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# On simultaneous approximation to a differentiable function and its derivative by Pál-type interpolation polynomials

Acta Mathematica Hungarica
Authors: T. F. Xie and S. P. Zhou
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# A remark on approximation by monotone sequences of polynomials

Acta Mathematica Hungarica
Authors: T. F. Xie and S. P. Zhou
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# The asymptotic property of approximation to |x| by Newman's rational operators

Acta Mathematica Hungarica
Authors: T.F. Xie and S.P. Zhou

## Abstract

Let
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$a = e^{ - 1/\sqrt n } ,p(x) = \Pi _{k = 1}^{n - 1} (a^k + x),r_n (x) = x\frac{{p(x) - p( - x)}} {{p(x) + p( - x)}}$$ \end{document}
. The present note gives the asymptotoc formula of max
\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} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\max }\limits_{|x| \leqq 1} \left| {|x| - r_n (x)} \right|$$ \end{document}
.
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# Polysaccharides and polyphenols in sea buckthorn leaf tea have synergistic impact on studied colonic strains in vitro and bacteria in vivo

Acta Alimentaria
Authors: W.M. Du, F.H. Wang, H.Y. Zhang, B.Z. Jiang, X.Y. Chen, W. Zhang, Y. Xie, and Z.T. Sheng

Present research on prebiotics focuses on either polysaccharides or polyphenols. This study compared the individual and combined impact of polysaccharide, quercetin, and gallic acid (GA) treatment on three human faecal strains. In vitro pure culturing and correlation analysis confirmed that the growth of both beneficial microbe B. longum subsp. longum (0.695, 0.205: R2, slope, respectively) and pathogenic C. perfringens (0.712, 0.085: R2, slope, respectively) increased due to polysaccharide treatment, and only GA treatment would inhibit C. perfringens (0.789, –0.165: R2, slope, respectively) growth. In vivo studies also revealed that genome copies of Bifidobacterium increased and C. perfringens decreased in the faeces, when a blend of the three nutrients rather than single polysaccharide or polyphenols were fed to rats. These data suggested that combined prebiotic treatment improved human faecal strain composition better than single treatment.

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