关于高等代数题解的五种方法

介绍处理高等代数习题的标准形式化方法、公理化方法、模型转换方法、形式统一性方法和形态联想方法,并给出实例加以说明.     

电感耦合等离子体原子发射光谱法(ICP-OES)测定铍铀伴生矿石中的铍

建立了电感耦合等离子体原子发射光谱法(ICP-OES)测定铍铀伴生矿石中的铍的方法,研究了酸溶-碱熔融法溶样过程中加入的焦硫酸钾,对ICP-OES法测定铍铀伴生矿石中的铍含量产生的基体干扰问题。主要阐述消除基体干扰的一些措施。从实验数据可知,控制称样量、焦硫酸钾加入量、定容体积和加标稀释倍数,能够有效消除焦硫酸钾对ICP-OES法测定结果的基体干扰,6次平行测定结果的相对标准偏差为3.4%,加标回收率为98.7%~104.4%,实验表明,方法准确、可靠。     

Standard Koszul standardly stratified algebras

In this paper, we prove that every standard Koszul (not necessarily graded) standardly stratified algebra is also Koszul. This generalizes a similar result of [3 Ágoston, I., Dlab, V., Lukács, E. (2003). Quasi-hereditary extension algebras. Algebras Represent. Theory 6:97–117.[Crossref], [Web of Science ®] , [Google Scholar]] on quasi-hereditary algebras.     

Analytic invariant curves for an iterative equation related to dissipative standard map

In this paper, we study existence of invariant curves of an iterative equation which is from dissipative standard map. By constructing an invertible analytic solution g (x ) of an auxiliary equation of the form invertible analytic solutions of the form g (λ g  ^? 1(x )) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < |λ | < 1, we focus on those λ on the unit circle S ¹, that is, |λ | = 1. We discuss not only those λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhancing Built-in Electric Fields for Efficient Photocatalytic Hydrogen Evolution by Encapsulating C60 Fullerene into Zirconium-Based Metal-Organic Frameworks

High-efficiency photocatalysts based on metal-organic frameworks (MOFs) are often limited by poor charge separation and slow charge-transfer kinetics. Herein, a novel MOF photocatalyst is successfully constructed by encapsulating C₆₀ into a nano-sized zirconium-based MOF, NU-901. By virtue of host-guest interactions and uneven charge distribution, a substantial electrostatic potential difference is set-up in C₆₀@NU-901. The direct consequence is a robust built-in electric field, which tends to be 10.7 times higher in C₆₀@NU-901 than that found in NU-901. In the catalyst, photogenerated charge carriers are efficiently separated and transported to the surface. For example, photocatalytic hydrogen evolution reaches 22.3 mmol g⁻¹ h⁻¹ for C₆₀@NU-901, which is among the highest values for MOFs. Our concept of enhancing charge separation by harnessing host-guest interactions constitutes a promising strategy to design photocatalysts for efficient solar-to-chemical energy conversion.     

Rhodium-Catalyzed Regio- and Diastereoselective [3+2] Cycloaddition of gem-Difluorinated Cyclopropanes with Internal Olefins

Direct synthesis of gem-difluorinated carbocyclic molecules represents a longstanding challenge in organic chemistry. Herein, a Rh-catalyzed [3+2] cycloaddition reaction between readily available gem-difluorinated cyclopropanes (gem-DFCPs) and internal olefins has been developed, enabling the efficient synthesis of gem-difluorinated cyclopentanes with good functional group compatibility, excellent regioselectivity and good diastereoselectivity. The resulting gem-difluorinated products can undergo downstream transformations to access various mono-fluorinated cyclopentenes and cyclopentanes. This reaction demonstrates the use of gem-DFCPs as a type of “CF₂” C3 synthon for cycloaddition under transition metal catalysis, which provides potential strategy for synthesizing other gem-difluorinated carbocyclic molecules.     

