Condensations of projective sets onto compacta

For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.

Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.

     

基于粗糙集理论的知识约简及应用实例

在保持分类能力不变的前提下 ,通过利用粗糙集理论中的知识约简方法 ,在保护知识库分类不变的条件下 ,删除其中不相关或不重要的知识 ,从而导出问题的决策 .利用基于决策表的粗糙集模型算法 ,实例分析如何数字化表示决策表 ,并对其进行属性约简和属性值的约简 ,从而提取决策规则 .     

HL-2M 装置供电系统研制

为满足 HL-2M 装置的供电需求,须配套建设相应的供电系统。通过仿真计算 HL-2M 装置的总体供 电需求,考虑到 HL-2A 装置现有的供电系统设备,提出了兼顾 HL-2A 和 HL-2M 装置供电需求的总体配置方案。介绍了国内首台 300MVA 立式交流脉冲发电机组、磁体电源、高压电源和电源控制系统的研制情况。     

Status Set Sequential Pattern Mining Considering Time Windows and Periodic Analysis of Patterns

The traditional sequential pattern mining method is carried out considering the whole time period and often ignores the sequential patterns that only occur in local time windows, as well as possible periodicity. Therefore, in order to overcome the limitations of traditional methods, this paper proposes status set sequential pattern mining with time windows (SSPMTW). In contrast to traditional methods, the item status is considered, and time windows, minimum confidence, minimum coverage, minimum factor set ratios and other constraints are added to mine more valuable rules in local time windows. The periodicity of these rules is also analyzed. According to the proposed method, this paper improves the Apriori algorithm, proposes the TW-Apriori algorithm, and explains the basic idea of the algorithm. Then, the feasibility, validity and efficiency of the proposed method and algorithm are verified by small-scale and large-scale examples. In a large-scale numerical example solution, the influence of various constraints on the mining results is analyzed. Finally, the solution results of SSPM and SSPMTW are compared and analyzed, and it is suggested that SSPMTW can excavate the laws existing in local time windows and analyze the periodicity of the laws, which solves the problem of SSPM ignoring the laws existing in local time windows and overcomes the limitations of traditional sequential pattern mining algorithms. In addition, the rules mined by SSPMTW reduce the entropy of the system.     

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.     

Assessment and Prediction of Water Resources Vulnerability Based on a NRS-RF Model: A Case Study of the Song-Liao River Basin,China

The vulnerability of water resources is an important criterion for evaluating the carrying capacity of water resources systems under the influence of climate change and human activities. Moreover, assessment and prediction of river basins’ water resources vulnerability are important means to assess the water resources security state of river basins and identify possible problems in future water resources systems. Based on the constructed indicator system of water resources vulnerability assessment in Song-Liao River Basin, this paper uses the neighborhood rough set (abbreviated as NRS) method to reduce the dimensionality of the original indicator system to remove redundant attributes. Then, assessment indicators’ standard values after dimensionality reduction are taken as the evaluation sample, and the random forest regression (abbreviated as RF) model is used to assess the water resources vulnerability of the river basin. Finally, based on data under three different future climate and socio-economic scenarios, scenario predictions are made on the vulnerability of future water resources. The results show that the overall water resources vulnerability of the Song-Liao River Basin has not improved significantly in the past 18 years, and the overall vulnerability of the Song-Liao River Basin is in the level V of moderate to high vulnerability. In the future scenario 1, the overall water resources vulnerability of the river basin will improve, and it is expected to achieve an improvement to the level III of moderate to low vulnerability. At the same time, the natural vulnerability and vulnerability of carrying capacity will increase significantly in the future, and the man-made vulnerability will increase slowly, which will deteriorate to the level V of moderate to high vulnerability under Scenario 3. Therefore, taking active measures can significantly reduce the vulnerability of nature and carrying capacity, but man-made vulnerability will become a bottleneck restricting the fragility of the overall water resources of the river basin in the future.     

基于学科素养论证分析2020年高考全国卷Ⅰ物理压轴题

2020年高考物理试题依托高考评价体系,结合物理学科特点,考试内容以学科素养考查为导向,即以物理观念、科学思维、科学探究、科学态度与责任的物理学科素养为导向,注重对核心物理概念和规律的考查,引导学生夯实学习发展的基础,促进中学重视培养学生的基础知识、基本技能以及提升学生的基本素养.基于物理学科素养,论证分析2020年高...     

On α-Limit Sets in Lorenz Maps

The aim of this paper is to show that α-limit sets in Lorenz maps do not have to be completely invariant. This highlights unexpected dynamical behavior in these maps, showing gaps existing in the literature. Similar result is obtained for unimodal maps on [0,1]. On the basis of provided examples, we also present how the performed study on the structure of α-limit sets is closely connected with the calculation of the topological entropy.     

Molecular properties with dual basis set methods

The dual basis set approach has proven to be very successful for accurately estimating total energies with large basis sets. This study extends the applications of this technique to the calculation of molecular properties, including energy derivatives with respect to nuclear positions and to an external electric field. All energy derivatives have been calculated numerically via finite-differences. Molecular gradients and Hessians as well as dipole moments and polarizabilites have been calculated at the HF and MP2 levels using two alternative versions of the dual basis set method. The accuracy of these approaches is discussed in the context of quality of basis sets used in calculations. It is shown that even quite poor results obtained with the 6-311G basis set are significantly improved in dual basis set calculations with the 6-311G(d,p) and 6-311G(3df,3dp) basis sets.     

Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.