We consider the product of a compact Riemannian manifold without boundary and null scalar curvature with a compact Riemannian manifold with boundary, null scalar curvature and constant mean curvature on the boundary. We use bifurcation theory to prove the existence of a infinite number of conformal classes with at least two non-homothetic Riemannian metrics of null scalar curvature and constant mean curvature of the boundary on the product manifold.

Elkin Cárdenas Díaz

Assuming Generalized Riemann's Hypothesis, Bach proved that the class group $\mathcal C\!\ell_{\mathbf K}$ of a number field ${\mathbf K}$ may be generated using prime ideals whose norm is bounded by $12\log^2\Delta_{\mathbf K}$, and by $(4+o(1))\log^2\Delta_{\mathbf K}$ asymptotically, where $\Delta_{\mathbf K}$ is the absolute value of the discriminant of ${\mathbf K}$. Under the same assumption, Belabas, Diaz y Diaz and Friedman showed a way to determine a set of prime ideals that generates $\mathcal C\!\ell_{\mathbf K}$ and which performs better than Bach's bound in computations, but which is asymptotically worse. In this paper we show that $\mathcal C\!\ell_{\mathbf K}$ is generated by prime ideals whose norm is bounded by the minimum of $4.01\log^2\Delta_{\mathbf K}$, $4\big(1+\big(2\pi e^{\gamma})^{-n_{\mathbf K}}\big)^2\log^2\Delta_{\mathbf K}$ and $4\big(\log\Delta_{\mathbf K}+\log\log\Delta_{\mathbf K}-(\gamma+\log 2\pi)n_{\mathbf K}+1+(n_{\mathbf K}+1)\frac{\log(7\log\Delta_{\mathbf K})}{\log\Delta_{\mathbf K}}\big)^2$. Moreover, we prove explicit upper bounds for the size of the set determined by Belabas, Diaz y Diaz and Friedman's algorithms, confirming that it has size $\asymp (\log\Delta_{\mathbf K}\log\log\Delta_{\mathbf K})^2$. In addition, we propose a different algorithm which produces a set of generators which satisfies the above mentioned bounds and in explicit computations turns out to be experimentally smaller than $\log^2\Delta_{\mathbf K}$ except for 7 out of 31000 fields.

Loïc Grenié Giuseppe Molteni

Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the "Rule of Four," initially used in calculus reform efforts, to a framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.

Carrie Diaz Eaton Hannah C. Highlander Kam D. Dahlquist M. Drew LaMar Glenn Ledder Richard C. Schugart

We will analyze the importance of varying the diffuse gas radial distribution on the resulting expected cosmic rays spectrum. We use the recent HI density data published by Nakanishi et al. (2004), and include them in the cosmic rays propagation code GALPROP (Strong & Moskalenko 1998). We will obtain those models that reproduce the characteristics shown by the cosmic rays data, and we will then extract information about the Galaxy structure.

M. Mollá M. Aguilar J. Alcaraz J. Berdugo J. Casaus C. Diaz E. Lanciotti C. Mañá J. Marin G. Martinez C. Palomares E. Sánchez I. Sevilla A. S. Torrentó

We consider the branching ratio for the process $t \to c \gamma$ in the context of the General Two Higgs Doublet Model type III. We find that taking into account reasonable values for the parameter $\tan \beta$ is possible to get values of this branching ratio up to orders of magnitude lying in the range of sensitivity of near future top quark experiments. For values of $B(t \to c \gamma) \sim 1-9 \times 10^{-5}$, values between 8-15 for $\tan \beta$ are allowed.

