Complexes constructed from chains of p-subgroups of a group G provide valuable tools in group theory, for the understanding of p-local structure, in algebraic topology, for the study of classifying spaces and mod-p group cohomology through homology decompositions, and in modular representation theory, where the Lefschetz module associated to the complex of all nonidentity p-subgroups can be reg...

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

let $g$ be a connected graph of order $3$ or more and $c:e(g)rightarrowmathbb{z}_k$‎ ‎($kge 2$) a $k$-edge coloring of $g$ where adjacent edges may be colored the same‎. ‎the color sum $s(v)$ of a vertex $v$ of $g$ is the sum in $mathbb{z}_k$ of the colors of the edges incident with $v.$ the $k$-edge coloring $c$ is a modular $k$-edge coloring of $g$ if $s(u)ne s(v)$ in $mathbb{z}_k$ for all pa...

We study the existence of unitriangular basic sets for symmetric group which behave nicely with respect to Mullineux involution. Such give a natural labelling modular irreducible representations. show that, any odd prime p, p-blocks weight 2 have stable we describe by studying combinatorics partitions in these blocks.

Background and purpose - Backside wear of the polyethylene insert in total knee arthroplasty (TKA) can produce clinically significant levels of polyethylene debris, which can lead to loosening of the tibial component. Loosening due to polyethylene debris could theoretically be reduced in tibial components of monoblock polyethylene design, as there is no backside wear. We investigated the effect...

BACKGROUND Reports of diverse outcomes in modular mini-keel tibial componentry for total knee arthroplasty (TKA) have raised concerns about early aseptic loosening. Cruciate-retaining (CR) prostheses, using mini-keel implants, have yet to be reported and compared to posterior-stabilizing (PS) designs. METHODS A retrospective, case-matched study of 91 consecutive TKAs (n = 46 CR; n = 45 PS pro...