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References [1] Kórus , P. 2010 Remarks on the uniform and L 1 -convergence of trigonometric series Acta Math. Hungar

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Bray, W. O. and Stanojevic, Č. V. , On weighted integrability of trigonometric series and L 1 -convergence of Fourier series, Proc. Amer. Math. Soc. 96 (1986), 53–61. MR 87e :42007

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Exploring antibiotic resistant mechanism by microcalorimetry

Determination of thermokinetic parameters of metallo-β-lactamase L1 catalyzing penicillin G hydrolysis

Journal of Thermal Analysis and Calorimetry
Authors: Hui-Zhou Gao, Qi Yang, Xiao-Yan Yan, Zhu-Jun Wang, Ji-Li Feng, Xia Yang, Sheng-Li Gao, Lei Feng, Xu Cheng, Chao Jia and Ke-Wu Yang

penicillin G [ 6 ]. The β-lactamases are divided into A, B, C, and D group [ 7 ], and the MβLs are group B enzymes which are Zn(II)-dependent [ 7 ], and the MβL L1 is a B3 group enzyme, it has been shown to bind 2 Zn(II) ions per monomer [ 8 ]. In an effort

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Abstract  

Our aim is to find the source why the logarithm sequences play the crucial role in the L 1-convergence of sine series. We define three new classes of sequences; one of them has the character of the logarithm sequences, the other two are the extensions of the class defined by Zhou and named Logarithm Rest Bounded Variation Sequences. In terms of these classes, extended analogues of Zhou’s theorems are proved.

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We generalize classical results concerning L 1 integrability, and tell a somewhat different story for sine series.

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We construct a sequence (n k) such that n k + 1n k → ∞ and for any ergodic dynamical system (X, Σ, �, T) and f ε L 1(�) the averages

\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} $$\lim _{N \to \infty } (1/N)\sum\nolimits_{k = 1}^N {f(T^{n_k } x)}$$ \end{document}
converge to X f d� for � almost every x. Since the above sequence is of zero Banach density this disproves a conjecture of J. Rosenblatt and M. Wierdl about the nonexistence of such sequences.

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The present note will present a different and direct way to generalize the convexity while keep the classical results for L 1-convergence still alive.

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We study 1-complemented subspaces of the sequence spaces ℓ1 andc 0. In ℓ1, 1-complemented subspaces of codimensionn are those which can be obtained as intersection ofn 1-complemented hyperplanes. Inc 0, we prove a characterization of 1-complemented subspaces of finite codimension in terms of intersection of hyperplanes.

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The aim of this paper is to prove that the Cesàro means of order α (0 < α < 1) of the Fourier series with respect to representative product systems converge to the function in L 1-norm, only for certain values of α which depend on some parameter of the representative product system.

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Abstract  

Suppose that f: ℝ → ℝ is a given measurable function, periodic by 1. For an α ∈ ℝ put M n α f(x) = 1/n+1 Σk=0 n f(x + ). Let Γf denote the set of those α’s in (0;1) for which M n α f(x) converges for almost every x ∈ ℝ. We call Γf the rotation set of f. We proved earlier that from |Γf| > 0 it follows that f is integrable on [0; 1], and hence, by Birkhoff’s Ergodic Theorem all α ∈ [0; 1] belongs to Γf. However, Γf\ℚ can be dense (even c-dense) for non-L 1 functions as well. In this paper we show that there are non-L 1 functions for which Γf is of Hausdorff dimension one.

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