Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Let be a ring. Given two positive integers and , an module is said to be -presented, if there is an exact sequence of -modules with is -generated. A submodule of a right -module is said to be -pure in , if for every -Presented left -module the canonical map is a monomorphism. An -module has the -pure intersection property if the intersection of any two -pure submodules is again -pure. In this paper we give some characterizations, theorems and properties of modules with the -pure intersection property.

Density Functional Theory at the generalized-gradient approximation level coupled with large unit cell method is used to simulate the electronic structure of (II-VI) zinc-blende cadmium sulfide nanocrystals that have dimensions 2-2.5 nm. The calculated properties include lattice constant, conduction and valence bands width, energy of the highest occupied orbital, energy of the lowest unoccupied orbital, energy gap, density of states etc. Results show that lattice constant and energy gap converge to definite values. However, highest occupied orbital, lowest unoccupied orbital fluctuates indefinitely depending on the shape of the nanocrystal.

the traumatic memory of their ancestors. The novel navigates sites of trauma, memory, and blues music while resisting the bourgeoisie-capitalist relationships that permeated not only white society but also African American communities. Jones’s novel presents the plight of an African American woman, Ursa, caught between the memory of her enslaved foremothers and her life in an emancipated world. The physical and spiritual exploitation of African American women who bear witness to the history of slavery in Corregidora materializes black women’s individuality. This article is framed by trauma studies as well as the Marxists’ concepts of commodification, accumulation, and production. Ursa, one of the Corregidora women, represents

Cryptographic applications demand much more of a pseudo-random-sequence
generator than do most other applications. Cryptographic randomness does not mean just
statistical randomness, although that is part of it. For a sequence to be cryptographically
secure pseudo-random, it must be unpredictable.
The random sequences should satisfy the basic randomness postulates; one of them is
the run postulate (sequences of the same bit). These sequences should have about the same
number of ones and zeros, about half the runs should be of length one, one quarter of length
two, one eighth of length three, and so on.The distribution of run lengths for zeros and ones
should be the same. These properties can be measured determinis

Electronic properties including (bond length, energy gap, HOMO, LUMO and density of state) as well as spectroscopic properties such like infrared, Raman scattering, force constant, reduced mass and longitu- dinal optical mode as a function of frequency are based on size and concentration of the molecular and nanostructures of aluminum nitride ALN, boron nitride BN and AlxB7-XN7 as nanotubes has calculated using Ab –initio approximation method dependent on density functional theory and generalized gradient approximation. The geometrical structure are calculated by using Gauss view 05 as a complementary program. Shows the energy gap of ALN, BN and AlxB7-XN7 as a function of the total number of atoms , start from smallest molecule to reached

    The electronic properties (such as energy gap HOMO levels. LUMO levels, density of state and density of bonds in addition to spectroscopic properties like IR spectra, Raman spectra, force constant and reduced masses as a function of frequency) of coronene C₂₄ and reduced graphene oxide C₂₄O_X , where x=1-5, were studied.. The  methodology employed was  Density Functional Theory (DFT) with Hybrid function B3LYP and 6-311G** basis sets. The energy gap was calculated for C₂₄ to be 3.5 eV and for C₂₄O_x was from 0.89 to 1.6862 eV  for x=1-5 ,respectively.   These energy gaps values are comparable to the measured gap of Graphene (1-2.2 eV). The spectroscopic propertie

    The electronic properties (such as energy gap HOMO levels. LUMO levels, density of state and density of bonds in addition to spectroscopic properties like IR spectra, Raman spectra, force constant and reduced masses as a function of frequency) of coronene C24 and reduced graphene oxide C24OX , where x=1-5, were studied.. The  methodology employed was  Density Functional Theory (DFT) with Hybrid function B3LYP and 6-311G** basis sets. The energy gap was calculated for C24 to be 3.5 eV and for C24Ox was from 0.89 to 1.6862 eV  for x=1-5 ,respectively.   These energy gaps values are comparable to the measured gap of Graphene (1-2.2 eV). The spectroscopic properties were  compared with experimental measurements, specificall