Low conversion copolymerization of N-vinyl-2-pyrrolidon M.W = (111.14) VP (monomer-1) has been conducted with acrylic acid AA and methymethacrylate MMA in ethanol at 70ºC , using Benzoyl peroxide BPO as initiator . The copolymer composition has been determined by elemental analysis. The monomer reactivity ratios have been calculated by the Kelen-Tudos and Finman-Ross graphical procedures . The derived reactivity ratios (r1 , r2 ) are : (0.51 , 4.85) for (VP / AA ) systems and (0.34 , 7.58) for (VP , MMA) systems , and found the reactivity ratios of the monomer AA , MMA is mor than the monomer VP in the copolymerization of (VP / AA) and (VP /MMA) systems respectly . The reactivity ratios values were used for microstructures calculation.

      Let  be a commutative ring with identity. The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule and a pseudo-2-absorbing submodules. A proper submodule  of an -module  is called pseudo primary-2-absorbing if whenever , for , , implies that either                  or  or . Many basic properties, examples and characterizations of these concepts are given. Furthermore, characterizations of pseudo primary-2-absorbing submodules in some classes of modules are introduced. Moreover, the behavior of a pseudo primary-2-absorbing submodul

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an

Our aim in this paper is to introduce the notation of nearly primary-2-absorbing submodule as generalization of 2-absorbing submodule where a proper submodule  of an -module  is called nearly primary-2-absorbing submodule if whenever , for , , ,  implies that either  or  or . We got many basic, properties, examples and characterizations of this concept. Furthermore, characterizations of nearly primary-2-absorbing submodules in some classes of modules were inserted. Moreover, the behavior of nearly primary-2-absorbing submodule under -epimorphism was studied.

Gallstone disease is one of the most common complications among diabetic patients especially type 2 DM. Till now, there is no specific and certain factor that explain the incidence of gallstones among type 2 diabetic patients and many risk factors are taken collectively to estimate its intensity and severity compared to non diabetic counter parts. This clinical study was designed to evaluate and report the incidence and severity of gallstones among type 2 diabetics and non diabetics regarding certain factors. 20 diabetic females and 20 diabetic males were collected as patients′ group and have had gallstones while 20 females and 20 males who have had gallstones without diabetes mellitus type 2 were collected as controls′ group

Laser drilling is capable of producing small, precisely positioned holes with high degree of reproductively. In this paper , IR millisecond Nd:YAG single pulsed laser was used to determine the effect of laser parameters on the drilled hole of the glass - fiber reinforced epoxy composite FR-4 sample of 2 mm in thickness . The type of laser source was GSI lumonics JK760TR Series laser 1.064μm system in a CNC cabin. The JK760TR series has a 0.3-50ms pulse length and a maximum repetition rate 500Hz with an average power of 600W. The investigation of single pulse laser drilling in this paper was based on theoretical and experimental solutions. In single pulse technique, the investigation included focal plane position fpp, pulse shap