Infrared Observations of AGN

We present results from an imaging and spectroscopic study of the dust properties of Seyfert galaxies in the 1-10um range. The data are compared to state of the art models of torus emission to constrain geometrical and physical properties of the obscuring medium.Comment: 2 pages, to appear in the IAU Symp.No.222 proceedings:"The Interplay among Black Holes, Stars and ISM in Galactic Nuclei", Gramado, Brazil, March 1-5, 200

High-order harmonic generation driven by chirped laser pulses induced by linear and non linear phenomena

We present a theoretical study of high-order harmonic generation (HHG) driven by ultrashort optical pulses with different kind of chirps. The goal of the present work is perform a detailed study to clarify the relevant parameters in the chirped pulses to achieve a noticeable cut-off extensions in HHG. These chirped pulses are generated using both linear and nonlinear dispersive media.The description of the origin of the physical mechanisms responsible of this extension is, however, not usually reported with enough detail in the literature. The study of the behaviour of the harmonic cut-off with these kind of pulses is carried out in the classical context, by the integration of the Newton-Lorentz equation complemented with the quantum approach, based on the integration of the time dependent Schr\"odinger equation in full dimensions (TDSE-3D), we are able to understand the underlying physics.Comment: 13 pages, 8 figure

Generalized Paley graphs equienergetic with their complements

We consider generalized Paley graphs $\Gamma(k,q)$, generalized Paley sum graphs $\Gamma^+(k,q)$, and their corresponding complements $\bar \Gamma(k,q)$ and $\bar \Gamma^+(k,q)$, for $k=3,4$. Denote by $\Gamma = \Gamma^*(k,q)$ either $\Gamma(k,q)$ or $\Gamma^+(k,q)$. We compute the spectra of $\Gamma(3,q)$ and $\Gamma(4,q)$ and from them we obtain the spectra of $\Gamma^+(3,q)$ and $\Gamma^+(4,q)$ also. Then we show that, in the non-semiprimitive case, the spectrum of $\Gamma(3,p^{3\ell})$ and $\Gamma(4,p^{4\ell})$ with $p$ prime can be recursively obtained, under certain arithmetic conditions, from the spectrum of the graphs $\Gamma(3,p)$ and $\Gamma(4,p)$ for any $\ell \in \mathbb{N}$, respectively. Using the spectra of these graphs we give necessary and sufficient conditions on the spectrum of $\Gamma^*(k,q)$ such that $\Gamma^*(k,q)$ and $\bar \Gamma^*(k,q)$ are equienergetic for $k=3,4$. In a previous work we have classified all bipartite regular graphs $\Gamma_{bip}$ and all strongly regular graphs $\Gamma_{srg}$ which are complementary equienergetic, i.e.\@ $\{\Gamma_{bip}, \bar{\Gamma}_{bip}\}$ and $\{\Gamma_{srg}, \bar{\Gamma}_{srg}\}$ are equienergetic pairs of graphs. Here we construct infinite pairs of equienergetic non-isospectral regular graphs $\{\Gamma, \bar \Gamma\}$ which are neither bipartite nor strongly regular.Comment: 22 page

The Waring's problem over finite fields through generalized Paley graphs

We show that the Waring's number over a finite field $\mathbb{F}_q$, denoted $g(k,q)$, when exists, coincides with the diameter of the generalized Paley graph $\Gamma(k,q)=Cay(\mathbb{F}_{q},R_k)$ with $R_k=\{x^k : x\in \mathbb{F}_q^*\}$. We find infinite new families of exact values of $g(k,q)$ from a characterization of graphs $\Gamma(k,q)$ which are also Hamming graphs previously proved by Lim and Praeger in 2009. Then, we show that every positive integer is the Waring number for some pair $(k,q)$ with $q$ not a prime. Finally, we find a lower bound for $g(k,p)$ with $p$ prime by using that $\Gamma(k,p)$ is a circulant graph in this case.Comment: 16 pages. Small additions and typos corrected. We added. at the end, a small subsection comparing our lower bound for Waring numbers with the other 3 lower bounds know

Potentials of metals in molten potassium bisulphate

The galvanic behaviour of various metals in molten potassium bisulphate has been investigated, using a hydrogen reference electrode at 260–280°C. A galvanic series is presented to indicate the probable direction of galvanic effects in corrosion cells.Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicada

The spectra of generalized Paley graphs of qℓ+1q^\ell+1 powers and applications

We consider a special class of generalized Paley graphs over finite fields, namely the Cayley graphs with vertex set $\mathbb{F}_{q^m}$ and connection set the nonzero $(q^\ell+1)$-th powers in $\mathbb{F}_{q^m}$, as well as their complements. We explicitly compute the spectrum of these graphs. As a consequence, the graphs turn out to be (with trivial exceptions) simple, connected, non-bipartite, integral and strongly regular (of Latin square type in half of the cases). By using the spectral information we compute several invariants of these graphs. We exhibit infinite families of pairs of equienergetic non-isospectral graphs. As applications, on the one hand we solve Waring's problem over $\mathbb{F}_q^m$ for the exponents $q^\ell+1$, for each $q$ and for infinite values of $\ell$ and $m$. We obtain that the Waring's number $g(q^\ell+1,q^m)=1$ or $2$, depending on $m$ and $\ell$, thus tackling some open cases. On the other hand, we construct infinite towers of Ramanujan graphs in all characteristics.Comment: 27 pages, 3 tables. A little modification of the title. Corollary 4.8 removed. Added Section 6 on "Energy". Minor typos corrected. Ihara zeta functions at the end correcte