日本线性代数教育的历史发展及启示

线性代数教育是大学数学的基础教育。本文系统地介绍了第二次世界大战以来,日本线性代数教育的发展,当今线性代数教育的研究内容、教学要求及存在的不足之处,并由此引起了对中国线性代数教育的思考。     

p-半单BCI-代数的导群列

引入了p-半单BCI-代数的导群和广义a-结合BCI-代数的导半群的概念,并给出了p-半单BCI-代数的一个导群列和广义a-结合BCI-代数的导半群列.     

The ubiquitous angle

Summary.  Previously we used the geometry of n -dimensional space to derive the paired samples t -test and its p -value. In the present paper we describe the 'ubiquitous' application of these results to single degree of freedom linear model hypothesis tests. As examples, we derive the p - and t -values for the independent samples t -test, for testing a contrast in an analysis of variance and for testing the slope in a simple linear regression analysis. An angle θ in n -dimensional space is again pivotal in the development of the ideas. The relationships between p , t , θ , F and the correlation coefficient are also described by using a 'statistical triangle'.     

BCI-代数的一类子代数

本文讨论了ＢＣＩ－代数Ｘ中满足条件０＊（０＊ｘｋ）＝ｘ的一类子代数的性质，给出了半单ＢＣＩ－代数的定义，讨论了这类ＢＣＩ－代数的结构和半群特征．     

Modular-transform based clustering

Spectral clustering uses eigenvectors of the Laplacian of the similarity matrix. It is convenient to solve binary clustering problems. When applied to multi-way clustering, either the binary spectral clustering is recursively applied or an embedding to spectral space is done and some other methods, such as K-means clustering, are used to cluster the points. Here we propose and study a K-way clustering algorithm – spectral modular transformation, based on the fact that the graph Laplacian has an equivalent representation, which has a diagonal modular structure. The method first transforms the original similarity matrix into a new one, which is nearly disconnected and reveals a cluster structure clearly, then we apply linearized cluster assignment algorithm to split the clusters. In this way, we can find some samples for each cluster recursively using the divide and conquer method. To get the overall clustering results, we apply the cluster assignment obtained in the previous step as the initialization of multiplicative update method for spectral clustering. Examples show that our method outperforms spectral clustering using other initializations.     

A Practical Implementation and Bayesian Estimation in Franklin's Randomized Response Procedure

A Bayesian estimator based on Franklin's randomized response procedure is proposed for proportion estimation in surveys dealing with a sensitive character. The method is simple to implement and avoids the usual drawbacks of Franklin's estimator, i.e., the occurrence of negative estimates when the population proportion is small. A simulation study is considered in order to assess the performance of the proposed estimator as well as the corresponding credible interval.     

自反代数的局部自同构

设Ａ为自反Ｂａｎａｃｈ空间Ｘ中一自反代数,使得在ＬａｔＡ中０＋≠０－且Ｘ－≠Ｘ,则Ａ的每一范数连续的满局部内自同构是自同构     

师范院校高等代数课程教学的几点认识

师范院校高等代数课程教学中如何提高教学质量,使学生通过这门课的学习获得相应的知识和能力,谈几点认识。     

Making hermeneutics explicit: how QCA supports an insightful dialogue between theory and cases

Typically, qualitative comparative analysis (QCA) is praised for its hermeneutic dialogue between theory and empirical cases. However, in reporting research with QCA, these hermeneutic processes will usually not be illustrated. This paper aims at showing clear how QCA induces this dialogue between theory and data. As an illustrative example, I use a research situation dealing with a genuine research question of Legislative Studies: the causes of party unity. Using the classical dichotomous and the MV-QCA approach, the paper mainly shows how to deal productively with contradictory theoretical statements and how stepping from simpler to more complex models adds explanation while still making clear further routes to improve insights into the substantive research topic: both theoretically and empirically. Finally, non-observed configuration (‘logical remainders’) will be used to simplify the resulting theory, and its theoretical and empirical plausibility will be evaluated. The whole paper makes explicit how the QCA approach forces researchers to reveal the dialogue between theory and cases – just as it was intended by the inventor of this analytical tool.     

加强能力培养 注重数学思想方法的运用

加强数学思想方法的研究不仅是培养高素质的数学人才的需要,更是培养复合型、创业型高级应用人才的需要。高等代数课程在培养学生抽象思维能力、逻辑推理能力、科学计算能力诸方面,起着非常重要的作用。本文从能力培养和数学思想方法在教学中的运用,以及在加强课程建设基础工作等方面,探索高等代数课程教育教学工作。