Constitutive Generalization of a Microstructure‐Based Model for Filled Elastomers

A microstructure‐based model of rubber reinforcement is presented describing filler‐induced stress softening and hysteresis by the breakdown and re‐aggregation of strained filler clusters. An extension of the previously introduced dynamic flocculation model, it considers incomplete deformation cycles that occur in the simulation of arbitrary deformation histories. For these inner cycles additional elastic stress contributions of clusters are taken into account. A constitutive generalization of the model is introduced by referring to the engineering concept of representative directions. This allows for an implementation of the model into FE codes. Fair agreement between measurement and simulation is obtained for CB‐filled EPDM, loaded along various deformation histories.

     

The fractional knowledge and algebraic reasoning of students with the first multiplicative concept

To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. Six students with each of three different multiplicative concepts participated. This paper reports on the fractional knowledge and algebraic reasoning of six students with the most basic multiplicative concept. The fractional knowledge of these students was found to be consistent with prior research, in that the students had constructed partitioning and iteration operations but not disembedding operations, and that the students conceived of fractions as parts within wholes. The students’ iterating operations facilitated their work on algebra problems, but the lack of disembedding operations was a significant constraint in writing algebraic equations and expressions, as well as in generalizing relationships. Implications for teaching these students are discussed.     

A simple proof of the generalized Ceva theorem by the principle of equilibrium

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics.     

On the content-dependence of prospective teachers’ knowledge: a case of exemplifying definitions

In this article, we demonstrate that prospective teachers’ content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers’ knowledge. We asked prospective secondary mathematics teachers to provide multiple examples of definitions of concepts from different areas of mathematics. We examined teacher-generated examples of concept definition and analysed individual and collective example spaces, focusing on their correctness and richness. We demonstrate differences in prospective teachers’ knowledge associated with defining mathematical concepts in geometry, algebra and calculus.     

离子色谱的新概念--不用化学试剂,只用水

不用化学试剂只用水的离子色谱（Reagent Free Ion Chromatography,RFIC）是2003年才问世的新一代色谱技术,荣获2003年Pitteon会议金奖。本文将详细讨论这一技术的基本原理和应用。     

"高分子化学"课程有关概念和公式研究

高分子化学是研究聚合反应机理和聚合方法的一门科学,是高分子科学的基础。基本概念确切,公式应用的条件明确,有助于学生对基本概念和基本理论的深入理解,有助于高分子设计和高分子合成的科学研究。     

基于扰动状态概念的结构性粘土本构模型研究

考虑结构性粘土的本构模型研究中存在的问题．引入了Desai C S的扰动状态概念,并对关键参数——扰动函数进行了扩展,增加了土体体积应变的影响,建立了结构性粘土的弹塑性扰动状态本构模型．最后通过三轴不排水剪切试验对模型进行了检验,结果表明该模型反映了上体的变形特征,说明在类似条件下能较好的满足工程实际的要求．     

综合集成研讨厅的几个示例

顺应于国际系统反思的浪潮,以钱学森为首的我国系统科学家于1990年正式提出了从定性到定量综合集成方法论用以处理以往还原论所无法解决的开放复杂巨系统问题.1992年钱学森又继而提出了综合集成研讨厅的概念(简称为HWMSE)作为该方法论的实践平台,其中特别强调利用信息技术的优势.此后,不断有HWMSE的研制来体现综合集成方法论的功力,同样也引来质疑.通过3个未自称为HWMSE的示例,包括国外实验室反恐系统、笔者提出的“在线会场”及众所周知的搜索引擎,对每一个示例阐明了其中含有的构成研讨厅的专家体系、机器体系与知识体系的内容及在该研讨厅中正在进行的综合集成复杂问题求解的活动.期望以此扩展对HWMSE功能的理解,促进HWMSE的推广和综合集成方法论的实践.     

The molecular composition of non-modified and acac-modified propoxide and butoxide precursors of zirconium and hafnium dioxides

Long-term storage at 0 °C of a paraffin-sealed flask with commercial 70 wt% solution of zirconium n-propoxide in n-propanol resulted in crystallization of an individual oxoalkoxide complex Zr₄O(OⁿPr)₁₄(ⁿPrOH)₂ in over 20% yield. The structure of this molecule can be described as a triangular Zr₃(μ₃-O)(OR)₁₀(ROH) core of 3 edge-sharing octahedrons with an additional Zr(OR)₄(ROH) unit attached through a pair of (μ-OR) bridges. Mass spectrometric and ¹H NMR investigation of the commercial samples of the most broadly applied zirconium and hafnium n-propoxides and n-butoxides indicate the presence of analogous species in the commercial alkoxide precursors. The content of oxo-alkoxide species in the commercial precursors has been estimated to be ~20% for n-propoxide and ~35% for zirconium n-butoxide. A new route has been presented for synthesis of the individual crystalline mixed ligand precursor [Zr(OⁿPr)(OⁱPr)₃(ⁱPrOH)]₂, from zirconium n-propoxide. A high yield has been observed (~90%), indicative of an almost complete precursor transformation. Mass spectrometry has shown that the synthesized mixed ligand precursor is dimeric, which makes it an attractive alternative to zirconium n-propoxide. Addition of 1 eq of Acetylacetone to zirconium or hafnium alkoxide precursors results in formation of dimeric [M(OR)₃(acac)]₂ in high yields. These species have limited stability (much higher for Hf than for Zr) and transform in solution into hydrolysis-insensitive M(acac)₄ through very unstable M(acac)₃(OR) intermediates containing 7-coordinated metal centers. This transformation can be followed kinetically in hydrocarbon solvents by ¹H NMR and is noticeably accelerated by addition of parent alcohols. The obtained results clearly reveal limited applicability of EXAFS and XANES techniques for the study of such systems, especially in the context of structure prediction. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

离子反应中几个问题的质疑

对离子反应的概念、离子反应的实质、离子方程式表示的意义及离子方程式的书写步骤产生质疑,指出这些问题并纠正。