A generalization of Hardy’s operator and an asymptotic Müntz–Szász Theorem

We prove an asymptotic version of the Muntz–Szasz theorem, and use it to prove that all monomial operators are vanishing preserving.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

A Bertini type theorem for pencils over finite fields

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.     

UPLC-Q/TOF-MS coupled with multivariate analysis for comparative analysis of metabolomic in Dendrobium nobile from different growth altitudes

Dendrobium nobile alkaloids (DNLA) and glycosides are the main active components extracted from Dendrobium nobile Lindl. (D. nobile) used for thousands of years in China. The pharmacological effects of the above chemical components are significantly different. D. nobile is mainly grown at an altitude ranging from 230 to 800 m in Chishui City, Northwest Guizhou Province. However, it is unclear whether the metabolite in D. nobile is influenced by the planting altitude. Hence, to reveal the different metabolite in D. nobile cultivated at the altitude of 336 m, 528 m, and 692 m, ultra-high performance liquid chromatography with Q/TOF-MS couple with multivariate analysis were developed. Using the orthogonal partial least squares-discriminant analysis, 19 different metabolites were discovered and then tentatively assigned their structures as alkaloids and glycosides by comparing mass spectrometry data with in-house database and literature. Moreover, the result of semiquantitative analysis showed the content of dendrobine that was belonged to alkaloids significantly increased at the altitude of 692 m, whereas the content of glycosides demonstrated an accumulation trend at the altitude of 528 m. The results could provide valuable information for the optimal clinical drug therapeutics and provide a reference for quality control.     

几个由积分形成的数列的极限

围绕着若干个由积分定义的数列展开讨论，求出了这些数列的极限，并指出它们是一些已知的数列极限的推广。     

Simultaneous quantification of 10 saponins in Chinese Shizhu Panax by UPLC-ESI-MS

A simple and rapid method was established and validated for the simultaneous quantification of 10 saponins, namely ginsenosides-Rb₁, Rb₂, Rb₃, Rc, Rd, Rg₁, Rg₂, Re, Rf and Notoginsenside R₁, in Chinese Shizhu Panax by ultra performance liquid chromatography coupled with an electrospray mass spectrometry (UPLC-ESI-MS). In addition, the contents of the analytes in different parts of Chinese Shizhu Panax were also analysed. The results showed that the concentration of saponins had a reference to the different parts of Chinese Shizhu Panax. The established method could be used as a new analytical approach for assessment of the quantity of Chinese Shizhu Panax.     

Systematic chemical profiling of a multicomponent Chinese herbal formula Huo Luo Xiao Ling Dan by ultra high performance liquid chromatography coupled with electrospray ionization quadrupoletime‐of‐flight mass spectrometry

Huo Luo Xiao Ling Dan, a Chinese herbal formula consisting of 11 different herbs, has been used in folk medicine for the treatment of arthritis and other chronic inflammatory diseases. However, the chemical compositions of Huo Luo Xiao Ling Dan are not completely characterized. In the present study, an ultra high performance liquid chromatography coupled with electrospray ionization quadrupole time‐of‐flight mass spectrometry method in positive and negative ion modes was employed to identify biochemical constitutes in Huo Luo Xiao Ling Dan. As a result, a total of 76 compounds including alkaloids, monoterpene glycosides, iridoids, phenolic acids, and tanshinones, coumarins, lactones, flavones, and their glycosides, triterpenes, and triterpene saponins were characterized by comparing the retention time and mass spectrometry data with reference standards within 5 ppm error or by reference to the reference literature. These results would provide the basis for a further in vivo study of Huo Luo Xiao Ling Dan and information for potential new drug candidates for treating arthritis and other chronic inflammatory diseases.