We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of...

In this paper, the buckling and vibration behaviour of functionally graded flexoelectric nanobeam is examined. The vibration and buckling formulations of functionally graded nanobeam are developed by using a new theory that’s presented exclusively for flexoelecteric nano-materials. So by considering Von-Karman strain and forming enthalpy equation based on displacement, polarization and electric...

The classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type s...

Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...

We generalize graded Hecke algebras to include a twisting twococycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke algebras. We prove that twisted graded Hecke algebras are particular types of deformations of a crossed product.

Let G be an abelian group and let R be a commutative G-graded super-ring (briefly, graded super-ring) with unity 1 6= 0. We say that a ∈ h(R), where h(R) is the set of homogeneous elements in R, is weakly prime to a graded superideal I of R if 0 6= r a ∈ I , where r ∈ h(R), then r ∈ I . If ν(I ) is the set of homogeneous elements in R that are not weakly prime to I , then we define I to be weak...

Biomaterials include bioceramics, biometals, biopolymers and biocomposites and they play important roles in the replacement and regeneration of human tissues. However, dense bioceramics and dense biometals pose the problem of stress shielding due to their high Young’s moduli compared to those of bones. On the other hand, porous biomaterials exhibit the potential of bone ingrowth, which will dep...

Let G and K be groupoids. We present the notion of a (Gα,Kβ)-set we prove duality theorem in this context, which extends for graded algebras by groups. For A unital G-graded algebra X finite split G-set, show that there is an isomorphism between category X-graded left A-modules A#αGX-modules. As application isomorphism, construct Morita context.

This paper studies dynamic stability of functionally graded beams with piezoelectric layers subjected to periodic axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The Young’s modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton’s principle, the governing dynamic equation is established. The eff...

Nonlinear behavior of a functionally graded cantilever beam is analyzed under non-uniform hygro-thermal effect. To solve this problem, finite element method is applied within plane solid continua. Total Lagrangian approach is utilized in the nonlinear kinematic relations. Newton-Raphson method with incremental displacement is used in nonlinear solution. Comparison study is performed. Effects of...