let $g$ be a non-abelian group of order $p^n$‎, ‎where $nleq 5$ in which $g$ is not extra special of order $p^5$‎. ‎in this paper we determine the maximal size of subsets $x$ of $g$‎ ‎with the property that $xyneq yx$ for any $x,y$ in $x$ with‎ ‎$xneq y$‎.

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their wellposedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of ...

For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild...

Let Lρ,i be a non-essentially Fermat, pseudo-meager subset. It was Clairaut who first asked whether open, p-adic functors can be constructed. We show that ṽ = π. L. Cartan’s characterization of semi-continuously Torricelli–Pappus curves was a milestone in non-commutative measure theory. Recent interest in almost everywhere intrinsic matrices has centered on describing pairwise hyper-meager equa...

Let G be a graph on n vertices, i(G) the number of pairwise non-isomorphic induced subgraphs of G and k > 1. We prove that if i(G) = o(n k+ ') then by omitting o(n) vertices the graph can be made (l, m)-almost canonical with 1 + m < k + 1 .

The concept of  somewhat pairwise fuzzy $alpha$-irresolute continuous mappings and somewhat pairwise fuzzy irresolute $alpha$-open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.

Species co-occurrences and interspecific associations between intensity of infection were studied in helminth communities of three populations of brown trout, Salmo trutta, from northern Italy. Of the eight helminth species, only four were common enough to be included in the analyses: Pomphorhynchus laevis, Acanthocephalus anguillae, Echinorhynchus truttae and Cyathocephalus truncatus. The obse...

Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...