决策单元的变更对共协调性的影响

本文将对共协调分析的灵敏度问题进行研究,着重探讨决策单元的变更对共协调性的影响。     

Students’ coordination of lower and higher dimensional units in the context of constructing and evaluating sums of consecutive whole numbers

This paper examines how three eighth grade students coordinated lower and higher dimensional units (e.g., composite units and pairs) in the context of constructing a formula for evaluating sums of consecutive whole numbers while solving combinatorics problems (e.g., 1 + 2 + ⋯ + 15 = (16 × 15)/2). The data is drawn from the beginning of an 8-month teaching experiment. The findings from the study include: (1) a framework for understanding how students coordinate lower and higher dimensional units; (2) identification of key learning that occurred as students made the transition between solving two kinds of combinatorics problems; and (3) identification of the links between the way students’ coordinated lower and higher dimensional units and their evaluation of sums of consecutive whole numbers. Implications for research and teaching are considered.     

Mg(C3O4H2)(H2O)2: A New Ultraviolet Nonlinear Optical Material Derived from KBe2BO3F2 with High Performance and Excellent Water-Resistance

Acquiring high-performance ultraviolet (UV) nonlinear optical (NLO) materials that simultaneously exhibit a strong second harmonic generation (SHG) coefficients, as short as possible SHG phase-matching (PM) wavelength and non-hygroscopic properties has consistently posed a significant challenge. Herein, through multicomponent modification of KBe₂BO₃F₂ (KBBF), an excellent UV NLO crystal, Mg(C₃O₄H₂)(H₂O)₂, was successfully synthesized in malonic system. This material possesses a unique 2D NLO-favorable electroneutral [Mg(C₃O₄H₂)₃(H₂O)₂]_∞ layer, resulting in the rare coexistence of a strong SHG response of 3×KDP (@1064 nm) and short PM wavelength of 200 nm. More importantly, it exhibits exceptional water resistance, which is rare among ionic organic NLO crystals. Theoretical calculations revealed that its excellent water-resistant may be originated from its small available cavity volumes, which is similar to the famous LiB₃O₅ (LBO). Therefore, excellent NLO properties and stability against air and moisture indicate it should be a promising UV NLO crystal.     

Thiophene-Containing Covalent Organic Frameworks for Overall Photocatalytic H2O2 Synthesis in Water and Seawater

H₂O₂ is a significant chemical widely utilized in the environmental and industrial fields, with growing global demand. Without sacrificial agents, simultaneous photocatalyzed H₂O₂ synthesis through the oxygen reduction reaction (ORR) and water oxidation reaction (WOR) dual channels from seawater is green and sustainable but still challenging. Herein, two novel thiophene-containing covalent organic frameworks (TD-COF and TT-COF) were first constructed and served as catalysts for H₂O₂ synthesis via indirect 2e⁻ ORR and direct 2e⁻ WOR channels. The photocatalytic H₂O₂ production performance can be regulated by adjusting the N-heterocycle modules (pyridine and triazine) in COFs. Notably, with no sacrificial agents, just using air and water as raw materials, TD-COF exhibited high H₂O₂ production yields of 4060 μmol h⁻¹ g⁻¹ and 3364 μmol h⁻¹ g⁻¹ in deionized water and natural seawater, respectively. Further computational mechanism studies revealed that the thiophene was the primary photoreduction unit for ORR, while the benzene ring (linked to the thiophene by the imine bond) was the central photooxidation unit for WOR. The current work exploits thiophene-containing COFs for overall photocatalytic H₂O₂ synthesis via ORR and WOR dual channels and provides fresh insight into creating innovative catalysts for photocatalyzing H₂O₂ synthesis.     

Problem solving activities of two middle school students with distinct levels of units coordination

The aim of this study is to investigate relationships between students’ arithmetical knowledge and their proportional reasoning. Two of seven students for whom we conducted clinical interviews were selected as participants in the study. An analysis of their solutions to four different types of multiplicative problems (equal sharing, reversible multiplicative relationship, fraction composition, and proportional relationship) was conducted. Based on the analysis, we found that the student who coordinated two three-level units structures prior to activity in the first three problem types could also solve the proportion problem using the units coordination. In contrast, the student who coordinated two three-level units structures only in activity in the first three problem types could not solve the proportion problem. Given the importance of units coordinating operations in solving diverse problems, implications for further research on students’ construction of proportional reasoning are discussed.     

Ring elements as sums of units

In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph Γ(R) is a power of 2.      

The Avogadro Constant for the Definition and Realization of the Mole

The International System of Units’ (SI) base unit of the quantity “amount of substance” is the mole (symbol: mol). After the revision of the SI to be implemented in 2019, when all SI units will be based solely on constants, the mole will be defined through a fixed value of the Avogadro constant N_A. One mole contains exactly 6.02214076 × 10²³ elementary entities, meaning the mole will no longer be linked to the kilogram. Currently, the mole is defined via the mass of exactly 0.012 kg of the ¹²C isotope which links it to the kilogram prototype. The history, changes, and implications of the revised definition of the mole are discussed here from the chemist's point of view. The ability to count entities such as atoms or molecules (precisely enough to enable a revision of the SI and preserve consistency of previous and future measurements) is crucial. This is achieved with the realization (Mise en Pratique) based on the X‐ray‐crystal density (XRCD) method (counting the atoms in a silicon sphere). The determination of N_A, focusing on the measurement of the molar mass of silicon highly enriched in the ²⁸Si isotope, with the lowest uncertainty so far, is presented.     

Absolute frequency and isotope shift measurements of the cooling transition in singly ionized indium

We report greater than two orders of magnitude improvements in the absolute frequency and isotope shift measurements of the In⁺ 5s^{2 1}S₀ (F = 9/2)–5s5p ³P₁ (F = 11/2) transition near 230.6 nm. The laser-induced fluorescence from a single In⁺ in a radio-frequency trap is detected. The fourth-harmonic of a semiconductor laser is used as the light source. The absolute frequency is measured with the help of a frequency comb referenced to a Cs atomic clock. The resulting transition frequencies for isotopes ¹¹⁵In⁺ and ¹¹³In⁺ are measured to be 1 299 648 954.54(10) MHz and 1 299 649 585.36(16) MHz, respectively. The deduced cooling transition frequency difference is 630.82(19) MHz. By taking into account of the hyperfine interaction, the isotope shift is calculated to be 695.76(1.68) MHz.     

A New 3-D Network Based on Large Mo18-Polyoxometalate Anionic Units and Alkaline Cations

The new polyoxomolybdate 1 was prepared from an aqueous solution by the reaction of Na2MoO4·H2O, NH2NH2·2HCl and HCOONa, and characterized by IR spectroscopy, elemental analysis and single-crystal X-ray structural analysis. Crystal data: C4H72ClMo18Na13O94, Mr = 3685.86, triclinic, space group P, a = 11.922(5), b = 15.003(5), c = 15.171(5) , α = 116.073(5), β = 112.593(5), γ = 93.342(5)o, V = 2164.3(14) 3, Z = 1, Dc = 2.828 g/cm3, F(000) = 1764, μ = 2.741 mm-1, R = 0.0349 and wR = 0.0875 (I > 2σ(I)). X-ray crystal structure analysis shows that 1 is constructed by Mo18 polyoxoanions linked by Na+ cations to form a fascinating 3D open framework with “guest” Na+ cations and formyl groups residing in the channels.