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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

The diabetic foot is considered one of the long term diabetes complications caused by a defect in blood vessel and nerve system. This requires dealing with diabetic foot with professional medical care, so as to prevent its development in advanced stages which could end to gangrene and amputation of the foot. This study has been initiated through follow-up of twelve patients with diabetes and the presence various occlusions in lower limb artery. One patient from them was chosen for investigation, this patient has stenosis in popliteal artery and presence multiple stenosis in superficial femoral artery. This study based on analysis present case of patient and prediction for progress stenosis in superficial femoral artery till arrive semi t

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

The green method was chosen for the preparation of nano iron oxide due to its simplicity, ease of preparation, and purity, compared to other methods. Nano iron oxide was made using a substance that causes precipitation and a coating from the alcoholic extract of orange leaves from Iraq. It was examined structurally and spectrally using several techniques, including X-ray diffraction, Fourier transform infrared spectroscopy, field-emission scanning microscopy (FESEM), energy-dispersive X-ray spectroscopy, and UV-Vis spectroscopy. The diagnosis proved that the nano iron oxide was successfully prepared in a spherical form and with an average size of 71.1 nm. The nano iron oxide particles were tested for their ability to remove crystal

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

In this paper Alx Ga1-x As:H films have been prepared by using new deposition method based on combination of flash- thermal evaporation technique. The thickness of our samples was about 300nm. The Al concentration was altered within the 0 x 40.
The results of X- ray diffraction analysis (XRD) confirmed the amorphous structure of all AlXGa1-x As:H films with x  40 and annealing temperature (Ta)<200°C. the temperature dependence of the DC conductivity GDC with various Al content has been measured for AlXGa1-x As:H films.
We have found that the thermal activation energy Ea depends of Al content and Ta, thus the value of Ea were approximately equal to half the value of optical gap.

This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient

Background: Since the invention of laser in 1960, lasers have been developed and approved in many fields. Lasers can now be regarded as practical tools with unique properties that have been utilized effectively in several applications in fields of medical and biological sciences.Objectives: The aim of the current study was to preparation of vaccines (live attenuated and killed) by irradiation of the bacteria by the low level diode laser.Methods: six bacterial isolates were isolated from human samples of diabetic foot infections, which used for preparation of vaccines. The experiment was conducted on fifteen adult male rabbits; they were divided into three groups with 5 rabbits each. Blood samples were collected from the marginal ear vein

This paper deals with calculate stresses in Knee-Ankle-Foot-Orthosis as a result of the effect vibration during gait cycle for patient wearing KAFO .Experimental part included measurement interface pressure between KAFO and leg due to action muscles and body weigh on Orthosis. also measurement acceleration result from motion of defected leg by accelerometer .Results of Experimental part used input in theoretical part so as to calculate stresses result from applying pressure and acceleration on KAFO by engineering analysis program ANSYS 14.Resultes show stresses values in upper KAFO greater than lower KAFO that is back to muscles more effective in thigh part lead to recoding pressure higher than pressure in shank part.