代数教科书中的“因式分解”沿革研究

1912年、1929年、1951年、2008年出版的数学教科书中的"因式分解"这一内容,在名词术语、内容方法、课程标准或大纲要求等方面即有相同点也有不同之处,展现了因式分解近百年来的沿革历程.因式分解内容方法在减少,难度在降低.目前的教科书的因式分解有待加强.     

基于随机游走增强型矩阵分解的混合服务预测

随着Web服务数量的急剧增长,如何在大量功能相似但非功能属性各异的服务中选择满足用户个性化需求的服务是亟需解决的问题。基于QoS（Quality of Service）预测的服务推荐方法成为研究热点。然而, QoS数据的稀疏性和“冷启动”问题阻碍其发展。针对当前主流的QoS预测模型预测精度不高和收敛速度较慢等问题,提出一种基于随机游走模型和矩阵分解技术的混合QoS预测方法。该方法首先基于矩阵分解获得用户及服务的潜因子矩阵,并将用户潜因子矩阵转化为用户相似度矩阵;然后基于用户相似度矩阵并结合Web服务的网络位置信息,使用随机游走模型提高用户相似度矩阵的准确性;最终结合协同过滤方法与矩阵分解模型进行QoS预测。在真实数据集上实验,结果表明,与当前主流的QoS预测方法相比,该方法具有更高的预测精度和效率。     

泛分解态射的加权Moore-Penros逆

讨论了带有泛分解态射的加权Moore-Penros逆,并给出了加权Moore-Penros逆存在的几个充要条件以及若干性质.     

整数因子分解方程

应用新的数学方法,通过对乘积分类,建立了描述乘积的一类不定方程,化为可解的二次同余方程,阐述该不定方程的计算量为O(nlog2n)的计算机算法,对密码破译与数论方法均有一定意义.给出任意非5k类奇数与方程的对应关系,根据方程确定变量有限连续取值区间,分类计算所有整数分解因子.论述所给分解程序的计算复杂性,讨论算法适合大数分解的理由.最后叙述筛法:求具有某一尾数一定范围内的复合数(素数)的方法.该算法把整数的素性检测和因子分解合二为一.具体特点:试除因子是连续整数的函数,用试除因子数列代替素数列作为整数素性检测序列.     

Web document summarization by exploiting social context with matrix co-factorization

In the context of social media, users usually post relevant information corresponding to the contents of events mentioned in a Web document. This information posses two important values in that (i) it reflects the content of an event and (ii) it shares hidden topics with sentences in the main document. In this paper, we present a novel model to capture the nature of relationships between document sentences and post information (comments or tweets) in sharing hidden topics for summarization of Web documents by utilizing relevant post information. Unlike previous methods which are usually based on hand-crafted features, our approach ranks document sentences and user posts based on their importance to the topics. The sentence-user-post relation is formulated in a share topic matrix, which presents their mutual reinforcement support. Our proposed matrix co-factorization algorithm computes the score of each document sentence and user post and extracts the top ranked document sentences and comments (or tweets) as a summary. We apply the model to the task of summarization on three datasets in two languages, English and Vietnamese, of social context summarization and also on DUC 2004 (a standard corpus of the traditional summarization task). According to the experimental results, our model significantly outperforms the basic matrix factorization and achieves competitive ROUGE-scores with state-of-the-art methods.     

Coupled matrix factorization and topic modeling for aspect mining

Aspect mining, which aims to extract ad hoc aspects from online reviews and predict rating or opinion on each aspect, can satisfy the personalized needs for evaluation of specific aspect on product quality. Recently, with the increase of related research, how to effectively integrate rating and review information has become the key issue for addressing this problem. Considering that matrix factorization is an effective tool for rating prediction and topic modeling is widely used for review processing, it is a natural idea to combine matrix factorization and topic modeling for aspect mining (or called aspect rating prediction). However, this idea faces several challenges on how to address suitable sharing factors, scale mismatch, and dependency relation of rating and review information. In this paper, we propose a novel model to effectively integrate Matrix factorization and Topic modeling for Aspect rating prediction (MaToAsp). To overcome the above challenges and ensure the performance, MaToAsp employs items as the sharing factors to combine matrix factorization and topic modeling, and introduces an interpretive preference probability to eliminate scale mismatch. In the hybrid model, we establish a dependency relation from ratings to sentiment terms in phrases. The experiments on two real datasets including Chinese Dianping and English Tripadvisor prove that MaToAsp not only obtains reasonable aspect identification but also achieves the best aspect rating prediction performance, compared to recent representative baselines.     

图簇GPnr的伴随多项式的恒等式及其因式分解

本文通过研究图的伴随多项式的重要恒等式与因式分解,给出了证明色等价图的结构性质.     

λK n,n的P5-因子分解

给出了平衡完全二部多重图λKn,n存在P5-因子分解的充分必要条件为n=0（mod 40/d）,其中d=gcd（λ,8）。     

整系数多项式因式分解的一种新方法

本文利用整系数多项式与正有理数的对应，将多项式因式分解通过对真分数序列筛选的办法求得因式．     

行列式在初等代数中的巧用

行列式虽是研究线性代数的一种重要工具,但是用行列式来解初等代数题还是少见的,文章介绍利用行列式巧解代数题的方法。