Novel Approach to Two-Component Analysis Based on the Generalized Calibration Strategy

The generalized calibration strategy (GCS), developed and previously applied to chemical analysis, has been adapted to two-component (2C) analysis. According to the 2C-GCS procedure, a set of 10 calibration solutions containing a sample and standards of two analytes in well-defined composition was diluted. The measurements performed at a given dilution stage allow the concentration of both analytes in a sample to be evaluated with six apparent concentrations calculated with various mathematical approaches. As a result, the method allows the detection, examination, and elimination of nonlinear and interference effects with multiplicative and additive characteristics. To perform 2C-GCS automatically and effectively, a dedicated flow sequential injection system was designed to be fully controlled by a computer. Caffeine and paracetamol were determined in synthetic and pharmaceutical samples using this calibration approach. The analytes were determined with good precision and accuracy with low consumption of sample and standard solutions. On the basis of this experimental model, the influence of effects and tendencies in the examined analytical system was detected and evaluated.     

两个广义伽玛分布之间新的Kullback-Leibler距离

在Kullback-Leibler距离的基础上,对Kullback-Leibler距离进行改进,给出了新的Kullback-Leibler距离,并讨论了它的性质.计算了两个不同广义伽玛分布之间新的Kullback-Leibler距离.推导出伽玛分布、Weibull分布、Rayleigh分布、正态分布、指数分布新的Kullback-Leibler距离.另外在新的KullbackLeibler距离下,还得到digamma函数Ψ(x)=(Γ'(x)/(Γ(x))为单调递增函数.     

Solitary wave solution of the generalized Hirota–Satsuma coupled KdV system

In this research, we find the exact traveling wave solutions involving parameters of the generalized Hirota–Satsuma couple KdV system according to the modified simple equation method with the aid of Maple 16. When these parameters are taken special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the modified simple equation method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.     

Erdélyi-type integrals for generalized hypergeometric functions with integral parameter differences

In this paper, we extend one of Erdélyi's classical integrals for the Gauss hypergeometric functions to a special class of generalized hypergeometric functions in which certain pairs of numerator and denomiator parameters differ by positive integers. Our main results are achieved by applying the fractional integration by parts and series manipulation technique. Some special cases are also pointed out which includes a new extension of a Thomae-type transformation.     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

On the symmetry analysis and conservation laws of the (1 + 1)‐dimensional Hénon–Lane–Emden system

We carry out a complete Lie symmetry analysis and Noether symmetry classification of the (1 + 1)‐dimensional H non–Lane–Emden system. It is shown that the principal Lie algebra, which is one dimensional, extends in several cases. It is also shown that four main cases transpire in the Noether classification with respect to the Lagrangian. In addition, conservation laws for the H non–Lane–Emden system are constructed. Furthermore, we briefly discuss the importance and the physical interpretation of these conserved vectors. Copyright © 2016 John Wiley & Sons, Ltd.