A Multi-Frequency Study of 3C309.1

Here we summarize our results from a detailed multi-frequency study of the QSO 3C309.1 based on the Very Long Baseline Array (VLBA) observations made in mid 1998. From our images, we find a curved jet extending up to 100 milliarcseconds (mas) to the east at low frequencies with two main components, A and B. A preliminary astrometric analysis (Ros and Lobanov 2001) provides a determination of the core position at different frequencies by phase-referencing to a nearby radio source, QSO S5 1448+76. The changes of the core position with frequency suggest high opacity close to the core caused by synchrotron self-absorption. Due to the large astrometric uncertainties we cannot draw any conclusions about the values of the opacity gradients at high frequencies. We believe that a detailed analysis of the frequency depedence of the core position will reveal the profile of the matter distribution in the broad line region, as was initially suggested by Lobanov (1998).Comment: To be published in the volume "Highlights of Spanish Astrophysics (III), Proceedings of the 5th Scientific Meeting of the Spanish Astronomical Society" of the Astrophysics and Space Science Library (Kluwer), J. Gallego, J. Zamorano, N. Cardiel (eds.), 1 page, 1 figure, no abstract, needs kapproc.st

Integrals of motion in the Many-Body localized phase

We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum $\{0,1\}$, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization-delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.Comment: 65 pages, 12 figures. Corrected typos, added reference

Multiband polarimetric and total intensity imaging of 3C345

We monitored the superluminal QSO 3C 345 at three epochs during a one-year period in 1995--1996, observing with the VLBA at 22, 15, 8.4, and 5 GHz. We imaged the radio source both in total and in polarized intensity. In the images at 5 and 8.4 GHz, the jet emission is traced up to 20 milliarcseconds (mas) from the jet core. In the 15 and 22 GHz images, we identify several enhanced emission regions moving at apparent speeds of 5c. Images of the linear polarized emission show predominantly an alignment of the electric vector with the extremely curved jet along the inner part of the high frequency jet. At 5 GHz, the jet shows remarkably strong fractional polarization (m~15%) with the electric vector perpendicular to the jet orientation.Comment: LaTeX file, 6 pages, 2 figures, needs "elsart" style package To be published in New Astronomy Reviews, special issue: Proceedings of the 4th EVN/JIVE VLBI Symposium, Eds. Garrett, M.A., Campbell, R.M., & Gurvits, L.

Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

R&D INVESTMENT AND FINANCIAL CONTRACTING IN SPANISH MANUFACTURIG FIRMS

This paper presents a model in which a firm with a degree of R&D specialization raises external funds to develop a two-period project that involves some non-verifiable returns (R&D-type of project). Taking into account a possible opportunistic behavior by the manager, we find out that the optimal firm's debt equity ratio is negatively related to the firm's degree of R&D specialization, its internal funds, and the output generated by the R&D project. Moreover, the expected R&D output of the firm is related negatively to the firm’s leverage and positively to the firm’s degree of R&D specialization as well as the amount of internal funds. The novelty of this work is to derive these results from strategic default consideration of the managers of firms specialized in R&D investments, as opposed to the standard collateral arguments concerning debt financing. This has a consequence of a lower growth of the firm’s debt-equity ratio once we compare firms specialized on R&D investments with others non specialized in these activities. We confirm our main theoretical findings making use of a Spanish data set of manufacturing firms during the period 1990-94.

On the length and area spectrum of analytic convex domains

Area-preserving twist maps have at least two different (p, q)-periodic orbits and every (p, q)-periodic orbit has its (p, q)-periodic action for suitable couples (p, q). We establish an exponentially small upper bound for the differences of (p, q)-periodic actions when the map is analytic on a (m, n)-resonant rotational invariant curve (resonant RIC) and p/q is 'sufficiently close' to m/n. The exponent in this upper bound is closely related to the analyticity strip width of a suitable angular variable. The result is obtained in two steps. First, we prove a Neishtadt-like theorem, in which the n-th power of the twist map is written as an integrable twist map plus an exponentially small remainder on the distance to the RIC. Second, we apply the MacKay-Meiss-Percival action principle. We apply our exponentially small upper bound to several billiard problems. The resonant RIC is a boundary of the phase space in almost all of them. For instance, we show that the lengths (respectively, areas) of all the (1, q)-periodic billiard (respectively, dual billiard) trajectories inside (respectively, outside) analytic strictly convex domains are exponentially close in the period q. This improves some classical results of Marvizi, Melrose, Colin de Verdiere, Tabachnikov, and others about the smooth case.Peer ReviewedPostprint (author's final draft