because of production process and constrains conditions, circular graphene sheet may be opposed to structural defect and pin hole, respectively. some of the defects and pin hole on a circular graphene sheet can be considered as an eccentric hole on the sheet. hence, analyzing behavior of circular graphene sheet with an eccentric hole is important. free vibration of an eccentric annular graphene...

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

1.1. Topological derivatives in shape optimization. Topological derivatives are introduced for linear problems in (Sokolowski and Zochowski, 1999) and for variational inequalities in (Sokolowski and Zochowski, 2005). The mathematical theory of asymptotic analysis is applied in (Nazarov and Sokolowski, 2003; 2006) for the derivation of topological derivatives in shape optimization of elliptic bo...

An experimental study was conducted to examine the aerodynamic and flow field characteristics of hyper-elliptic cambered span (HECS) wings and compare results with more conventional configurations used for induced drag reduction. Previous preliminary studies, indicating improved L/D characteristics when compared to an elliptical planform prompted this more detailed experimental investigation. B...

the drilling is well known as one of the most common hole making processes in the industry.due to close tolerance requirement for drilled holes in the most of work pieces, onlinecontrolling of the diameter of drilled holes seems to be necessary. in the current work, an onlinedimensional controlling system was developed for drilling process. doing this, drilling processwas executed in different ...

We study tidal disruption of white dwarfs in elliptic orbits with the eccenticity $\sim 1/3$--$2/3$ by a non-spinning supermassive black hole mass $M_{\rm BH}=10^5M_\odot$ fully general relativistic simulations targeting extreme mass-ratio inspiral leading eventually to disruption. Numerical-relativity are performed employing suitable formulation which weak self-gravity is accurately solved. re...

by the mordell-weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎there is no known algorithm for finding the rank of this group‎. ‎this paper computes the rank of the family $ e_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

This paper develops and analyzes a finite element method for a nonlinear singular elliptic equation arising from the black hole theory in the general relativity. The nonlinear equation, which was derived and analyzed by Huisken and Ilmanen in [14], represents a level set formulation for the inverse mean curvature flow describing the evolution of a hypersurface whose normal velocity equals the r...