Graded identities of block-triangular matrices

Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading induced by an $n$-tuple of elements of a group $G$ such that the neutral component corresponds to the diagonal of $UT(d_1,\dots,d_n)$. In particular, we prove that the monomial identities of such algebra follow from the ones of degree up to $2n-1$. Our results generalize for infinite fields of arbitrary characteristic, previous results in the literature which were obtained for fields of characteristic zero and for particular $G$-gradings. In the characteristic zero case we also generalize results for the algebra $UT(d_1,\dots, d_n)\otimes C$ with a tensor product grading, where $C$ is a color commutative algebra generating the variety of all color commutative algebras.Comment: 24 pages and 39 references. We have added section 5 in the text about tensor products by color commutative superalgebra

South-South Cooperation in Times of Global Economic Crisis

For South-South cooperation, the current moment of global economic downturn is one of anxiety. South-South cooperation was born with the Non-Aligned Movement. It went through a latent period, but re-emerged in the 1990s and early 2000s. The momentum gathered when a handful of middle-income countries such as Brazil, India, Mexico and South Africa were set to improve their position as global players. They had developed some relatively successful social programmes, which they sought to share with other developing countries. Considering that conventional North-South cooperation had turned out to be of limited effectiveness, South-South cooperation gained further impetus.South-South Cooperation in Times of Global Economic Crisis

Regular black holes in f(G)f(G) gravity

In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case.Comment: 22 pages, 25 figures.Version published in EPJ

New York?s Brand-new Conditional Cash Transfer Programme: What if it Succeeds?

In 2007, emulating the Mexican experience, Mayor Bloomberg decided that New York City should also have its own conditional cash transfer programme (CCT). He named the programme Opportunity NYC after the Mexican Oportunidades. Is Opportunity NYC just one more CCT in the plethora of existing programmes? Or will it influence the way educational reforms have been traditionally conceptualized?New York?s Brand-new Conditional Cash Transfer Programme: What if it Succeeds?