A new family of maximal curves

In this article we construct for any prime power $q$ and odd $n \ge 5$, a new $\mathbb{F}_{q^{2n}}$-maximal curve $\mathcal X_n$. Like the Garcia--G\" uneri--Stichtenoth maximal curves, our curves generalize the Giulietti--Korchm\'aros maximal curve, though in a different way. We compute the full automorphism group of $\mathcal X_n$, yielding that it has precisely $q(q^2-1)(q^n+1)$ automorphisms. Further, we show that unless $q=2$, the curve $\mathcal{X}_n$ is not a Galois subcover of the Hermitian curve. Finally, we find new values of the genus spectrum of $\mathbb{F}_{q^{2n}}$-maximal curves, by considering some Galois subcovers of $\mathcal X_n$

Weierstrass semigroups on the Giulietti-Korchm\'aros curve

In this article we explicitly determine the structure of the Weierstrass semigroups $H(P)$ for any point $P$ of the Giulietti-Korchm\'aros curve $\mathcal{X}$. We show that as the point varies, exactly three possibilities arise: One for the $\mathbb{F}_{q^2}$-rational points (already known in the literature), one for the $\mathbb{F}_{q^6} \setminus \mathbb{F}_{q^2}$-rational points, and one for all remaining points. As a result, we prove a conjecture concerning the structure of $H(P)$ in case $P$ is an $\mathbb{F}_{q^6} \setminus \mathbb{F}_{q^2}$-rational point. As a corollary we also obtain that the set of Weierstrass points of $\mathcal{X}$ is exactly its set of $\mathbb{F}_{q^6}$-rational points

Muintir na Tire Seeks Funding for Rural Sociology in 1960s Ireland

working paperMuintir na Tire’s role in the emergence of the discipline of Sociology in Ireland is usually acknowledged with reference to the Limerick Rural Survey (1958-64) that it initiated, part-funded and published. In the first half of the 1960s the movement also put proposals to the Irish government and sought US foundation grants for a centre or institute that would operate in the field of rural sociology and form part of Muintir na Tire’s organisational structure. Although Taoiseach Sean Lemass was positively disposed towards these initatives, opposition from the Departments of Agriculture, Education and Finance prevailed against them and Muintir na Tire was ultimately to find itself completely excluded from participation in the state-resourced institutional arrangements for carrying out social/sociological research in Ireland

Heat maximal function on a Lie group of exponential growth

Let G be the Lie group R^2\rtimes R^+ endowed with the Riemannian symmetric space structure. Let X_0, X_1, X_2 be a distinguished basis of left-invariant vector fields of the Lie algebra of G and define the Laplacian \Delta=-(X_0^2+X_1^2+X_2^2). In this paper, we show that the maximal function associated with the heat kernel of the Laplacian \Delta is bounded from the Hardy space H^1 to L^1. We also prove that the heat maximal function does not provide a maximal characterization of the Hardy space H^1.Comment: 18 page

Boundedness from H^1 to L^1 of Riesz transforms on a Lie group of exponential growth

Let $G$ be the Lie group given by the semidirect product of $R^2$ and $R^+$ endowed with the Riemannian symmetric space structure. Let $X_0, X_1, X_2$ be a distinguished basis of left-invariant vector fields of the Lie algebra of $G$ and define the Laplacian $\Delta=-(X_0^2+X_1^2+X_2^2)$. In this paper we consider the first order Riesz transforms $R_i=X_i\Delta^{-1/2}$ and $S_i=\Delta^{-1/2}X_i$, for $i=0,1,2$. We prove that the operators $R_i$, but not the $S_i$, are bounded from the Hardy space $H^1$ to $L^1$. We also show that the second order Riesz transforms $T_{ij}=X_i\Delta^{-1}X_j$ are bounded from $H^1$ to $L^1$, while the Riesz transforms $S_{ij}=\Delta^{-1}X_iX_j$ and $R_{ij}=X_iX_j\Delta^{-1}$ are not.Comment: This paper will be published in the "Annales de l'Institut Fourier

Public Perception of Risk Management in Environmental Controversies: A U.K. Case Study

Drs. Simosi and Allen focus on issues arising from an environmental dispute in the U.K. Their case study findings are discussed in the context of existing environmental decision-making procedures in the U.K

Measuring group switching in the European Parliament: Methodology, data and trends (1979-2009)

Party group switching in the European Parliament (ep), where parliamentarians individually or collectively switch from one party group to the other, is a well-known contributor to the volatility of the ep party system. We present a new dataset that contains party group information on all meps from 1979 to 2009. As a first step to a more comprehensive analysis of the phenomenon of party group switching in the ep we describe characteristics of all switches that have occurred in these six legislatures, with a focus on the trends across time, variety between member states, party groups, and ideological party families