Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

B3LYP/6-31G, DFT method was applied to hypothetical study the design of six carbon nanotube materials based on [8]circulene, through the use of cyclic polymerization of two and three molecules of [8]circulene. Optimized structures of [8]circulene have saddle-shaped. Design of six carbon nanotubes reactions were done by thermodynamically calculating (Δ S, Δ G and Δ H) and the stability of these hypothetical nanotubes depending on the value of HOMO energy level. Nanotubes obtained have the most efficient gap energy, making them potentially useful for solar cell applications.

Photonic Crystal Fiber Interferometers (PCFIs) are greatly used
for sensing applications. This work presents the fabrication and
characterization of a relative humidity sensor based on Mach-
Zehnder Interferometer (MZI), which operates in reflection mode.
The humidity sensor operation based on the adsorption and
desorption of water vapour at the silica-air interface within the PCF.
The fabrication of this sensor is simple, it only includes splicing and
cleaving the PCF with SMF.PCF (LMA-10) with a certain length
spliced to SMF (Corning-28).
The spectrum of PCFI exhibits good sensitivity to humidity
variations. The PCFI response is observed for a range of humidity
values from (27% RH to 85% RH), the positi