‎let $g$ be a finite group‎. ‎the degree pattern of $g$ denoted by‎ ‎$d(g)$ is defined as follows‎: ‎if $pi(g)={p_{1},p_{2},...,p_{k}}$ such that‎ ‎$p_{1}

Let $p$ be an odd prime and let $n$ a positive integer with $p\nmid n$. For any $r$ $\lambda \in \{1, 2, 3\}$ \lambda $, we have $$ \sum _{k=0}^{p^{r}n-1}\frac {\left (\frac 12\right )_k}{k!}\cdot \frac {4^k}{\lambda ^

Let Ω ⊆ ℝ 2 be a domain, let X rearrangement invariant space and f ∈ W 1 (Ω, ) homeomorphism between (Ω). Then there exists sequence of diffeomorphisms k converging to in the ).