Improvement of 1D off-axis computer-generated holograms

Creation of Fresnel off-axis computer-generated holograms and improvement of images reconstructed from the holograms are described. To improve the reconstructed images, we have created the holograms with high construct diffraction patterns by using a histogram method. From reconstruction experiments of the holograms, clear images have been obtained and 3D images have been seen directly with eyes.     

Applications of operator identities to the multiple q-binomial theorem and q-Gauss summation theorem

In this paper, we first give an interesting operator identity. Furthermore, using the q-exponential operator technique to the multiple q-binomial theorem and q-Gauss summation theorem, we obtain some transformation formulae and summation theorems of multiple basic hypergeometric series.     

On a finite difference scheme for Burgers’ equation

In this paper we study properties of numerical solutions of Burger’s equation. Burgers’ equation is reduced to the heat equation on which we apply the Douglas finite difference scheme. The method is shown to be unconditionally stable, fourth order accurate in space and second order accurate in time. Two test problems are used to validate the algorithm. Numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well.     

半群OCK_n的理想的极大子半群

设X_n={1,2,…,n}并赋予自然数序,OCK_n是X_n上的具有核连续的保序变换半群.将考虑OCK_n的理想OCK(n,r)={α∈OCK_n:|imα|≤r}(3≤r≤n-1),并得到了OCK(n,r)的极大子半群的完全分类.     

关于对称不定线性方程组Ax=b的一种求解算法

本文针对系数矩阵A具有少数几个正(负)特征值的对称不定性方程组Ax=b构造了一个有效的稳定算法.这个算法充分利用了矩阵的对称性及具有少数几个正(或负)特征值的特点,其运算量与Cholesky方法相当,大约为?个乘法和加法,所用贮存单元为?.从第四节的数值例子可以看出在上述假定条件下用本算法求解较Parlett和Reid算法要好些.尤其对A又是大型稀疏矩阵更为有效.     

The PyPES library of high quality semi‐global potential energy surfaces

In this article, we present a Python‐based library of high quality semi‐global potential energy surfaces for 50 polyatomic molecules with up to six atoms. We anticipate that these surfaces will find widespread application in the testing of new potential energy surface construction algorithms and nuclear ro‐vibrational structure theories. To this end, we provide the ability to generate the energy derivatives required for Taylor series expansions to sixth order about any point on the potential energy surface in a range of common coordinate systems, including curvilinear internal, Cartesian, and normal mode coordinates. The PyPES package, along with FORTRAN, C, MATLAB and Mathematica wrappers, is available at http://sourceforge.net/projects/pypes-lib . © 2015 Wiley Periodicals, Inc.     

Synthesis, ring transformations, IR-, NMR and DFT study of heterocycles with two ferrocenyl units

Cyclization of 1,5-bis(ferrocenylmethylidene)thiocarbonohydrazide with DMAD afforded diastereomeric dimethyl-thiazole-4,5-dicarboxylates. The cis-isomer undergoes ring opening and recyclization to a thiazolone derivative. A further thiazolone was obtained from this precursor with ethyl chloroacetate employing a bifunctional organocatalyst. Due to its propensity to dehydrogenation evidenced by DFT calculations, the studied thiocarbonohydrazide underwent oxidative cyclizations under different conditions to yield a 1,3,4-thiadiazole and a 1,2,4-triazole derivative, respectively. Thermal isomerisation of 1,3,4-thiadiazole into 1,2,4-triazole was also observed. The DMAD-mediated cyclizations of the S-metylated thiocarbonohydrazide and the 1,5-bis(ferrocenylmethylideneamino)guanidine gave 1,2,4-triazole derivatives and a 4-pyrimidone, respectively. The structure of the new compounds was established by IR and NMR spectroscopy, including HMQC, HMBC and DEPT measurements. The solid state structure of a triazole was revealed by single crystal X-ray analysis.     

Maintaining the predictive abilities of multivariate calibration models by spectral space transformation

In quantitative on-line/in-line monitoring of chemical and bio-chemical processes using spectroscopic instruments, multivariate calibration models are indispensable for the extraction of chemical information from complex spectroscopic measurements. The development of reliable multivariate calibration models is generally time-consuming and costly. Therefore, once a reliable multivariate calibration model is established, it is expected to be used for an extended period. However, any change in the instrumental response or variations in the measurement conditions can render a multivariate calibration model invalid. In this contribution, a new method, spectral space transformation (SST), has been developed to maintain the predictive abilities of multivariate calibration models when the spectrometer or measurement conditions are altered. SST tries to eliminate the spectral differences induced by the changes in instruments or measurement conditions through the transformation between two spectral spaces spanned by the corresponding spectra of a subset of standardization samples measured on two instruments or under two sets of experimental conditions. The performance of the method has been tested on two data sets comprising NIR and MIR spectra. The experimental results show that SST can achieve satisfactory analyte predictions from spectroscopic measurements subject to spectrometer/probe alteration, when only a few standardization samples are used. Compared with the existing popular methods designed for the same purpose, i.e. global PLS, univariate slope and bias correction (SBC) and piecewise direct standardization (PDS), SST has the advantages of implementation simplicity, wider applicability and better performance in terms of predictive accuracy.     

Studies on the Synthesis and Characterization of Pd?TiO2?SiO2 Nanocomposite for Electroanalytical Applications

A nanocomposite of Pd? TiO₂? SiO₂ is developed through a sol‐gel process from the reaction products of titanium isopropoxide followed by mixing the same with palladium linked 3‐glycidoxypropyltrimethoxysilane. The reaction product is sonicated and calcinated to obtain the nanocomposite of Pd? TiO₂? SiO₂. The calcination at 600 °C yielded an amorphous structure whereas at 900 °C it resulted into a nanocrystalline structure. The nanocomposite of palladium was further characterized by TEM, XRD, IR and EDS. The material acts as an efficient electrocatalyst. Electrocatalysis of ascorbic acid is observed at 0.1 V vs. Ag/AgCl, shows linearity between 1 µM and 1 mM in 0.1 M phosphate buffer (pH 7.0).