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
Our aim is to find the source why the logarithm sequences play the crucial role in the L1-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.
We study 1-complemented subspaces of the sequence spaces ℓ1 andc0. In ℓ1, 1-complemented subspaces of codimensionn are those which can be obtained as intersection ofn 1-complemented hyperplanes. Inc0, we prove a characterization of 1-complemented subspaces of finite codimension in terms of intersection of hyperplanes.
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 L1-norm, only for certain values of α which depend on some parameter of the representative product system.
Suppose that f: ℝ → ℝ is a given measurable function, periodic by 1. For an α ∈ ℝ put Mnαf(x) = 1/n+1 Σk=0nf(x + kα). Let Γf denote the set of those α’s in (0;1) for which Mnαf(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-L1 functions as well. In this paper we show that there are non-L1 functions for which Γf is of Hausdorff dimension one.