Let $I\subset S=K[x_1,\dots,x_n]$ be a squarefree monomial ideal, $K$ field. The $k$th power $I^{[k]}$ of $I$ is the ideal $S$ generated by all monomials belonging to $I^k$. biggest integer $k$ such that $I^{[k]}\ne(0)$ called grade and it denoted $\nu(I)$. $d_k$ minimum degree $I^{[k]}$. Then, $\text{depth}(S/I^{[k]})\ge d_k-1$ for $1\le k\le\nu(I)$. normalized depth function defined as $g_{I}...

Abstract Let ϕ be a normalized convex function defined on open unit disk D . For unified class of analytic functions which satisfy the second order differential subordination f′ ( z ) + αzf″ ≺ for all z ∈ , we investigate distortion theorem and grow...

In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacem...