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The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module $M$, there exists a module $K\in \sigma \left[M\right]$ such that $K\oplus N$ is weakly injective in $\sigma \left[M\right]$, for any $N\in \sigma \left[M\right]$. Similarly, if $M$ is projective and right perfect in $\sigma \left[M\right]$, then there exists a module $K\in \sigma \left[M\right]$ such that $K\oplus N$ is weakly projective in $\sigma \left[M\right]$, for any $N\in \sigma \left[M\right]$. Consequently, over a right perfect ring every module is a direct summand of a weakly projective module. For...

In this paper, we further the study of $\theta$-compactness a generalization of quasi-H-closed sets and its applications to some forms of continuity using $\theta$-open and $\delta$-open sets. Among other results, it is shown a weakly $\theta$-retract of a Hausdorff space $X$ is a $\delta$-closed subset of $X$.

The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes $ℳ$ of modules in $\sigma \left[M\right]$ we study when direct sums of modules from $ℳ$ satisfies a property $\mathbb{P}$ in $\sigma \left[M\right]$. In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.

A right $R$-module $M$ is called a generalized q.f.d. module if every M-singular quotient has finitely generated socle. In this note we give several characterizations to this class of modules by means of weak injectivity, tightness, and weak tightness that generalizes the results in [sanh1], Theorem 3. In particular, it is shown that a module $M$ is g.q.f.d. iff every direct sum of $M$-singular $M$-injective modules in $\sigma \left[M\right]$ is weakly injective iff every direct sum of $M$-singular weakly tight is weakly tight iff...

In this paper we consider three measures of overlap, namely Matusia’s measure $\rho$, Morisita’s measure $\lambda$ and Weitzman’s measure $\Delta$. These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...

In this paper we consider three measures of overlap, namely Matusia's measure , Morisita's measure and Weitzman's measure . These measures are usually used in quantitative ecology and stress-strength models of reliability analysis. Herein we consider two Weibull distributions having the same shape parameter and different scale parameters. This distribution is known to be the most flexible life distribution model with two parameters. Monte Carlo evaluations are used to study the bias and precision...