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.     

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。     

HgCdTe薄膜的输运特性及其应力调控

窄禁带直接带隙半导体材料碲镉汞(Hg1–xCdxTe)是一种在红外探测与自旋轨道耦合效应基础研究方面都具有重要应用意义的材料.本文对单晶生长的体材料Hg0.851Cd0.149Te进行阳极氧化以形成表面反型层,将样品粘贴在压电陶瓷上减薄后进行磁输运测试,在压电陶瓷未加电压时观察到了明显的SdH振荡效应.对填充因子与磁场倒数进行线性拟合,获得样品反型层二维电子气的载流子浓度为ns=1.25×10^16m^-2.在不同磁场下,利用压电陶瓷对样品进行应力调控,观测到具有不同特征的现象,分析应是样品中存在二维电子气与体材料两个导电通道.零磁场下体材料主导的电阻的变化应来源于应力导致的带隙的改变;而高场下产生类振荡现象的原因应为应力导致的二维电子气能级的分裂.     

Event-triggered based $$\pmb {L_{2}-L_{\infty }}$$L2-L∞ filtering for multiagent systems with Markovian jumping topologies under time-varying delays

Nonlinear Dynamics - In this article, we analyze the $$L_{2}-L_{\infty }$$ filtering of multiagent systems for Markovian switch topologies under time-varying delays with an influence of...     

黏弹性接触界面端附近的奇异应力场

研究蠕变加载条件下线黏弹性材料接触界面端附近的奇异应力场问题.考虑接触界面的摩擦,假设界面端的滑移方向不改变,相对滑移量微小,且其与位移同量级,由此线性化局部边界条件,根据对应原理得到Laplace变换域中的界面端应力场,导出时域中奇异应力场的卷积积分表达式.对卷积积分核函数进行数值反演,考虑接触材料的两类组合,一是持久模量具有量级上的差异,另一是持久模量接近相同.算例结果证实核函数可以用准弹性法求得的解析式较准确地近似.在此基础上,利用积分中值定理,并引入各应力分量的修正系数,得到黏弹性奇异应力场的简化式.结合核函数的数值反演结果分析修正系数表达式的取值范围,得到如下结论,若两相接触材料的持久模量相差很大,可以采用准弹性解的解析式较准确地描述界面端的奇异应力场;一般情况下,应力场不存在统一的奇异值和应力强度系数,当采用类似于准弹性解的表达式近似给出黏弹性应力场时,可以估计此近似描述的误差限.文中最后采用有限元分析黏弹性板端部嵌入部位的应力场,算例包括了黏弹性板与弹性金属支承、黏弹性板与黏弹性垫层所形成的滑移接触界面端,利用黏弹性有限元的数值结果验证理论分析所得结论的有效性.