Zeros of real polynomials

We study vector subspaces of the set of zeros of real valued symmetric odd polynomials and of real homogeneous polynomials of low degree.     

Real elements in T n (K)

We study the real elements in triangular matrix groups. We describe some classes of elements that are real in T _n (K) – the groups of upper triangular matrices over a commutative field K. From the obtained results there follow some applications for finding real elements in general linear groups – GL _n (K).     

基于光线光学的非线性自聚焦现象的仿真分析

采用光线光学方法对非线性自聚焦现象进行仿真, 能够从宏观上直观地体现强激光的传输过程, 同时避免采用近轴近似、自相似近似等. 本文采用在光传输路径上垂直于光轴切片的方法, 将光的非线性传输转化为切片上的光对折射率的调制作用和切片间的线性传输. 在切片端面上统计光强后对量化误差进行了抑制, 而线性传输过程采用了亚当斯法求解光线方程从而解决了龙格库塔法等不能用于非线性光传输仿真的问题. 仿真结果显示, 强激光自聚焦在轴上有多个焦点, 且第一个焦点的位置随光功率的增大而更靠近入射位置; 由于追迹的是实际光线, 故可以得到近轴区以外区域自聚焦及成丝(环)的情况, 这对于强激光系统安全是有重要意义的. 利用已有的同样基于光线追迹方法的光学设计、仿真软件, 可以把非线性自聚焦介质和线性介质结合起来, 仿真光在实际强激光系统中的传输. 关键词： 实际光线追迹 非线性自聚焦 光传输仿真     

Anodic Oxidation of α‐Lipoic Acid at a Glassy Carbon Electrode and Its Determination in Dietary Supplements

Abstract

Direct electrochemistry of alpha‐lipoic acid (ALA) was performed at a glassy carbon electrode using cyclic, differential pulse and square wave voltammetry over a wide range of pH. The oxidation of ALA is an irreversible process, pH independent, and involves the charge transfer of one electron. The diffusion coefficient of ALA was calculated from the results obtained at pH 6.9 in 0.1 M phosphate buffer and was shown to be D ₀=1.1×10^?5 cm² s^?1. The limits of detection (LOD) and quantification (LOQ) calculated from the results obtained at this pH are 1.8 and 6.1 µM, respectively.

The lipoic acid content in two dietary supplements samples, a syrup containing ALA and capsules of ALA, has been determined directly at the glassy carbon electrode by differential pulse voltammetry using the standard addition method.     

Quantum principal bundles over quantum real projective spaces

Two hierarchies of quantum principal bundles over quantum real projective spaces are constructed. One hierarchy contains bundles with U(1)$U\left(1\right)$ as a structure group, the other has the quantum group S_Uq(2)$S{U}_q\left(2\right)$ as a fibre. Both hierarchies are obtained by the process of prolongation from bundles with the cyclic group of order 2 as a fibre. The triviality or otherwise of these bundles is determined by using a general criterion for a prolongation of a comodule algebra to be a cleft Hopf–Galois extension.     

基于PCA-VAR模型的房地产信贷政策调控效应分析

有效的房地产调控,既要实现稳定房价、控制房地产开发投资过快增长等调控目标,同时也不会对宏观经济带来过大的负面影响.在分析各类房地产调控政策传导机制的基础上,通过构建PCA-VAR模型,并综合运用了协整分析、Granger因果检验、方差分解和脉冲效应分析等方法,细致测算了房地产信贷政策对房地产市场和宏观经济的影响,据此为我国实施房地产调控提供政策建议.     

基于实Schur分解的实正规矩阵特征值的变分特征

在实Schur分解的基础上,构造一新特征量表示正规矩阵特征值的虚部最大值,同时表示了所有实部.