Three predictions on July 2012 Federal Elections in Mexico based on past regularities

Electoral systems are subject of study for physicist and mathematicians in last years given place to a new area: sociophysics. Based on previous works of the author on the Mexican electoral processes in the new millennium, he found three characteristics appearing along the 2000 and 2006 preliminary dataset offered by the electoral authorities, named PREP: I) Error distributions are not Gaussian or Lorentzian, they are characterized for power laws at the center and asymmetric lobes at each side. II) The Partido Revolucionario Institucional (PRI) presented a change in the slope of the percentage of votes obtained when it go beyond the 70% of processed certificates; hence it have an improvement at the end of the electoral computation. III) The distribution of votes for the PRI is a smooth function well described by Daisy model distributions of rank $r$ in all the analyzed cases, presidential and congressional elections in 2000, 2003 and 2006. If all these characteristics are proper of the Mexican reality they should appear in the July 2012 process. Here I discuss some arguments on why such a behaviors could appear in the present processComment: 6 pages, one tabl

On Types of Elliptic Pseudoprimes

We generalize the notions of elliptic pseudoprimes and elliptic Carmichael numbers introduced by Silverman to analogues of Euler-Jacobi and strong pseudoprimes. We investigate the relationships among Euler Elliptic Carmichael numbers , strong elliptic Carmichael numbers, products of anomalous primes and elliptic Korselt numbers of Type I: The former two of these are introduced in this paper, and the latter two of these were introduced by Mazur (1973) and Silverman (2012) respectively. In particular, we expand upon a previous work of Babinkostova et al. by proving a conjecture about the density of certain elliptic Korselt numbers of Type I that are products of anomalous primes.Comment: Revised for publication. 33 page

Plausible families of compact objects with a Non Local Equation of State

We investigate the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. It is explored how their physical variables change as the family-parameter varies. The models studied correspond to anisotropic spherical matter configurations having a non local equation of state. This particular type of equation of state with no causality problems provides, at a given point, the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in General Relativity, we obtain that those models become more stable as the family parameter increases

Nonmeasurable subgroups of compact groups

In 1985 S.~Saeki and K.~Stromberg published the following question: {\it Does every infinite compact group have a subgroup which is not Haar measurable?} An affirmative answer is given for all compact groups with the exception of some metric profinite groups known as strongly complete. In this spirit it is also shown that every compact group contains a non-Borel subgroup