Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

Conventional dosage forms for topical and transdermal drug delivery have several disadvantages related mainly to its poor skin permeation and patient compliance. Many approaches have been developed to improve these dosage forms. Film forming drug delivery systems represents a recent advancement in this field. It provides improved patient compliance with enhanced skin permeation of drugs. In its simplest form, these consist of a polymeric solution, usually in a supersaturated state, in a suitable solvent. A plasticizer is usually added to improve the flexibility and enhance the tensile strength to the film. It is also possible to control and sustain the drug release from the films by controlling the polymeric content, concentration o

A prepared PMMA/Anthracene film of thickness 70μm was irradiated under reduced pressure ~10-3 to 60Coγ-ray dose of (0.1mrad-10krad) range. The optical properties of the irradiated films were evaluated spectrophotometrically. The absorption spectrum showed induced absorption changes in the 200-400nm range. At 359nm, where there is a decrease in radiation-induced absorption, the optical density as a function of absorbed dose is linear from 10mrad-10Krad.It can therefore, be used as radiation dosimeter for gamma ray in the range 10mrd-10krad

In this work, the effect of atomic ratio on structural and optical properties of SnO₂/In₂O₃ thin films prepared by pulsed laser deposition technique under vacuum and annealed at 573K in air has been studied.  Atomic ratios from 0 to 100% have been used. X-ray diffraction analysis has been utilized to study the effect of atomic ratios on the phase change using XRD analyzer and the crystalline size and the lattice strain using Williamson-Hall relationship. It has been found that the ratio of 50% has the lowest crystallite size, which corresponds to the highest strain in the lattice. The energy gap has increased as the atomic ratio of indium oxide increased.