The Frequency Distribution of Semi-major Axis of Wide Binaries. Cosmogony and Dynamical Evolution

The frequency distribution f(a) of semi-major axis of double and multiple systems, as well as their eccentricities and mass ratios, contain valuable fossil information about the process of star formation and the dynamical history of the systems. In order to advance in the understanding of these questions, we have made an extensive analysis of the frequency distribution f (a) for wide binaries (a>25 AU) in the various published catalogues, as well as in our own (Poveda et al., 1994; Allen et al., 2000; Poveda & Hernandez, 2003). Based upon all these studies we have established that the frequency f(a) is function of the age of the system and follows Oepik's distribution f(a) ~ 1/a in the range of 100 AU < a < a[c](t), where a[c](t) is a critical semi-major axis beyond which binaries have dissociated by encounters with massive objects. We argue that the physics behind the distribution f(a) ~ 1/a is a process of energy relaxation, analogous to that present in stellar clusters (secular relaxation) or in spherical galaxies (violent relaxation). The frequency distribution of mass ratios in triple systems as well as the existence of runaway stars, indicate that both types of relaxation are important in the process of binary and multiple star formation.Comment: International Astronomical Union. Symposium no. 240, held 22-25 August, 2006 in Prague, Czech Republi

On the equivalence between MV-algebras and ll-groups with strong unit

In "A new proof of the completeness of the Lukasiewicz axioms"} (Transactions of the American Mathematical Society, 88) C.C. Chang proved that any totally ordered $MV$-algebra $A$ was isomorphic to the segment $A \cong \Gamma(A^*, u)$ of a totally ordered $l$-group with strong unit $A^*$. This was done by the simple intuitive idea of putting denumerable copies of $A$ on top of each other (indexed by the integers). Moreover, he also show that any such group $G$ can be recovered from its segment since $G \cong \Gamma(G, u)^*$, establishing an equivalence of categories. In "Interpretation of AF $C^*$-algebras in Lukasiewicz sentential calculus" (J. Funct. Anal. Vol. 65) D. Mundici extended this result to arbitrary $MV$-algebras and $l$-groups with strong unit. He takes the representation of $A$ as a sub-direct product of chains $A_i$, and observes that $A \overset {} {\hookrightarrow} \prod_i G_i$ where $G_i = A_i^*$. Then he let $A^*$ be the $l$-subgroup generated by $A$ inside $\prod_i G_i$. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang's result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product $l$-group $\prod_i G_i$, avoiding entirely the notion of good sequence.Comment: 6 page

The process μ→νeeνˉμ\mu \to \nu_{e}e\bar{\nu}_{\mu} in the 2HDM with flavor changing neutral currents

We consider the process $\mu \to \nu_{e}e\bar{\nu}_{\mu}$in the framework of a two Higgs doublet model with flavor changing neutral currents (FCNC). Since FCNC generates in turn flavor changing charged currents in the lepton sector, this process appears at tree level mediated by a charged Higgs boson exchange. From the experimental upper limit for this decay, we obtain the bound $| \xi_{\mu e}/m_{H^{\pm}}| \leq 3.8\times 10^{-3}$ where$\xi_{\mu e}$refers to the mixing between the first and second lepton generations, and $m_{H^{\pm}}$denotes the mass of the charged Higgs boson. This bound is independent on the other free parameters of the model. In particular, for $m_{H^{\pm}}\simeq 100$GeV we get $| \xi_{e\mu}|$ $\lesssim 0.38$Comment: 2 pages, no figure

A Double Classification of Common Pitfalls in Ontologies

The application of methodologies for building ontologies has improved the ontology quality. However, such a quality is not totally guaranteed because of the difficulties involved in ontology modelling. These difficulties are related to the inclusion of anomalies or worst practices in the modelling. In this context, our aim in this paper is twofold: (1) to provide a catalogue of common worst practices, which we call pitfalls, and (2) to present a double classification of such pitfalls. These two products will serve in the ontology development in two ways: (a) to avoid the appearance of pitfalls in the ontology modelling, and (b) to evaluate and correct ontologies to improve their quality