Abstract:
This article examines inequalities between and within 57 countries, categorized by income levels, for efficiency in pro-duction and output per worker for 1965 and 1990. Regression analysis was also employed as a basis of convergence from which countries were evaluated for their potential to actual performance in efficiency and output over a span of 25 years. The findings indicate that gaps between the groups of countries widened as compared to gaps within the groups. Convergence was found to increase between the groups of countries as their income levels rose.

Abstract:
The present study was designed to examine the ways power relations influence politeness strategies in disagreement. The study was an attempt to find out whether different power status of people influencethe the choice of appropriate politeness strategies and speech act of disagreement by Iranian EFL learners, in a university setting. A Discourse Completion Test (DCT) was utilized to elicit the required data. The sample included 20 Iranian upper-intermediate EFL learners who were selected based on their scores on a proficiency test. The DTC consists of five scenarios in which the subjects are expected to disagree with two higher statuses and two with peers and one with a lower status. Selection of disagreement situations in DCT was based on relative power and status of people. The main frameworks used for analyzing data were the taxonomy from Muntigl and Turnbull (1995) for counting and analyzing the utterances of disagreement and Brown and Levinson’ (1987) theory of politeness. It was found that EFL learners employ different kind of politeness strategies in performing this face threatening speech act. When performing the speech act of disagreement, they used more direct and bald on record strategies. The findings of this study provide some evidences for the relation between the type and frequency of disagreement and choice of politeness strategies associated with people with different power status. It concludes by arguing that the results can be closely related with learning contexts and textbook contents and some suggestions were put forward regarding the issue.It is also hoped that the findings of this study will provide some worthwhile knowledge into the teaching and training of communication skills in EFL courses. Furthermore, this study may reveal some cultural differences between Iranian societies and others.

Abstract:
In the present paper we extend and improve the results of \cite{bl, br} for the tensor square of Lie algebras. More precisely, for any Lie algebra $L$ with $L/L^2$ of finite dimension, we prove $L\otimes L\cong L\square L\oplus L\wedge L$ and $Z^{\wedge}(L)\cap L^2=Z^{\otimes}(L)$. Moreover, we show that $L\wedge L$ is isomorphic to derived subalgebra of a cover of $L$, and finally we give a free presentation for it.

Abstract:
For every $p$-group of order $p^n$ with the derived subgroup of order $p^m$, Rocco in \cite{roc} has shown that the order of tensor square of $G$ is at most $p^{n(n-m)}$. In the present paper not only we improve his bound for non-abelian $p$-groups but also we describe the structure of all non-abelian $p$-groups when the bound is attained for a special case. Moreover, our results give as well an upper bound for the order of $\pi_3(SK(G, 1))$.

Abstract:
For every finite $p$-group $G$ of order $p^n$ with derived subgroup of order $p^m$, Rocco in \cite{roc} proved that the order of tensor square of $G$ is at most $p^{n(n-m)}$. This upper bound has been improved recently by author in \cite{ni}. The aim of the present paper is to obtain a similar result for a non-abelian nilpotent Lie algebra of finite dimension. More precisely, for any given $n$-dimensional non-abelian nilpotent Lie algebra $L$ with derived subalgebra of dimension $m$ we have $\mathrm{dim} (L\otimes L)\leq (n-m)(n-1)+2$. Furthermore for $m=1$, the explicit structure of $L$ is given when the equality holds.

Abstract:
It has been proved in \cite{ge} for every $p$-group of order $p^n$, $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$, where $t(G)\geq 0$. In \cite{be, el, zh}, the structure of $G$ has been characterized for $t(G)=0,1,2,3$ by several authors. Also in \cite{sa}, the structure of $G$ characterized when $t(G)=4$ and $Z(G)$ is elementary abelian. This paper is devoted to classify the structure of $G$ when $t(G)=4$ without any condition.

Abstract:
Let $G$ be a finite $p$-group of order $p^n$. It is known that $|\mathcal{M}(G)|=p^{\f{1}{2}n(n-1)-t(G)}$ and $t(G)\geq 0$. The structure of $G$ characterized when $t(G)\leq 4$ in \cite{be,el,ni,sa,zh}. The structure description of $G$ is determined in this paper for $t(G)=5$.

Abstract:
The author in $($On the order of Schur multiplier of non-abelian $p$-groups. J. Algebra (2009).322: 4479--4482$)$ showed that for any $p$-group $G$ of order $p^n$ there exists a nonnegative integer $s(G)$ such that the order of Schur multiplier of $G$ is equal to $p^{\f{1}{2}(n-1)(n-2)+1-s(G)}$. Furthermore, he characterized the structure of all non-abelian $p$-groups $G$ when $s(G)=0$. The present paper is devoted to characterization of all $p$-groups when $s(G)=2$.

Abstract:
For a finite dimensional Lie algebra $L$, it is known that $s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L)$ is non negative. Moreover, the structure of all finite nilpotent Lie algebras is characterized when $s(L)=0,1$ in \cite{ni,ni4}. In this paper, we intend to characterize all nilpotent Lie algebra while $s(L)=2.$