Pre-university students square-root from squared things: A commognitive account of apparent conflicts within learners' mathematical discourses

This study explores the grasp of square roots among eleven students in a remedial mathematics course, with a special focus on where the same student generated apparently conflicting responses. Building on the commognitive framework, the analysis distinguished between routines that individual students consistently implemented in situations where roots “stood alone” and where they were incorporated in more compound exercises, where roots were extracted from square numbers and from squared radicands, where roots were applied to monomials and binomials, and where parameters named with different letters were involved. Differences were found in routines’ degree of objectification, procedures, and tasks. These differences are explained with a theoretical account, suggesting that what may seem as a conflict within a student’s discourse could be a sensible difference of actions taken in situations that this student construed as different. The contribution of this study to the body of knowledge on teaching and learning of roots and to commognitive research is discussed.     

均值-方差准则下的多期最优保险投资(英文)

近年来,最优保险投资问题吸引了越来越多的注意。一般这个问题是在连续时间框架下来研究的。本文针对这一问题建立离散时间的最优控制模型。应用动态规划原理求解模型对应的近似问题,得到了最优投资策略和投资有效边界的解析表达形式。本文得到的最优投资策略和投资有效边界均依赖于承保参数。通过数值例子分析了承保参数对最优投资策略和有效边界的影响。     

Characterization and gas adsorption of a novel three‐dimensional metal–organic framework (MOF) generated from a new polydentate fluorene‐bridged ligand

A polydentate ligand bridged by a fluorene group, namely 9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene (L), has been prepared under solvothermal conditions in acetonitrile. Crystals of the three‐dimensional metal–organic framework (MOF) poly[[[μ₃‐9,9‐bis(2‐hydroxyethyl)‐2,7‐bis(pyridin‐4‐yl)fluorene‐κ³N:N′:O]bis(methanol‐κO)(μ‐sulfato‐κ²O:O′)nickel(II)] methanol disolvate], {[Ni(SO₄)(C₂₇H₂₄N₂O₂)(CH₃OH)]·2CH₃OH}_n, (I), were obtained by the solvothermal reaction of L and NiSO₄ in methanol. The ligand L forms a two‐dimensional network in the crystallographic bc plane via two groups of O—H…N hydrogen bonds and neighbouring two‐dimensional planes are completely parallel and stack to form a three‐dimensional structure. In (I), the Ni^II ions are linked by sulfate ions through Ni—O bonds to form inorganic chains and these Ni‐containing chains are linked into a three‐dimensional framework via Ni—O and Ni—N bonds involving the polydentate ligand L. With one of the hydroxy groups of L coordinating to the Ni^II atom, the torsion angle of the hydroxyethyl group changes from that of the uncoordinated molecule. In addition, the adsorption properties of (I) with carbon dioxide were investigated.     

Ultrasound assisted synthesis of amide functionalized metal-organic framework for nitroaromatic sensing

Nano plates of zinc(II) based metal-organic framework (MOF) were prepared via ultrasonic method without any surfactants at room temperature and atmospheric pressure. Control of particle size and morphology was enhanced in this synthesis method. Nano plates of an interpenetrated amide-functionalized metal-organic framework, [Zn₂(oba)₂(bpfb)]·(DMF)₅, TMU-23, (H₂oba = 4,4′-oxybis(benzoic acid); bpfb = N,N′-bis-(4-pyridylformamide)-1,4-benzenediamine, DMF = N,N-dimethyl formamide), was synthesized under ultrasound irradiation in different concentrations of initial precursor. The nano structure and morphology of the synthesized MOF were characterized by Field Emission Scanning Electron Microscopy (FE-SEM), powder X-ray diffraction, thermo gravimetric analysis (TGA), elemental analysis and FTIR spectroscopy. Moreover, Fluorescence emissions of nanoplates have been studied. Amide-functionalized MOF shows high selectivity for sensing of nitroaromatic compounds such as nitrophenol, nitroaniline, and nitrobenzene in acetonitrile solution. Fluorescence intensity decreased with increasing contents of nitroaromatics in acetonitrile solution due to fluorescence quenching effect.     

Two-Dimensional MOF and COF Nanosheets: Synthesis and Applications in Electrochemistry

Metal–organic framework (MOF) and covalent organic framework (COF) nanosheets are a new type of two-dimensional (2D) materials with unique design principles and various synthesis methods. They are considered ideal electrochemical devices due to the ultrathin thickness, easily tunable molecular structure, large porosity and other unique properties. There are two common methods to synthesize 2D MOF/COF nanosheets: bottom-up and top-down. The top-down strategy mainly includes ultrasonic assisted exfoliation, electrochemical exfoliation and mechanical exfoliation. Another strategy mainly includes interface synthesis, modulation synthesis, surfactant-assisted synthesis. In this Review, the development of ultrathin 2D nanosheets in the field of electrochemistry (supercapacitors, batteries, oxygen reduction, and hydrogen evolution) is introduced, and their unique dimensional advantages are highlighted.     

