We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

0266-3538/$ see front matter 2011 Elsevier Ltd. A doi:10.1016/j.compscitech.2011.01.009 ⇑ Corresponding author. E-mail address: [email protected] (G.J. Nie). We present a technique to tailor materials for functionally graded (FG) linear elastic hollow cylinders and spheres to attain through-the-thickness either a constant hoop (or circumferential) stress or a constant in-plane shear stress. The...

We studied the evolution of elliptic heavy SF6 gas cylinder surrounded by air when accelerated by a planar Mach 1.25 shock. A multiple dynamics imaging technology has been used to obtain one image of the experimental initial conditions and five images of the time evolution of elliptic cylinder. We compared the width and height of the circular and two kinds of elliptic gas cylinders and analyzed...

The objective of this paper is to provide guidance for the design of the thick-walled cylinder made up of transversely isotropic material so that collapse of cylinder due to influence of internal and external pressure can be avoided. The concept of transition theory based on Lebesgue strain measure has been used to simplify the constitutive equations. Results have been analyzed theoretically an...

In this research, static stresses analysis of boron nitride nano - tube reinforced composite (BNNTRC) cylinder made of poly - vinylidene fluoride (PVDF) subjected to non - axisymmetric thermo - mechanical loads and applied voltage is developed. The surrounded elastic medium is modelled by Pasternak foundation. Composite structure is modeled based on piezoelectric fiber reinforced composite (PFR...