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.

Abstract

           We produced a study in Estimation for Reliability of the Exponential distribution based on the Bayesian approach. These estimates are derived using Bayesian approaches. In the Bayesian approach, the parameter of the Exponential distribution is assumed to be random variable .we derived bayes estimators of reliability under four types when the prior distribution for the scale parameter of the Exponential distribution is: Inverse Chi-squar

Anticyclone of synoptic studies that influence weather and climate of Iraq, The aim of
the study is to clarify the effect variation of repetition of Anticyclone and effect on thermal
characteristic in Iraq were pressure level has been analyzed (1000) millibars and that because
of pressure level is the closet to the earth surface and the clarity of climatic phenomenon
based on a systematic analysis of synoptic seeking maps and observation and (12:00)
according to timing GMT for five climatic stations which is (Mosul, Kirkuk, Baghdad, Rutba,
and Basra) and so far three consecutive climatic cycles which is first climatic cycle for period
(1986-1976). and second climatic cycle for period (1997-1987) and third climatic cy

This paper deal with the estimation of the shape parameter (a) of Generalized Exponential (GE) distribution when the scale parameter (l) is known via preliminary test single stage shrinkage estimator (SSSE) when a prior knowledge (a₀) a vailable about the shape parameter as initial value due past experiences as well as suitable region (R) for testing this prior knowledge.

The Expression for the Bias, Mean squared error [MSE] and Relative Efficiency [R.Eff(×)] for the proposed estimator are derived. Numerical results about beha

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2⁺ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. ⁴⁰Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f_7/2, 2p_3/2, 1f_5/2, and 2p_1/2 orbits. Model space is used to present calculations using FPBM intera

represent websites link support of human communicate and cohesion of cultures different depending on their languages and their environments around, it was the evolution of one of the most important means of communication of services for electronic networks, the Internet active role in containing the world Bbodqh science and knowledge to Taatlaqah cultures from which derives its intellectual and cognitive cupboards continuity and as a link language for each those environmental Altdadat, linguistic, religious, political, economic . We all know that these electronic means difficult promise ring intellectual and mental connectivity for the masses polarized without being of the image as an element Kravekaa supporter of the electronic media an

     In front of the serious deterioration of the elements of the environment, new convictions arose the need to integrate into the global environmental concerns as being one and the issue of shared responsibility and the impact of this conviction, the evolution of the environment protection law in many countries, including Algeria. Due to the multiplicity of perceptions about the environmental result of multiple scientific disciplines, the legislative concept emerged to protect the environment, which includes prevention and rational management and conservation and restoration and repair.

    Environmental planning for the various governments and countries aims to avert disasters and achieve the

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

This study aims to conduct an exhaustive comparison between the performance of human translators and artificial intelligence-powered machine translation systems, specifically examining the top three systems: Spider-AI, Metacate, and DeepL. A variety of texts from distinct categories were evaluated to gain a profound understanding of the qualitative differences, as well as the strengths and weaknesses, between human and machine translations. The results demonstrated that human translation significantly outperforms machine translation, with larger gaps in literary texts and texts characterized by high linguistic complexity. However, the performance of machine translation systems, particularly DeepL, has improved and in some contexts