Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

Effective restoration of the U_A(1) symmetry with temperature and density

We investigate the full U(3)$\otimes$U(3) chiral symmetry restoration, at finite temperature and density, on the basis of a quark model which incorporates the most relevant properties of QCD in this context: explicit and spontaneous breaking of chiral symmetry and axial U$_A$(1) symmetry breaking. A specific lattice-inspired behavior of the topological susceptibility, combined with the convergence of chiral partners, signals the onset of an effective chiral symmetry restoration. The results suggest that the axial part of the symmetry is restored before the possible restoration of the full U(3)$\otimes$U(3) chiral symmetry can occur. This conclusion is valid in the context of both finite temperature and density.Comment: 5 pages, 2 figures; PRD versio

Euclidean thermal spinor Green's function in the spacetime of a straight cosmic string

Within the framework of the quantum field theory at finite temperature on a conical space, we determine the Euclidean thermal spinor Green's function for a massless spinor field. We then calculate the thermal average of the energy-momentum tensor of a thermal bath of massless fermions. In the high-temperature limit, we find that the straight cosmic string does not perturb the thermal bathComment: 11 pages, latex, no figure

The new clash of generation

Unlike in the sixties, today's clash of generations is not about creating (post-)materialistic values. It is about human species survival. The fear of decay (of the Empire through war) and the hope of revolution ( coming back a new to a starting configuration) are similar. Social State´s financial sustainability or the new generation of energy sources are partial problems. How to have justice for all, including the environment?, that´s a global problem. The main and also repressed question is about how climate change will impose new ways of living on us all.Political and cognitive alienation from the main human problems is pushing emotional responses in different directions. Alienation closes political systems from population and from it springs populist irrationality in politics, racist and sexist scapegoating, consumers street uprisings, etc. Considering the regulatory function of the law over technology, social exclusion, war, one can assess the way modern law focuses on intergeneration relationships and how a healthy environment has been dismissed as a human right. For this propose one will consider the ongoing legal attempts to criminalize ecocide.info:eu-repo/semantics/publishedVersio