In this study, a radiation pattern reconfigurable microstrip antenna is designed and fabricated. The antenna’s radiation pattern is directed in 9 different angles by employing a radiating patch and embedding complementary split ring resonators (CSRR) on the ground plane. The radiating patch is of circular shape, while for CSRR elements both circular and rectangular shapes are investigated. The ...

Ring rolling is one of the most significant methods for producing rings with highly precise dimensions and superior qualities such as high strength uniformity, all accomplished without wasting any materials. In this article, we have achieved analytical formulas for calculating the pressure and shear friction over the contact arcs between the rollers and ring in the ring rolling process for the ...

Let R be a commutative ring with identity and M be a unitary R-module. Let : S(M) −! S(M) [ {;} be a function, where S(M) is the set of submodules ofM. Suppose n 2 is a positive integer. A proper submodule P of M is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 R and x 2 M and a1 . . . an−1x 2P(P), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x 2 P...

let $r$ be a commutative noetherian ring with non-zero identity, $fa$ an ideal of $r$, and $x$ an $r$--module. here, for fixed integers $s, t$ and a finite $fa$--torsion $r$--module $n$, we first study the membership of $ext^{s+t}_{r}(n, x)$ and $ext^{s}_{r}(n, h^{t}_{fa}(x))$ in the serre subcategories of the category of $r$--modules. then, we present some conditions which ensure the exi...

A commutative ring R is said to satisfy property (P) if every finitely generated proper ideal of R admits a non-zero annihilator. In this paper we give some necessary and sufficient conditions that a ring satisfies property (P). In particular, we characterize coherent rings, noetherian rings and P-coherent rings with property (P).