Throughout this paper, every groups are finite. The prime graph of a group $G$ is denoted by $Gamma(G)$. Also $G$ is called recognizable by prime graph if for every finite group $H$ with $Gamma(H) = Gamma(G)$, we conclude that $Gcong H$. Until now, it is proved that if $k$ is an odd number and $p$ is an odd prime number, then $PGL(2,p^k)$ is recognizable by prime graph. So if $k$ is even, the r...

‎This article presents a systematic study for structure of finite wavelet frames‎ ‎over prime fields‎. ‎Let $p$ be a positive prime integer and $mathbb{W}_p$‎ ‎be the finite wavelet group over the prime field $mathbb{Z}_p$‎. ‎We study theoretical frame aspects of finite wavelet systems generated by‎ ‎subgroups of the finite wavelet group $mathbb{W}_p$.

The prime graph of a finite group $G$ is denoted by $Gamma(G)$ whose vertex set is $pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $Gamma(H)=Gamma(G)$, in while $Hnotcong G$. In this paper, we consider finite groups with the same prime gr...

‎let $r$ be a domain with quotiont field $k$‎, ‎and‎ ‎let $n$ be a submodule of an $r$-module $m$‎. ‎we say that $n$ is‎ ‎powerful (strongly primary) if $x,yin k$ and‎ ‎$xymsubseteq n$‎, ‎then $xin r$ or $yin r$ ($xmsubseteq n$‎ ‎or $y^nmsubseteq n$ for some $ngeq1$)‎. ‎we show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $m$‎, ‎also we show tha...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prim...

in this paper we introduce the concept of weakly prime ternary subsemimodules of a ternary semimodule over a ternary semiring and obtain some characterizations of weakly prime ternary subsemimodules. we prove that if $n$ is a weakly prime subtractive ternary subsemimodule of a ternary $r$-semimodule $m$, then either $n$ is a prime ternary subsemimodule or $(n : m)(n : m)n = 0$. if $n$ is a $q$-...

We prove, without assuming the Generalized Riemann Hypothesis, but with at most one exception, that an irreducible cyclic code c(p, m, v) with v prime and p of index 2 modulo v is a two-weight code if and only if it is a semiprimitive code or it is one of the six sporadic known codes. The result is proved without any exception for index-two irreducible cyclic c(p, m, v) codes with v prime not c...

Let $G= (V,E)$ be a $(p,q)$-graph. A bijection $f: Eto{1,2,3,ldots,q }$ is called an edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ where $f^+(u) = sum_{uwin E} f(uw)$. Moreover, a bijection $f: Eto{1,2,3,ldots,q }$ is called a semi-edge-prime labeling if for each edge $uv$ in $E$, we have $GCD(f^+(u),f^+(v))=1$ or $f^+(u)=f^+(v)$. A graph that admits an  ...