A Highly Stable (4, 8)-Connected Tb-MOF Exhibiting Efficiently Luminescent Sensing towards Nitroimidazole Antibiotics

A robust 4,8-connected Tb-based metal-organic framework (Tb-MOF) with paddle wheel-shaped {Tb₂(COO)₄} subunits extended by C₃-symmetric 3,3',3''-[1,3,5-benzenetriyltris(carbonylimino)]tris-benzoate connector was hydrothermally synthesized, showing highly environmental stability, good dispersion and intense green emission in water system. Resulting critically from the well suppressed absorption towards the excitation energy, the Tb-MOF exhibits rapid and efficient fluorescent response towards nitroimidazole antibiotics with strong quenching constants and low detection limits of 1.59 × 10⁴ m ^–1 and 2.4 μM for metronidazole as well as 1.62 × 10⁴ m ^–1 and 2.9 μM for dimetridazole. Moreover, the sensitive and selective identification of the Tb-MOF has strong anti-interference and excellent regeneration ability, which endows the promising applications of the Tb-MOF as fluorescent sensing materials.     

A self-penetrating and chemically stable zinc (ii)-organic framework as multi-responsive chemo-sensor to detect pesticide and antibiotics in water

Guided by the self-penetrating features can improve the stability of metal organic frameworks (MOFs), an unprecedented 3D self-penetrated framework, {[Zn (tptc)_0.5(bimb)]·H₂O}_n ( NUC-6 , here NUC corresponding to North University of China), with 3D (4,4)-c {8⁶} net, was designed. Benefit from the high chemical stability and excellent luminescent property, NUC-6 can be act as an efficient multi-response chemo-sensor in detecting dichloronitroaniline pesticide and nitrofuran antibiotics in water with the detection limits are 116 ppb for DCN pesticide, 16 ppb for NFT antibiotic, and 12 ppb for NTZ antibiotic. Besides, the mechanisms of luminescence quenching were revealed from the viewpoint of internal filter effect (IFE) and photo-induced electron transfer (PET), implied by the optical spectroscopy and quantum chemical calculation. This work provides a promising strategy to design stable MOFs by improving the self-penetrating features and to expand their practical applications in the detection of organic pollutants in aqueous medium.     

国内外化学相异构想研究的进展与启示*

国内外有关化学学科的相异构想研究主要包括对学生相异构想进行诊断及其原因分析,以及开发有效的教学模式或策略对学生相异构想进行概念转变。通过对国内外相关研究现状的分析,为相异构想的后续研究提供思路。     

New Supercage Metal–Organic Framework Based on Allopurinol Ligands Showing Acetylene Storage and Separation

To develop efficient adsorbent materials for storage and separation of C₂H₂, an unprecedented supercage MOF, [Me₂NH₂]⋅[Zn₃(ALP)(TDC)_2.5]⋅3.5DMF⋅2 H₂O ( 1 ) was constructed through medicinal molecule allopurinol (ALP) and S-containing 2,5-thiophenedicarboxylic acid (H₂TDC). 1 contains a novel linear trinuclear cluster that is composed by ALP and carboxylates and forms a final uncommon 5-connected yfy topological framework. The framework possesses three types of interlinked cages decorated by rich functional sites, and reveals not only high adsorption capacity for C₂H₂ but also excellent selective separation for C₂H₂/CO₂ and C₂H₂/CH₄ at 298 K. Dynamic breakthrough experiments on C₂H₂/CO₂ (1:1) mixture and C₂H₂/CH₄ (1:1) mixture also demonstrated the potential of the material to separate C₂H₂ from CO₂ or CH₄ mixtures. Molecular simulations were also studied to identify the different CO₂- and C₂H₂- binding sites in 1 , such as carboxylate groups, S atoms and carbonyl groups.     

Nanostructured BiVO4 Derived from Bi-MOF for Enhanced Visible-light Photodegradation

BiVO4,a promising visible-light responding photocatalyst,has aroused extensive research interest because of inexpensiveness and excellent chemical stability.However,its main drawback is the poor photoinduced charge-transfer dynamics.Building nanostructures is an effective way to tackle this problem.Herein,we put forward a new method to prepare nanostructured BiVO4 from Bi-based metal-organic frameworks[Bi-MOF(CAU-17)]precursor.The as-prepared material has a rod-like morphology inherited from the Bi-MOF sacrificial template and consists of small nanoparticle as building blocks.Compared with its counterparts prepared by conventional methods,MOF-derived nanostructured BiVO4 shows better light absorption ability,narrower bandgap,and improved electrical conductivity as well as reduced recombination.Consequently,BiVO4 nanostructure demonstrates high photocatalytic activity under visible light towards the degradation of methylene blue.Methylene blue can be degraded up to 90%within 30 min with a reaction rate constant of 0.058 min-1.Moreover,the cycling stability of the catalyst is excellent to withstand unchanged degradation efficiency for at least 5 cycles.