ABSTRACT We deduce the dynamic frequency-domain-lattice Green’s function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the continuous limiting case which represents an elastic 1D exponentially graded material. The discrete model yields closed form expressions for the N × N Green...

We study a multilevel additive Schwarz method for the h-p version of the Galerkin boundary element method with geometrically graded meshes. Both hypersingular and weakly singular integral equations of the first kind are considered. As it is well known the h-p version with geometric meshes converges exponentially fast in the energy norm. However, the condition number of the Galerkin matrix in th...

In this paper, plane thermo-elastic solutions are presented for the problem of a crack in two bonded homogeneous orthotropic media with a graded interfacial zone. The graded interfacial zone is treated as a nonhomogeneous interlayer having spatially varying thermo-elastic moduli between dissimilar, homogeneous orthotropic half-planes, which is assumed to vary exponentially in the direction perp...

In this paper we are concerned with the numerical analysis of the collocation method based on graded meshes of second kind integral equations on the real line of the form φ(s)=ψ(s)+ ∫ R κ(s − t)z(t)φ(t) dt, s ∈R, where κ ∈ L1(R), z ∈ L∞(R), and ψ ∈ BC(R), the space of bounded continuous complex-valued functions on R, are assumed known and the function φ ∈ BC(R) is to be determined. We introduce...

‎let $g$ be a group with identity $e.$ let $r$ be a $g$-graded‎ ‎commutative ring and $m$ a graded $r$-module‎. ‎in this paper‎, ‎we‎ ‎introduce several results concerning graded classical prime‎ ‎submodules‎. ‎for example‎, ‎we give a characterization of graded‎ ‎classical prime submodules‎. ‎also‎, ‎the relations between graded‎ ‎classical prime and graded prime submodules of $m$ are studied‎.‎

let  be a graded ring and  be a graded -module. we define a topology on graded prime spectrum  of the graded -module  which is analogous to that for , and investigate several properties of the topology.

In this study, the mechanical behaviours of thick-walled hollow functionally graded material (FGM) cylinder subjected to uniform pressures at inner and outer surfaces are proposed. The FGM has variable geometric profile, thickness properties like elastic modulus mass density all assumed vary radially according exponentially-varying functions in radial direction. With help infinitesimal elastici...

Graded path quantifiers have been recently introduced and investigated as a useful framework for generalizing standard existential and universal path quantifiers in the branching-time temporal logic CTL (GCTL), in such a way that they can express statements about a minimal and conservative number of accessible paths. These quantifiers naturally extend to paths the concept of graded world modali...

Abstract Signature is an infinite graded sequence of statistics known to characterize geometric rough paths. While the use signature in machine learning successful low-dimensional cases, it suffers from curse dimensionality high-dimensional as number features truncated transform grows exponentially fast. With idea Convolutional Neural Network, we propose a novel neural network address this prob...

A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness directio...