弹簧参与的微小振动一定是简谐运动吗

振动和波动是生活中的一种非常普遍而重要的运动形式,其中简谐振动是最简单、最基本的运动,弹簧振子是研究简谐运动的最基本模型.在研究弹簧参与的微小振动时,部分学生不能很好的判定弹簧参与的微小振动是否为简谐运动.本文讨论了系统作简谐运动的充要条件,并通过4个具体例子详细分析了弹簧参与的微小振动.     

Effects of carbon contents on morphology and electrical properties of Li2MnSiO4/C prepared by a vacuum solid-state method

To improve the electrochemical performance of Li₂MnSiO₄ with low electric conductivity, the Li₂MnSiO₄/C composite are synthesized by a vacuum solid-state reaction of a mixture of SiO₂, LiCH₃COO, Mn(CH₃COO)₂ and designed mass of C₆H₁₂O₆ · H₂O as carbon sources. The crystalline structure and morphology of products are analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM) and laser scattering technology (LS) respectively. The tested results show that carbon doping decrease the crystallite sizes of products, but keep the aggregation of the particles and made the impurity increased instead. The results of constant current charge-discharge prove that the mixed carbon improve Li⁺ transmission performance and decrease inner polatization resistance of Li₂MnSiO₄ materials, but can not prevent the collapse of Li₂MnSiO₄ crystal structure. While the galvanostatic intermittent titration technique (GITT) results demonstrate that the primary reason for the improved electrochemical performance can be attributed to increased Li-ion diffusion coefficient $(D_{Li^ + } )$ as a result from carbon doping.     

Exceedingly Fast Copper(II)‐Promoted ortho CH Trifluoromethylation of Arenes using TMSCF3

The direct ortho‐trifluoromethylation of arenes, including heteroarenes, with TMSCF₃ has been accomplished by a copper(II)‐promoted C? H activation reaction which completes within 30 minutes. Mechanistic investigations are consistent with the involvement of C? H activation, rather than a simple electrophilic aromatic substitution (S_EAr), as the key step.     

Divergent Total Synthesis of Euphoranginol C,Euphoranginone D,ent-Trachyloban-3β-ol,ent-Trachyloban-3-one,Excoecarin E,and ent-16α-Hydroxy-atisane-3-one

A divergent synthetic approach to biogenetically related diterpenoids such as ent-kauranes, ent-trachylobanes, ent-beyerane, and ent-atisane has been developed. The unified synthetic route involves the De Mayo reaction to rapidly generate the bicyclo[3.2.1]-octane moiety of ent-kaurane. The key reactions also include bioinspired nucleophilic cyclopropanation generating the [3.2.1.0^2,7]-tricyclic core of ent-trachylobane and regioselective cyclopropane fragmentation furnishing ent-beyerane and ent-atisane through the nucleophilic attack and protonation of the cyclopropane ring. This strategy enables the asymmetric total syntheses of six diterpenoids from the commercially available geraniol.     

A Supported Bismuth Halide Perovskite Photocatalyst for Selective Aliphatic and Aromatic C–H Bond Activation

Direct selective oxidation of hydrocarbons to oxygenates by O₂ is challenging. Catalysts are limited by the low activity and narrow application scope, and the main focus is on active C−H bonds at benzylic positions. In this work, stable, lead-free, Cs₃Bi₂Br₉ halide perovskites are integrated within the pore channels of mesoporous SBA-15 silica and demonstrate their photocatalytic potentials for C−H bond activation. The composite photocatalysts can effectively oxidize hydrocarbons (C₅ to C₁₆ including aromatic and aliphatic alkanes) with a conversion rate up to 32900 μmol g_cat⁻¹ h⁻¹ and excellent selectivity (>99 %) towards aldehydes and ketones under visible-light irradiation. Isotopic labeling, in situ spectroscopic studies, and DFT calculations reveal that well-dispersed small perovskite nanoparticles (2–5 nm) possess enhanced electron–hole separation and a close contact with hydrocarbons that facilitates C(sp³)−H bond activation by photoinduced charges.     

Palladium‐Catalyzed Asymmetric [4+3]‐Cyclization Reaction of Fused 1‐Azadienes with Amino‐trimethylenemethanes: Highly Stereoselective Construction of Chiral Fused Azepines

Summary of main observation and conclusion A Pd-catalyzed asymmetric aromative[4+3]-cyclization reaction of amino-trimethylenemethanes(TMM,1d,ip3-oles)with fused 1-azadienes has been developed.This method enables access to the synthetically importance and biologically active benzofuran fused azepines and indeno-azepines in excellent efficiency and stereoselectivity(up to 95%yield,99%ee,>19:1 dr).     

具有高机械强度的掺Er3+∶TeO2-Nb2O5玻璃的光谱性质研究

熔制了掺铒碲铌玻璃样品(100-XTeO2-XNb2O5(X=5,10,15,20 mol%),测试了其密度、折射率、转变温度、析晶温度、维氏机械强度、吸收光谱、荧光光谱、荧光寿命等参量。利用Judd-Ofelt和McCumber理论分别计算了铒离子强度参量Ωt (t=2, 4, 6)和受激发射截面σemi的大小,研究了掺铒碲铌玻璃样品光谱参量对Nb2O5成分的依赖性,并与典型的碲锌钠玻璃（75TeO2-20ZnO-5Na2O）在热学、机械强度、光谱性质和放大品行四个方面进行了比较.     

不同溶剂中番茄红素的荧光光谱及其特性研究

用970CRT荧光光度计测定了番茄红素在正己烷、乙酸乙酯、四氢呋喃、氯仿、丙酮和苯等6种溶剂中的荧光光谱以及番茄红素在四氢呋喃溶液中不同浓度下的荧光光谱。对所测光谱分析得出:6种溶剂中荧光光谱的最大峰值波长(λmax)分别为542.5 nm5、48.2 nm5、55.0 nm、555.7 nm、556.4 nm和565.7 nm,由于溶剂效应,随溶剂极性由小到大,荧光光谱的最大峰值波长(λmax)逐渐红移,由这些峰值波长计算得出相应的番茄红素分子在6种溶剂中的跃迁能ET分别为220.5 kJ/mol2、18.2 kJ/mol2、15.6 kJ/mol2、15.3 kJ/mol2、14.9 kJ/mol和211.5 kJ/mol,可见跃迁能ET也随溶剂极性增大而降低;当番茄红素在四氢呋喃溶液中的质量浓度低于50μg/ml时,溶液的荧光强度随溶液浓度增加而增大,当质量浓度高于50μg/ml时,由于番茄红素的激发态分子与基态分子相互作用,荧光强度反而减小;在浓度低于80μg/ml的溶液中,番茄红素的荧光光谱除最大峰值外还有三个较小峰值,据此计算得出相应的番茄红素分子的跃迁能分别为E(T1)=278.2 kJ/mol、E(T2)=260.2 kJ/mol和E(T3)=239.3 kJ/mol。