Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, $u_t=J*u-u:=Lu$, in an exterior domain, $\Omega$, which excludes one or several holes, and with zero Dirichlet data on $\mathbb{R}^N\setminus\Omega$. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is $L$-harmonic, $Lu=0$, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behavior can be presented in a unified way through a suitable global approximation

ON GAUGINO CONDENSATION WITH FIELD-DEPENDENT GAUGE COUPLINGS

We study in detail gaugino condensation in globally and locally supersymmetric Yang-Mills theories. We focus on models for which gauge-neutral matter couples to the gauge bosons only through nonminimal gauge kinetic terms, for the cases of one and several condensing gauge groups. Using only symmetry arguments, the low-energy expansion, and general properties of supersymmetry, we compute the low energy Wilson action, as well as the (2PI) effective action for the composite {\it classical} superfield U\equiv\langle \Tr\WW \rangle, with $W_\alpha$ the supersymmetric gauge field strength. The 2PI effective action provides a firmer foundation for the approach of Veneziano and Yankielowicz, who treated the composite superfield, $U$, as a quantum degree of freedom. We show how to rederive the Wilson action by minimizing the 2PI action with respect to $U$. We determine, in both formulations and for global and local supersymmetry, the effective superpotential, $W$, the non-perturbative contributions to the low-energy K\"ahler potential $K$, and the leading higher supercovariant derivative terms in an expansion in inverse powers of the condensation scale. As an application of our results we include the string moduli dependence of the super- and K\"ahler potentials for simple orbifold models.Comment: 54 pages, plain te

Brans-Dicke-type theories and avoidance of the cosmological singularity

We tudy flat Friedmann-Robertson-Walker cosmology in Brans-Dicke-type theories of gravitation with minimal coupling between the scalar field and the matter fields in the Einstein frame (general relativity with an extra scalar field) for arbitrary values of the Brans-Dicke parameter $\omega>-{3/2}$. It is shown that the cosmological singularity occuring in the Einstein frame formulation of this theory is removed in the Jordan frame in the range $-{3/2}<\omega<\leq-{4/3}$. This result is interpreted in the ligth of a viewpoint (first presented in reference gr-qc/9905071) asserting that both Jordan frame and Einstein frame formulations of general relativity are physically equivalent. The implications of the obtained result for string theory are outlined.Comment: 9 pages, LaTeX, no figures. Improved version accepted for publication in PR

Radiative Electroweak Symmetry-Breaking Revisited

In the absence of a tree-level scalar-field mass, renormalization-group methods permit the explicit summation of leading-logarithm contributions to all orders of the perturbative series within the effective potential for $SU(2)\times U(1)$ electroweak symmetry. This improvement of the effective potential function is seen to reduce residual dependence on the renormalization mass scale. The all-orders summation of leading logarithm terms involving the dominant three couplings contributing to radiative corrections is suggestive of a potential characterized by a plausible Higgs boson mass of 216 GeV. However, the tree potential's local minimum at $\phi =0$ is restored if QCD is sufficiently strong.Comment: revtex, 4 pages, 1 eps figure embedded in manuscript. Updated version contains additional comments and corrects minor error

Near-brane SU(6) origin Higgs in Scherk-Schwarz breaking of five-dimensional SU(6) GUT

The symmetry breaking of five-dimensional SU(6) GUT is realized by Scherk-Schwarz mechanisms through trivial and pseudo nontrivial orbifold S1/Z2 breakings to produce dimensional deconstruction 5D SU(6) \rightarrow4D SU(6). The latter also induces near-brane weakly-coupled SU(6) Baby Higgs to further break the symmetry into SU(3)C \otimes SU(3)H \otimes U(1)C. The model successfully provides a scenario of the origin of (Little) Higgs from GUT scale, produces the (intermediate and light) Higgs boson with the most preferred range and establishes coupling unification and compactification scale correctly.Comment: 23 pages, 5 figure

Dual geometries and spacetime singularities

The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity may be avoided in its dual representation (Weyl-type general relativity). This dual representation provides a singularity-free picture of the World that is physicaly equivalent to the canonical general relativistic one.Comment: 11 pages, LaTeX, no figures, version accepted for publication in PR

The absolute age of the globular cluster M15 using near-infrared adaptive optics images from PISCES/LBT

We present deep near-infrared (NIR) J, Ks photometry of the old, metal-poor Galactic globular cluster M\,15 obtained with images collected with the LUCI1 and PISCES cameras available at the Large Binocular Telescope (LBT). We show how the use of First Light Adaptive Optics system coupled with the (FLAO) PISCES camera allows us to improve the limiting magnitude by ~2 mag in Ks. By analyzing archival HST data, we demonstrate that the quality of the LBT/PISCES color magnitude diagram is fully comparable with analogous space-based data. The smaller field of view is balanced by the shorter exposure time required to reach a similar photometric limit. We investigated the absolute age of M\,15 by means of two methods: i) by determining the age from the position of the main sequence turn-off; and ii) by the magnitude difference between the MSTO and the well-defined knee detected along the faint portion of the MS. We derive consistent values of the absolute age of M15, that is 12.9+-2.6 Gyr and 13.3+-1.1 Gyr, respectively.Comment: 13 pages, 8 figures, ApJ accepte

evaluation of liver fibrosis concordance analysis between noninvasive scores apri and fib 4 evolution and predictors in a cohort of hiv infected patients without hepatitis c and b infection

Background. There is lack of data on the incidence of liver fibrosis (LF) progression in patients with human immunodeficiency virus (HIV) monoinfection and risk factors for LF. Methods. We performed an observational prospective study in a cohort of HIV-infected patients who had initiated highly active antiretroviral therapy (HAART). FIB-4 and aspartate aminotransferase (AST)-to-platelet ratio index (APRI) were assessed. The concordance between the 2 scores was assessed by weighted kappa coefficient. Kaplan-Meier analysis was used to estimate the incidence of LF. Cox regression analysis was used to assess the predictors of transition. Results. A total of 1112 patients were observed for a mean of 2249 days of follow-up. The concordance between FIB-4 and APRI was moderate (kappa = .573). The incidence of transition to higher FIB-4 classes was 0.064 (95% confidence interval [CI], 0.056―0.072) per person-year of follow-up (PYFU), whereas the incidence of transition to higher APRI classes was 0.099 (95% CI, 0.089-0.110) per PYFU. The incidence of transition to FIB-4 >3.25 was 0.013 per PYFU (95% CI, 0.010-0.017) and 0.018 per PYFU (95% CI, 0.014―0.022) for APRI >1.5. In multivariate analyses, for transition to higher classes, HIV RNA level 3.25 and APRI> 1.5 as study outcomes. Conclusions. Overall, our results suggest a possible benefit associated with earlier HAART initiation, provided that the effectiveness of HAART is sustained and treatment with DDX is avoided

Low-level viraemia, measured as viraemia copy-years, as a prognostic factor for medium–long-term all-cause mortality: a MASTER cohort study

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