On Minimal Asymptotic Bases

Mathematical Notes - Let $$\mathbb N$$ denote the set of all nonnegative integers, and let $$A\subseteq\mathbb N$$ . Let $$h,n\in\mathbb N$$ , $$h\ge 2$$ and $$r_h(A,n)=\#\{(a_1,\dots,a_h)\in...     

On the first eigenvalue of the mean finsler-laplacian

In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.     

STEAM教育跨学科思维评价研究——基于化学师范生的实证分析

跨学科思维是个体在解决复杂问题时,基于学科知识间的内在联系寻找问题解决方案的思维方式。基于SOLO分类理论和STEM教育的“融合斜面”构建跨学科思维评价框架,采用NVivo12分析软件依据“STEAM金字塔结构框架”对93位化学师范生的STEAM项目的任务分解资料进行编码和统计,分析化学师范生跨学科思维发展水平。以期为进一步寻求化学师范生跨学科思维高水平发展的策略提供参考。     

不同版本高中化学教科书中学生必做实验的分析与启示——基于“科学探究与创新意识”素养

以人教版、苏教版、鲁科版(2019年版)和沪科版(2020年版)高中化学教科书中的学生必做实验文本为研究对象,基于“科学探究与创新意识”素养构建高中化学教科书中学生必做实验文本的分析框架,分析和比较4个版本教科书中学生必做实验文本“科学探究与创新意识”素养的体现及其异同,为学生必做实验教学提供启示和建议。     

A Triply Negatively Charged Nanographene Bilayer with Spin Frustration

We report on the largest open-shell graphenic bilayer and also the first example of triply negatively charged radical π-dimer. Upon three-electron reduction, bilayer nanographene fragment molecule (C₉₆H₂₄Ar₆)₂ (Ar=2,6-dimethylphenyl) ( 1 ₂) was transformed to a triply negatively charged species 1 ₂^3.−, which has been characterized by single-crystal X-ray diffraction, electron paramagnetic resonance (EPR) spectroscopy and magnetic properties on a superconducting quantum interference device (SQUID). 1 ₂^3.− features a 96-center-3-electron (96c/3e) pancake bond with a doublet ground state, which can be thermally excited to a quartet state. It consists of 34 π-fused rings with 96 conjugated sp² carbon atoms. Spin frustration is observed with the frustration parameter f>31.8 at low temperatures in 1 ₂^3.−, which indicates graphene upon reduction doping may behave as a quantum spin liquid.     

Photosynthesis of Benzonitriles on BiOBr Nanosheets Promoted by Vacancy Associates

Photocatalytic organic functionalization reactions represent a green, cost-effective, and sustainable synthesis route for value-added chemicals. However, heterogeneous photocatalysis is inefficient in directly activating ammonia molecules for the production of high-value-added nitrogenous organic products when compared with oxygen activation in the formation of related oxygenated compounds. In this study, we report the heterogeneous photosynthesis of benzonitriles by the ammoxidation of benzyl alcohols (99 % conversion, 93 % selectivity) promoted using BiOBr nanosheets with surface vacancy associates. In contrast, the main reaction of catalysts with other types of vacancy sites is the oxidation of benzyl alcohol to benzaldehyde or benzoic acid. Experimental measurements and theoretical calculations have demonstrated a specificity of vacancy type with respect to product selectivity, which arises from the adsorption and activation of NH₃ and O₂ that is required to promote subsequent C−N coupling and oxidation to nitrile. This study provides a better understanding of the role of vacancies as catalytic sites in heterogeneous photocatalysis.