Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.     

分块算子矩阵的加权EP

本文在加权广义Schur补的基础上, 引入并研究了Hilbert空间上分块算子矩阵的加权Moore-Penrose逆和加权EP. 进一步, 给出了加权EP算子在算子方程中的一个应用.     

Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

A note on the weighted norm inequality for the one-sided maximal operator

Let be the one-sided maximal function. In this note we obtain some necessary and sufficient conditions in order that the weighted weak type inequality holds for . Meanwhile, some necessary or sufficient conditions for the weighted inequality for are given.

     

结合视觉Transformer和CNN的道路裂缝检测方法

提出了一种结合视觉Transformer和CNN的道路裂缝检测方法。利用CNN来捕获局部的细节信息,同时利用视觉Transformer来捕获全局特征。通过设计的Fusion特征融合模块将两者提取的特征有机地结合在一起,从而解决了单独使用CNN或视觉Transformer方法存在的局限。最终将结果传递至交互式解码器,生成道路裂缝的检测结果。实验结果表明,无论是在公开的数据集上还是在自建的数据集上,相较于单独使用CNN或视觉Transformer的方法,所提出的方法在道路裂缝检测任务中有更好的效果。     

加权量子搜索算法及其相位匹配条件研究

目前的Grover算法在无序数据库中搜索多个目标时,得到不同目标的几率是相等的,不考虑各个目标重要程度的差异;并且当目标数超过数据库记录总数的四分之一时,搜索到目标的几率迅速下降,当目标数超过记录总数的一半时,算法失效.针对这两个问题,首先提出一种基于加权目标的搜索算法.根据各子目标的重要程度,为每个子目标赋予一个权系数,应用这些权系数将多个子目标表示成一个量子叠加态,这样可使得到每个子目标的几率等于其自身的权系数;其次,提出自适应相位匹配条件,该条件中两次相位旋转的方向相反,大小根据目标量子叠加态和系统初始状态的内积决定.当该内积大于等于((3-√5)/8)^1/2时,至多只需两步搜索,即可以恒等于1的几率得到搜索目标.实验表明,算法及其相位匹配条件是有效的.     

Weighted Cumulative Past Extropy and Its Inference

This paper introduces and studies a new generalization of cumulative past extropy called weighted cumulative past extropy (WCPJ) for continuous random variables. We explore the following: if the WCPJs of the last order statistic are equal for two distributions, then these two distributions will be equal. We examine some properties of the WCPJ, and a number of inequalities involving bounds for WCPJ are obtained. Studies related to reliability theory are discussed. Finally, the empirical version of the WCPJ is considered, and a test statistic is proposed. The critical cutoff points of the test statistic are computed numerically. Then, the power of this test is compared to a number of alternative approaches. In some situations, its power is superior to the rest, and in some other settings, it is somewhat weaker than the others. The simulation study shows that the use of this test statistic can be satisfactory with due attention to its simple form and the rich information content behind it.     

Relative Entropy of Distance Distribution Based Similarity Measure of Nodes in Weighted Graph Data

Many similarity measure algorithms of nodes in weighted graph data have been proposed by employing the degree of nodes in recent years. Despite these algorithms obtaining great results, there may be still some limitations. For instance, the strength of nodes is ignored. Aiming at this issue, the relative entropy of the distance distribution based similarity measure of nodes is proposed in this paper. At first, the structural weights of nodes are given by integrating their degree and strength. Next, the distance between any two nodes is calculated with the help of their structural weights and the Euclidean distance formula to further obtain the distance distribution of each node. After that, the probability distribution of nodes is constructed by normalizing their distance distributions. Thus, the relative entropy can be applied to measure the difference between the probability distributions of the top d important nodes and all nodes in graph data. Finally, the similarity of two nodes can be measured in terms of this above-mentioned difference calculated by relative entropy. Experimental results demonstrate that the algorithm proposed by considering the strength of node in the relative entropy has great advantages in the most similar node mining and link prediction.     

基于社会网络增量的动态社区组织探测

在现实世界中,社会网络结构并不是一成不变的,而是随着时间的推移不断变化,同样社区作为社会网络的一个本质特性也是如此。为了揭示真实的网络社区结构,该文提出一种基于属性加权网络的增量式动态社区发现算法,将网络的属性信息融合在拓扑图中,定义了节点与社区之间的拓扑势吸引,利用网络相对于前一时刻的改变量不断更新完善当前时刻社区结构。通过在真实网络数据上进行实验仿真,证明此算法能够更有效、更实时地发现有意义的社区结构,并具有较小的时间复杂性。