T(1,2,n)∪(s∪i=0 CPi)及补图的匹配唯一性

本文研究了图的匹配唯一性，给出了T（1，2，n）∪（S∪i=0CPi）及补图匹配唯一的充要条件．     

局部对称空间的伪脐点子流形的内蕴刚性积分不等式

研究了局部对称空间的紧致的脐子流形，得到了这种子流形的关于截面曲率和Ricci曲率的两个内蕴积分不等式。     

图搜索的A*算法和SQL方法

本文介绍一般图的搜索算法的两种具体实现方法,“A*算法”使用启发函数选点扩展;“数据库”方法利用数据库存储图中原始数据,再借助功能强大的SQL语言来完成搜索．     

Clustering dense graphs: A web site graph paradigm

Typically graph-clustering approaches assume that a cluster is a vertex subset such that for all of its vertices, the number of links connecting a vertex to its cluster is higher than the number of links connecting the vertex to the remaining graph. We consider a cluster such that for all of its vertices, the number of links connecting a vertex to its cluster is higher than the number of links connecting the vertex to any other cluster. Based on this fundamental view, we propose a graph-clustering algorithm that identifies clusters even if they contain vertices more strongly connected outside than inside their cluster; hence, the proposed algorithm is proved exceptionally efficient in clustering densely interconnected graphs. Extensive experimentation with artificial and real datasets shows that our approach outperforms earlier alternate clustering techniques.     

Re-examining lexical and semantic attention: Dual-view graph convolutions enhanced BERT for academic paper rating

Automatically assessing academic papers has enormous potential to reduce peer-review burden and individual bias. Existing studies strive for building sophisticated deep neural networks to identify academic value based on comprehensive data, e.g., academic graphs and full papers. However, these data are not always easy to access. And the content of the paper rather than other features outside the paper should matter in a fair assessment. Furthermore, while BERT models can maintain general semantics by pre-training on large-scale corpora, they tend to be over-smoothing due to stacked self-attention layers among unfiltered input tokens. Therefore, it is nontrivial to figure out distinguishable value of an academic paper from its limited content. In this study, we propose a novel deep neural network, namely Dual-view Graph Convolutions Enhanced BERT (DGC-BERT), for academic paper acceptance estimation. We combine the title and abstract of the paper as input. Then, a pre-trained BERT model is employed to extract the paper’s general representations. Apart from hidden representations of the final layer, we highlight the first and last few layers as lexical and semantic views. In particular, we re-examine the dual-view filtered self-attention matrices via constructing two graphs, respectively. After that, two multi-hop Graph Convolutional Networks (GCNs) are separately employed to capture pivotal and distant dependencies between the tokens. Moreover, the dual-view representations are facilitated by each other with biaffine attention modules. And a re-weighting gate is proposed to further streamline the dual-view representations with the help of the original BERT representation. Finally, whether the submitted paper could be acceptable is predicted based on the original language model features cooperated with the dual-view dependencies. Extensive data analyses and the full paper based MHCNN studies provide insights into the task and structural functions. Comparison experiments on two benchmark datasets demonstrate that the proposed DGC-BERT significantly outperforms alternative approaches, especially the state-of-the-art models like MHCNN and BERT variants. Additional analyses reveal significance and explainability of the proposed modules in the DGC-BERT. Our codes and settings have been released on Github (https://github.com/ECNU-Text-Computing/DGC-BERT).     

A new deep graph attention approach with influence and preference relationship reconstruction for rate prediction recommendation

Graph neural networks have been frequently applied in recommender systems due to their powerful representation abilities for irregular data. However, these methods still suffer from the difficulties such as the inflexible graph structure, sparse and highly imbalanced data, and relatively shallow networks, limiting rate prediction ability for recommendations. This paper presents a novel deep dynamic graph attention framework based on influence and preference relationship reconstruction (DGA-IPR) for recommender systems to learn optimal latent representations of users and items. The entire framework involves a user branch and an item branch. An influence-based dynamic graph attention (IDGA) module, a preference-based dynamic graph attention (PDGA) module, and an adaptive fine feature extraction (AFFE) module are respectively constructed for each branch. Concretely, the first two attention modules concentrate on reconstructing influence and preference relationship graphs, breaking imbalanced and fixed constraints of graph structures. Then a deep feature aggregation block and an adaptive feature fusion operation are built, improving the network depth and capturing potential high-order information expressions. Besides, AFFE is designed to acquire finer latent features for users and items. The DGA-IPR architecture is formed by integrating IDGA, PDGA, and AFFE for users and items, respectively. Experiments reveal the superiority of DGA-IPR over existing recommendation models.     

数形结合及其应用

“数”与“形”是数学的基本研究对象,他们之间存在着对立统一的辨证关系。数形结合是一种重要的数学思想,是人们认识．理解．掌握数学的意识,它是我们解题的重要手段,是根据数理与图形之间的关系,认识研究对象的数学特征,寻求解决问题的方法的一种数学思想。它是在一定的数学知识．数学方法的基础上形成的．它对理解．掌握．运用数学知识和数学方法,解决数学问题能起到促进和深化的作用。切实把握好数形结合的思想是学好数学的关键之一。文章先阐述了数形结合的原则及途径,再在从数形结合思想在数学解题中的应用角度分类谈了几个方面的应用。     

确定水泵工况点的C程序设计

排水设备选型设计的关键是确定工况点，利用计算机技术，模拟水泵性能曲线，绘制管路特性曲线，读取工况参数，可准确、合理地确定工况点。     

基于知识图谱的国外儿童青少年身体活动研究可视化分析

文章以web of science^TM核心合集数据库中收录的2017年到2020年间以儿童青少年身体活动为主题的文献信息为研究数据来源,运用文献资料法和Cite Space知识图谱分析国外儿童青少年身体活动研究外部特征和基本情况,解析当前儿童青少年身体活动研究的经典引文,揭示研究热点。国外儿童青少年身体活动的研究呈现出跨众多学科且多领域之间相互交叉的态势;研究来源期刊种类丰富多样,涉及学科领域广泛;美国和澳大利亚虽发文量最多,中心性较低;英格兰、新加坡和南非其研究影响力较高;大学是该研究领域的核心机构;儿童青少年的体质和健康问题,锻炼对儿童体质和健康的干预尤其是对肥胖儿童青少年体质健康干预与慢性病方面研究是国际上关注的焦点;身体活动水平对非传染性疾病的预防方案的制定和实施、儿童和青少年身体活动准则的制定、儿童青少年久坐行为与多项身体以及心理健康指标之间的关系等研究构成了该领域的经典被引文献。     

电子商务中混合数据加密技术的研究

由于电子商务拥有了更加丰富的信息、更加简单方便的交易和更加低廉的成本,受到了广大用户的欢迎。然而,现今阻碍电子商务快速发展的最大问题则是安全问题,数据加密技术是保证电子商务安全的核心技术,是电子商务安全技术的重要组成部分。目前使用的数据加密技术主要分成两种：对称加密技术和非对称加密技术。文章通过剖析数据加密技术中的RSA和DES算法的特点和缺点,提出一种混合加密算法用以规避两者的缺陷。