In this paper the diagrams and divided power of the place polarization
(k )
ij  , with
its capelli identities have been used, to study the complex of Lascoux in case of the
partition (4,4,4).

     The main purpose of this paper is to study the application of weyl module and resolution in the case skew- shapes (6, 5) / (1, 0) and (6, 5) / (2, 0) by using contracting homotopy and the 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).

In the partition theory, there is more then one form of representation of dedication, most notably the Abacus diagram, which gives an accurate and specific description. In the year 2019, Mahmood and Mahmood presented the idea of merging more than two plans, and then the following question was raised: Is the process of separating any somewhat large diagram into smaller schemes possible? The general formula to split e-abacus diagram into two or more equal or unequal parts was achieved in this study now.

In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.

     The Syriac language is one of the ancient Semitic languages that appeared in the first century AD. It is currently used in a number of cities in Iraq, Turkey, and others. In this research paper, we tried to apply the work of  Ali and Mahmood 2020  on the letters and words in the Syriac language to find a new encoding for them and increase the possibility of reading the message by other people.

Constructing a fine 3D geomodel for complex giant reservoir is a crucial task for hydrocarbon volume assessment and guiding for optimal development. The case under study is Mishrif reservoir of Halfaya oil field, which is an Iraqi giant carbonate reservoir. Mishrif mainly consists of limestone rocks which belong to Late Cenomanian age. The average gross thickness of formation is about 400m. In this paper, a high-resolution 3D geological model has been built using Petrel software that can be utilized as input for dynamic simulation. The model is constructed based on geological, geophysical, pertophysical and engineering data from about 60 available wells to characterize the structural, stratigraphic, and properties distri