in this article, finite difference method (fdm) is used to solve sixth-order derivatives of differential equations in buckling analysis of nanoplates due to coupled surface energy and non-local elasticity theories. the uniform temperature change is used to study thermal effect. the small scale and surface energy effects are added into the governing equations using eringen’s non-local elasticity...

Let $\mathcal{X}$ be a Banach space with fundamental biorthogonal system and let $\mathcal{Y}$ the dense subspace spanned by vectors of system. We prove that admits $C^\infty$-smooth norm locally depends on finitely many coordinates (LFC, for short), as well polyhedral coordinates. As consequence, we also finite, $\sigma$-uniformly discrete LFC partitions unity $C^1$-smooth LUR norm. This theor...

Abstract Given a purely non-atomic, finite measure space $$(\Omega ,\Sigma ,\nu )$$ ( Ω , Σ ν ) , it is proved that for every closed, infinite-dimensional subspace V of $$L_p(\nu L</m...

in this paper, a new smooth second order sliding mode control is proposed. this algorithm is a modified form of super twisting algorithm. the super twisting guarantees the asymptotic stability, but the finite time stability of proposed method is proved with introducing a new particular lyapunov function. the proposed algorithm which is able to control nonlinear systems with matched structured u...