‎Suppose G is a group of order p^2q^2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, ‎respectively‎. ‎In this paper‎, ‎we show that up to isomorphism‎, ‎there are four groups of order p^2q^2 when Q and P are cyclic‎, ‎three groups when Q is a cyclic and P is an elementary ablian group‎, ‎p^2+3p/2+7 groups when Q is an elementary ablian group an...

lexicographic ordering by spectral moments ($s$-order) among all trees is discussed in this‎ ‎paper‎. ‎for two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{t}_n^{p‎, ‎q}={t‎: ‎t$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. furthermore, ‎the last four trees‎, ‎in the $s$-order‎, ‎among $mathscr{t}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...

در این پژوهش، برای نخستین بار کشور، جداسازی لیزری ایزوتوپ C13 از راه گسست چندفوتونی ایزوتوپ- گزین مولکول‌های گاز HCl2CF مقیاس آزمایشگاهی به انجام رسید. کار، تپ‌های یک لیزر 2TEA CO کوک‌پذیر که با برش­گر پلاسمایی کوتاه‌سازی شده‌اند، شاریدگی 2J/cm 50 درون اتاقک تابش‌دهی کانونی شدند. تابش‌‌دهی نیز فشار mbar 10-20 نسبت‌های HCl: He2CF برابر 1:5 و 1:10 پر شده بود. نشان داده شد فراوانی فرآورده‌ی 4F2C ک...

The Padmakar-Ivan (PI) index of a graph G is the sum over all edges uv of G of the number of edges which are not equidistant from u and v. In this paper, the notion of vertex PI index of a graph is introduced. We apply this notion to compute an exact expression for the PI index of Cartesian product of graphs. This extends a result by Klavzar [On the PI index: PI-partitions and Cartesian product...