Let R be a commutative ring with identity and let Mbe a unitary R-module. We shall say that a proper submodule N of M is nearly S-primary (for short NS-primary), if whenever , , with  implies that either  or there exists a positive integer n, such that , where  is the Jacobson radical of M. In this paper we give some new results of NS-primary submodule. Moreover some characterizations of these classes of submodules are obtained.

This study was carried out in the Center of Endocrinology and Diabetes in Baghdad during the period between October 2019 to February 2020. The aim was to measure the level of some apoptosis markers and some autoimmune antibodies related to the thyroid gland in Iraqi patients with hyperthyroidism and evaluate the correlation between all the measured parameters. The study included 88 patients who were divided into three groups; group 1 included 30 newly diagnosed hyperthyroidism patients (24 females, 6 males); group 2 included  30 patients of hyperthyroidism who were under treatment (28, 2 males); group 3 included 28 healthy individuals as control group (22 females, 6 males).

     Most of the patient's ages

In the recent decade, injection of nanoparticles (NPs) into underground formation as liquid nanodispersions has been suggested as a smart alternative for conventional methods in tertiary oil recovery projects from mature oil reservoirs. Such reservoirs, however, are strong candidates for carbon geo-sequestration (CGS) projects, and the presence of nanoparticles (NPs) after nanofluid-flooding can add more complexity to carbon geo-storage projects. Despite studies investigating CO2 injection and nanofluid-flooding for EOR projects, no information was reported about the potential synergistic effects of CO2 and NPs on enhanced oil recovery (EOR) and CGS concerning the interfacial tension (γ) of CO2-oil system. This study thus extensively inves

   In this paper, we introduce a new type of functions in bitopological spaces, namely, (1,2)*-proper functions. Also, we study the basic properties and characterizations of these functions . One of the most important of equivalent definitions to the (1,2)*-proper functions is given by using (1,2)*-cluster points of filters . Moreover we define and study (1,2)*-perfect functions and (1,2)*-compact functions in bitopological spaces and we study the relation between (1,2)*-proper functions and each of (1,2)*-closed functions , (1,2)*-perfect functions and (1,2)*-compact functions and we give an example when the converse may not be true .
 

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 approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

Let be a unitary left R-module on associative ring with identity. A submodule of is called -annihilator small if , where is a submodule of , implies that ann( )=0, where ann( ) indicates annihilator of in . In this paper, we introduce the concepts of -annihilator-coessential and - annihilator - coclosed submodules. We give many properties related with these types of submodules.

The shape for even-even (54Xe 118≤ A ≤ 140 and 82Pb 204 ≤ A ≤ 210 ) nuclei have been studied and investigated through the deformation parameters and δ , these deformation parameters were calculated by two different methods. The first one is nucleus quadrupole deformation parameter β2 from reduced transition probability B(E2)↑ for 0+→2+1 transitions and the second is nucleus quadrupole deformation parameters δ from quadrupole moment Qo.The relationship between two deformation parameters ( , ) and neutrons magic number (N=82 & 126) was studied through plotting the deformation parameters ( , ) as a function of neutrons number , from this relationship we can see very cleary that the deformation of nucleus decreased when th

   In this paper, we introduce new classes of sets called g *sD -sets , g *sD −α -sets , g *spreD − sets , g *sbD − -sets and g *sD −β -sets . Also, we study some of their properties and relations among them . Moreover, we use these sets to define and study some associative separation axioms .
 

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .

Let  be a commutative ring with identity and  be an -module. In this work, we present the concept of semi--maximal sumodule as a generalization of -maximal submodule.

We present that a submodule  of an -module  is a semi--maximal (sortly --max) submodule if  is a semisimple -module (where  is a submodule of ). We  investegate some properties of these kinds of modules.