Let R be a commutative ring with identity 1 ¹ 0, and let M be a unitary left module over R. A submodule N of an R-module M is called essential, if whenever N ⋂ L = (0), then L = (0) for every submodule L of M. In this case, we write N ≤e M. An R-module M is called extending, if every submodule of M is an essential in a direct summand of M. A submodule N of an R-module M is called semi-essential (denoted by N ≤sem M), if N ∩ P ≠ (0) for each nonzero prime submodule P of M. The main purpose of this work is to determine and study two new concepts (up to our knowledge) which are St-closed submodules and semi-extending modules. St-closed submodules is contained properly in the class of closed submodules, where a submodule N of

In this work the concept of semi-generalized regular topological space was introduced and studied via semi generalized open sets. Many properties and results was investigated and studied, also it was shown that the quotient space of semi-generalized regular topological space is not, in general semi-generalizedspace.

Dans la langue française, une forme d'auxiliarité, composée de deux éléments cohérents l'auxiliant et l'auxilié, fournit, en effet, à la phrase une diversité significative et structurale. L'auxiliarité, renvoie à l'unification de deux éléments grammaticaux afin de localiser l'énoncé sur l'axe du temps, d'aspect ou de mode. É. Benveniste définit l'auxiliarité en : « Il s'agit d'une forme linguistique unitaire qui se réalise, à travers des paradigmes entiers, en  deux éléments, dont chacun assume une partie des fonctions grammaticales, et qui sont à la fois liés et autonomes, distincts et complémentaires »[1]. Ces deux éléments d'auxiliarité possèden

In this work a chemical sensor was built by using Plane Wave Expansion (PWE) modeling technique by filling the core of 1550 hollow core photonic crystal fiber with chloroform that has different concentrations after being diluted with distilled water. The minimum photonic bandgap width is.0003 and .0005 rad/sec with 19 and 7 cells respectively and a concentration of chloroform that filled these two fibers is 75%.

Hollow core photonic bandgap fibers provide a new geometry for the realization and enhancement of many nonlinear optical effects. Such fibers offer novel guidance and dispersion properties that provide an advantage over conventional fibers for various applications. Dispersion, which expresses the variation with wavelength of the guided-mode group velocity, is one of the most important properties of optical fibers. Photonic crystal fibers (PCFs) offer much larger flexibility than conventional fibers with respect to tailoring of the dispersion curve. This is partly due to the large refractive-index contrast available in the silica/air microstructures, and partly due to the possibility of making complex refractive-index structure over the fibe

The increasing requirement and use of dental implant treatments has rendered dental implantology indispensable in dentistry. The aim of this study is to determine the optimum concentration of calcium silicate to be incorporated into a polyetherketoneketone (PEKK) matrix used as an implant material to enhance the bioactivity and mechanical properties of the composite compared with unmodified PEKK. In this study, different weight percentage (wt%) of micro-calcium silicate (m-CS) is incorporated into PEKK with ethanol as a binder. Subsequently, the mixture is dried in a forced convection oven at 120°C and poured into customized molds to fabricate a bioactive composite via compression molding (310°C, 15 MPa, and 20 min holding time

 Polyaniline organic Semiconductor polymer was prepared by oxidation polymerization by adding hydrochloric acid concentration of 0.1M and potassium per sulfate concentration of 0.2M to 0.1M of aniline at room temperature, the polymer was deposited at glass substrate, the structural and optical properties were studies through UV-VIS, IR, XRD measurements, films have been operated as a sensor of vapor  H₂SO₄ and HCl  acids.