Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

Let R be any ring with identity, and let M be a unitary left R-module. A submodule K of M is called generalized coessential submodule of N in M, if Rad( ). A module M is called generalized hollow-lifting module, if every submodule N of M with is a hollow module, has a generalized coessential submodule of N in M that is a direct summand of M. In this paper, we study some properties of this type of modules.

Let R be a commutative ring with unity. Let W be an R-module, for K≤F, where F is a submodule of W and K is said to be R-annihilator coessential submodule of F in W (briefly R-a-coessential) if  (denoted by K  F in W). An R-module W is called strongly hollow -R-annihilator -lifting module (briefly, strongly hollow-R-a-lifting), if for every submodule F of W with  hollow, there exists a fully invariant direct summand K of W such that K  F in W. An R - module W is called strongly R - annihilator - ( hollow - lifting ) module ( briefly strongly R - a - ( hollow - lifting ) module ), if for every submodule F of W with   R - a - hollow, there exists a fully invariant direct summand K o

The present work aims to improve the flux of forward osmosis with the use of Thin Film Composite membrane by reducing the effect of polarization on draw solution (brine solution) side.This study was conducted in two parts. The first is under the effect of polarization in which the flux and the water permeability coefficient (A) were calculated. In the second part of the study the experiments were repeated using a circulating pump at various speeds to make turbulence and reduce the effect of polarization on the brine solution side.
A model capable of predicting water permeability coefficient has been derived, and this is given by the following equations:
Z=Z₀ +C.R.T/9.8(d²/D²+1) [Exp. [-9.8(d

Aim: The present study aims to improve the poor water solubility of zaltoprofen which is a non-steroidal anti-inflammatory drug (NSAIDs) with a potent analgesic effect using solid dispersion then formulate it as a hollow type suppository to be more convenient for geriatric patients. Materials and Method: Zaltoprofen solid dispersions were prepared by solvent evaporation technique in different zaltoprofen: Soluplus® ratios. Results: Among the formulations tested, zaltoprofen solid dispersion preparation using 1:5 (zaltoprofen: Soluplus®) ratio showed the highest solubility and selected for further investigation. Solid dispersion characterization was evaluated by differential scanning calorimetry (DSC), X-ray diffraction study (XRD) and Fou

A computational investigation has been carried out on the design and properties of the electrostatic mirror. In this research, we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The electron beam path under zero magnification condition had been investigated as mirror trajectory with the aid of fourth – order – Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. each optical element in optical system has suffer from the chromatic aberration, for this case, it is use to operate the mirror in optical system at various values

The aim of this work is to study reverse osmosis characteristics for copper sulfate hexahydrate (CuSO4.6H2O), nickel sulfate hexahydrate (NiSO4.6H2O) and zinc sulfate hexahydrate (ZnSO4.6H2O) removal from aqueous solution which discharge from some Iraqi factories such as Alnasser Company for mechanical industries. The mode of operation of reverse osmosis was permeate is removed and the concentrate of metals solution is recycled back to the feed vessel. Spiral-wound membrane is thin film composite membrane (TFC) was used to conduct this study on reverse osmosis. The variables studied are metals concentrations (50 – 150 ppm) and time (15 – 90 min). It was found that increasing the time results in an increase in concentration of metal in p

Fiber‐reinforced elastic laminated composites are extensively used in several domains owing to their high specific stiffness and strength and low specific density. Several studies were performed to ascertain the factors that affect the composite plates’ dynamic properties. This study aims to derive a mathematical model for the dynamic response of the processed composite material in the form of an annular circular shape made of polyester/E‐glass composite. The mathematical model was developed based on modified classical annular circular plate theory under dynamic loading, and all its formulas were solved using MATLAB 2023. The mathematical model was also verified with real experimental work involving the vibration test of the f