Size effect of Ruderman-Kittel-Kasuya-Yosida interaction mediated by electrons in nanoribbons

We calculated the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the magnetic impurities mediated by electrons in nanoribbons. It was shown that the RKKY interaction is strongly dependent on the width of the nanoribbon and the transverse positions of the impurities. The transverse confinement of electrons is responsible for the above size effect of the RKKY interaction. It provides a potential way to control the RKKY interaction by changing nanostructure geometry

The non-abelian squares are not context-free

Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free

Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids

In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex associated with that finite element pair. The finite element spaces involved consist of piecewise polynomials only, and the divergence-free condition is imposed in a primal formulation. Combined with some existing results, these constructions can be generated onto grids that consist of both triangular and quadrilateral cells

Book review: Refugees, capitalism and the British state: implications for social workers, volunteers and activists

"Refugees, Capitalism and the British State: Implications for Social Workers, Volunteers and Activists." Tom Vickers. Ashgate. 2012. --- In this period of economic crisis, public sector cuts, and escalating class struggles, Marxist theory offers social workers and service users important tools to help understand the structures of oppression they face and to devise effective means of resistance. This book uses Marxism’s lost insights, reinterpreting them for the current context by focusing on one particular section of the international working class: refugees and asylum seekers in Britain. Shuo Liu finds that this book offers a unique understanding of the refugee’s position in Britain, and is a valuable contribution to the anti-racism effort