In this paper, we study some properties of φ-prime submodules andwe give another charactrization for it. For given N and K a moduleM with ⊆ N, prove that is submodule if only N/Kis φ_K-prime submodule. Finally, show any finite sum isφ-prime.

Objective(s): In this work, pomegranate juice was used as a capping agent for self- assembly to form particles-like Au nanostructures in the presence of AuHCl4.3H2O as aurate source. Besides, to investigate the concentration effect of pomegranate juice as the green capping agent on the morphology and particle size of final products several experiments were...

A geometric charactrization of the equation found by Hietarinta and Viallet, which satisfies the singularity confinement criterion but which exhibits chaotic behavior, is presented. It is shown that this equation can be lifted to an automorphism of a certain rational surface and can therefore be considered to be a realization of a Cremona isometry on the Picard group of the surface. It is also ...

A Graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their compliments. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing intersecting bi-i...