The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

Starting from bis (4,4'-diamino phenoxy) ethan(1), a variety of phenolicschiff bases (methylolic, etheric, epoxy) derivatives have been synthesized. All proposed structure were supported by FTIR, 1H-NMR, 13C-NMR Elemental analysis, some derivatives evaluated by thermal analysis (TGA).

      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

The charge density distributions (CDD) and the elastic electron
scattering form factors F(q) of the ground state for some even mass
nuclei in the 2s 1d shell ( Ne Mg Si 20 24 28 , , and S 32 ) nuclei have
been calculated based on the use of occupation numbers of the states
and the single particle wave functions of the harmonic oscillator
potential with size parameters chosen to reproduce the observed root
mean square charge radii for all considered nuclei. It is found that
introducing additional parameters, namely 1 , and , 2  which
reflect the difference of the occupation numbers of the states from
the prediction of the simple shell model leads to a remarkable
agreement between the calculated an

The estimation of the regular regression model requires several assumptions to be satisfied such as "linearity". One problem occurs by partitioning the regression curve into two (or more) parts and then joining them by threshold point(s). This situation is regarded as a linearity violation of regression. Therefore, the multiphase regression model is received increasing attention as an alternative approach which describes the changing of the behavior of the phenomenon through threshold point estimation. Maximum likelihood estimator "MLE" has been used in both model and threshold point estimations. However, MLE is not resistant against violations such as outliers' existence or in case of the heavy-tailed error distribution. The main goal of t

Some Results on Fuzzy Zariski

Topology  on Spec(J.L)