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# О линейных методах суммирования рядов Фурье-Лапласа. II

Analysis Mathematica
Author: Tang Ping

## Abstract

Let Σn be the unit sphere inR n for somen≥3 with centre at the origin, L(Σn) the space of all functions integrable on Σn. We prove a theorem on the representation of functions by singular integrals at double Lebesgue points, which is analogous to a theorem by D. K. Faddeev in the one-dimensional case. On the basis of this theorem, we give necessary and sufficient conditions for the fulfillment of the relation

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\lim }\limits_{x \to \infty } U_N (f,x,\Lambda ) = f(x)$$ \end{document}
for an arbitrary integrable functionf at its double Lebesgue pointsx, where byU N (f, x Λ) we denote the linear means of the Fourier-Laplace series off defined by means of the triangular matrix
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\Lambda = \left\{ {\lambda _k^{(N)} :N = 0,1,...;k = 0,1...,N + 1;\lambda _k^{(N)} = 1,\lambda _{N + 1}^{(N)} = 0} \right\}$$ \end{document}

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# О линеиных методах суммирования рядов Фуряе-Лапласа

Analysis Mathematica
Authors: Tang Ping and Тан Пин

## Abstract

В работе докаэывается достаточное условие для ограниченности функции Лебега линеиных средних рядов Фуряе-Лапласа. Иэ него и ранее полученнои Калянеем оценки выведены необходимые и достаточные условия сходимости линеиных средных рядов Фуря’е-Лапласа непрерывных функции, определенных на единичнои сфере в Rn (n>-3) с центром в начале координат. Это является аналогом иэвестного реэулятата Николяского для тригонометрических рядов.

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# Determination of adriamycin content in pectin–adriamycin conjugate in a two-phase reaction system by high-performance liquid chromatography

Acta Chromatographica
Authors: Maosheng Ran, Ping Xie, Xiaohai Tang, Guangfu Zeng and Jinliang Yang

Open access

# The comprehensive competitiveness evaluation of American universities in Bridge Engineering

Scientometrics
Authors: Yuan Wang, Ruimin Ma, Tianhao Tang, Xia Liu, Ping Xie, Jianxin Wang, Jianxiang Liu, Haideng Zhou and Siwei Zhang

## Abstract

This article explores a method of evaluating the comprehensive competitiveness of American universities in Bridge Engineering, which is beneficial for students’ picking up an ideal university for further study in America. Making use of ESI database, SCI database and EI database as well as the ranking of American universities from U.S. News and World Report, the author evaluates the comprehensive competitiveness of American universities in Bridge Engineering, and then develops the ranking of comprehensive competitiveness of American universities in Bridge Engineering specialty. From the ranking, the author reaches the conclusion that American universities such as University of Illinois-Urbana-Champaign and Georgia Institute of Technology and so on, have comparatively higher international influence and competitiveness in the field of Bridge Engineering.

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# Analysis of chloramphenicol in drinking water using an evaporation preparative step and isotope dilution liquid chromatography–tandem mass spectrometry

Acta Chromatographica
Authors: Yonggang Li, Xiaohong Liu, Rui Zhang, DerGer ZomPa, Ping Luo, Lin Tang, Xiao Liu, Yan Zhou and Sheng Wen

A reliable isotope dilution method for the determination of chloramphenicol (CAP) in drinking water was developed by using an evaporation preparative step. Each sample was monitored by ultrahigh-pressure liquid chromatography (UHPLC) coupled to tandem mass spectrometry (MS/MS) using an electrospray ionization interface (ESI) in negative ion modes. Recoveries of spiked samples were in the range from 93.2% to 95.7% with intra-day relative standard deviation lower than 6.7% and inter-day relative standard deviation lower than 8.2%. Limit of quantification (LOD) was 0.002 ng/mL. The developed method was successfully applied to the analysis of CAP in drinking water of Shannan region of Tibet.

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