Products of two 1ϕ1 series and implications

An expansion formula into bivariate formal power series is established that implies, as consequences, three remarkable identities of partial theta functions due to Warnaar (2003), Schilling–Warnaar (2002) and Andrews–Warnaar (2007).     

A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

Unified approach to photo-and electro-production of mesons with arbitrary spins

A new approach to identify the independent amplitudes along with their partial wave multipole expansions, for photo-and electro-production is suggested, which is generally applicable to mesons with arbitrary spin-parity. These amplitudes facilitate direct identification of different resonance contributions.      

Using Short Wave Visible–Near Infrared Reflectance Spectroscopy to Predict Soil Properties and Content

In this study, short wave visible–near infrared reflectance spectroscopy was evaluated for prediction of diverse soil properties related to four different soil series of several regions in Jiangxi, China. A total of 240 soil samples were collected for the calibration (n = 168) and prediction (n = 72) sets. The used wavelength range of short wave visible–near infrared reflectance spectroscopy is 325–1075 nm. Partial least squares regression and back propagation neural network were used to develop models for soil properties such as organic matter and extractable forms of calcium, magnesium, and potassium. Performance of these models was also compared and analyzed. The input of back propagation neural network was the first six principal components resulted from the principal component analysis and the optimal number of latent variables obtained from partial least squares regression. The overall results showed that the performance of partial least squares regression model was inferior to all back propagation neural network models. The best prediction was obtained with latent variables as input of back propagation neural network model for organic matter (determination coefficient = 0.84 and relative predictive determinant = 2.38), which was classified as very good model predictions. The prediction of calcium, magnesium, and potassium was classified as fair (determination coefficient = 0.56–0.68 and relative predictive determinant = 1.51–1.61), where quantitative predictions were considered possible. It is recommended to adopt latent variables as input for back propagation neural network model predicting soil properties with short wave visible–near infrared reflectance spectroscopy. In conclusion, short wave visible–near infrared reflectance spectroscopy was variably successful in estimating soil properties and showed potential for substituting laboratory analyses.     

激光多普勒自主测速仪天线安装误差对测速精度的影响

为了减小激光多普勒自主测速仪天线安装误差引起的测速误差,以多普勒频移原理为基础,通过旋转矩阵的复合变换推导出测速误差与安装误差间的函数关系,分析了三个安装误差角对三维测速精度的影响,并对旋转矩阵采用Bursa模型线性化后在整体最小二乘准则下给出安装误差角的最优估计,从而实现测速误差的补偿。仿真结果表明:测速误差随速度的增大而增大,影响纵向、横向测速精度的主要因素是偏航角,影响垂向测速精度的主要因素是纵倾角,补偿后三维测速误差显著减小。     

High resolution gamma-ray spectroscopy of the27Al(p,γ)28Si resonance reaction

High resolution gamma-ray spectra have been measured from the²⁷Al (p,γ)²⁸Si reaction for the resonances atE _p=2·482, 2·511 and 2·735 MeV at ϑ _pγ=0°, 30°, 55° and 90° using a Ge (Li) gamma spectrometer. From the spectra and the angular distributions the properties of the resonance states have been obtained. These states are the isobaric analogues of the levels at 4·69, 4·75 and 4·93MeV levels respectively in the parent nucleus A²⁸l.     

网格模型PDE曲面重建中的边界曲线构造

利用偏微分方程(PDE)进行曲面拟合是计算机图形学研究领域中的常用方法,该类方法通过选取适当的边界条件来构造PDE,用PDE的解来表示几何曲面.基于网格简化方法和离散曲面测地线计算等技术,提出一种从网格模型提取PDE曲面片边界条件曲线的方法.首先,对复杂模型进行简化并分片处理;通过计算离散曲面的测地线为每个分片定义相应的PDE边界条件曲线,进而构造复杂模型的PDE拟合表面.最后,通过细分方法建立原模型的多分辨率表示.实验表明,该方法可以对具有不同几何复杂度的网格模型进行处理,产生具有细分连通性的多分辨网格模型.     

Preparation of partially functionalised resorcinarene derivatives

The conditions for synthesis of mono-, di- and trifunctionalised resorcinarenes by catalysed Mannich reaction are described. A series of these compounds are functionalised with different functional groups.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.     

股本稀释效应下的认股权证定价模型与数值方法

本文研究了在股本稀释效应下认股权证的定价问题.假设随机利率服从Vasicek模型,利用Δ-对冲方法建立了权证价格所满足的偏微分方程.然后,通过计价单位变换,将偏微分方程降维,求得了权证价格的显式解,并给出了一种较好的数值计算方法,可运用市场的可观测变量来计算权证价值.