(+)-儿茶素金属配合物的结构、红外光谱和反应活性

用密度泛函理论(DFT)B3LYP方法, 对非金属原子和金属原子分别采用6-311+G(d,p)基组和LANL2DZ基组, 计算并分析了(+)-儿茶素(Cc, C₁₅H₁₄O₆)及其与金属形成的配合物分子(M-Cc, M=Ca, Zn, Cd, Cu, Al, Cr)的几何构型、红外光谱和反应活性的异同. 计算结果表明, M-Cc的分子结构、红外光谱与反应活性均不同于其前体Cc. 形成金属配合物后, 取代基团及结构的改变使得红外光谱有所差异. 前线分子轨道及概念DFT指数计算结果显示, 一些M-Cc体系的反应活性要强于Cc单体. 金属离子的不同使得配合物的各指数有所差异. 这些结果将为进一步认识(+)-儿茶素及其相关化合物的结构、红外光谱和反应活性提供有益启示.     

Observation‐based missing data methods for exploratory data analysis to unveil the connection between observations and variables in latent subspace models

This paper introduces a class of methods to infer the relationship between observations and variables in latent subspace models. The approach is a modification of the recently proposed missing data methods for exploratory data analysis (MEDA). MEDA is useful to identify the structure in the data and also to interpret the contribution of each latent variable. In this paper, MEDA is augmented with dummy variables to find the data variables related to a given deviation detected among observations, for instance, the difference between one cluster of observations and the bulk of the data. The MEDA extension, referred to as observation‐based MEDA or oMEDA, can be performed in several ways, one of which is theoretically shown to be equivalent to a comparison of means between groups. The use of the proposed approach is demonstrated with a number of examples with simulated data and a real data set of archeological artifacts. Copyright © 2011 John Wiley & Sons, Ltd.     

Fractions as Subtraction: An Activity‐Oriented Perspective from Elementary Children

A sample of third‐, fourth‐, and fifth‐grade student responses to the question “What is a fraction?” were examined to gain an understanding of how children in upper elementary grades make sense of fractions. Rather than measure children's understanding of fractions relative to mathematically conventional part–whole constructions of fractions, we attempted to understand children's actions and processes. A small but nontrivial group of children used subtraction (takeaway and removal) as a framework for understanding how fractions were created and written. An analysis of the content of their responses as well as a comparison of the performance of these children with that of children who used other ways of describing fractions suggests that the use of subtraction may be a reasonable (or at least not harmful) way for children to begin to access concepts related to fractions. Also, this study suggests that attention to children's understanding through the lens of children's activity might reveal ways of thinking and insights that are masked when we compare children's thinking in more structured research settings.     

Investigating statistical approximations with computer graphics

This paper describes the use of interactive computer graphics software to explore the notion of the approximation of one statistical distribution by another. In particular, the authors illustrate how such programs can be used to investigate the normal approximation to the binomial distribution, the Poisson approximation to the binomial distribution, the convergence of t‐distributions to the normal distribution, and the limiting behaviour of the chi‐squared distribution. The discussions include possible methods using such programs, either in a classroom setting on a demonstration basis or on an individual student basis for independent study in a computer laboratory setting.     

Experienced engineers becoming mathematics teachers: preliminary perceptions of mathematics teaching

Engineers who choose to change careers and become mathematics teachers are a specific group as far as their mathematics learning in the context of engineering and their previous work experience are concerned. Regarding mathematics, they mainly engaged in applied mathematics associated with engineering, which is a highly practical field. This research explores experienced engineers’ perceptions of mathematics teaching-related topics, before starting their studies in a pre-service mathematics teacher preparation programme. This research explores their perceptions of mathematics as a discipline, mathematics teaching and mathematical understanding. The qualitative research involves three mechanical engineers, two industrial management engineers, and an electrical engineer. Semi-structured interviews were conducted before the beginning of the programme, and analysed qualitatively. The participants view engineering as an applied and changing discipline while perceiving mathematics as closed, rigorous, accurate, systematic, theoretical and as a tool for engineering. They mostly address general features of mathematics teaching while expressing a more multifaceted view of mathematical understanding. Due to the specific characteristics of the participants, this study may contribute to planning mathematics teacher preparation programmes for engineers.     

