对称与数学

引述了自然界、科学技术领域和日常生活中普遍存在的对称现象 ,说明对称是宇宙和自然界的基本属性 ,也是事物生存发展的自然规律 ,然后简要介绍了对称方法在数学中的应用     

物质结构课程教学改革的思考与实践

本文针对师专化学系物质结构课程的教学目的和现状,提出改革教学的思路,并从优化教材的知识结构,突出讲授内容的实用性和注重化学史和方法论的介绍以培养学生的能力入手,阐述了作者几年来从事物质结构教学改革的实践和体会．     

论语文教学中的美育

语文教学美育需综合教学论、接受美学、教育心理学和语言美学的理论资源。在语文美育实施过程中作为审美客体的汉语言文学的形式美与审美主体具有异质同构性,作为审美主体的教师和学生的审美心理结构特征及审美心理活动各有其特点。在美育实施中教师与学生必须信息对称交流,并充分发挥各自审美心理活动的优势,在大美育的环境内实施语文美育,以便相得益彰,收效最佳。     

Spherical symmetry: An elementary justification

Summary The present paper includes characterizations of the conditions of spherical symmetry and of centered spherical symmetry. These characterizations provide an empirical justification for the above mentioned conditions of symmetry.     

垂直管理体制下地方政府与环保部门的权责对称取向

当前,严峻的生态环境形势以及环境治理困境倒逼环保管理体制改革,省级以下环保机构监测监察执法实行垂直管理正是结合全面深化改革背景下的一种应然的理性选择。基于地方政府限权和环保部门放权的分析框架认为,环保部门实行垂直管理体制虽然能突破"属地管理"和"双重领导"带来的执法困境,但并不能完全抵制地方政府以其他形式进行合法性行政干预造成的权责不对称。因此,应通过加强"权责匹配"与"执法下沉"协同规避"地方化";突出"责任倒查"与"执法督察"结合强化"行政问责";注重"跨部门合作"与"社会参与"互动实现"协同治理"等方式动态调整地方政府限权与环保部门放权之间的平衡点,进而实现地方政府与环保部门权责对称。     

Label‐ and Level‐Invariant Graphical Log‐Linear Models

We introduce two types of graphical log‐linear models: label‐ and level‐invariant models for triangle‐free graphs. These models generalise symmetry concepts in graphical log‐linear models and provide a tool with which to model symmetry in the discrete case. A label‐invariant model is category‐invariant and is preserved after permuting some of the vertices according to transformations that maintain the graph, whereas a level‐invariant model equates expected frequencies according to a given set of permutations. These new models can both be seen as instances of a new type of graphical log‐linear model termed the restricted graphical log‐linear model, or RGLL, in which equality restrictions on subsets of main effects and first‐order interactions are imposed. Their likelihood equations and graphical representation can be obtained from those derived for the RGLL models.     

Gender Mainstreaming: An Assessment of Its Conceptual Value for Gender Equality

Evaluations of gender mainstreaming show that there has been limited change to gender equality and it has been very fragmented across EU countries. Therefore, the purpose of this article is to evaluate the heuristic and conceptual value of the term gender mainstreaming as a metaphor for gender equality. Our results from applying an image‐schematic model of metaphor evaluation show that gender mainstreaming represents a nonsensical metaphor for gender equality. We conclude with recommendations for reconceptualizing gender mainstreaming.     

R-Symmetry and the Power Functions of the Tests for Inverse Gaussian Means

The two-parameter Inverse Gaussian (IG) distribution is often appropriate for modeling non negative right-skewed data due to the striking similarities with the Gaussian distribution in its basic properties and inference methods. There are about 40 such G-IG analogies developed in literature and were most recently tabulated by Mudholkar and Wang. Of these, the earliest and most commonly noted similarities are the significance tests based on student's t and F distribution for the homogeneity of one, two or several means of the IG populations. However, unlike the corresponding tests in Gaussian theory, little is known about the power function of the basic tests. In this article, we employ the IG-related root-reciprocal IG distribution and a notion of Reciprocal Symmetry to establish the monotonicity of the power function of the test of significance for the IG mean.     

The “wrong skewness” problem in stochastic frontier models: A new approach

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generalizing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and nondegenerate efficiency measures. We discuss the statistical properties of the model, and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958–2005 and show that for a number of years our model suggests technical efficiencies well below the frontier while the classical one estimates no inefficiency in those years.     

Testing symmetry based on empirical likelihood

In this paper, we propose a general kth correlation coefficient between the density function and distribution function of a continuous variable as a measure of symmetry and asymmetry. We first propose a root-n moment-based estimator of the kth correlation coefficient and present its asymptotic results. Next, we consider statistical inference of the kth correlation coefficient by using the empirical likelihood (EL) method. The EL statistic is shown to be asymptotically a standard chi-squared distribution. Last, we propose a residual-based estimator of the kth correlation coefficient for a parametric regression model to test whether the density function of the true model error is symmetric or not. We present the asymptotic results of the residual-based kth correlation coefficient estimator and also construct its EL-based confidence intervals. Simulation studies are conducted to examine the performance of the proposed estimators, and we also use our proposed estimators to analyze the air quality dataset.