for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

Abstract Within this study, self-lubricating and triboactive (Cr,Al)N+Mo:S coatings were developed investigated for the deposition on components in a low-temperature physical vapor (PVD) hybrid process. Therefore, direct current magnetron sputtering (dcMS) high power pulse (HPPMS) PVD combined by using an industrial coating machine. Hereby, it was possible to deposit dense smooth triboactive, n...

Let $G$ be an abelian group with identity $e$. $R$ a $G$-graded commutative ring identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $S$-prime submodules modules over rings. We investigate some properties class their homogeneous components. $N$ submodule such that $(N:_{R}M)\cap S=\emptyset $. say is \textit{a }$S$...

Let $G$ be a group, $R$ $G$-graded commutative ring with identity, $M$ graded $R$-module and $S\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, new concept $S$-primary submodules is introduced as generalization Primary well $S$-prime $M$. Also, some properties class are investigated.

The aim of this study was to deyelop a noyel hydroxyapatite (HA) coating method on zirconia using glass coating technique. A borosi)icate glass, the mixture of the glass ttnd HA (3e, 50, 70, and 90 mass%), and the 100% HA were coated on two kinds of zirconia discs and fired at 900-950'C. After the final coating, the surface of the sample was etched for 3 min in an acid-mixture of 3% HF and 5%HN...

by virtue of a complete set of two displacement potentials, an analytical derivation of the elastostatic green’s functions of an exponentially graded transversely isotropic bi-material full-space was presented. three-dimensional point-load green’s functions for stresses and displacements were given in line-integral representations. the formulation included a complete set of transformed stress-p...

in this research controlled coating of magnetite (fe3o4) nanoparticles with sio2 was investigated. the fe3o4 nanoparticles were synthesized via chemical co-precipitation and then coated by silica according to stober method. effects of tetra ethyl ortho silicate (teos) concentration and ethanol to teos on the coating thickness were investigated. x-ray powder diffraction, fourier transform infrar...

A nanostructural hydroxyapatite (HA) coating was deposited to the porous Ti6Al4V acetabular cup implants using a room temperature electrophoretic deposition (EPD) process in order to achieve the improved bonding strength between the implants and cells, fast healing, good corrosion resistance and long-term stability after implantation. The micropores created in the coating will improve the bioac...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring and $M$ graded $R$-module. In this paper, we introduce the concept of primary-like submodules as new generalization primary ideals give some basic results about modules. Special attention has been paid, when satisfies gr-primeful property, to find extra properties these submodules.