de Sitter–Gödel–de Sitter phase transition (dGd) is a possible geometrical in the very early universe. It induces fluctuations with possibly observable traces on matter and radiation fields. Here we present simulation based dGd to investigate perturbations which could be along standard inflationary cosmic microwave background distribution of large-scale structure. The power spectrum characteriz...

Abstract We prove that, for almost all $r \leq N^{1/2}/\log^{O(1)}N$, any given $b_1 \ (\mathrm{mod}\ r)$ with $(b_1, r) = 1$, and $b_2 $(b_2, we have that natural numbers $2n N$ \equiv b_1 + b_2 can be written as the sum of two prime p_1 p_2$, where $p_1 $p_2 r)$. This improves previous result which required N^{1/3}/\log^{O(1)}N$ instead N^{1/2}/\log^{O(1)}N$. also improve some other results c...

Let $G$ be a finite group and $pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ with vertex set $pi(G)$ and two distinct vertices $p$ and $q$ in $pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $psim q$. Let $|G= p_1^{alpha_1}cdot p_2^{alpha_2}cdots p_k^{alpha_k}$, where $p_1

Abstract The paper contains the study of weighted $$L^{p_1}\times L^{p_2}\times \ldots \times L^{p_m}\rightarrow L^p$$ L p 1 × 2 … m → ...