Ergodic Transport Theory, periodic maximizing probabilities and the twist condition

The present paper is a follow up of another one by A. O. Lopes, E. Oliveira and P. Thieullen which analyze ergodic transport problems. Our main focus will a more precise analysis of case where the maximizing probability is unique and is also a periodic orbit. Consider the shift T acting on the Bernoulli space \Sigma={1, 2, 3,.., d}^\mathbb{N} $and$A:\Sigma \to \mathbb{R} a Holder potential. Denote m(A)=max_{\nu is an invariant probability for T} \int A(x) \; d\nu(x) and, \mu_{\infty,A}, any probability which attains the maximum value. We assume this probability is unique (a generic property). We denote \T the bilateral shift. For a given potential Holder A:\Sigma \to \mathbb{R}, we say that a Holder continuous function W: \hat{\Sigma} \to \mathbb{R} is a involution kernel for A, if there is a Holder function A^*:\Sigma \to \mathbb{R}, such that, A^*(w)= A\circ \T^{-1}(w,x)+ W \circ \T^{-1}(w,x) - W(w,x). We say that A^* is a dual potential of A. It is true that m(A)=m(A^*). We denote by V the calibrated subaction for A, and, V^* the one for A^*. We denote by I^* the deviation function for the family of Gibbs states for \beta A, when \beta \to \infty. For each x we get one (more than one) w_x such attains the supremum above. That is, solutions of V(x) = W(w_x,x) - V^* (w_x)- I^*(w_x). A pair of the form (x,w_x) is called an optimal pair. If \T is the shift acting on (x,w) \in {1, 2, 3,.., d}^\mathbb{Z}, then, the image by \T^{-1} of an optimal pair is also an optimal pair. Theorem - Generically, in the set of Holder potentials A that satisfy (i) the twist condition, (ii) uniqueness of maximizing probability which is supported in a periodic orbit, the set of possible optimal w_x, when x covers the all range of possible elements x in \in \Sigma, is finite

Comment on Ricci Collineations of Static Spherically Symmetric Spacetimes

We present a counter example to a theorem given by Amir {\em et al.} J. Math. Phys. {\bf 35}, 3005 (1994). We also comment on a misleading statements of the same reference.Comment: 4 pages,LaTex fil

Radiative non-isothermal Bondi accretion onto a massive black hole

In this paper, we present the classical Bondi accretion theory for the case of non-isothermal accretion processes onto a supermassive black hole (SMBH), including the effects of X-ray heating and the radiation force due to electron scattering and spectral lines. The radiation field is calculated by considering an optically thick, geometrically thin, standard accretion disk as the emitter of UV photons and a spherical central object as a source of X-ray emission. In the present analysis, the UV emission from the accretion disk is assumed to have an angular dependence, while the X-ray/central object radiation is assumed to be isotropic. This allows us to build streamlines in any angular direction we need to. The influence of both types of radiation is evaluated for different flux fractions of the X-ray and UV emissions with and without the effects of spectral line driving. We find that the radiation emitted near the SMBH interacts with the infalling matter and modifies the accretion dynamics. In the presence of line driving, a transition resembles from pure type 1 & 2 to type 5 solutions (see Fig2.1 of Frank etal. 2002), which takes place regardless of whether or not the UV emission dominates over the X-ray emission. We compute the radiative factors at which this transition occurs, and discard type 5 solution from all our models. Estimated values of the accretion radius and accretion rate in terms of the classical Bondi values are also given. The results are useful for the construction of proper initial conditions for time-dependent hydrodynamical simulations of accretion flows onto SMBH at the centre of galaxies.Comment: 10 pages, 10 figures, Accepted to be published in A&

A new determination of the Pomeron intercept in hard processes

A method allowing for a direct comparison of data with theoreticalpredictions is proposed for forward jet production at HERA. It avoids thereconstruction of multi-parton contributions by expressing the experimentalcuts directly as correction factors on the QCD forward jet cross-section. Anapplication to the determination of the {\it effective} Pomeron intercept inthe BFKL-LO parametrization from $d\sigma/dx$ data at HERA leads to a good fitwith a significantly higher {\it effective} intercept, $\alpha_P= 1.43 \pm0.025 (stat.) \pm 0.025 (syst.),$ than for proton (total and diffractive)structure functions. It is however less than the value of the pomeron interceptusing dijets with large rapidity intervals obtained at Tevatron. We alsoevaluate the rapidity veto contribution to the higher order BFKL corrections.The method can be extended to other theoretical inputs

Variable stars in the globular cluster M28 (NGC 6626)

We present a new search for variable stars in the Galactic globular cluster M28 (NGC 6626). The search is based on a series of BVI images obtained with the SMARTS Consortium's 1.3m telescope at Cerro Tololo Inter-American Observatory, Chile. The search was carried out using the ISIS v2.2 image subtraction package. We find a total of 25 variable stars in the field of the cluster, 9 being new discoveries. Of the newly found variables, 1 is an ab-type RR Lyrae star, 6 are c-type RR Lyrae, and 2 are long-period/semi-regular variables. V22, previously classified as a type II Cepheid, appears as a bona-fide RRc in our data. In turn, V20, previously classified as an ab-type RR Lyrae, could not be properly phased with any reasonable period. The properties of the ab-type RR Lyrae stars in M28 appear most consistent with an Oosterhoff-intermediate classification, which is unusual for bona-fide Galactic globulars clusters. However, the cluster's c-type variables do not clearly support such an Oosterhoff type, and a hybrid Oosterhoff I/II system is accordingly another possibility, thus raising the intriguing possibility of multiple populations being present in M28. Coordinates, periods, and light curves in differential fluxes are provided for all the detected variables.Comment: A&A, in pres