Analytical and Numerical investigation of natural convection in a heated cylinder using Homotopy Perturbation Method

Homotopy Perturbation Method (HPM) has been applied to solve a nonlinear heat transfer problem. Natural convection around an isothermal horizontal cylinder was studied. Heat transfer coefficient and specific heat coefficient were assumed to be dependent on temperature. Outcomes were compared with solution of heat transfer equation with constant properties. Solutions of HPM were compared with numerical results for different cases, and variation of Nusselt number was obtained and investigated.

A new characterization of the projective linear groups by the Sylow numbers

Let G be a finite group, pi (G) be the set of primes p such that G contains an element of order p and n_{p}(G) be the number of Sylow p-subgroup of G, that is, n_{p}(G)=|Syl_{p}(G)|. Set NS(G):=\{n_{p}|p\in \pi (G)\}, the set of the all of the number of Sylow subgroups of G. In this paper, we show that the linear groups PSL(2, q) are recognizable by NS(G) and order. Also we prove that if NS(G)=NS(PSL(2,8)$), then G is isomorphic to PSL(2,8) or Aut(PSL(2,8))

CHARACTERIZATION OF PROJECTIVE GENERAL LINEAR GROUPS

Abstract. Let G be a finite group and πe(G) be the set of element orders of G. Let k ∈ πe(G) and s k be the number of elements of order k in G. Set nse(G):={s k |k ∈ πe(G)}. In this paper, it is proved if |G| = |PGL2(q)|, where q is odd prime power and nse(G) = nse(PGL2(q)), then G ∼ = PGL2(q)

Characterization of projective general linear groups

Let $G$ be a finite group and $pi_{e}(G)$ be the set of element orders of $G$. Let $k in pi_{e}(G)$ and $s_{k}$ be the number of elements of order $k$ in $G$. Set nse($G$):=${ s_{k} | k in pi_{e}(G)}$. In this paper, it is proved if $|G|=|$ PGL$_{2}(q)|$, where $q$ is odd prime power and nse$(G)=$nse$($PGL$_{2}(q))$, then $G cong$PGL$

A New Characterization of PSL(2, 27)

abstract: Let G be a group and πe(G) be the set of element orders of G. Let k ∈ πe(G) and m k be the number of elements of order k in G. Set nse(G):={m k |k ∈ πe(G)}. In this paper, we prove if G is a group such that nse(G)=nse(PSL(2, 27)), then G ∼ =PSL(2, 27). Key Words: Element order, set of the numbers of elements of the same order, Sylow subgroup

Characterization of the alternating groups by their order and one conjugacy class length

summary:Let $G$ be a finite group, and let $N(G)$ be the set of conjugacy class sizes of $G$. By Thompson's conjecture, if $L$ is a finite non-abelian simple group, $G$ is a finite group with a trivial center, and $N(G)=N(L)$, then $L$ and $G$ are isomorphic. Recently, Chen et al.\ contributed interestingly to Thompson's conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li's PhD dissertation). In this article, we investigate validity of Thompson's conjecture under a weak condition for the alternating groups of degrees $p+1$ and $p+2$, where $p$ is a prime number. This work implies that Thompson's conjecture holds for the alternating groups of degree $p+1$ and $p+2$

On the average number of Sylow subgroups in finite groups

summary:We prove that if the average number of Sylow subgroups of a finite group is less than $\tfrac {41}{5}$ and not equal to $\tfrac {29}{4}$, then $G$ is solvable or $G/F(G)\cong A_{5}$. In particular, if the average number of Sylow subgroups of a finite group is $\tfrac {29}{4}$, then $G/N\cong A_{5}$, where $N$ is the largest normal solvable subgroup of $G$. This generalizes an earlier result by Moretó et al