THE HIT PROBLEM OF RANK FIVE IN A GENERIC DEGRE

Nguyen Sum — 2024-07-22

Let Ek be an elementary abelian 2-group of rank k and let BEk be the classifying space of Ek. Then, Pk := H∗(BEk) ∼ = F2[x1, x2, . . . , xk], a polynomial algebra in k generators x1, x2, . . . , xk, with the degree of each xi being 1. This algebra is regarded as a module over the mod-2 Steenrod algebra, A. We study the Peterson hit problem of finding a minimal set of generators for A-module Pk. It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of A-generators for P5 in terms of the admissible monomials for the case of the generic degree m = 2d+2 + 2d+1 - 3 with d ⩾ 6.

SELECTIVE INERTIAL BLOCK-ITERATIVE SCHEMES FOR A CLASS OF VARIATIONAL INEQUALITIES AND APPLICATIONS

Nguyen Thi Quynh Anh — 2024-07-22

Our purpose in this paper is to present inertial block-iterative schemes with selective technique for finding a solution of a variational inequality problem over the set of common fixed points of a finite family of demiclosed quasinonexpansive mappings in Hilbert spaces. First, we introduce a basic scheme and show that any sequence, generated by this scheme, converges weakly to a point in the common fixed point set. Then, based on a specific combination of the scheme with the steepest-descent method, we propose new schemes, strong convergence of which is proved without the approximately shrinking and boundedly regular assumptions on the mappings and their fixed point sets, respectively, that are usually required recently in literature. An application to study a networked system and computational experiments are given for illustration and comparison

East West Math

THE HIT PROBLEM OF RANK FIVE IN A GENERIC DEGRE

SELECTIVE INERTIAL BLOCK-ITERATIVE SCHEMES FOR A CLASS OF VARIATIONAL INEQUALITIES AND APPLICATIONS