Boundedness, compactness and Schatten-class membership of weighted composition operators

The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class membership is also considered; as a result, stronger forms of the two main results of a recent paper of Gunatillake are derived. Finally, weighted composition operators on weighted Bergman spaces $\mathcal{A}^2 \alpha(\mathbb{D})$ are considered, and the results of Harper and Smith, linking their properties to those of Carleson embeddings, are extended to this situation.Comment: 12 page

Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer new insights into decoherence, dynamics of quantum entanglement, and quantum chaos.Comment: 12 pages, 7 figures, to appear in Physical Review

Reionization: Characteristic Scales, Topology and Observability

Recently the numerical simulations of the process of reionization of the universe at z>6 have made a qualitative leap forward, reaching sufficient sizes and dynamic range to determine the characteristic scales of this process. This allowed making the first realistic predictions for a variety of observational signatures. We discuss recent results from large-scale radiative transfer and structure formation simulations on the observability of high-redshift Ly-alpha sources. We also briefly discuss the dependence of the characteristic scales and topology of the ionized and neutral patches on the reionization parameters.Comment: 4 pages, 5 figures (4 in color), to appear in Astronomy and Space Science special issue "Space Astronomy: The UV window to the Universe", proceedings of 1st NUVA Conference ``Space Astronomy: The UV window to the Universe'' in El Escorial (Spain

Spiral Galaxies Rotation Curves with a Logarithmic Corrected Newtonian Gravitational Potential

We analyze the rotation curves of 10 spiral galaxies with a newtonian potential corrected with an extra logarithmic term, using a disc modelization for the spiral galaxies. There is a new constant associated with the extra term in the potential. The rotation curve of the chosen sample of spiral galaxies is well reproduced for a given range of the new constant. It is argued that this correction can have its origin from string configurations. The compatibility of this correction with local physics is discussed.Comment: Latex file, 6 pages, 20 figure

Maxwell's field coupled nonminimally to quadratic torsion: Induced axion field and birefringence of the vacuum

We consider a possible (parity conserving) interaction between the electromagnetic field $F$ and a torsion field $T^\alpha$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and {\it quadratic} in torsion. These two classes are displayed explicitly. The first class of the type $\sim F T^2$ yields (undesirable) modifications of the Maxwell equations. The second class of the type $\sim F^2 T^2$ doesn't touch the Maxwell equations but rather modifies the constitutive tensor of spacetime. Such a modification can be completely described in the framework of metricfree electrodynamics. We recognize three physical effects generated by the torsion: (i) An axion field that induces an {\em optical activity} into spacetime, (ii) a modification of the light cone structure that yields {\em birefringence} of the vacuum, and (iii) a torsion dependence of the {\em velocity of light.} We study these effects in the background of a Friedmann universe with torsion. {\it File tor17.tex, 02 August 2003}Comment: 6 page

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a 'mini-' state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.Comment: Invited talk at the Fifth Stromlo Symposium: Disks, Winds & Jets - from Planets to Quasars. Accepted for publication in Astrophysics & Space Scienc

A Hedged Monte Carlo Approach to Real Option Pricing

In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.Comment: 25 pages, 14 figure

Extrapolating SMBH correlations down the mass scale: the case for IMBHs in globular clusters

Empirical evidence for both stellar mass black holes M_bh<10^2 M_sun) and supermassive black holes (SMBHs, M_bh>10^5 M_sun) is well established. Moreover, every galaxy with a bulge appears to host a SMBH, whose mass is correlated with the bulge mass, and even more strongly with the central stellar velocity dispersion sigma_c, the `M-sigma' relation. On the other hand, evidence for "intermediate-mass" black holes (IMBHs, with masses in the range 1^2 - 10^5 M_sun) is relatively sparse, with only a few mass measurements reported in globular clusters (GCs), dwarf galaxies and low-mass AGNs. We explore the question of whether globular clusters extend the M-sigma relationship for galaxies to lower black hole masses and find that available data for globular clusters are consistent with the extrapolation of this relationship. We use this extrapolated M-sigma relationship to predict the putative black hole masses of those globular clusters where existence of central IMBH was proposed. We discuss how globular clusters can be used as a constraint on theories making specific predictions for the low-mass end of the M-sigma relation.Comment: 14 pages, 3 figures, accepted for publication in Astrophysics and Space Science; fixed typos and a quote in Sec.

Radiation Hydrodynamical Instabilities in Cosmological and Galactic Ionization Fronts

Ionization fronts, the sharp radiation fronts behind which H/He ionizing photons from massive stars and galaxies propagate through space, were ubiquitous in the universe from its earliest times. The cosmic dark ages ended with the formation of the first primeval stars and galaxies a few hundred Myr after the Big Bang. Numerical simulations suggest that stars in this era were very massive, 25 - 500 solar masses, with H II regions of up to 30,000 light-years in diameter. We present three-dimensional radiation hydrodynamical calculations that reveal that the I-fronts of the first stars and galaxies were prone to violent instabilities, enhancing the escape of UV photons into the early intergalactic medium (IGM) and forming clumpy media in which supernovae later exploded. The enrichment of such clumps with metals by the first supernovae may have led to the prompt formation of a second generation of low-mass stars, profoundly transforming the nature of the first protogalaxies. Cosmological radiation hydrodynamics is unique because ionizing photons coupled strongly to both gas flows and primordial chemistry at early epochs, introducing a hierarchy of disparate characteristic timescales whose relative magnitudes can vary greatly throughout a given calculation. We describe the adaptive multistep integration scheme we have developed for the self-consistent transport of both cosmological and galactic ionization fronts.Comment: 6 pages, 4 figures, accepted for proceedings of HEDLA2010, Caltech, March 15 - 18, 201

The Relativistic Factor in the Orbital Dynamics of Point Masses

There is a growing population of relativistically relevant minor bodies in the Solar System and a growing population of massive extrasolar planets with orbits very close to the central star where relativistic effects should have some signature. Our purpose is to review how general relativity affects the orbital dynamics of the planetary systems and to define a suitable relativistic correction for Solar System orbital studies when only point masses are considered. Using relativistic formulae for the N body problem suited for a planetary system given in the literature we present a series of numerical orbital integrations designed to test the relevance of the effects due to the general theory of relativity in the case of our Solar System. Comparison between different algorithms for accounting for the relativistic corrections are performed. Relativistic effects generated by the Sun or by the central star are the most relevant ones and produce evident modifications in the secular dynamics of the inner Solar System. The Kozai mechanism, for example, is modified due to the relativistic effects on the argument of the perihelion. Relativistic effects generated by planets instead are of very low relevance but detectable in numerical simulations