Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

In this work, a comparative analysis for the behavior and pattern of the variations of the IF2 and T Ionospheric indices was conducted for the minimum and maximum years of solar cycles 23 and 24. Also, the correlative relationship between the two ionospheric indices was examined for the seasonal periods spanning from August 1996 to November 2008 for solar cycle 23 and from December 2008 to November 2019 for solar cycle 24. Statistical calculations were performed to compare predicted values with observed values for the selected indices during the tested timeframes. The study's findings revealed that the behavior of the examined indices exhibited almost similar variations throughout the studied timeframe. The seasonal variations were

        Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

    The aim of this study was the isolation and characterization of Klebsiella pneumonia from 160 urine samples of patients hospitalized in children hospital in AL-Ramadi Proveng during October 2006 to May 2008. Also determination of the susceptibility of K. pneumoniae against a number of antibiotics to explain resistance mechanism for these antibiotics by using interpretative reading to avoid using it in treatment.           Forty two isolates were detected as K. pneumoniae with resistance to a number of antibiotics . These isolates were  tested to determine their sensitivities to a wide number of antibiotics which included  β-lactum group and aminoglicosides

 Let R be a commutative ring with 10 and M is a unitary R-module . In this paper , our aim is to continue studying 2-absorbing submodules which are introduced by  A.Y. Darani and F. Soheilina . Many new properties and characterizations are given .

Our aim in this paper is to introduce the notation of nearly primary-2-absorbing submodule as generalization of 2-absorbing submodule where a proper submodule  of an -module  is called nearly primary-2-absorbing submodule if whenever , for , , ,  implies that either  or  or . We got many basic, properties, examples and characterizations of this concept. Furthermore, characterizations of nearly primary-2-absorbing submodules in some classes of modules were inserted. Moreover, the behavior of nearly primary-2-absorbing submodule under -epimorphism was studied.

  In this paper it was presented the idea quasi-fully cancellation fuzzy modules and we will denote it by  Q-FCF(M), condition universalistic idea quasi-fully cancellation modules It .has been circulated to this idea quasi-max fully cancellation fuzzy modules and we will denote it by Q-MFCF(M). Lot of results and properties have been studied in this research.