Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

An aircraft's landing stage involves inherent hazards and problems associated with many factors, such as weather, runway conditions, pilot experiences, etc. The pilot is responsible for selecting the proper landing procedure based on information provided by the landing console operator (LCO). Given the likelihood of human decisions due to errors and biases, creating an intelligent system becomes important to predict accurate decisions. This paper proposes the fuzzy logic method, which intends to handle the uncertainty and ambiguity inherent in the landing phase, providing intelligent decision support to the pilot while reducing the workload of the LCO. The fuzzy system, built using the Mamdani approach in MATLAB software, considers critical

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

In this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti

In this paper by using δ-semi.open sets we introduced the concept of weakly δ-semi.normal and δ-semi.normal spaces . Many properties and results were investigated and studied. Also we present the notion of δ- semi.compact spaces and we were able to compare with it δ-semi.regular spaces

The importance of knowledge is represented in the use of various sources of information, the corresponding to the same level of importance is the use of modern means and technologies in the delivery and investment of these sources to the beneficiaries, among these means and technologies are the multimedia that deal with most of the human senses, but the most important of which is sight and hearing, if these are invested the means in the field of education will give many positive results, such as the speed of receiving information, its clarity, and its freedom from impurities and influences, as well as its stability in memory as it is based on nderstanding, not memorization. On this basis, the experience of supporting the education process

A new Schiff base o-hydroxybenzylidene-1-phenyl-2,3-dimethyl-4-amino-3-pyrazolin-5-on (HL) ,have been prepared and characterization.(HL) has been used as a chelating ligand to prepare a number of metal complexes VO(II) ,Cr(III) ,Mn(II),Fe(II),Hg(II) and UO2(II) .and mixed ligands complexes have been prepared between o-hydroxybenzylidene-1-phenyl-2,3-dimethyl-4-amino-3-pyrazolin-5-on and 8- hydroxy quinoline with VO(II),Zn(II),Cd(II), Hg(II) and UO2(II) the prepared complexes were isolated and characterized by (FT-IR)and (UV-Vis) spectroscopy. Elemental analysis (C.H.N) Chloride contents, Flame atomic absorption technique. in addition to magnetic susceptibility and conductivity measurement. Molar ratio measurement in solution gave comparabl

New ligand of N-(pyrimidin-2-yl carbamothioyl)acetamide was synthesized and its complexes with (VO(II), Mn (II), Cu (II), Zn (II), Cd (II) and Hg (II) are formed with confirmation of their structures on the bases of spectroscopic analyses. Antimicrobial activity of new complexes are studied against Gram positive S. aureus and Gram negative E. coli, Proteus, Pseudomonas. The octahedral geometrical structures are proved depending on the outcomes from the preceding procedures. Keywords: pyrimidin-2-amine, acetyl isothiocyanate, complexes, Antimicrobial activity