In this paper, there are two main objectives. The first objective is to study the relationship between the density property and some modules in detail, for instance; semisimple and divisible modules. The Addition complement has a good relationship with the density property of the modules as this importance is highlighted by any submodule N of M has an addition complement with Rad(M)=0. The second objective is to clarify the relationship between the density property and the essential submodules with some examples. As an example of this relationship, we studied the torsion-free module and its relationship with the essential submodules in module M.

Electronic properties such as density of state, energy gap, HOMO (the highest occupied molecular orbital) level, LUMO (the lowest unoccupied molecular orbital) level and density of bonds, as well as spectroscopic properties like infrared (IR), Raman scattering, force constant, and reduced masses for coronene C₂₄, reduced graphene oxide (rGO) C₂₄O₅and interaction between C₂₄O₅and NO₂gas molecules were investigated. Density functional theory (DFT) with the exchange hybrid function B3LYP with 6-311G** basis sets through the Gaussian 09 W software program was used to do these calculations. Gaussian view 05 was em

This study was undertaken to provide more insight on the optimum injection temperature used for the production of PE crates, thereby saving time and money, and improving part quality. The work included processing trails of HDPE crates in an injection
molding machine at five temperatures ranged from 220 to 300°C. Both Rheological and mechanical characterization was conducted in order to understand the effect of injection temperature on the properties of crates. Oven aging was also applied for (4 weeks) to evaluate the long-term thermal stability. The results revealed that producing the crates at a temperature range of (260-280 °C) gives the best rheological and mechanical result. The lowest drop in thermal stability has been observed

Ab – initio density function theory (DFT) calculations coupled with Large Unit Cell (LUC) method were carried out to evaluate the electronic structure properties of III-V zinc blend (GaAs). The nano – scale that have dimension (1.56-2.04)nm. The Gaussian 03 computational packages has been employed through out this study to compute the electronic properties include lattice constant, energy gap, valence and conduction band width, total energy, cohesive energy and density of state etc. Results show that the total energy and energy gap are decreasing with increase the size of nano crystal . Results revealed that electronic properties converge to some limit as the size of LUC increase .

Density functional theory (DFT) with B3LYP level and 6-311G[Formula: see text] basis sets for light atoms like N and O and SDD basis sets for heavy atoms like Sn is used to examine the interaction of tin dioxide nanocrystals with nitrogen dioxide as a function of temperature from 273[Formula: see text]K to 373[Formula: see text]K through a Gaussian 09W software program. Gibbs free energy, enthalpy, and entropy of activation and reaction are calculated. The situation of transition of SnO₂ clusters toward nitrogen dioxide is investigated. According to the findings, the activation energy of SnO₂ clusters with nitrogen dioxide increases as the temperature rises (in negative value). Gauss view 0

Cerium oxide CeO2, or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the effect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,

Cerium oxide (CeO2), or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the eect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,