we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

let $g=(v,e)$ be a connected simple graph. a labeling $f:v to z_2$ induces two edge labelings $f^+, f^*: e to z_2$ defined by $f^+(xy) = f(x)+f(y)$ and $f^*(xy) = f(x)f(y)$ for each $xy in e$. for $i in z_2$, let $v_f(i) = |f^{-1}(i)|$, $e_{f^+}(i) = |(f^{+})^{-1}(i)|$ and $e_{f^*}(i) = |(f^*)^{-1}(i)|$. a labeling $f$ is called friendly if $|v_f(1)-v_f(0)| le 1$. for a friendly labeling $f$ of...

modern societies belief life insurance scheme, which is designed to be backbone of man survival, ensure financial security and offers readymade source of long term capital financing for the infrastructural project is capable of combating the besetting problem of man so that life can be made easy and continuous. the dramatic increase in competition within the insurance sector and the needs of in...

the image of a brand is the first word or image that is evoked in the mind of costumers immediately after hearing the brand name. the purpose of paying attention to the brand image is to ensure the proper mentality of consumers toward the brand. the components such as suitability, services, brand, variety, quality, and atmosphere form the brand image. the relationship between the brand image an...

background and purpose: faculty members are the most important assets and resources of each country and information literacy refers to a set of capabilities that enable people to recognize the need for information and after placement and access to information needed, they evaluate and effectively use them, and since scientific production is one of the important indicators of faculty members’ pe...

in laboratory experiments the toxicity of acetone was investigated against four species of stored-product insects. in empty-space trials, estimates of the lethal concentrations of acetone (lc, 72-h exposure) for 50% mortality against adults of the lesser grain borer, rhizopertha dominica (f.), red flour beetle, tribolium castaneum (herbst), rice weevil, si-tophilus oryzae (l.) and eggs of the a...

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...

This paper presents an overview of new approaches in rapid product development in production networks from design points of view. The manufacturing industries are changing their focus to global sourcing as a means to improve performance and enhance competitiveness. Some partnerships created with this strategy improve product development through collaborative design. With the advent of e-Commerc...

Let R be a commutative ring with identity and M an R-module. The Scalar-Product Graph of M is defined as the graph GR(M) with the vertex set M and two distinct vertices x and y are adjacent if and only if there exist r or s belong to R such that x = ry or y = sx. In this paper , we discuss connectivity and planarity of these graphs and computing diameter and girth of GR(M). Also we show some of...