The Additional Symmetries for the BTL and CTL Hierarchies

The Toda lattice (TL) hierarchy was first introduced by K.Ueno and K.Takasaki in \cite{uenotaksasai} to generalize the Toda lattice equations\cite{toda}. Along the work of E. Date, M. Jimbo, M. Kashiwara and T. Miwa \cite{DJKM} on the KP hierarchy, K.Ueno and K.Takasaki in \cite{uenotaksasai} develop the theory for the TL hierarchy: its algebraic structure, the linearization, the bilinear identity, $\tau$ function and so on. Also the analogues of the B and C types for the TL hierarchy, i.e. the BTL and CTL hierarchies, are considered in \cite{uenotaksasai}, which are corresponding to infinite dimensional Lie algebras $\textmd{o}(\infty)$ and $\textmd{sp}(\infty)$ respectively. In this paper, we will focus on the study of the additional symmetries for the BTL and CTL hierarchies.Comment: 13 page

Cosmological implications of dwarf spheroidal chemical evolution

The chemical properties of dwarf spheroidals in the local group are shown to be inconsistent with star formation being truncated after the reionization epoch (z~8). Enhanced levels of [Ba/Y] in stars in dwarf spheroidals like Sculptor indicate strong s-process production from low-mass stars whose lifetimes are comparable with the duration of the pre-reionization epoch. The chemical evolution of Sculptor is followed using a model with SNeII and SNeIa feedback and mass- and metallicity-dependent nucleosynthetic yields for elements from H to Pb. We are unable to reproduce the Ba/Y ratio unless stars formed over an interval long enough for the low-mass stars to pollute the interstellar medium with s-elements. This robust result challenges the suggestion that most of the local group dwarf spheroidals are fossils of reionization and supports the case for large initial dark matter halos.Comment: 7 pages, 4 figures. Accepted for publication in ApJ. Minor changes following referee repor

Open questions on prominences from coordinated observations by IRIS, Hinode, SDO/AIA, THEMIS, and the Meudon/MSDP

Context. A large prominence was observed on September 24, 2013, for three hours (12:12 UT -15:12 UT) with the newly launched (June 2013) Interface Region Imaging Spectrograph (IRIS), THEMIS (Tenerife), the Hinode Solar Optical Telescope (SOT), the Solar Dynamic Observatory Atmospheric Imaging Assembly (SDO/AIA), and the Multichannel Subtractive Double Pass spectrograph (MSDP) in the Meudon Solar Tower. Aims. The aim of this work is to study the dynamics of the prominence fine structures in multiple wavelengths to understand their formation. Methods. The spectrographs IRIS and MSDP provided line profiles with a high cadence in Mg II and in Halpha lines. Results. The magnetic field is found to be globally horizontal with a relatively weak field strength (8-15 Gauss). The Ca II movie reveals turbulent-like motion that is not organized in specific parts of the prominence. On the other hand, the Mg II line profiles show multiple peaks well separated in wavelength. Each peak corresponds to a Gaussian profile, and not to a reversed profile as was expected by the present non-LTE radiative transfer modeling. Conclusions. Turbulent fields on top of the macroscopic horizontal component of the magnetic field supporting the prominence give rise to the complex dynamics of the plasma. The plasma with the high velocities (70 km/s to 100 km/s if we take into account the transverse velocities) may correspond to condensation of plasma along more or less horizontal threads of the arch-shape structure visible in 304 A. The steady flows (5 km/s) would correspond to a more quiescent plasma (cool and prominence-corona transition region) of the prominence packed into dips in horizontal magnetic field lines. The very weak secondary peaks in the Mg II profiles may reflect the turbulent nature of parts of the prominence.Comment: 15 pages, 14 figure

A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension

For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N=2 supersymmetric extension of the Harry Dym hierarchy is constructed, and is further shown to be linked to one of the N=2 supersymmetric KdV equations through superconformal transformation. The bosonic limit of this new N=2 supersymmetric Harry Dym equation is related to a coupled system of KdV-MKdV equations.Comment: 9 page

A Photometric Study of the Young Stellar Population Throughout the lambda Orionis Star-Forming Region

We present VRI photometry of 320,917 stars with 11 < R < 18 throughout the lambda Orionis star-forming region. We statistically remove the field stars and identify a representative PMS population throughout the interior of the molecular ring. The spatial distribution of this population shows a concentration of PMS stars around lambda Ori and in front of the B35 dark cloud. Few PMS stars are found outside these pockets of high stellar density, suggesting that star formation was concentrated in an elongated cloud extending from B35 through lambda Ori to the B30 cloud. We find a lower limit for the global stellar mass of about 500 Mo. We find that the global ratio of low- to high-mass stars is similar to that predicted by the field initial mass function, but this ratio varies strongly as a function of position in the star-forming region. Locally, the star-formation process does not produce a universal initial mass function. We construct a history of the star-forming complex. This history incorporates a recent supernova to explain the distribution of stars and gas today.Comment: 42 pages, 11 figures; to appear in the Astronomical Journa

From Cavity Electromechanics to Cavity Optomechanics

We present an overview of experimental work to embed high-Q mesoscopic mechanical oscillators in microwave and optical cavities. Based upon recent progress, the prospect for a broad field of "cavity quantum mechanics" is very real. These systems introduce mesoscopic mechanical oscillators as a new quantum resource and also inherently couple their motion to photons throughout the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio

Ehrenfest time in the weak dynamical localization

The quantum kicked rotor (QKR) is known to exhibit dynamical localization in the space of its angular momentum. The present paper is devoted to the systematic first--principal (without a regularizer) diagrammatic calculations of the weak--localization corrections for QKR. Our particular emphasis is on the Ehrenfest time regime -- the phenomena characteristic for the classical--to--quantum crossover of classically chaotic systems.Comment: 27 pages, 9 figure