313 research outputs found
Asymptotics of the number of threshold functions on a two-dimensional rectangular grid
Let , . It is well-known that the number of
(two-dimensional) threshold functions on an rectangular grid is
{eqnarray*} t(m,n)=\frac{6}{\pi^2}(mn)^2+O(m^2n\log{n})+O(mn^2\log{\log{n}})=
\frac{6}{\pi^2}(mn)^2+O(mn^2\log{m}). {eqnarray*} We improve the error term by
showing that t(m,n)=\frac{6}{\pi^2}(mn)^2+O(mn^2). $
Polymer dynamics in time-dependent periodic potentials
Dynamics of a discrete polymer in time-dependent external potentials is
studied with the master equation approach. We consider both stochastic and
deterministic switching mechanisms for the potential states and give the
essential equations for computing the stationary state properties of molecules
with internal structure in time-dependent periodic potentials on a lattice. As
an example, we consider standard and modified Rubinstein-Duke polymers and
calculate their mean drift and effective diffusion coefficient in the two-state
non-symmetric flashing potential and symmetric traveling potential. Rich
non-linear behavior of these observables is found. By varying the polymer
length, we find current inversions caused by the rebound effect that is only
present for molecules with internal structure. These results depend strongly on
the polymer type. We also notice increased transport coherence for longer
polymers.Comment: 22 pages, 7 figure
The arithmetic derivative and Leibniz-additive functions
An arithmetic function is Leibniz-additive if there is a completely
multiplicative function , i.e., and for
all positive integers and , satisfying
for all positive integers and . A motivation for the present study is
the fact that Leibniz-additive functions are generalizations of the arithmetic
derivative ; namely, is Leibniz-additive with . In this paper,
we study the basic properties of Leibniz-additive functions and, among other
things, show that a Leibniz-additive function is totally determined by the
values of and at primes. We also consider properties of
Leibniz-additive functions with respect to the usual product, composition and
Dirichlet convolution of arithmetic functions
‘At least they are welcome in my home!’ : Contentious hospitality in home accommodation of asylum seekers in Finland
This article discusses hospitality towards asylum seekers as a political and contentious act. Accommodating asylum seekers in local homes is one of the pro-asylum mobilisations that emerged across Europe following the 'summer of migration'. Based on interviews with local hosts in Finland, this article demonstrates that offering accommodation is often motivated by an explicit mistrust in state asylum policies and a will to make a statement in support of the right to asylum. Home accommodation challenges the norm of housing asylum seekers in reception centres, isolated from the rest of society. Thus, it provides valuable social and spatial resources in the struggle for asylum. Departing from the understanding that questions of asylum and home are inherently political, and following feminist citizenship theorisation that connects the domestic with the political, this article and the concept contentious hospitality contribute to challenging the discursive division between public and private.Peer reviewe
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