Topology of the elliptical billiard with the Hooke's potential

Using Fomenko graphs, we present a topological description of the elliptical billiard with Hooke's potential.Comment: 9 pages, 5 figures; added discussion on the stability of closed orbit

Divisor class groups of rational trinomial varieties

We give an explicit description of the divisor class groups of rational trinomial varieties. As an application, we relate the iteration of Cox rings of any rational variety with torus action of complexity one to that of a Du Val surface.Comment: 17 page

Examining the interaction between vertical and horizontal dimensions of state transformation

Two dimensions of state transformation often analysed separately can be identified as vertical authority shifts between different levels of government and horizontal authority transfers between state and non-state domains. This article firstly reviews three existing approaches that highlight links between vertical and horizontal state transformation: multi-level governance, policy networks and sections of the rescaling literature. However, these approaches do not yet provide a framework sufficient to enable a more thorough and detailed examination of the relationship between these two dimensions. The article thus proceeds to develop a multifaceted framework in order to facilitate further research into this relationship, a necessity if we are to understand more fully whether vertical and horizontal authority shifts complement or contradict one another within the transformation of the state's role in governing society and economy

Some factorizations in the twisted group algebra of symmetric groups

In this paper we will give a similar factorization as in \cite{4}, \cite{5}, where the autors Svrtan and Meljanac examined certain matrix factorizations on Fock-like representation of a multiparametric quon algebra on the free associative algebra of noncommuting polynomials equiped with multiparametric partial derivatives. In order to replace these matrix factorizations (given from the right) by twisted algebra computation, we first consider the natural action of the symmetric group $S_{n}$ on the polynomial ring $R_{n}$ in $n^2$ commuting variables $X_{a\,b}$ and also introduce a twisted group algebra (defined by the action of $S_{n}$ on $R_{n}$) which we denote by ${\mathcal{A}(S_{n})}$. Here we consider some factorizations given from the left because they will be more suitable in calculating the constants (= the elements which are annihilated by all multiparametric partial derivatives) in the free algebra of noncommuting polynomials

The open method of coordination – effectively preventing welfare state retrenchment?

This article re-examines the division between "optimists" and "pessimists" within the literature on the Open Method of Coordination’s (OMC) effectiveness. Each of those "camps" tends to focus on a different question. "Optimists" are more concerned with the question of whether the OMC exerts an influence on the national level and through which mechanisms, whilst "pessimists" concentrate on the question of whether the OMC can "strengthen" EU social policy and therefore European welfare states. This article combines these two perspectives and argues that the OMC is indeed capable of influencing national policies through the dissemination of ideas and "learning" as the "optimists" stress. However, policy "learning" at the member state level is shaped and constrained by a variety of internal and external pressures. Against the hopes of most of the OMC "optimists", this makes the OMC largely ineffective in preventing welfare state retrenchme

Quantifying galaxy morphology

How do the different shapes of galaxies arise? Milena Pawlik describes work to identify the role of galaxy mergers and starbursts in galactic evolution.Publisher PDFPeer reviewe