Rodolfo A. Diaz R. Martinez J-Alexis Rodriguez

We show that the minimal R-parity breaking model characterized by an effective bilinear violation of R-parity in the superpotential is consistent with minimal N=1 supergravity unification with radiative breaking of the electroweak symmetry and universal scalar and gaugino masses. This one-parameter extension of the MSSM-SUGRA model provides therefore the simplest reference model for the breaking of R-parity and constitutes a consistent truncation of the complete dynamical models with spontaneous R-parity breaking proposed previously. We comment on the lowest-lying CP-even Higgs boson mass and discuss its minimal N=1 supergravity limit, determine the ranges of $\tan\beta$ and bottom quark Yukawa couplings allowed in the model, as well as the relation between the tau neutrino mass and the bilinear R-parity violating parameter.

Marco A. Diaz Jorge C. Romao Jose W. F. Valle

We study gauge and Yukawa coupling unification in the simplest extension of the Minimal Supersymmetric Standard Model (MSSM) which incorporates R-Parity violation through a bilinear superpotential term. Contrary to what happens in the MSSM, we show that bottom-tau unification at the scale M_GUT where the gauge couplings unify can be achieved for any value of tan(beta) by choosing appropriately the sneutrino vacuum expectation value. In addition, we show that bottom-tau-top unification occurs in a slightly wider tan(beta) range than in the MSSM.

Marco A. Diaz J. Ferrandis Jorge C. Romao Jose W. F. Valle

Minimal R-parity violating supergravity predicts a value for $alpha_s(M_Z)$ smaller than in the case with conserved R-parity, and therefore closer to the experimental world average. We show that the R-parity violating effect on the $alpha_s$ prediction comes from the larger two-loop b-quark Yukawa contribution to the renormalization group evolution of the gauge couplings which characterizes R-parity violating supergravity. The effect is correlated to the tau neutrino mass and is sensitive to the initial conditions on the soft supersymmetry breaking parameters at the unification scale. We show how a few percent effect on $alpha_s(M_Z)$ may naturally occur even with tau neutrino masses as small as indicated by the simplest neutrino oscillation interpretation of the atmospheric neutrino data from Super-Kamiokande.

M. A. Diaz J. Ferrandis J. C. Romao J. W. F. Valle

Flavor violating Higgs signals, such as the top FCNC decay $t\to ch^0$ and the LFV Higgs decay $h^0\to \tau\mu$, have been studied at the LHC. These signals can arise within the general Two-Higgs doublet model (THDM), where each Higgs doublet couples to all fermions types through Yukawa matrices $Y^f_1$ and $Y^f_2$. The Yukawa matrices can be assumed to have the same form or they could have different structures. In this paper we study the case when both $Y^f_1$ and $Y^f_2$ have completely different forms, but in such a way that they complement to produce a specific hermitian mass matrix. We find that for specific four-zero textures, the Flavor Violating Higgs couplings depend only on the free parameters $\tan \beta$, $\gamma_f$ and the fermion masses. We use the current bounds on the low energy processes, to derive constraints on the Heavy Higgs boson mass, $\tan \beta$ and $\gamma_f$. Then, we use these constraints to evaluate the LFV Higgs decays, which reach Branching ratios that could be tested at the LHC.

M. A. Arroyo-Ureña J. Lorenzo Diaz-Cruz Enrique Diaz Javier A. Orduz-Ducuara

In this paper we investigate bubble nucleation in a disordered Landau-Ginzburg model. First we adopt the standard procedure to average over the disordered free energy. This quantity is represented as a series of the replica partition functions of the system. Using the saddle-point equations in each replica partition function, we discuss the presence of a spontaneous symmetry breaking mechanism. The leading term of the series is given by a large-N Euclidean replica field theory. Next, we consider finite temperature effects. Below some critical temperature, there are N real instantons-like solutions in the model. The transition from the false to the true vacuum for each replica field is given by the nucleation of a bubble of the true vacuum. In order to describe these irreversible processes of multiple nucleation, going beyond the diluted instanton approximation, an effective model is constructed, with one single mode of a bosonic field interacting with a reservoir of N identical two-level systems.

R. Acosta Diaz N. F. Svaiter C. A. D. Zarro