It is known that one can improve the accuracy of the finite element solution of partial differential equation (PDE) by uniformly refining a triangulation. Similarly, one can uniformly refine a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [4]. It is demonstrated that the numerical solution of Poisson equation based on the pentagonal refinement scheme ou...

In the past decades, exactly recovering the intrinsic data structure from corrupted observations, which is known as robust principal component analysis (RPCA), has attracted tremendous interests and found many applications in computer vision. Recently, this problem has been formulated as recovering a low-rank component and a sparse component from the observed data matrix. It is proved that unde...

in this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (fdm). the uniform temperature change is utilized to study thermal effect. the surface energy effects are taken into account using the gurtin-murdoch’s theory. using the principle of virtual work, the...

in this article, finite difference method (fdm) is used to study the size-dependent free vibration characteristics of rectangular nanoplates considering the surface stress effects. to include the surface effects in the equations, gurtin-murdoch continuum elasticity approach has been employed. the effects of surface properties including the surface elasticity, surface residual stress and surface...

We prove a gluing formula for the Donaldson invariants of the connected sum of two four-manifolds along a surface of genus 2. We also prove a finite type condition for manifolds containing a surface of genus 2, self-intersection zero and representing an odd homology class.

In this article, Finite Element Method (FEM) and Eulerian-Lagrangies Algorithm (ELA) formulation were used to numerically simulate the impact of several low-velocity projectiles with water surface. Material models which were used to express behavior of air and water included Null material model. For the projectiles, rigid material model were applied. Results were validated by analyzing the impa...

In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the Gurtin-Murdoch’s theory. Using the principle of virtual work, the...