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.     

一类图的伴随多项式的因式分解及色性

通过研究一类S-型图的伴随多项式的因式分解,证明了这类图的补图的色等价图的结构性质和非色唯一性.     

对称M矩阵的并行不完全分解预条件

J.H.Yun提出了一种新的计算块三对角M矩阵预条件的算法,这种方法具有天然的并行性,解决了ILU分解不易并行化的缺点,能有效节约计算时间。以对称M矩阵作为例子,将以上方法推广到一般的对称M矩阵,使得在构造这一类矩阵的不完全分解预条件方法时,能够更加快速有效。关于预条件子的定理及其证明将会被给出。最后,数值实验将会被用来验证我们的定理结论。     

EDMH: Efficient discrete matrix factorization hashing for multi-modal similarity retrieval

Hashing has been an emerging topic and has recently attracted widespread attention in multi-modal similarity search applications. However, most existing approaches rely on relaxation schemes to generate binary codes, leading to large quantization errors. In addition, amounts of existing approaches embed labels into the pairwise similarity matrix, leading to expensive time and space costs and losing category information. To address these issues, we propose an Efficient Discrete Matrix factorization Hashing (EDMH). Specifically, EDMH first learns the latent subspaces for individual modality through matrix factorization strategy, which preserves the semantic structure representation information of each modality. In particular, we develop a semantic label offset embedding learning strategy, improving the stability of label embedding regression. Furthermore, we design an efficient discrete optimization scheme to generate compact binary codes discretely. Eventually, we present two efficient learning strategies EDMH-L and EDMH-S to pursue high-quality hash functions. Extensive experiments on various widely-used databases verify that the proposed algorithms produce significant performance and outperform some state-of-the-art approaches, with an average improvement of 2.50% (for Wiki), 2.66% (for MIRFlickr) and 2.25% (for NUS-WIDE) over the best available results, respectively.     

浅谈定积分在不等式证明与因式分解中应用

定积分是高中新课程体系中一个新增加的重要内容,很多教师在该部分内容的教学时都与高中其他知识点割裂开来,殊不知,定积分在高中阶段解题中具有广泛的应用,本文以定积分在不等式证明和因式分解中应用为例,探讨定积分在高中解题中的应用。     

二次型理论在中学数学中的应用

二次型是高等代数的重要内容之一,通过研究二次型的结构及性质,借助例子说明二次型在多项式因式分解、判断二次曲线的形状及计算椭圆面积等方面的应用。     

Search result diversification on attributed networks via nonnegative matrix factorization

Search result diversification is an effective way to tackle query ambiguity and enhance result novelty. In the context of large information networks, diversifying search result is also critical for further design of applications such as link prediction and citation recommendation. In previous work, this problem has mainly been tackled in a way of implicit query intent. To further enhance the performance on attributed networks, we propose a novel search result diversification approach via nonnegative matrix factorization. Our approach encodes latent query intents as well as nodes as representation vectors by a novel nonnegative matrix factorization model, and the diversity of the results accounts for the query relevance and the novelty w.r.t. these vectors. To learn the representation vectors of nodes, we derive the multiplicative updating rules to train the nonnegative matrix factorization model. We perform a comprehensive evaluation on our approach with various baselines. The results show the effectiveness of our proposed solution, and verify that attributes do help improve diversification performance.     

基于实时新闻分析的馆藏资源推荐方法研究

如何在信息时代增加馆藏资源的可见度,提高馆藏资源的利用率,是一个急需研究和解决的问题。实时新闻和图书馆馆藏资源间的连接可以提高图书馆馆藏资源的可见度,增加图书馆馆藏资源的利用率,为用户提供丰富、全面的阅读资料和专业知识,帮助用户形成全面、深入阅读和思考的良好习惯。基于快数据处理技术的实时新闻分析和馆藏资源推荐框架,通过分析网络实时新闻获取用户感兴趣的话题,应用快数据处理技术、潜在语义分析、非负矩阵分解、权重矩阵分解等方法对数据进行语义分析和处理,对图书馆馆藏资源进行相关话题的分类和推荐。对OCLC的百万数据集和雅虎新闻的分析和实验表明,这种资源推荐框架和方法有较好的应用效果。图2。表1。     

二分图的正交[0，ki]1^m-因子分解

设G是二分图,k1,k2,…,km是正整数。若二分图G的边能划分成m个边不交的[0,k1]-因子F1,…,[0,k]-因子Fm,则称F^-={F1,…,Fm}是二分图G的一个[0,ki]1^m-因子分解,又若H是二分图G的一个有m条边的子图,若时任意的1≤i≤m有｜E（H）∩E（Fi）｜=1,则称F^-与H是正交的。本文主要研究二分图的正交[0,ki]1^m-因子分解,并给出一个结果。     

Super number roots and factorizations for a kind of polynomial

~~Super number roots and factorizations for a kind of polynomial@邱学绍$Information and Computation Department, Zhengzhou Institute of Light Industry, Zhengzhou450002, P.R. China~~