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 ...

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the...

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.

We offer a comprehensive theory of pH response of a coupled ISFET sensor to show that the maximum achievable response is given by ΔV/ΔpH = 59 mV/pH × α, where 59 mV/pH is the intrinsic Nernst response and α an amplification factor that depends on the geometrical and electrical properties of the sensor and transducer nodes. While the intrinsic Nernst response of an electrolyte/site-binding inter...

Polyhedral nanostructures are widely used to enable localized surface plasmon resonance (LSPR). In practice, vertices of such structures are almost always truncated due to limitations of nanofabrication processes. This paper studies the effects of vertex truncation of polyhedral nanostructures on the characteristics of LSPR sensing. The optical properties and sensing performance of triangular n...

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...

BACKGROUND Functional neuroimaging experiments have implicated prefrontal cortex (PFC) in memory processes. Several studies of schizophrenic patients have shown failure of activation in the dorsolateral region of PFC (DLPFC). We used a graded memory challenge to characterize functional neuroanatomical differences between schizophrenic and control subjects. The graded manipulation of task demand...

Laser-based flexible fabrication (LBFF), a solid free form fabrication (SFF) method based on laser-cladding process, was developed as an alternative to conventional machining methods for producing dies and molds. LBFF is similar to processes such as LENS with additional features including shaped beam profile, quasi-coaxial powder delivery, and functionally graded materials. It uses a high-power...