Let  be an R-module, and let  be a submodule of . A submodule  is called -Small submodule () if for every submodule  of  such that  implies that . In our work we give the definition of -coclosed submodule and -hollow-lifiting modules with many properties.

     Kp index correlates with the many magnetosphere properties, which are used to measure the level of magnetic activity. In the solar system, the two different planets, Mercury with weak magnetic field and Jupiter with strong magnetic field, are selected for this study to calculate the planet's magnetosphere radius (R_MP) which represents the size of magnetosphere compared with solar activity through Kp index,  through two types of geomagnetic conditions; quiet and strong for the period (2016-2018). From the results, we found that there are reversible relations between them during strong geomagnetic storms, while there are direct relations during quiet geomagnetic conditions. Also it is found that the

هدف البحث إلى التعرف على الانكسار النفسي فضلاً عن التعرف على الفروق في الانكسار النفسي بين الطلبة على وفق متغير الجنس (ذكر – انثى) والمرحلة الدراسية (أول- رابع)، تألفت عينة البحث من (120) طالبا وطالبة من طلبة الجامعة، وتم تطبيق مقياس البحث - مقياس (الانكسار النفسي) وهو (من إعداد الباحثة)، وقد اسفرت نتائج البحث عن: - إن طلبة الجامعة ليس لديهم انكسار نفسي. - عدم وجود فروق في الانكسار النفسي على وفق متغير الجنس أو متغير

  Let M be an R-module, where R is commutative ring with unity. In this paper we study the behavior of strongly hollow and quasi hollow submodule in the class of strongly comultiplication modules. Beside this we give the relationships between strongly hollow and quasi hollow submodules with V-coprime, coprime, bi-hollow submodules.

In this paper, we introduce and study the concepts of hollow – J–lifting modules and FI – hollow – J–lifting modules as a proper generalization of both hollow–lifting and J–lifting modules . We call an R–module M as hollow – J – lifting if for every submodule N of M with is hollow, there exists a submodule K of M such that M = K Ḱ and K N in M . Several characterizations and properties of hollow –J–lifting modules are obtained . Modules related to hollow – J–lifting modules are  given .

    In this paper, we formulate and study a new property, namely indeterminacy (neutrosophic) of the hollow module. We mean indeterminacy hollow module is neutrosophic hollow module B (shortly Ne(B)) such that it is not possible to specify the conditions for satisfying it.  Some concepts have been studied and introduced, for instance, the indeterminacy local module, indeterminacy divisible module, indeterminacy indecomposable module and indeterminacy hollow-lifting module. Also, we investigate that if Ne(B) is an indeterminacy divisible module with no indeterminacy zero divisors, then any indeterminacy submodule Ne(K) of Ne(B) is an indeterminacy hollow module. Further, we study the relationship between the indeterminacy of hollow an

     As a result of changes in the chemical properties of the Shatt al-Arab River, especially in the last decade, as well as the lack of rainfall and the effect of seawater intrusion into the Shatt al-Arab, this study was conducted to investigate the possible changes in the water pipelines like corrosive and scaling which Shatt al-Arab River is the source of water supply for domestic use. Domestic water samples were collected from 10 various locations in Basrah to study the water's tendency to be corrosive or form scales along the pipelines. The Langelier Index, Ryznar Index, Larson-Skold Index, and Saturation Index were used to determine the corrosivity potential of water based on physical and chemical parameters. Most domestic wate

     The concept of a small f- subm was presented in a previous study. This work introduced a concept of a hollow f- module, where a module is said to be hollow fuzzy when every subm of it is a small f- subm. Some new types of hollow modules are provided namely, Loc- hollow f- modules as a strength of the hollow module, where every Loc- hollow f- module is a hollow module, but the converse is not true. Many properties and characterizations of these concepts are proved, also the relationship between all these types is researched. Many important results that explain this relationship are demonstrated also several characterizations and properties related to these concepts are given.