A representation theorem for integral rigs and its applications to residuated lattices

We prove that every integral rig in Sets is (functorially) the rig of global sections of a sheaf of really local integral rigs. We also show that this representation result may be lifted to residuated integral rigs and then restricted to varieties of these. In particular, as a corollary, we obtain a representation theorem for pre-linear residuated join-semilattices in terms of totally ordered fibers. The restriction of this result to the level of MV-algebras coincides with the Dubuc-Poveda representation theorem.Comment: Manuscript submitted for publicatio

Critical behavior of ferromagnetic pure and random diluted nanoparticles with competing interactions: variational and Monte Carlo approaches

The magnetic properties and critical behavior of both ferromagnetic pure and metallic nanoparticles having concurrently atomic disorder, dilution and competing interactions, are studied in the framework of an Ising model. We have used both the free energy variational principle based on the Bogoliubov inequality and Monte Carlo simulation. As a case of study for random diluted nanoparticles we have considered the Fe$_{0.5}$Mn$_{0.1}$Al$_{0.4}$ alloy characterized for exhibiting, under bulk conditions, low temperature reentrant spin glass (RSG) behavior and for which experimental and simulation results are available. Our results allow concluding that the variational model is successful in reproducing features of the particle size dependence of the Curie temperature for both pure and random diluted particles. In this last case, low temperature magnetization reduction was consistent with the same type of RSG behavior observed in bulk in accordance with the Almeida-Thouless line at low fields and a linear dependence of the freezing temperature with the reciprocal of the particle diameter was also obtained. Computation of the correlation length critical exponent yielded the values $\nu=0.926\pm 0.004$ via Bogoliubov and$\nu =0.71\pm 0.04$ via Monte Carlo. This fact indicates that even though thermodynamical models can be indeed used in the study of nanostructures and they can reproduce experimental features, special attention must be paid regarding critical behavior. From both approaches, differences in the $\nu$ exponent with respect to the pure Ising model agree with Harris and Fisher arguments.Comment: 11 pages, 11 figures. Submitted to Phys. Rev.

Induction of stimulative parthenocarpy in Vitis vinifera L.

Stimulative parthenocarpy was induced in two varieties of Vitis vinifera L. Flame Tokay and Rose Muscat (local variety) out of eight varieties studied.In F l a m e T o k a y the delay or inhibition of bhe abscission of the calyptra and parthenocarpic development of the berries, was obtained with pre-bloom treatments (3 days before beginning of bloom) of 4CPA 30 ppm + KGA3 30 ppm. Induction and growth ,of parthenocarpic berries was most pronounced after post-bloom sprays (7 days after the end of bloom) with BA 1500 ppm + KGA3 80 ppm or 4CPA 30 ppm. A parthenocarpic development of the berries was also obtained with postbloom treatments of KGA3 at concentrations of 50 to 100 ppm. BA (Benzyladenine) alone had only a slight effect on the development of parthenocarpic berries. However, the results were surprisingly satisfactory when applied in combination with gibberellin (KGA3 80 ppm) or auxins. Treatments at bloom or after bloom with BA 800 ppm + KGA3 80 ppm increased bhe number of berries and cluster weight. Applications of BA 800 ppm + KGA3 80 ppm to Rose Musca t at the beginning of bloom resulted in clusters with practically all berries seedless. The artificially accelerated growth of the berries may provoke abortion of all the recently fecundated ovules and the non viability of the not fecundated ones. Clusters of the treated plants with an average of 520 flowers originated 501 parbhenocarpic berries (96%), whereas the control with an average 635 flowers per cluster gave a percentage of seeded + seedless berries of 14% only {95 berries per cluster). BA applied with auxin or gibberellin-like substances in full-bloom or after bloom produced seedless berries, which were smaller in size than the seeded berries of unsprayed clusters

The Spin-Orbit Evolution of GJ 667C System: The Effect of Composition and Other Planet's Perturbations

Potentially habitable planets within the habitable zone of M-dwarfs are affected by tidal interaction. We studied the tidal evolution in GJ 667C using a numerical code we call TIDEV. We reviewed the problem of the dynamical evolution focusing on the effects that a rheological treatment, different compositions and the inclusion of orbital perturbations, have on the spin-down time and the probability to be trapped in a low spin-orbit resonance. Composition have a strong effect on the spin-down time, changing, in some cases, by almost a factor of 2 with respect to the value estimated for a reference Earth-like model. We calculated the time to reach a low resonance value (3:2) for the configuration of 6 planets. Capture probabilities are affected when assuming different compositions and eccentricities variations. We chose planets b and c to evaluate the probabilities of capture in resonances below 5:2 for two compositions: Earth-like and Waterworld planets. We found that perturbations, although having a secular effect on eccentricities, have a low impact on capture probabilities and noth- ing on spin-down times. The implications of the eccentricity variations and actual habitability of the GJ 667C system are discussed.Comment: 15 pages, 9 figures, 4 tables. Accepted for publication in MNRAS - V