this research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. heat conduction equation in cylindrical coordinate system is solved. thermal conductivity coefficient is graded along the radial direction. by considering a symmetric distribution of temperature, loading and boundary conditions, strain-displacement and stress-strain relations can b...

Let $G$ be a group with identity $e$. $R$ $G$-graded commutative ring, $M$ graded $R$-module and $A\subseteq h(R)$ multiplicatively closed subset of $R$. In this paper, we introduce the concept $A$-2-absorbing submodules as generalization 2-absorbing $A$-prime $M.$ We investigate some properties class submodules.

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

In this paper, we introduce the theory of local cohomology and duality to Notherian connected cochain DG algebras. We show that notion functor can be used detect Gorensteinness a homologically smooth algebra. For any Gorenstein locally finite algebra $${\cal A}$$ , define group homomorphism $${\rm{Hdet}}:{\rm{Au}}{{\rm{t}}_{dg}}\left( {\cal A} \right) \to {k^ \times }$$ called homological deter...