Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.     

浮升力和流动加速对超临界CO2管内流动传热影响

基于单相流体的概念,超临界流体的异常传热行为已经被研究很多年了,但是关于其流动传热机理仍没有统一的认识.本文通过理论分析和实验研究了超临界二氧化碳在竖直管内向上流动过程中,浮升力和流动加速效应对其流动结构和传热过程的影响.结果表明,没有确凿的实验证据表明超临界流体的异常传热行为是浮升力和流动加速直接导致的,存在的估计浮升力和流动加速效应准则均是在常物性流体的基础上,做了大量假设得出的,不同的研究者采用浮升力和流动加速准则分析超临界流体的传热恶化得出的结论不一致.最后,基于拟沸腾理论分析超临界流体的传热恶化过程,提出超临界沸腾数区分了超临界流体正常传热与恶化传热的转换边界,为超临界流体流动传热研究提供新思路,超临界沸腾数对建立用于不同技术的超临界流体动力循环的最佳运行条件具有重要意义.     

Sulfonic acid-functionalized Fe3O4-supported magnetized graphene oxide quantum dots: A novel organic-inorganic nanocomposite as an efficient and recyclable nanocatalyst for the synthesis of dihydropyrano[2,3-c]pyrazole and 4H-chromene derivatives

In this research, the main emphasis has been focused on the preparation of a novel Fe₃O₄-supported propane-1-sulfonic acid-grafted graphene oxide quantum dots (Fe₃O₄@GOQD-O-(propane-1-sulfonic acid)) that it was readily synthesized via a five-step procedure as a hitherto unreported magnetic nanocatalyst. This newly prepared Fe₃O₄@GOQD-O-(propane-1-sulfonic acid) nanocomposite was structurally well-established by different analytical techniques including Fourier transform infrared (FT-IR), X-ray diffraction (XRD), energy-dispersive X-ray (EDX), thermal gravimetric analysis (TGA), field emission gun-scanning electron microscope (FESEM), high-resolution transmission electron microscopy (HRTEM) and vibrating sample magnetometer (VSM) analyses. The high catalytic performance of this nanocomposite was exhibited in one-pot synthesis of dihydropyrano[2,3-c]pyrazole and 4H-chromene derivatives under mild conditions. Low reaction times, excellent yields of the products, benignity of the catalyst, easy reaction work-up and magnetic recyclability of the catalyst are the main advantages of the present protocol. Also, our research indicated that the Fe₃O₄@GOQD-O-(propane-1-sulfonic acid) could be reused up to five times without considerable loss of catalytic activity.     

Photoinduced Decarboxylative Amino-Fluoroalkylation of Maleic Anhydride

A photoinduced decarboxylative three-component coupling reaction involving amine, maleic anhydride, and fluorinated alkyl iodides has been developed, leading to synthetically valuable fluoroalkyl-containing acrylamides with a high E selectivity. A broad array of substrates including monoprotected amino acid are capable coupling partners. Preliminary mechanistic studies suggest a stepwise process. This reaction represents the first example of photoinduced decarboxylative difunctionalization of maleic anhydride.     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

Real-time accurate Free-Form Deformation in terms of triangular Bezier surfaces

We implemented accurate FFD in terms of triangular Bezier surfaces as matrix multiplications in CUDA and rendered them via OpenGL. Experimental results show that the proposed algorithm is more efficient than the previous GPU acceleration algorithm and tessel- lation shader algorithms.     

Corona[5]arenes Accessed by a Macrocycle-to-Macrocycle Transformation Route and a One-Pot Three-Component Reaction

Corona[5]arenes, a novel type of macrocyclic compound that is composed of alternating heteroatoms and para-arylenes, were synthesized efficiently by two distinct methods. In a macrocycle-to-macrocycle transformation approach, S₆-corona[3]arene[3]tetrazine underwent sequential S_NAr reactions with HS-C₆H₄-X-C₆H₄-SH (X=S, CH₂, CMe₂, SO₂, and O) to produce the corresponding corona[3]arene[2]tetrazines. Different corona[3]arene[2]tetrazine compounds were also constructed in a straightforward manner by a one-pot three-component reaction of HS-C₆H₄-X-C₆H₄-SH (X=S, CH₂, CMe₂, SO₂, and O) with diethyl 2,5-dimercaptoterephthalate and 2 equiv of 3,6-dichlorotetrazine under very mild conditions. All corona[5]arenes adopted 1,2,4-alternate conformational structures in the crystalline state yielding similar nearly regular pentagonal cavities. Both the cavity size and the electronic property of the acquired macrocycles were fine-tuned by the nature of the bridging element X.     

Visible-Light-Driven Three-Component Reaction of Unactivated Alkenes Enables Access to Monofluoro γ-Amino Acids

A strategy for the synthesis of diverse protected α-monofluoro-γ-amino acid derivatives has been developed. This reaction assembles a simple enamide, quinoxalin-2(1H)-one, and diethyl 2-bromo-2-fluoromalonate through a three-component reaction driven by visible light. The advantages of this protocol include the simplicity of its operation, mild conditions, high functional group tolerance, and applicability to a wide variety of substrates. The synthesis of this fluorine-containing amino acid derivative has significant value for potential applications in medicinal chemistry and chemical biology.     

镍催化α,β-不饱和醛的选择性α,β-双芳基化反应

三组分双官能化反应是一种高效、简便构建C―C键、C―X键的方式. 双键广泛存在于众多有机化合物中, 对双键的双官能化反应研究有巨大的应用潜力. 本工作以Ni(COD)₂为催化剂, 以芳基溴化镁、芳基溴化物为芳基化试剂, 实现了3-芳基-2-丙烯醛亚胺中碳碳双键的双芳基化反应. 该反应建立了一个新的镍催化α,β-不饱和醛的α,β-双芳基化方法, 可以高度区域选择性地向底物分子中引入两个不同取代的芳环, 得到多种2,3,3-三芳基丙醛骨架的产物. 利用这一反应作为核心步骤实现了天然产物Quebecol的简便合成. 机理研究表明, 该反应可能经历了亲核加成、金属交换、还原消除的历程.