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 purpose of this research was to investigate the beneficial effects of phosphatidylcholine in reducing changes in both lipid and protein profiles in addition to atherogenic index in adult rats with fructose-induced metabolic syndrome. Thirty-six mature Wistar Albino female rats (Rattus norvegicus) (aged 12-15 weeks and weighing 200±10 g) were divided randomly into four groups (G1, G2, G3, and G4); then variable treatments were orally administered for 62 days as follows: G1 (Control group), received distilled water; G2, treated with phosphatidylcholine (PC) orally (1 g/kg BW); G3 (Fr), orally dosed with 40% fructose and 25% fructose mixed with drinking water; G4 (Fr+PC), were also intubated with 40% fr

A new data for Fusion power density has been obtained for T-3He and T-T fusion reactions, power density is a substantial term in the researches related to the fusion energy generation and ignition calculations of magnetic confined systems. In the current work, thermal nuclear reactivities, power densities of a fusion reactors and the ignition condition inquiry are achieved by using a new and accurate formula of cross section, the maximum values of fusion power density for T-3He and TT reaction are 1.1×107 W/m3 at T=700 KeV and 4.7×106 W/m3 at T=500 KeV respectively, While Zeff suggested to be 1.44 for the two reactions. Bremsstrahlung radiation has also been determined to reaching self- sustaining reactors, Bremsstrahlung values are 4.5×

Copula modeling is widely used in modern statistics. The boundary bias problem is one of the problems faced when estimating by nonparametric methods, as kernel estimators are the most common in nonparametric estimation. In this paper, the copula density function was estimated using the probit transformation nonparametric method in order to get rid of the boundary bias problem that the kernel estimators suffer from. Using simulation for three nonparametric methods to estimate the copula density function and we proposed a new method that is better than the rest of the methods by five types of copulas with different sample sizes and different levels of correlation between the copula variables and the different parameters for the function. The