Let R be a commutative ring with unity. In this paper we introduce the notion of chained fuzzy modules as a generalization of chained modules. We investigate several characterizations and properties of this concept

  Let R be a commutative ring with unity. In this paper we introduce and study fuzzy distributive modules and fuzzy arithmetical rings as generalizations of (ordinary) distributive modules and arithmetical ring. We give some basic properties about these concepts.  

     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 .

Recently, the theory of Complex Networks gives a modern insight into a variety of applications in our life. Complex Networks are used to form complex phenomena into graph-based models that include nodes and edges connecting them. This representation can be analyzed by using network metrics such as node degree, clustering coefficient, path length, closeness, betweenness, density, and diameter, to mention a few. The topology of the complex interconnections of power grids is considered one of the challenges that can be faced in terms of understanding and analyzing them. Therefore, some countries use Complex Networks concepts to model their power grid networks. In this work, the Iraqi Power Grid network (IPG) has been modeled, visua

 In this paper, we proved the existence and uniqueness of the solution of nonlinear Volterra fuzzy integral equations of the second kind.
 

In this study Microwave and conventional methods have been used to extract and estimate pectin and its degree of esterification from dried grapefruit and orange peels. Acidified solution water with nitric acid in pH (1.5) was used. In conventional method, different temperature degrees for extraction pectin from grape fruit and orange(85 ,90 , 95 and 100?C) for 1 h were used The results showed grapefruit peels contained 12.82, 17.05, 18.47, 15.89% respectively, while the corresponding values were 5.96, 6.74, 7.41 and 8.00 %, respectively in orange peels. In microwave method, times were 90, 100, 110 and 120 seconds. Grapefruit peels contain 13.86, 16.57, 18.69, and 17.87%, respectively, while the corresponding values were of 6.53, 6.68, 7.2