The main aim of this paper is to study the application of Weyl module resolution in the case of two rows, which will be specified in the skew- partition (6, 6)/(1,1) and (6,6)/(1,0), by using the homological Weyl (i.e. the contracting homotopy and place polarization).

     The aim of this work is to survey the two rows resolution of Weyl module and locate the terms and the exactness of the Weyl Resolution in the case of skew-shape (8,6)/(2,1).

The aim of this work is to study the application of Weyl module resolution in the case of two rows, which will be specified in the partition (7, 6) and skew- partition (7,6)/(1,0)  by using the homological Weyl (i.e. the contracting homotopy and place polarization).

The purpose of this paper is to study the application of Weyl module’s resolution in the case of two rows which will be specified in the partitions (7, 7) and (7, 7) / (1, 0), using the homological Weyl (i.e. the contracting homotopy and place polarization).

Let R be a ring with identity and M be a right unitary R-module. In this paper we
introduce the notion of strongly coretractable modules. Some basic properties of this
class of modules are investigated and some relationships between these modules and
other related concepts are introduced. 

     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 .

     The question asked by all researchers is when solar panels will replace the national grid, especially in the domestic sector. In this study, a rooftop stand-alone solar electric system is designed to provide all the electrical power to a house in Baghdad-Iraq, using a (How to design PV system) simulation program. The feasibility of this system compared to the performance of the national electric grid and the system of private diesel generators is determined. The proposed solar system capacity is (25 kW), and the space required and the energy payback time are (360 m² and 7.82 years), respectively. By using the current system, the net CO₂ mitigation amount is 499,518.2 tons for 30-year. The kilowatt-hour cost

     In this paper we introduce the notions of t-stable extending and strongly t-stable extending modules. We investigate properties and characterizations of each of these concepts. It is shown that a direct sum of t-stable extending modules is t-stable extending while with certain conditions a direct sum of strongly t-stable extending is strongly t-stable extending. Also, it is proved that under certain condition, a stable submodule of t-stable extending (strongly t-stable extending) inherits the property.

      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.