The list Ramsey number R ℓ ( H , k ) ${R}_{\ell }(H,k)$ recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical number. They showed that if $H$ fixed r $r$ -uniform hypergraph not -partite colors $k$ goes to infinity, e Ω ≤ O ${e}^{{\rm{\Omega }}(\sqrt{k})}\le {R}_{\ell }(H,k)\le {e}^{O(k)}$ . We prove = Θ }(H,k)={e}^{{\rm{\Theta }}(k)}$ ...

For the first time, structural dynamics and vibrational stability of a viscoelastic axially functionally graded (AFG) beam with both spinning axial motions subjected to an load are analyzed, aim enhance performance bi-gyroscopic systems. A detailed parametric study is also performed emphasize influence various key factors such as material distribution type, viscosity coefficient, coupled rotati...

Let G be a group with identity e. Let R be a G-graded commutative ring and let M be a graded R-module. The graded classical prime spectrum Cl.Specg(M) is defined to be the set of all graded classical prime submodule of M. The Zariski topology on Cl.Specg(M); denoted by ϱg. In this paper we establish necessary and sufficient conditions for Cl.Specg(M) with the Zariski topology to be a Noetherian...