高中化学“次氯酸盐的性质”的项目式教学*——84消毒液的使用指南

以“84消毒液的使用指南”为主题,开展高中化学“次氯酸盐的性质”的教学。学生通过完成“一张图说清消毒剂”“探究84消毒液的漂白效果与酸碱性的关系”“探究84消毒液的漂白效果与光照的关系”“探究84消毒液的漂白效果与温度的关系”“84消毒液与酒精混合会有氯气吗”等5个项目任务,理解了次氯酸盐的性质及漂白原理,培养了学生的文献检索能力、实验探究能力以及发展了学生的高阶思维能力。将文献查阅与学生实验相结合,让学生在真实问题的解决中,完成次氯酸盐的性质等相关知识的内化,是顺利完成本项目教学的关键。     

Mobility of small molecules in membrane materials based on copolyimide P84

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False theta functions and companions to Capparelli's identities

Capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions, which were motivated by the calculation of characters for the standard modules of certain affine Lie algebras and by vertex operator theory. These identities were subsequently proved and refined by Andrews, who related them to Jacobi theta functions, and also by Alladi–Andrews–Gordon, Capparelli and Tamba–Xie. In this paper we prove two new companions to Capparelli's identities, where the evaluations are expressed in terms of Jacobi theta functions and false theta functions.     

Quantum key distribution transmitter chip based on hybrid-integration of silica and lithium niobates

A quantum key distribution transmitter chip based on hybrid-integration of silica planar light-wave circuit (PLC) and lithium niobates (LN) modulator PLC is presented. The silica part consists of a tunable directional coupler and 400-ps delay line, and the LN part is made up of a Y-branch, with electro-optic modulators on both arms. The two parts are facet-coupled to form an asymmetric Mach-Zehnder interferometer. We successfully encode and decode four BB84 states at 156.25-MHz repetition rate. Fast phase-encoding of 0 or $\pi $ is achieved, with interference fringe visibilities 78.53% and 82.68% for states $|+\rangle$ and $|-\rangle$, respectively. With the aid of an extra off-chip LN intensity modulator, two time-bin states are prepared and the extinction ratios are 18.65 dB and 15.46 dB for states $|0\rangle$ and $|1\rangle$, respectively.     

Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

Curve forecasting by functional autoregression

This paper deals with the prediction of curve-valued autoregression processes. It develops a novel technique, predictive factor decomposition, for the estimation of the autoregression operator. The technique is based on finding a reduced-rank approximation to the autoregression operator that minimizes the expected squared norm of the prediction error.Implementing this idea, we relate the operator approximation problem to the singular value decomposition of a combination of cross-covariance and covariance operators. We develop an estimation method based on regularization of the empirical counterpart of this singular value decomposition, prove its consistency and evaluate convergence rates.The method is illustrated by an example of the term structure of the Eurodollar futures rates. In the sample corresponding to the period of normal growth, the predictive factor technique outperforms the principal components method and performs on a par with custom-designed prediction methods.     

Nonlinear wave propagation along periodic-loaded transmission line

A high frequency transmission line periodically loaded with varactor diodes is presented to study nonlinear wave propagation. The nonlinearity and dispersion characteristics are experimentally and theoretically analysed. Experimental results on shock wave formation and harmonic frequency generation are found to be in good agreement with theoretical predictions. The influence of dispersion on second-harmonic frequency generation is particularly discussed yielding large values of the efficiency.     

Characteristics of CO2 TE-amplifiers with different UV preionization at superatmospheric pressure with doping additives

The attainable maximum pressure and the small signal gain are compared at pressures up to 3 bar in a TE-CO₂ laser amplifier with two preionization systems. It is found that doping with tripropylamine increases the attainable pressure for glow discharges but decreases the small signal gain. At slightly superatmospheric pressure and low doping amount the simple lamberton-Pearson device gives the best results. For constant input energy the inversion grows with increasing total pressure.     

Low-frequency scattering by rectangular dielectric particles

The field scattered by a homogeneous isotropic dielectric particle illuminated by a low-frequency plane electromagnetic wave is expressed in terms of a single polarizability tensor which is a function of only the geometry of the particle and a material parameter τ representing either the relative permittivity or permeability of the dielectric. The mathematical formulation is specialized to the case of a rectangular parallelepiped and numerical techniques are developed for computing the tensor elements. Specific data are presented for the tensor elements of rectangular parallelepipeds having square cross sections and are compared to the results obtained for spheroids and right circular cylinders of similar dimensions.