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.
Objective: To evaluate the functional outcome of percutaneous cross two K wires fixation for Gartland types II and III fractures of humerus. Methodology: This prospective study included80 patients with supracondylar humeral fracture, who underwent closed reduction and fixation by two crossed Kirschner wires. We included children with age < 15 years with closed fractures with Gartland types II and III, while the patient with vascular injury, open, irreducible fractures were excluded. The patients were following up for 6 months and assessed functionally by Flynn’s criteria. Results: The mean age of patients was 8.1 years. Trauma while child playing was the main mechanism of injury in 43 (59.8%) children and 46 (57.5%) fractures were of the
... Show MoreWe introduced the nomenclature of orthogonal G -m-derivations and orthogonal generalized G -m-derivations in semi-prime G -near-rings and provide a few essentials and enough provision for generalized G -n-derivations in semi-prime G -near-rings by orthogonal.
In this research, a variable stiffness actuator is proposed to enhance the damping of the mechanical vibrating system. The frequency response analysis of the vibrating system is dependant in order to analyze and synthesis this semi-active damping, where the suggested process is using active filter to estimate the present frequency of the vibration system, and this will limit the value of the stiffness of the vibrated system. Two active filter s are needed, low-pass-filter (LPF) to choose the higher stiffness of the actuator at small frequencies as well as more damping and high-pass-filter (HPF) to choose the lower stiffness of the actuator at high frequencies as well as more damping, and so
... Show MoreTo evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult
... Show MoreLet R be a commutative ring with non-zero identity element. For two fixed positive integers m and n. A right R-module M is called fully (m,n) -stable relative to ideal A of , if for each n-generated submodule of Mm and R-homomorphism . In this paper we give some characterization theorems and properties of fully (m,n) -stable modules relative to an ideal A of . which generalize the results of fully stable modules relative to an ideal A of R.
In this paper, analyzing the non-dimensional Magnesium-hydrodynamics problem Using nanoparticles in Jeffrey-Hamel flow (JHF) has been studied. The fundamental equations for this issue are reduced to a three-order ordinary differential equation. The current project investigated the effect of the angles between the plates, Reynolds number, nanoparticles volume fraction parameter, and magnetic number on the velocity distribution by using analytical technique known as a perturbation iteration scheme (PIS). The effect of these parameters is similar in the converging and diverging channels except magnetic number that it is different in the divergent channel. Furthermore, the resulting solutions with good convergence and high accuracy for the d
... Show MoreThe research dealt with a comparative study between some semi-parametric estimation methods to the Partial linear Single Index Model using simulation. There are two approaches to model estimation two-stage procedure and MADE to estimate this model. Simulations were used to study the finite sample performance of estimating methods based on different Single Index models, error variances, and different sample sizes , and the mean average squared errors were used as a comparison criterion between the methods were used. The results showed a preference for the two-stage procedure depending on all the cases that were used
The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.