Non standard parametrizations and adjoint invariants of classical groups

We obtain local parametrizations of classical non-compact Lie groups where adjoint invariants under maximal compact subgroups are manifest. Extension to non compact subgroups is straightforward. As a by-product parametrizations of the same type are obtained for compact groups. They are of physical interest in any theory gauge invariant under the adjoint action, typical examples being the two dimensional gauged Wess-Zumino-Witten-Novikov models where these coordinatizations become of extreme usefulness to get the background fields representing the vacuum expectation values of the massless modes of the associated (super) string theory.Comment: 11 pages, latex file, La Plata preprint Th-99/01. Minor changes in the introduction, version to appear in Physics Letters

Differences between sources of government expenditure in education and health, Tanzania

Reliable data on government expenditure in priority sectors, such as health and education, is a key ingredient into the analysis of public policy effectiveness. This brief note has two primary goals: (i) to document the increasing divergence over time between various official Tanzanian data sources on spending in these two sectors, and (ii) to outline possible explanations for this divergence and highlight its consequences for social expenditure analysis

A note on the non-commutative Chern-Simons model on manifolds with boundary

We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical consistency and gauge invariance lead necessary to the introduction of $K_0$-space of square integrable functions null together with all their derivatives at the origin. Furthermore the requirement of closure of $K_0$ under the *-product leads to the introduction of a novel notion of the *-product itself in regions where a boundary is present, that in turn yields the complexification of the gauge group and to consider chiral waves in one sense or other. The canonical quantization of the theory is sketched identifying the physical states and the physical operators. These last ones include ordinary NC Wilson lines starting and ending on the boundary that yield correlation functions depending on points on the one-dimensional boundary. We finally extend the definition of the *-product to a strip and comment on possible relevance of these results to finite Quantum Hall systems.Comment: 15 pages, references added, to appear in International Journal of Modern Physic

Fearless: Kevin Lugo

This summer, recent graduate Kevin Lugo will bike over 4,000 miles across the country to benefit the Ulman Cancer Fund for Young Adults. His choice to bike for seventy days from Baltimore to Seattle makes him fearless! His goal is to raise $7,476 for the organization, and he reached that goal last night (although more donations are always welcome in support of fighting cancer)! Kevin explains that when he studied abroad in Denmark in the fall of 2011, he “fell in love with sustainable transportation, especially cycling.” Not only does his fearless endeavor raise money to fight cancer, but he is also supporting healthy environmental practices. [excerpt

On competitive discrete systems in the plane. I. Invariant Manifolds

Let $T$ be a $C^{1}$ competitive map on a rectangular region $R\subset \mathbb{R}^{2}$. The main results of this paper give conditions which guarantee the existence of an invariant curve $C$, which is the graph of a continuous increasing function, emanating from a fixed point $\bar{z}$. We show that $C$ is a subset of the basin of attraction of $\bar{z}$ and that the set consisting of the endpoints of the curve $C$ in the interior of $R$ is forward invariant. The main results can be used to give an accurate picture of the basins of attraction for many competitive maps. We then apply the main results of this paper along with other techniques to determine a near complete picture of the qualitative behavior for the following two rational systems in the plane. $$x_{n+1}=\frac{\alpha_{1}}{A_{1}+y_{n}},\quad y_{n+1}=\frac{\gamma_{2}y_{n}}{x_{n}},\quad n=0,1,...,$$ with $\alpha_1,A_{1},\gamma_{2}>0$ and arbitrary nonnegative initial conditions so that the denominator is never zero. $$x_{n+1}=\frac{\alpha_{1}}{A_{1}+y_{n}},\quad y_{n+1}=\frac{y_{n}}{A_{2}+x_{n}},\quad n=0,1,...,$$ with $\alpha_1,A_{1},A_{2}>0$ and arbitrary nonnegative initial conditions.Comment: arXiv admin note: text overlap with arXiv:0905.1772 by other author