Trigonometric Parallaxes of Massive Star Forming Regions: III. G59.7+0.1 and W 51 IRS2

We report trigonometric parallaxes for G59.7+0.1 and W 51 IRS2, corresponding to distances of 2.16^{+0.10}_{-0.09} kpc and 5.1^{+2.9}_{-1.4} kpc, respectively. The distance to G59.7+0.1 is smaller than its near kinematic distance and places it between the Carina-Sagittarius and Perseus spiral arms, probably in the Local (Orion) spur. The distance to W 51 IRS2, while subject to significant uncertainty, is close to its kinematic distance and places it near the tangent point of the Carina-Sagittarius arm. It also agrees well with a recent estimate based on O-type star spectro/photometry. Combining the distances and proper motions with observed radial velocities gives the full space motions of the star forming regions. We find modest deviations of 5 to 10 km/s from circular Galactic orbits for these sources, both counter to Galactic rotation and toward the Galactic center.Comment: 16 pages, 6 figures; to appear in the Astrophysical Journa

Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in random environment

The objective of the present paper is to establish exponential large deviation inequalities, and to use them to show exponential concentration inequalities for the free energy of a polymer in general random environment, its rate of convergence, and an expression of its limit value in terms of those of some multiplicative cascades.Comment: 25 page

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

Language Models as a Service: Overview of a New Paradigm and its Challenges

Some of the most powerful language models currently are proprietary systems, accessible only via (typically restrictive) web or software programming interfaces. This is the Language-Models-as-a-Service (LMaaS) paradigm. In contrast with scenarios where full model access is available, as in the case of open-source models, such closed-off language models present specific challenges for evaluating, benchmarking, and testing them. This paper has two goals: on the one hand, we delineate how the aforementioned challenges act as impediments to the accessibility, replicability, reliability, and trustworthiness of LMaaS. We systematically examine the issues that arise from a lack of information about language models for each of these four aspects. We conduct a detailed analysis of existing solutions and put forth a number of considered recommendations, and highlight the directions for future advancements. On the other hand, it serves as a comprehensive resource for existing knowledge on current, major LMaaS, offering a synthesized overview of the licences and capabilities their interfaces offer

Modules of Abelian integrals and Picard-Fuchs systems

We give a simple proof of an isomorphism between the two $\mathbb{C}[t]$-modules: the module of relative cohomologies $\Lambda^2/dH\land \Lambda^1$ and the module of Abelian integrals corresponding to a regular at infinity polynomial $H$ in two variables. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.Comment: A separate section discusses Fuchsian properties of the Picard-Fuchs system, Morse condition exterminated. Few errors were correcte

Modelling Circumbinary Gas Flows in Close T Tauri Binaries

Young close binaries open central gaps in the surrounding circumbinary accretion disc, but the stellar components may still gain mass from gas crossing through the gap. It is not well understood how this process operates and how the stellar components are affected by such inflows. Our main goal is to investigate how gas accretion takes place and evolves in close T Tauri binary systems. In particular, we model the accretion flows around two close T Tauri binaries, V4046 Sgr and DQ Tau, both showing periodic changes in emission lines, although their orbital characteristics are very different. In order to derive the density and velocity maps of the circumbinary material, we employ two-dimensional hydrodynamic simulations with a locally isothermal equation of state. The flow patterns become quasi-stable after a few orbits in the frame co-rotating with the system. Gas flows across the circumbinary gap through the co-rotating Lagrangian points, and local circumstellar discs develop around both components. Spiral density patterns develop in the circumbinary disc that transport angular momentum efficiently. Mass is preferentially channelled towards the primary and its circumstellar disc is more massive than the disc around the secondary. We also compare the derived density distribution to observed line profile variability. The line profile variability tracing the gas flows in the central cavity shows clear similarities with the corresponding observed line profile variability in V4046 Sgr, but only when the local circumstellar disc emission was excluded. Closer to the stars normal magnetospheric accretion may dominate while further out the dynamic accretion process outlined here dominates. Periodic changes in the accretion rates onto the stars can explain the outbursts of line emission observed in eccentric systems such as DQ Tau.Comment: Accepted for publication in MNRA

On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem

We prove that the number of limit cycles generated by a small non-conservative perturbation of a Hamiltonian polynomial vector field on the plane, is bounded by a double exponential of the degree of the fields. This solves the long-standing tangential Hilbert 16th problem. The proof uses only the fact that Abelian integrals of a given degree are horizontal sections of a regular flat meromorphic connection (Gauss-Manin connection) with a quasiunipotent monodromy group.Comment: Final revisio

Hadronic Regge Trajectories: Problems and Approaches

We scrutinized hadronic Regge trajectories in a framework of two different models --- string and potential. Our results are compared with broad spectrum of existing theoretical quark models and all experimental data from PDG98. It was recognized that Regge trajectories for mesons and baryons are not straight and parallel lines in general in the current resonance region both experimentally and theoretically, but very often have appreciable curvature, which is flavor-dependent. For a set of baryon Regge trajectories this fact is well described in the considered potential model. The standard string models predict linear trajectories at high angular momenta J with some form of nonlinearity at low J.Comment: 15 pages, 9 figures, LaTe

Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y