin threads may provide a useful model for studying the properties of contractile systems. The development of highly sensitive positional feedback transducers has enabled the properties of these threads to be measured reproducibly. Potential applications include such systems as ventricle, smooth muscle and non-muscle preparations, from which it is difficult to obtain suitable fibres for mechanical studies. In addition, studies with chemically modified myosins may provide new insights into the relationships between the biochemical and mechanical events in the cross-bridge cycle. However, there are indications that the mechanical properties of actomyosin threads differ from those of intact fibres in several important respects. For example, contraction velocity is proportional to isometric tension in threads, but is independent of filament density in intact fibres. We have now determined the force-velocity characteristics of actomyosin threads prepared from muscles with known differences in their physiological contraction velocities. No direct relationships could be found between the velocity characteristics of the threads and those of intact muscle. We conclude that the measured velocities of threads reflect properties of the actomyosins other than cross-bridge cycling times, thus severely limiting the usefulness of this technique for comparative purposes.     

无平均数集与无模n平均数集

我们称Ｚｎ＝｛０,１,…,ｎ－１｝的一个子集Ｘ是无模ｎ平均数集,如果对于所有｛ｘ,ｙ,ｚ｝Ｘ,ｘ＋ｙ≠２ｚ（ｍｏｄｎ）。我们记ｒ（ｎ）＝ｍａｘ｛｜Ｘ｜｜Ｘ是无模ｎ平均数集｝,Ｒ′（ｎ）＝ｍａｘ｛｜Ｘ｜｜Ｘ是无模ｎ平均数集,且对于所有｛ｘ,ｙ｝Ｘ,２Ｘ≠２ｙ（ｍｏｄｎ）｝。在本文中,我们证明了：当ｎ为奇数时,Ｒ′（ｎ）＝Ｒ（ｎ）,Ｒ（２ｎ）＝２Ｒ（ｎ）;当ｌ≥２ｎ－１时,Ｒ′（ｌ）≥ｒ（ｎ）;当ｌ≥２ｎ－２时,Ｒ（ｌ）≥ｒ（ｎ）;Ｒ′（ｎ）≤Ｒ（ｎ）≤ｒ（ｎ）