Nonlinear elliptic equations involving the p-Laplacian with mixed Dirichlet-Neumann boundary conditions

In this paper, a nonlinear differential problem involving the p-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results

Improved Action Functionals in Non-Perturbative Quantum Gravity

Models of gravity with variable G and Lambda have acquired greater relevance after the recent evidence in favour of the Einstein theory being non-perturbatively renormalizable in the Weinberg sense. The present paper builds a modified Arnowitt-Deser-Misner (ADM) action functional for such models which leads to a power-law growth of the scale factor for pure gravity and for a massless phi**4 theory in a Universe with Robertson-Walker symmetry, in agreement with the recently developed fixed-point cosmology. Interestingly, the renormalization-group flow at the fixed point is found to be compatible with a Lagrangian description of the running quantities G and Lambda.Comment: Latex file. Record without file already exists on SLAC-SPIRES, and hence that record and the one for the present arxiv submission should become one record onl

Role of Noise in a Market Model with Stochastic Volatility

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES effect in our model with stochastic volatility. We investigate the role of the correlation between the two noise sources on the NES effect.Comment: 13 pages, 6 figures, Eur. Phys. J. B, in pres

Cosmological Perturbations in Renormalization Group Derived Cosmologies

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $\Lambda$ is presented. A gauge-invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, $G$, and $\Lambda$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $\Lambda$ vary according to renormalization group equations in the vicinity of a fixed point.Comment: 22 pages, revtex, subeqn.sty, to appear on IJMP

Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity

We discuss a mechanism that induces a time-dependent vacuum energy on cosmological scales. It is based on the instability induced renormalization triggered by the low energy quantum fluctuations in a Universe with a positive cosmological constant. We employ the dynamical systems approach to study the qualitative behavior of Friedmann-Robertson-Walker cosmologies where the cosmological constant is dynamically evolving according with this nonperturbative scaling at low energies. It will be shown that it is possible to realize a "two regimes" dark energy phases, where an unstable early phase of power-law evolution of the scale factor is followed by an accelerated expansion era at late times.Comment: 26 pages, 4 figures. To appear in New Journal of Physic

The neutron star in Cassiopeia A: equation of state, superfluidity, and Joule heating

The thermomagnetic evolution of the young neutron star in Cassiopea A is studied by considering fast neutrino emission processes. In particular, we consider neutron star models obtained from the equation of state computed in the framework of the Brueckner-Bethe-Goldstone many-body theory and variational methods, and models obtained with the Akmal-Pandharipande-Ravenhall equation of state. It is shown that it is possible to explain a fast cooling regime as the one observed in the neutron star in Cassiopea A if the Joule heating produced by dissipation of the small-scale magnetic field in the crust is taken into account. We thus argue that it is difficult to put severe constraints on the superfluid gap if the Joule heating is considered.Comment: 4 pages, 2 figures, to appear on A&A Letter

Networks of equities in financial markets

We review the recent approach of correlation based networks of financial equities. We investigate portfolio of stocks at different time horizons, financial indices and volatility time series and we show that meaningful economic information can be extracted from noise dressed correlation matrices. We show that the method can be used to falsify widespread market models by directly comparing the topological properties of networks of real and artificial markets.Comment: 9 pages, 8 figures. Accepted for publication in EPJ