Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2

Stellar structures in the outer regions of M33

We present Subaru/Suprime-Cam deep V and I imaging of seven fields in the outer regions of M33. Our aim is to search for stellar structures corresponding to extended HI clouds found in a recent 21-cm survey of the galaxy. Three fields probe a large HI complex to the southeastern (SE) side of the galaxy. An additional three fields cover the northwestern (NW) side of the galaxy along the HI warp. A final target field was chosen further north, at a projected distance of approximately 25 kpc, to study part of the large stellar plume recently discovered around M33. We analyse the stellar population at R > 10 kpc by means of V, I colour magnitude diagrams reaching the red clump. Evolved stellar populations are found in all fields out to 120' (~ 30 kpc), while a diffuse population of young stars (~ 200 Myr) is detected out to a galactocentric radius of 15 kpc. The mean metallicity in the southern fields remains approximately constant at [M/H] = -0.7 beyond the edge of the optical disc, from 40' out to 80'. Along the northern fields probing the outer \hi disc, we also find a metallicity of [M/H] = -0.7 between 35' and 70' from the centre, which decreases to [M/H] = -1.0 at larger angular radii out to 120'. In the northernmost field, outside the disc extent, the stellar population of the large stellar feature possibly related to a M33-M31 interaction is on average more metal-poor ([M/H] = -1.3) and older (> 6 Gyr). An exponential disc with a large scale-length (~ 7 kpc) fits well the average distribution of stars detected in both the SE and NW regions from a galactocentric distance of 11 kpc out to 30 kpc. The stellar distribution at large radii is disturbed and, although there is no clear correlation between the stellar substructures and the location of the HI clouds, this gives evidence for tidal interaction or accretion events.Comment: 13 pages, 13 figures. Accepted for publications in Astronomy and Astrophysics; minor revisions of the tex

Chemical compositions of six metal-poor stars in the ultra-faint dwarf spheroidal galaxy Bo\"otes I

Ultra-faint dwarf galaxies recently discovered around the Milky Way (MW) contain extremely metal-poor stars, and might represent the building blocks of low-metallicity components of the MW. Among them, the Bo\"otes I dwarf spheroidal galaxy is of particular interest because of its exclusively old stellar population. We determine chemical compositions of six red giant stars in Bo\"otes I, based on the high-resolution spectra obtained with the High Dispersion Spectrograph mounted on the Subaru Telescope. Abundances of 12 elements, including C, Na, alpha, Fe-peak, and neutron capture elements, were determined for the sample stars. The abundance results were compared to those in field MW halo stars previously obtained using an abundance analysis technique similar to the present study. We confirm the low metallicity of Boo-094 ([Fe/H]=-3.4). Except for this star, the abundance ratios ([X/Fe]) of elements lighter than zinc are generally homogeneous with small scatter around the mean values in the metallicities spanned by the other five stars (-2.7-2.7 show no significant enhancement of carbon. The [Mg/Fe] and [Ca/Fe] ratios are almost constant with a modest decreasing trend with increasing [Fe/H] and are slightly lower than the field halo stars. The [Sr/Fe] and [Sr/Ba] ratios also tend to be lower in the Bo\"otes I stars than in the halo stars. Our results of small scatter in the [X/Fe] ratios for elements lighter than zinc suggest that these abundances were homogeneous among the ejecta of prior generation(s) of stars in this galaxy.Comment: 16 pages, 12 figures. Accepted to A&A, language correcte

Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain

We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound F5PNN. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective S=1/2 XXZ chain and a possibility of the field-induced incommensurate long range order.Comment: 4 pages, 5 figures, replaced with revised version accepted to PR

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl