基于串并联电阻法的半偏思想测量电表内阻

利用中学物理实验中半偏法测量电表内阻的思想,通过给电表并联和串联电阻,调节串并联电阻的阻值使电表指针达到满偏和半偏的方法测量电表内阻,拓展了测量电表内阻的方法。     

Synthesis and characterization of chiral poly(alkyl isocyanates) by coordination polymerization using a chiral half‐titanocene complex

A new chiral half‐titanocene complex, [CpTiCl₂(O‐(S)?2‐Bu)], is synthesized and characterized by ¹H and ¹³C NMR spectroscopy. This complex is employed for the coordination polymerization of n‐butyl and n‐hexyl‐ isocyanate leading to chiral polymers, as revealed by their CD spectra. Only the left‐handed helix is produced, due to the chiral (S)?2‐butoxy group, which is bound to the polymer chain end. The polymerization of 3‐(triethoxysilyl)propyl isocyanate produces less soluble polymers. On the other hand, phenyl isocyanate reacts slowly with the complex leading quantitatively and selectively to triphenyl isocyanurate. 2‐Ethylhexyl isocyanate is slowly and selectively cyclotrimerized in the presence of the half‐titanocene complex. However, a statistical copolymer of 2‐ethylhexyl isocyanate and hexyl isocyanate is produced. The reaction of benzyl isocyanate with the complex leads to a mixture of low molecular weight polymer and cyclotrimer. The polymers are characterized using SEC, NMR, and CD spectroscopy and their thermal properties are investigated by TGA/DSC analysis. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2141–2151     

Integral quantizations with two basic examples

The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical–quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl–Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half-plane viewed as the corresponding phase space.     

光栅衍射实验中测量光栅常数的两种辅助方法

衍射光栅可以将不同波长的光在空间上分离开,在光谱分析领域中有广泛应用.利用光栅的衍射来测量光栅常数是大学物理实验中的一个典型实验,而本文介绍的正是光栅衍射实验中的两个有趣现象:一是旋转光栅时,谱线的偏转角存在一个最小值;二是光栅旋转到一定角度时,衍射光斑会逐渐消失在视野中.论文从理论上分析解释这两种现象,并设计出两种测量光栅常数的方法,在实验上进行验证.与传统的用最小偏转角测光栅常数的方法相比,本文重点分析了由判定最小偏转角位置偏差所带来的影响,并提出了对称旋转测量的方法来进一步减小误差.     

Oscillation and non‐oscillation results for solutions of perturbed half‐linear equations

The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.     

双暴露面的阶段充填体孤柱需求强度模型及影响因素

阶段充填体孤柱侧壁均暴露、处于双轴受力状态，易发生剪切破坏.为合理确定其所需强度值，根据Terzaghi松散地压理论和滑楔体极限平衡理论，建立了孤柱需求强度数学计算模型，分析了需求强度的影响因素.结果表明:阶段充填体孤柱需求强度值与采场埋深和结构参数呈正相关，与充填体内摩擦角、充填体-围岩接触面摩擦系数和摩擦角呈负相关.该研究成果对指导矿山充填配比设计、防止地表塌陷和环境保护等具有现实意义.     

Development of non‐bonded interaction parameters between graphene and water using particle swarm optimization

New Lennard‐Jones parameters have been developed to describe the interactions between atomistic model of graphene, represented by REBO potential, and five commonly used all‐atom water models, namely SPC, SPC/E, SPC/Fw, SPC/Fd, and TIP3P/Fs by employing particle swarm optimization (PSO) method. These new parameters were optimized to reproduce the macroscopic contact angle of water on a graphene sheet. The calculated line tension was in the order of 10⁻¹¹ J/m for the droplets of all water models. Our molecular dynamics simulations indicate the preferential orientation of water molecules near graphene–water interface with one O H bond pointing toward the graphene surface. Detailed analysis of simulation trajectories reveals the presence of water molecules with ≤∼1, ∼2, and ∼4 hydrogen bonds at the surface of air–water interface, graphene–water interface, and bulk region of the water droplet, respectively. Presence of water molecules with ≤∼1 and ∼2 hydrogen bonds suggest the existence of water clusters of different sizes at these interfaces. The trends observed in the libration, bending, and stretching bands of the vibrational spectra are closely associated with these structural features of water. The inhomogeneity in hydrogen bond network of water at the air–water and graphene–water interface is manifested by broadening of the peaks in the libration band for water present at these interfaces. The stretching band for the molecules in water droplet shows a blue shift as compared to the pure bulk water, which conjecture the presence of weaker hydrogen bond network in a droplet. © 2017 Wiley Periodicals, Inc.     

Recursive condition for positivity of the angle for multivariate stationary sequences

In this note a recursive type condition for positivity of the angle between past and future for -variate stationary sequences is provided. In the case it gives a simple different proof of a result due to Solev and Tserkhtsvadze on basicity of bivariate stationary sequences.