Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of M is called St-closed in M, if N has no proper semi-essential extension in M, i.e if there exists a submodule K of M such that N is a semi-essential submodule of K, then N = K. We investigate the main properties of this type of submodules, and discuss some results that are useful in our work. The class of semi-extending modules is a generalization to the notion of extending modules, where an R-module M is called semi-extending, if every submodule of M is a semi-essential in a direct summand of M. Various properties of semi-extending modules are obtained, and we study the relationships between this class of modules and other related concepts.
An accurate assessment of the pipes’ conditions is required for effective management of the trunk sewers. In this paper the semi-Markov model was developed and tested using the sewer dataset from the Zublin trunk sewer in Baghdad, Iraq, in order to evaluate the future performance of the sewer. For the development of this model the cumulative waiting time distribution of sewers was used in each condition that was derived directly from the sewer condition class and age data. Results showed that the semi-Markov model was inconsistent with the data by adopting ( 2 test) and also, showed that the error in prediction is due to lack of data on the sewer waiting times at each condition state which can be solved by using successive conditi
... Show MoreTests were performed on Marshall samples and were implemented for permanent deformation and resilient modulus (Mr) under indirect tensile repeated loading (ITRL), with constant stress level. Two types of liquid asphalt (cutback and emulsion) were tried as recycling agents, aged materials that were reclaimed from field (100% RAP), samples were prepared from the aged mixture, and two types of liquid asphalt (cutback and emulsion) with a weight content of 0.5% were utilized to prepare a recycled mixture. A group of twelve samples was prepared for each mixture; six samples were tested directly for ITRL test (three samples at 25˚C and three samples at 40˚C), an average value for ITRL for every three samples was calculated (
... Show MoreBackground: 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
... Show MoreLight isotopes, especially closed shell nuclei, have significance in thermonuclear reactions of the Carbon-Nitrogen-Oxygen (CNO) cycle in stars. In this research, 12C(p, γ) 13N and 14N(p, γ) 15O reactions have been calculated by means of Matlab codes to find the reaction rate across a temperature range of 0.006 to 10 GK using non-resonant parts, as well as the astrophysical S- factor S(E) at low energies. It was concluded that the high binding energy of 12C and 14N nuclei make the reaction less probable thus enabling other competitive processes to develop, which enhances the probability of other competitive proton reactions in the CNO cycle.
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
... Show MoreBackground: 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
... Show MoreThis paper presents thermal characteristics analysis of a modified Closed Wet Cooling Tower (CWCT) based on heat and mass transfer principles to improve the performance of this tower in Iraq. A prototype of CWCT optimized by added packing was designed, manufactured and tested for cooling capacity of 9 kW. Experiments are conducted to explore the effects of various operational and conformational parameters on the thermal performance. In the test section, spray water temperature and both dry bulb temperature and relative humidity of the air measured at intermediate points of the heat exchanger and packing. Heat exchangers consist of four rows and eight columns for an inline tubes arrangement and six rows and five columns f
... Show MoreIn this paper, the concept of fully stable Banach Algebra modules relative to an ideal has been introduced. Let A be an algebra, X is called fully stable Banach A-module relative to ideal K of A, if for every submodule Y of X and for each multiplier ?:Y?X such that ?(Y)?Y+KX. Their properties and other characterizations for this concept have been studied.