The numerical evaluation of the error term in Gaussian quadrature rules

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.     

三聚氰胺金属(II)配合物的结构、紫外-可见光谱和反应活性

三聚氰胺是婴幼儿“肾结石事件”的重要前体. 本文选取几个典型的二价金属离子与三聚氰胺(L)形成的三聚氰胺金属配合物ML2(OH)2(M=Ca, Mg, Zn, Cu, Ni, Fe), 使用密度泛函理论(DFT)、含时DFT和概念DFT等工具, 系统地计算和比较了ML2(OH)2的结构、紫外-可见光谱和反应性质的异同. 模拟结果揭示了ML2(OH)2的结构、光谱及其反应性质是一类不同于其前体L, 形成ML2(OH)2配合物后, 将有较高的亲电指数和较低的化学硬度以及呈现红外吸收峰红移; 在这些典型的二价金属配合物中, 金属M离子电荷与配体O和N原子之间的电荷、以及与金属M离子和配体原子之间的二级微扰相互作用能, 配合物最低空轨道能级与其亲电反应指数、最低空轨道能级与化学硬度指数等方面, 存在着一系列定量的相关关系, 相关系数(R2)达0.889-0.997; 前线分子轨道模拟结果表明, ML2(OH)2体系反应活性的差异源于金属离子对前线轨道贡献有所不同, FeL2(OH)2、CuL2(OH)2、NiL2(OH)2等过渡金属离子的配合物中, 金属离子贡献较多, 共价性成分较多. 这些结果将为进一步理解人体内三聚氰胺致结石的成因提供有益的启示.     

概念密度泛函理论及近来的一些进展

概念密度泛函理论(又称密度泛函活性理论或化学密度泛函理论)是密度泛函理论(DFT)的化学活性理论. 本文对其理论框架和最新进展进行了概述, 包括电负性、硬度、软度、福井函数、亲电性, 及其从这些概念中得到的原理. 介绍了二元描述符和立体效应定量描述的新进展, 并对今后的发展作出了展望.     

理科职前教师科学模型理解的调查研究

就科学模型的理解对553名理科职前教师进行问卷调查。结果发现：（1）职前教师对科学模型的认识处于中上水平,仍需进一步提高;（2）科学模型的多个维度之间职前教师的理解水平相当;（3）职前教师对科学模型的认识并非随年级逐渐递增,具有不稳定性、反复性;（4）专业学习内容的差异对教师科学模型的认识有着重要影响;（5）科学模型的认识性别差异不明显。基于此提出了关于理科职前教师教育中加强科学模型教学的3点启示。     

Interpretation of environmental tracer data for conceptual understanding of groundwater flow: an application for fractured aquifer systems in the Kłodzko Basin,Sudetes, Poland

Environmental isotopes and hydrogeological data have been used for the construction of a conceptual model of fresh groundwater flow in the K?odzko Basin, Sudetes, Poland. The model has allowed the verification of a groundwater circulation scheme resulting from the general morphological assumptions and the recharge role to the surrounding mountains. Combined interpretation of the tritium ages and the isotopic altitude effect allowed determining the volume of water-bearing rock V_r and hydrogeological parameters of systems drained by springs and wells. Prior to the final determination of the recharge zone of individual objects, calculations were made for the thickness of the flow zone (h) and the distance from the recharge zone to the drainage point (L). The recharge areas for springs are located within a distance of 1–1.5 km and are characterized by a width of 0.75–1.65 km. The recharge area of wells is located in significantly longer distances of 2.1–12 km but yet definitely lower width. The recharge of groundwater from the Western direction seems to be obvious for all the wells and springs located westward from Nysa K?odzka River. The eastern component of the recharge appeared during the interpretation of the well in D?ugopole.

Dedicated to Professor Peter Fritz on the occasion of his 80th birthday