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.

Abstract

Friction stir welding is a relatively new joining process, which involves the joining of metals without fusion or filler materials. In this study, the effect of welding parameters on the mechanical properties of aluminum alloys AA2024-T351 joints produced by FSW was investigated.

Different ranges of welding parameters, as input factors, such as welding speed (6 - 34 mm/min) and rotational speed (725 - 1235 rpm) were used to obtain their influences on the main responses, in terms of elongation, tensile strength, and maximum bending force. Experimental measurements of main responses were taken and analyzed using DESIGN EXPERT 8 experimental design software which was used to develop t

A numerical study of the double-diffusive laminar natural convection in a right triangular solar collector has been investigated in present work. The base (absorber) and glass cover of the collector are isothermal and isoconcentration surfaces, while the vertical wall is considered adiabatic and impermeable. Both aiding and opposing buoyancy forces have been studied. Governing equations in vorticity-stream function form are discretized via finite-difference method and are solved numerically by iterative successive under relaxation (SUR) technique. Computer code for MATLAB software has been developed and written to solve mathematical model. Results in the form of streamlines, isotherms, isoconcentration, average Nusselt, and average Sherw

   The aim of this work is to detect the best operating conditions that effect on the removal of Cu²⁺, Zn²⁺, and Ni²⁺ ions from aqueous solution using date pits in the batch adsorption experiments. The results have shown that the Al-zahdi Iraqi date pits demonstrated more efficient at certain values of operating conditions of adsorbent doses of 0.12 g/ml of aqueous solution, adsorption time 72 h, pH solution 5.5 ±0.2, shaking speed  300 rpm, and smallest adsorbent particle size needed for removal of metals.  At the same time the particle size of date pits has a little effect on the adsorption at low initial concentration of heavy metals. The adsorption of metals increases with increas

Two- dimensional numerical simulations are carried out to study the elements of observing a Dirac point source and a Dirac binary system. The essential features of this simulation are demonstrated in terms of the point spread function and the modulation transfer function. Two mathematical equations have been extracted to present, firstly the relationship between the radius of optical telescope and the distance between the central frequency and cut-off frequency of the optical telescope, secondly the relationship between the radius of the optical telescope and the average frequency components of the modulation transfer function.

 In the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The

The present work describes numerical and experimental investigation of the heat transfer characteristics in a plate-fin, having built-in piezoelectric actuator mounted on the base plate (substrate). The geometrical configuration considered in the present work is representative of a single element of the plate-fin and triple fins. Air is taken as the working fluid. A performance data for a single rectangular fin and triple fins are provided for different frequency levels (5, 30 and
50HZ) , different input power (5,10,20,30,40 and 50W) and different inlet velocity (0.5, 1, 2, 3, 4, 5 and 6m/s) for the single rectangular fin and triple fins with and without oscillation. The investigation was also performed with different geometrical fin

The Wheat husk is one of the common wastes abundantly available in the Middle East countries especially in Iraq. The present study aimed to evaluate the Wheat husk as low cost material, eco-friendly adsorbents for the removal of the carcinogenic dye (Congo red dye) from wastewater by investigate the effect of, at different conditions such as, pH(3-10), amount of adsorbents (1-2.3gm/L),and particle size (125-1000) μm, initial Congo red dye concentration(10, 25 , 50 and 75mg/l)  by batch experiments. The results showed that the removal percentage of dye increased with increasing adsorbent dosage, and decreasing particle size. The maximum removal and uptake reached (91%) , 21.5mg/g, respectively for 25 initial concent

In this paper, integrated quantum neural network (QNN), which is a class of feedforward

neural networks (FFNN’s), is performed through emerging quantum computing (QC) with artificial neural network(ANN) classifier. It is used in data classification technique, and here iris flower data is used as a classification signals. For this purpose independent component analysis (ICA) is used as a feature extraction technique after normalization of these signals, the architecture of (QNN’s) has inherently built in fuzzy, hidden units of these networks (QNN’s) to develop quantized representations of sample information provided by the training data set in various graded levels of certainty. Experimental results presented here show that