The (b; c)-inverse in semigroups and rings with involution

We first prove that if a is both left (b; c)-invertible and left (c; b)- invertible, then a is both (b; c)-invertible and (c; b)-invertible in a *-monoid, which generalizes the recent result about the inverse along an element by L. Wang and D. Mosić [Linear Multilinear Algebra, Doi.org/10.1080/03081087. 2019.1679073], under the conditions (ab)* = ab and (ac)* = ac: In addition, we consider that ba is (c; b)-invertible, and at the same time ca is (b; c)-invertible under the same conditions, which extend the related results about Moore- Penrose inverses studied by J. Chen, H. Zou, H. Zhu, and P. Patrício [Mediterr J. Math., 2017, 14: 208] to (b; c)-inverses. As applications, we obtain that under condition (a²)* = a²; a is an EP element if and only if a is one-sided core invertible, if and only if a is group invertible.     

Further results on several types of generalized inverses

Let R be an associative ring with unity 1 and let a,b,c∈R. In this paper, several characterizations for hybrid (b,c)-inverses of a are given. Also, the hybrid (b,c)-inverse of a is characterized by the group inverse of ab, under certain hypothesis. In particular, existence criteria for the the inverse along an element are obtained. Finally, we get the double commutant property and the reverse order law of annihilator (b,c)-inverses.     

相对于环的自同态的(b, c)-逆

研究了相对于环的自同态的$(b, c)$-逆的相对性质.在更一般地条件下, 定义了一类新的广义逆, 即$\alpha$-$(b, c)$-逆. 通过具体例子说明了$\alpha$-$(b, c)$-逆与$(b, c)$-逆是完全不同的两类广义逆, 并研究了$\alpha$-$(b, c)$-逆与$(b, c)$-逆等价的条件. 此外, 还研究了$\alpha$-$(b, c)$-逆的强clean分解. 这些研究结果统一和推广了$(b, c)$- 逆上的若干已知结果.     

广义加权Bloch空间与QK(p,q)空间之间的复合算子

设φ是复平面上的单位圆盘D上的全纯自映射,0＜p＜∞,q＞-2,α＞0.本文给出广义加权Bloch空间与QK(p,q)空间之间的复合算子的有界性和紧性.     

Fixed points of (α,ψ)‐contractions in Hausdorff partial metric spaces

The concept of (α,ψ)‐contractions was introduced by Samet et al. in this paper, we introduce (α,ψ)‐generalized contractions in a Hausdorff partial metric space. We discuss its significance and obtain some common fixed point theorems for a pair of self‐mappings. Some examples are given to support the theory.     

Weighted composition operators from F（p,q, s） spaces to Bers-type spaces in the unit ball

This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.     

Coding‐theoretic constructions for (t,m,s)‐nets and ordered orthogonal arrays

(t,m,s)‐nets are point sets in Euclidean s‐space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi‐Monte Carlo methods and coding theory. The ambient space is a metric space generalizing the Hamming space of coding theory. We denote it by NRT space (named after Niederreiter, Rosenbloom and Tsfasman). Our main results are generalizations of coding‐theoretic constructions from Hamming space to NRT space. These comprise a version of the Gilbert‐Varshamov bound, the (u,u+υ)‐construction and concatenation. We present a table of the best known parameters of q‐ary (t,m,s)‐nets for qε{2,3,4,5} and dimension m≤50. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 403–418, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10015     

A nearfield-free definition of regular Hughes planes and some embeddings of PG(3,q) in Hughes planes of order q 4

We give a nearfield-free definition of some finite and infinite incidence systems by means of half-points and half-lines and show that they are projective planes. We determine a planar ternary ring for these planes and use it to determine the full collineation group and to demonstrate some embeddings of these planes among themselves. We show that these planes include all finite regular Hughes planes and many infinite ones. We also show that PG(3, q) embeds in Hu(q ⁴) (and show infinite versions of this embedding). Dan Hughes 80th Birthday.