Let V (d, n) be the number of permutations p of {1, 2, . . . , n} that satisfy |pi−i| 6 d for all i. Generating functions for V (d, n), for fixed d, are given.

in the present paper, an exact solution for transient response of an infinitely long functionally graded thick-walled cylinder subjected to dynamic pressures at the boundary surfaces is presented for arbitrary initial conditions. the cylinder is assumed to have a plane-strain condition and the dynamic pressures are assumed to be imposed uniformly and axisymmetrically on the boundary surfaces. m...

In this paper, the effects of carbon nanotube (CNT) orientation and aggregation on the static behavior of functionally graded nanocomposite cylinders reinforced by CNTs are investigated based on a mesh-free method. The used nanocomposites are made of the straight CNTs that are embedded in an isotropic polymer as matrix. The straight CNTs are oriented, randomly or aligned or local aggregated int...

the main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by özkoç and aslım cite{10} called weakly $er$-open functions and $e$-$theta$-open functions. moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing to...

In this paper static analysis of orthotropic functionally graded material (FGM) cylinders with finite length was carried out by a mesh-free method. MLS shape functions are used for approximation of displacement field in the weak form of equilibrium equation and essential boundary conditions are imposed by transformation method. In this simulation, an ax symmetric model is used. Mechanical prope...