Throughout this paper, we introduce the notion of weak essential F-submodules of F-modules as a generalization of  weak essential submodules. Also we study the homomorphic image and inverse image of weak essential F-submodules.

Background: Calcaneus is a spongy cancellous bone with rich blood supply , its fracture heals more rapidly providing no occurrence of infection and soft tissue injury around ,no gross malposition of fragments. The associated pain leads to a major impairment in life quality. The aim of treatment for calcaneal fractures is the decrease of pain and rebuilding of walking ability for patients with normal foot shape and the ability to wear normal foot wear. To reduce complications, a minimally invasive technique for the treatment of displaced intra-articular fractures of the calcaneus was preferred to use. The purpose of this study was to determine whether the closed reduction and percutaneous K. wire fixation of displaced intra-art

This work provides an analysis of the thermal flow and behavior of the (load-free) refrigerator compartment. The main goal was to compare the thermal behavior inside the refrigerator cavity to the freezer door (home refrigerator) effect and install a fan on the freezer door while neglecting the heat transmitted by thermal radiation. Moreover, the velocity distribution, temperature, and velocity path lines are theoretically studied. This was observed without affecting the shelves inside the cabinet and the egg and butter places on the refrigerator door as they were removed and the aluminum door replaced with a glass door. This study aims to expand our knowledge about the temperature and flow fields of this refrigerator mo

Background: Calcaneus is a spongy cancellous bone with rich blood supply , its fracture heals more rapidly providing no occurrence of infection and soft tissue injury around ,no gross malposition of fragments. The associated pain leads to a major impairment in life quality. The aim of treatment for calcaneal fractures is the decrease of pain and rebuilding of walking ability for patients with normal foot shape and the ability to wear normal foot wear. To reduce complications, a minimally invasive technique for the treatment of displaced intra-articular fractures of the calcaneus was preferred to use.

The purpose of this study was to determine whether the closed reduction and percutaneous K. wire fixation of displ

The aim of this paper is introducing the concept of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal. Some properties of (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal have been studied and another characterizations have been given. The relationship of (ɱ,ɳ) strong full stability B-Algebra-module related to an ideal that states,  a B- -module Ӽ is (ɱ,ɳ)- strong full stability B-Algebra-module related to an ideal  , if and only if  for any two ɱ-element sub-sets and of Ӽ^ɳ, if , for each j = 1, …, ɱ,  i = 1,…, ɳ  and   implies _Ạɳ( ) _Ạɳ(  have been proved..

      In order to increase the amount of solar radiation reaching a solar panel, and hence increase its performance, a tracking system might be used. A prototype of an efficient and portable solar tracking system, for home applications was constructed. The Arduino Uno Microcontroller is utilized to drive the proposed tacking system. The results of area under curve show that at certain circumstances, the open-loop tracking system is more efficient as compared with fixed one, while  the closed-loop tracker is slightly efficient than open-loop tracker.

The heat and mass transfer coefficients of the indirect contact closed circuit cooling tower, ICCCCT, were investigated experimentally. Different experiments were conducted involving the controlling parameters such as air velocity, spray water to air mass flow rate ratio, spray water flow rate, ambient air wet bulb temperature and the provided heat load to investigate their effects on the performance of the ICCCCT. Also the effect of using packing on the performance of the ICCCCT was investigated. It was noticed that these parameters affect the tower performance and the use of packing materials is a good approach to enhance the performance for different operational conditions. Correlations for mass and heat transfer coefficients are pres

     Let R be a commutative ring with 1 and M be a left unitary R-module. In this paper, we give a generalization for the notions of compressible (retractable) Modules. We study s-essentially compressible (s-essentially retractable). We give some of their advantages, properties, characterizations and examples. We also study the relation between s-essentially compressible   (s-essentially retractable modules) and some classes of modules.

In this paper ,we introduce hollow modules with respect to an arbitrary submodule .Let M be a non-zero module and T be a submodule of M .We say that M is aT-hollow module if every proper submodule K of M such that T ⊈ K is a T-small submodule of M .We investigate the basic properties of a T-hollow module