Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...

Abstract Functionally graded materials raise considerable interest in the biomedical research. In particular, gyroid structures are suitable for bone tissue engineering applications, allowing to emulate porosity of inner part bone. this frame, mechanical properties 17–4 PH steel gyroids made by additive manufacturing have been investigated. Three design methods implemented, i.e., thickness grad...

TITLE: Functionally-graded sandwich design of the armor protecting a hot-vent gastropod AUTHORS (FIRST NAME, LAST NAME): Haimin Yao1, Ming Dao1, Timothy Imholt2, Subra Suresh1, Christine Ortiz1 INSTITUTIONS (ALL): 1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambirdge, MA, USA. 2. Raytheon, Inc, Marlboro, MA, USA. ABSTRACT BODY: Recently, a gastropo...

Information on soil type and thickness becomes important in planning land use for various purposes, both agriculture infrastructure. Measurements to identify this information have been developed using methods, one of which is the ultrasonic wave method. However, measurement layer carried out by knowing speed propagation layer. Generally, measurements, assumption a constant used. situations wher...

– We have derived the local electric field inside graded metal-dielectric composite films with weak nonlinearity analytically, which further yields the effective linear dielectric constant and third-order nonlinear susceptibility of the graded structures. As a result, the composition-dependent gradation can produce a broad resonant plasmon band in the optical region, resulting in a large enhanc...

Synthetic fibrillar adhesives inspired by nature, most commonly by the gecko lizard, have been shown to strongly and repeatedly attach to smooth surfaces. These adhesives, mostly of monolithic construction, perform on par with their natural analogues on smooth surfaces but exhibit far inferior adhesive performance on rough surfaces. In this paper, we report on the adhesive performance of functi...

in the presented work, sulfur concrete and rubber were used for producing functionally graded materials (fgm). the physical and mechanical properties of sulfur concrete and rubber were changed continuously across the thickness. on one side, there was just rubber and, on the other, there was pure sulfur; the properties of each substance were moved to reach another. this kind of material was cons...