The Second Welfare Theorem with public goods in general economies

In this paper we prove a general version of the Second Welfare Theorem for a non-convex and non-transitive economy, with public goods and other externalities in consumption. For this purpose we use the sub-gradient to the distance function (normal cone) to define the pricing rule in this general context.Non-convex separation, Second Welfare Theorem, public goods, externalities.

Constraining a possible time-variation of the gravitational constant through "gravitochemical heating" of neutron stars

A hypothetical time-variation of the gravitational constant $G$ would make neutron stars expand or contract, so the matter in their interiors would depart from beta equilibrium. This induces non-equilibrium weak reactions, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of $G$ is balanced by the ongoing reactions. Using the surface temperature of the nearest millisecond pulsar (PSR J0437$-$4715) inferred from ultraviolet observations and results from theoretical modelling of the thermal evolution, we estimate two upper limits for this variation: (1) $|\dot G/G| < 2 \times 10^{-10}\mathrm{yr}^{-1},$ if the fast, "direct Urca" reactions are allowed, and (2) $|\dot G/G|<4\times 10^{-12}\mathrm{yr}^{-1},$ considering only the slower, "modified Urca" reactions. The latter is among the most restrictive upper limits obtained by other methods.Comment: IAU 2009 JD9 conference proceedings. MmSAIt, vol.80, in press. Paolo Molaro & Elisabeth Vangioni, eds. - 4 pages, 2 figure

KIC 9821622: An interesting lithium-rich giant in the Kepler field

We report the discovery of a new exceptional young lithium-rich giant, KIC 9821622, in the \textit{Kepler} field that exhibits an unusually large enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements. From high-resolution spectra obtained with GRACES at Gemini North, we derived fundamental parameters and detailed chemical abundances of 23 elements from equivalent widths and synthesis analysis. By combining atmospheric stellar parameters with available asteroseismic data, we obtained the stellar mass, radius, and age. The data analysis reveals that KIC 9821622 is a Li-rich (A(Li)$_{NLTE}$ = 1.80 $\pm$ 0.2) intermediate-mass giant star ($M$ = 1.64 $M_{\odot}$) located at the red giant branch near the luminosity bump. We find unexpectedly elevated abundances of Fe-peak and \textit{r}-process elements. In addition, as previously reported, we find that this is a young star (2.37 Gyr) with unusually high abundances of $\alpha$-elements ([$\alpha$/Fe] = 0.31). The evolutionary status of KIC 9821622 suggests that its Li-rich nature is the result of internal fresh Li that is synthesized through the Cameron-Fowler mechanism near the luminosity bump. However, its peculiar enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements opens the possibility of external contamination by material enriched by a supernova explosion. Although it is less likely, planet accretion cannot be ruled out.Comment: Letter, 6 pages, 3 figures, Accepted for publication in A&A. - Some language editing include

Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies

In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex economies, a recent result obtained by one of the authors, introduces conditions which, when applied to the convex case, give for Banach commodity spaces the well-known result of decentralization by continuous prices of pareto optimal allocations under an interiority condition. In this paper, in order to prove a different version of the Second Welfare Theorem, we reinforce the conditions on the commodity space, assumed here to be a Banach lattice, and introduce a nonconvex version of the properness assumptions on preferences and the total rpoduction set. Applied to the convex case, our result becomes the usual Second Welfare Theorem when properness assumptions replace the interiority condition. The proof uses a Hahn-Banach Theorem generalization by Borwein-Jofré which allows to separate nonconvex sets in general Banach spaces.Second welfare theorem; nonconvex economies; Banach spaces; subdifferential; Banach lattices; Properness assumptions

Pablo Neruda: mito y poesía

Se examina la relación entre el discurso poético y el discurso mítico en los poemas de Neruda. Se analiza primero el rechazo de la realidad social degradada y la alabanza de la naturaleza, ya sea en su dimensión vegetal, mineral u oceánica. A continuación, se estudian los mitos del tiempo, concentrándose en la estructura del día y del año, para concluir con el mito fundacional del cambio del tiempo, acontecido por el acceso traumático del continente americano a la historia de Occidente. Finalmente, se examinan los espacios sagrados y el ciclo de la materia, especialmente en el caso del mar y la tierra. Se descubre también la imagen genésica nerudiana, de índole heliocéntrica, y se concluye con una síntesis acerca de los mitos nerudianos y su significació