电感耦合等离子体质谱（ICP-MS）法测定黄精中15种稀土元素及其指纹图谱绘制

为了准确测定黄精中稀土元素的含量,采用电感耦合等离子体质谱（ICP-MS）法同时测定黄精中15种稀土元素（La、Ce、Pr、Nd、Pm、Sm、Eu、Gd、Tb、Dy、Ho、Er、Tm、Yb、Lu）的含量,进而绘制稀土元素指纹图谱,以稀土元素含量的平均值构建黄精稀土元素标准指纹图谱,作为鉴定黄精中药材的参考依据。黄精样品采用微波消解法处理后,通过在线引入内标溶液,采用ICP-MS法测定15种稀土元素的含量,采用OriginPro 2021绘制稀土元素指纹图谱和进行主成分分析,采用SPSS 26.0进行聚类分析。15种稀土元素的线性关系、重复性、精密度良好,平均加标回收率在97.0%~103.3%,相对标准偏差小于等于1.74%。黄精中Ce、La、Nd含量相对较高,Ce含量为53.02～2004.58 μg/kg,位居第一。聚类分析和主成分分析结果表明,样品聚为2类,同一产地的样品能够较好地聚在一起。黄精药材中15种稀土元素的指纹图谱具有相似的分布形态,具有较强的特征性和一致性,相似度均大于0.950。该方法操作简单,准确可靠,能满足实验分析要求,可为黄精的质量控制和药理研究提供参考;建立的指纹图谱可用于黄精的鉴别。     

Si内标-X射线衍射法定量测定铁矿中Fe3O4、Fe2O3和SiO2

铁矿物相的准确定量对矿物价值评价及选冶工艺研究有重要作用,现有化学法流程复杂效率低,X射线衍射全谱拟合法可溯源性差,结果准确性难以评价和验证。本研究建立了以Si为内标,以Cu靶X射线为辐射光源,步进扫描方式获得衍射谱图,以待测相含量为横坐标,待测相与内标相峰面积比值为纵坐标建立校准曲线,以曲线对铁矿中Fe3O4、Fe2O3和SiO2物相进行定量的方法。试验对制样条件、扫描参数、内标物选择、积分方式、重叠峰校正等进行了优化选择,结果表明,试样全部通过45 μm标准筛,Si内标比例为10%,步进长度0.01°,步进时间30S,选择对Fe3O4（311）、Fe2O3（104）、SiO2（011）和Si（111）的衍射峰进行积分强度计算,可获得最优结果。在选定工作条件下,Fe3O4在1.07～100%范围内线性相关系数(R2)为0.9953,相对标准偏差(RSD)1.1%～13.2% (n=6),加标回收率99.7 %~114.8 %,检出限(LOD)4.29%;Fe2O3在1.51～100%范围内线性相关系数(R2)为0.9991,相对标准偏差(RSD)2.8%～10.6% (n=6),加标回收率87.1%~112.2%,检出限(LOD)2.56%;SiO2在0.79～29.72 %范围内线性相关系数(R2)为0.9957,相对标准偏差(RSD)3.2%～10.3% (n=6),加标回收率86.6%~98.9%,检出限(LOD)0.68%。方法易溯源、准确性易评价和验证,适合开展标准化检测和应用。     

硫代硫酸钠标准溶液配制中标定基准物质的优化选择

对硫代硫酸钠标准溶液配制实验中不同基准物质的标定效果进行了对比研究,结合试剂用量、反应时间、显著性检验等分析说明不同基准物质所产生的结果:重铬酸钾、碘酸钾、溴酸钾均可实现对硫代硫酸钠溶液的标定。其中溴酸钾作为标定的基准物质时,试剂用量少,反应时间短,实验费用低且终点易于观察。双侧t检验符合统计学要求,更适用于硫代硫酸钠溶液标定,有望引入学生实验。     

N-Tosylhydrazone as an oxidizing directing group for the redox-neutral access to isoquinolines via Cp1Co(III)-Catalyzed C–H/N–N activation

Herein, an efficient and economic access has been revealed for the synthesis of isoquinolines via C–H bond activation strategy by using comparatively inexpensive and versatile cobalt catalyst. A hardly investigated directing group, N-tosylhydrazone has been effectively applied as an internal oxidant for an annulation reaction with internal alkynes via C–H/N–N bond functionalization. This catalytic protocol works for the extensive variety of substrates in moderate to excellent yields under external oxidant-free conditions. Additionally, the proposed protocol has advantages such as broad substrate coverage with significant product yields, readily synthesized substrates as well as scalability up to the gram quantity which further improves the competency of the methodology.