Polynomial bounds for automorphisms groups of foliations

Let $(X, \mathcal{F})$ be a foliated surface and $G$ a finite group of automorphisms of $X$ that preserves $\mathcal{F}$. We investigate invariant loci for $G$ and obtain upper bounds for its order that depends polynomially on the Chern numbers of $X$ and $\mathcal{F}$. As a consequence, we estimate the order of the automorphism group of some foliations under mild restrictions. We obtain an optimal bound for foliations on the projective plane which is attained by the automorphism groups of the Jouanolou's foliations.Comment: To appear in Revista Matem\'atica Iberoamerican

A standard form for generator matrices with respect to the Niederreiter-Rosenbloom-Tsfasman metric

In this note, we present an analogue for codes in vector spaces with a Rosenbloom-Tsfasman metric of the well-known standard form of generator matrices for codes in spaces with the Hamming metric

Foliations on the projective plane with finite group of symmetries

Let $\mathcal{F}$ denote a singular holomorphic foliation on $\mathbb{P}^2$ having a finite automorphism group \mbox{aut}(\mathcal{F}). Fixed the degree of $\mathcal{F}$, we determine the maximal value that |\mbox{aut}(\mathcal{F})| can take and explicitly exhibit all the foliations attaining this maximal value. Furthermore, we classify the foliations with large but finite automorphism group.Comment: Minor changes, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sc

Thermodynamic Properties of Static and Rotating Unparticle Black Holes

In this paper we find analytical expressions for thermodynamic quantities of scalar (tensor) and vector unparticle static black holes. We also find rotating solutions to these systems and analyse their thermodynamics. First we consider the static case with a spherically symmetric source for both the vector and scalar (tensor) unparticles. We obtain thus analytical expressions to the principal thermodynamic quantities: Hawking temperature, entropy, heat capacity and free energy. For the scalar (tensor) case we find that the black hole presents a residual value for the entropy when its radius goes to zero but the other thermodynamic quantities give, for any horizon radius, a thermodynamically unstable behavior similar to the standard black hole. For the vector case we find a richer structure in the region in which the horizon radius is less than the characteristic length of the unparticle theory. We identify a phase transition and a region where the black hole can be thermodynamically stable. Following, we show that the mentioned modifications in the standard gravity are formally similar to those ones present in the black holes with quintessence. With this we also show, notwithstanding, that the unparticles cannot be a source of quintessence. By using this similarity we find two different rotating solutions to the unparticle black holes based on works by Ghosh and Toshmatov {\it et al}. For both cases we compute the Hawking temperature and in the ungravity dominated regime we find, as in the static cases, a fractalization of the event horizon. For the Gosh-like solution the fractal dimension depends on the polar angle and on the rotation of the source. For the Toshmatov-like one it is equal to the static case and therefore the fractalization is not dependent on the rotation of the source.Comment: Minor correction

Non-periodic bifurcation for surface diffeomorphisms

We prove that a "positive probability" subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles $\mathcal{H}$ is constituted by Kupka-Smale diffeomorphisms: all periodic points are hyperbolic and their invariant manifolds intersect transversally. Lack of hyperbolicity arises from the presence of a tangency between a stable manifold and an unstable manifold, one of which is not associated to a periodic point. All these diffeomorphisms that we construct lie on the boundary of the same connected component of $\mathcal{H}$.Comment: 31 pages, 5 figure

Spin filtering by ferromagnetic nanowires

We show that electrical current flowing through nanowires made of ferromagnetic disordered alloys can become highly spin polarized.Comment: 4 pages, 2 figures, RevTeX

Polynomial Invariant Theory and Shape Enumerator of Self-Dual Codes in the NRT-Metric

In this paper we consider self-dual NRT-codes, that is, self-dual codes in the metric space endowed with the Niederreiter-Rosenbloom-Tsfasman (NRT-metric). We use polynomial invariant theory to describe the shape enumerator of a binary self-dual, doubly even self-dual, and doubly-doubly even self dual NRT-code $C\subseteq M_{n,2}(\mathbb{F}_{2})$. Motivated by these results we describe the number of invariant polinomials that we must find to describe the shape enumerator of a self-dual NRT-code of $M_{n,s}(\mathbb{F}_{2})$. We define the ordered flip of a matrix $A\in M_{k,ns}(\mathbb{F}_{q})$ and present some constructions of self-dual NRT-codes over $\mathbb{F}_{q}$. We further give an application of ordered flip to the classification of bidimensional self-dual NRT-codes

Shannon Entropy and Kullback-Leibler Divergence in Multivariate Log Fundamental Skew-Normal and Related Distributions

This paper mainly focuses on studying the Shannon Entropy and Kullback-Leibler divergence of the multivariate log canonical fundamental skew-normal (LCFUSN) and canonical fundamental skew-normal (CFUSN) families of distributions, extending previous works. We relate our results with other well known distributions entropies. As a byproduct, we also obtain the Mutual Information for distributions in these families. Shannon entropy is used to compare models fitted to analyze the USA monthly precipitation data. Kullback-Leibler divergence is used to cluster regions in Atlantic ocean according to their air humidity level.Comment: 21 page

Coherent control of optical injection of spin and currents in topological insulators

Topological insulators have surface states with a remarkable helical spin structure, with promising prospects for applications in spintronics. Strategies for generating spin polarized currents, such as the use of magnetic contacts and photoinjection, have been the focus of extensive research. While several optical methods for injecting currents have been explored, they have all focused on one-photon absorption. Here we consider the use of both a fundamental optical field and its second harmonic, which allows the injection of spin polarized carriers and current by a nonlinear process involving quantum interference between one- and two-photon absorption. General expressions are derived for the injection rates in a generic two-band system, including those for one- and two-photon absorption processes as well as their interference. Results are given for carrier, spin density and current injection rates on the surface of topological insulators, for both linearly and circularly polarized light. We identify the conditions that would be necessary for experimentally verifying these predictions.Comment: 10 pages, 4 figure

All-optical injection of charge, spin and valley currents in monolayer transition metal dichalcogenides

Monolayer transition metal dichalcogenides have recently become a playground for spin- and valleytronics research. Their low energy spectrum can be described by Dirac cones on the corners of Brillouin zone, but the physical properties are richer than those of graphene since the spin degeneracy is lifted and the optical selection rules are valley dependent. This has been exploited for the optical injection of spin and valley polarized currents by the application of static electric fields. In this paper we consider an all-optical method for the injection of charge, spin and valley polarized currents. The presence of both a fundamental optical field and its second harmonic can lead to the injection of currents due to a nonlinear effect involving the quantum interference between one- and two-photon absorption processes. We analyze how the injected quantities can be controlled through the parameters of the incident light fields, allowing capabilities of control beyond those achieved with static fields, and discuss the conditions for experimental verification of our results.Comment: 8 pages, 3 figures. arXiv admin note: text overlap with arXiv:1401.124