二元二次因式分解的简便方法

给出二元二次多项式F(x,y)=ax^2 bxy cy^2 dx ey f在实数范围内因式分解的一种简便方法。利用这种方法，还可以简便地分解多元二次多项式。     

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.     

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。     

以谱分解方法对随机摄动系统进行最优性能分析

We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.     

大整数分解算法及其并行实现

讨论大整数解的一些算法，并讨论它们的并行实现．可以看出，大多数分解算法非常适合并行计算．叙述了在微机上实现二次筛法和椭圆曲线法的情况     

基于NMF与SVM的粘连种子分类研究

为促进农业向精准农业、智慧农业方向发展,针对种业中衡量种子质量的重要指标千粒重,为提高其精确度,提出基于非负矩阵分解与支持向量机的粘连种子分类算法,在利用机器视觉与图像识别等技术进行种子颗粒计数时,解决种子因严重粘连（经图像预处理、形态学操作等仍粘连）使系统出现误判,导致计数结果误差较大的问题。实验以玉米种子为研究对象,研究3种常见粘连类型。采用基于NMF的方法实现种子粘连图像有效特征的提取,再运用SVM构建多分类器,解决种子粘连类型的三分类问题,最后通过实验验证,该方法的分类准确率为98%。     

完全数问题的探讨

利用数的标准分解式给出了一个数为完全数的必要条件，以及若奇完全数存在，则a为（4n＋1）^4k＋1 a^2 1形式的数，其中4n＋l为素数，且a1不含4n＋1型的素因子。     

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).     

一种基于隐式信任感知的MOOCs推荐方法

[目的/意义]随着MOOCs迅猛发展和普及,如何利用智能推荐技术为学习者从海量的MOOC中"寻找最佳课程"成为MOOC发展中需要解决的重要课题。[方法/过程]基于自我知觉理论和学习行为投入框架,充分利用学习行为日志和评分数据挖掘学习者之间的隐式信任关系,并通过信任传播建立MOOC社区信任网络,从而构建动态结合兴趣和隐式信任感知的混合推荐方法。为解决数据稀疏问题,提出基于信任的联合概率矩阵分解模型(TA-PMF),将课程评分矩阵、信任关系矩阵的分解相结合来挖掘用户及课程潜在特征,进而实现评分预测。[结果/结论]真实数据集测试结果表明,与显性评分值相比,学习行为投入信息对信任度构建贡献权重达到0.7;TA-PMF方法对MOOC推荐具有较好的适用性,且能在一定程度上缓解冷启动问题。