整系数多项式因式分解的一种矩阵方法及程序设计语言

矩阵论是高等代数中最重要的内容之一,本文利用矩阵的知识给出整系数多项式因式分解的一个充分必要条件,同时还针对r=1的情况给出了相应的程序设计语言.     

形如(p~p+1)/(p+1)的素数

设p是奇素数 ,证明 :当p >3,且p≡ 3(mod4 )时 ,(pp+1) / (p +1)都不是素数     

Kn,n的P5—因子分解

本给出了平衡完全二部图Kn,n存在P5－因子分解的充分必要条件：n=0(mod40).     

基于Sylvester结式消元低次拼接条件的研究

根据拼接中的主曲面和辅助曲面方程,利用同伦映射方法构造出含有单位区间变元的代数方程,应用Sylvester结式方法消去变元得到拼接曲面表达式.然后,假设该曲面表达式能够进行因式分解,分析G0和G1次光滑拼接中拼接曲面的次数最低时辅助曲面S（hi）应满足的条件.最后,运用Grobner基理论判断分解因式后各因式是否在主曲面和辅助曲面生成的理想中,从而得出符合条件的低次拼接曲面.     

多项式因式分解与线性空间直和分解的关系

利用线性变换的最小多项式的因式分解,得到线性空间的线性变换的不变子空间的直和分解．反过来由线性空间的任一线性变换的不变子空间的直和分解,也能得到线性变换的最小多项式的不可约因式分解,给出了相关定理及其证明。     

TDTMF: A recommendation model based on user temporal interest drift and latent review topic evolution with regularization factor

This paper constructs a novel enhanced latent semantic model based on users’ comments, and employs regularization factors to capture the temporal evolution characteristics of users’ potential topics for each commodity, so as to improve the accuracy of recommendation. The adaptive temporal weighting of multiple preference features is also improved to calculate the preferences of different users at different time periods using human forgetting features, item interest overlap, and similarity at the semantic level of the review text to improve the accuracy of sparse evaluation data. The paper conducts comparison experiments with six temporal matrix-based decomposition baseline methods in nine datasets, and the results show that the accuracy is 31.64% better than TimeSVD++, 21.08% better than BTMF, 15.51% better than TMRevCo, 13.99% better than BPTF, 9.24% better than TCMF, and 3.19% better than MUTPD ,which indicates that the model is more effective in capturing users’ temporal interest drift and better reflects the evolutionary relationship between users’ latent topics and item ratings.     

A stock rank prediction method combining industry attributes and price data of stocks

Stock forecasting has always been challenging as the stock market is affected by a combination of factors. Temporal Convolutional Network (TCN) based on convolutional structure has been widely used in time series prediction in recent years, but the dilated causal convolution structure leaves it unable to effectively learn the dependencies between data at different time points. This paper proposes a method for stock ranking prediction. To enhance the ability of TCN to handle dependencies within series, we first develop a channel-time dual attention module (CTAM). In conjunction with TCN to process complex historical stock price data, CTAM can adaptively learn the importance of multiple price nature series of stocks and model the dependencies between the data at different times. On the other hand, due to the market industry rotation, some stocks with specific industry attributes may become market preference for a period time. To apply the industry attributes to the stock prediction, we construct an industry-stock Pearson correlation matrix and extract a vector that fully characterizes the industry attributes of stocks from it through a matrix factorization algorithm. Furthermore, the historical market preference is modeled according to the industry attribute of the stocks to generate the dynamic correlation between stocks and market preference, and this correlation is combined with the historical price features extracted by TCN for stock ranking prediction. We conduct experiments on three datasets of 950 constituent stocks of the Shanghai Stock Exchange Index, 750 constituent stocks of the Shenzhen Stock Exchange 1000 Index and 486 stocks of the S&P500 to demonstrate the effectiveness of the proposed method. On the Shanghai Stock Exchange Index dataset, the Investment Return Ratio (IRR) obtained by using the predict results of our method to guide the exchange reached 1.416, and the Sharpe Ratio (SR) reached 2.346. On the Shenzhen Stock Exchange Index dataset, the IRR reached 1.434 and the Sharpe ratio reached 2.317. On the S&P500, the IRR reached 1.491 and the Sharpe ratio reached 2.031.     

基于盲源分离理论的图像加密算法概述

随着盲源分离理论的日渐成熟,其应用领域也越来越广泛,尤其在图像加密领域中,提出了基于独立分量分析(ICA)、基于非负矩阵分解(NMF)的加密新方法,以及盲源分离加密与混沌结合的加密方法等。本子将对以上基于盲源分离理论的加密新方法进行具体阐述。     

自适应非负矩阵分解的人脸识别方法研究

在单样本或者小样本的人脸识别系统中,常常会面临样本数量不足的问题,为解决少样本情况下的分类精度,以及利用原始特征或者目标特点重构的虚拟样本过于单一等问题,提出一种自适应非负矩阵分解（NMF）的人脸识别方法。该方法首先在矩阵分解过程中构造不同矩阵维度和迭代次数参数下的重构样本;然后利用QR分解稀疏表示方法进行人脸分类;最后,通过选取最优参数组合,调整重构样本,直至达到最佳分类效果。在ORL、Yale和AR 3个数据库上的实验结果表明,该算法在最佳参数下,尤其是单样本情况下对比基于原样本方法的准确率平均提高了约5%,最高提高了约10%～15%。     

矩阵分解技术在电影推荐系统中的应用

随着大数据、移动互联网的快速发展,推荐系统成为解决网络信息过载的有力工具.为解决传统推荐系统由于没有将社交网络中用户关系考虑进去而导致的稀疏矩阵、冷启动等问题,提出一种基于矩阵分解技术的电影推荐系统算法MFMRS.该算法充分考虑到社交网络中用户之间的关系对推荐结果的影响,通过设置特征参数、损失函数、随机梯度下降等方法对...