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).

    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule  of an -module  is called an approximaitly semi-prime submodule of  , if whenever , where ,  and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are

     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

     Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.

An attempt was made to evaluate the PV performance of one-axis daily tracking and fixed system for Baghdad, Iraq. Two experimental simulations were conducted on a PV module for that purpose. Measurements included incident solar radiation, load voltage and load current. The first experiment was carried out for six months of winter half of year to simulate the one-axis daily tracking. The azimuth angle was due south while the tilt angle was being set to optimum according to each day of simulation. The second experiment was done at one day to simulate the PV module of fixed angles. It is found that there is a significant power gain of 29.6% for the tracking system in respect to the fixed one. The one-axis daily tracking was much more effect

Let M be an R-module, where R is a commutative ring with unity. A submodule N of M is called e-small (denoted by N e  M) if N + K = M, where K e  M implies K = M. We give many properties related with this type of submodules.

Let M be an R-module, where R be a commutative;ring with identity. In this paper, we defined a new kind of submodules, namely; ET-coessential and ET-Coclosed submodules of M. Let T be a submodule of M. Let K  H  M, K  is called  ET-Coessential of H in M (K⊆_ET.ce H), if     . A submodule H is called ET- coclosed in M of H has no proper coessential submodule in M, we denote by  (K⊆_ET.cc H) , that is, K⊆_ET.ce H implies that   K = H. In our work, we introduce;some properties of ET-coessential and ET-coclosed submodules of M.

The goal of this research is to introduce the concepts of Large-coessential submodule and Large-coclosed submodule, for which some properties are also considered. Let M  be an R-module and K, N are submodules of M such that , then K is said to be Large-coessential submodule, if . A submodule N of M is called Large-coclosed submodule, if K is Large-coessential submodule of N in M, for some submodule K of N, implies that  .

      In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout this work, we assume that    is a commutative ring with identity and  is a left unitary R- module. A  proper submodule  of  is called a quasi-radical semi prime submodule (for short Q-rad-semiprime), if     for   ,   ,and then  . Where   is the intersection of all prime submodules of .