Identification of Very Red Counterparts of SiO Maser and OH/IR Objects in the GLIMPSE Survey

Using the 3.6/4.5/5.8/8.0 micron images with 1.2 arcsec pixel resolution from the Spitzer/GLIMPSE survey, we investigated 23 masing and 18 very red objects that were not identified in the 2MASS survey. Counterparts for all selected objects were found in the GLIMPSE images. Color indices in these IR bands suggest the presence of a high-extinction layer of more than a few tenths of a solar mass in front of the central star. Furthermore, radio observations in the SiO and H2O maser lines found characteristic maser-line spectra of the embedded objects, e.g., the SiO J=1-0 line intensity in the v=2 state stronger than that of the v=1 state, or very widespread H2O maser emission spectra. This indicates that these objects are actually enshrouded by very thick circumstellar matter, some of which cannot be ascribed to the AGB wind of the central star. Individually interesting objects are discussed, including two newly found water fountains and an SiO source with nebulosity.Comment: High resolution figures available at ftp://ftp.nro.nao.ac.jp/nroreport/no653.pdf.gz. ApJ No. 655 no.1 issue in pres

Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs

We present formulas for the Clebsch-Gordan coefficients and the Racah coefficients for the root of unity representations ($N$-dimensional representations with $q^{2N}=1$) of $U_q(sl(2))$. We discuss colored vertex models and colored IRF (Interaction Round a Face) models from the color representations of $U_q(sl(2))$. We construct invariants of trivalent colored oriented framed graphs from color representations of $U_q(sl(2))$.Comment: 39 pages, January 199

XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

A Measurement of Proper Motions of SiO Maser Sources in the Galactic Center with the VLBA

We report on the high-precision astrometric observations of maser sources around the Galactic Center in the SiO J=1--0 v=1 and 2 lines with the VLBA during 2001 -- 2004. With phase-referencing interferometry referred to the radio continuum source Sgr A*, accurate positions of masers were obtained for three detected objects: IRS 10 EE (7 epochs), IRS 15NE (2 epochs), and SiO 6 (only 1 epoch). Because circumstellar masers of these objects were resolved into several components, proper motions for the maser sources were derived with several different methods. Combining our VLBA results with those of the previous VLA observations, we obtained the IRS 10EE proper motion of 76+-3 km s^{-1} (at 8 kpc) to the south relative to Sgr A*. Almost null proper motion of this star in the east--west direction results in a net transverse motion of the infrared reference frame of about 30+-9 km s^{-1} to the west relative to Sgr A*. The proper-motion data also suggests that IRS 10EE is an astrometric binary with an unseen massive companion.Comment: High-res. figures are available at ftp://ftp.nro.nao.ac.jp/nroreport/no656.pdf.gz . PASJ 60, No. 1 (2008) in pres

Magnetic susceptibility and low-temperature specific-heat of integrable 1-D Hubbard model under open-boundary conditions

The magnetic susceptibility and the low-temperature specific heat of the 1-dimensional Hubbard model under the integrable open-boundary conditions are discussed through the Bethe ansatz with the string hypothesis. The contributions of the boundary fields to both the susceptibility and the specific heat are obtained, and their exact expressions are analytically derived.Comment: 14 pages, Latex, No figures, to appear in J. Phys. A: Gen. & Mat

On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

The knotting probability is defined by the probability with which an $N$-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of $N$. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be $2.5 \times 10^5$ on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

A gapless charge mode induced by the boundary states in the half-filled Hubbard open-chain

We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with L sites, where only one of the boundary sites has a different value of chemical potential. We consider the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. By an analytic method we show that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. It follows that there is a ``surface phase transition'' at some critical value p_c; when p<p_c all the charge excitations have the gap for the half-filled band, while there exists a massless charge mode when p>p_c.Comment: Revtex, 25 pages, 3 eps figures; Full revision with Appendixes adde

Correlation between Infrared Colors and Intensity Ratios of SiO Maser Lines

We present the results of SiO millimeter-line observations of a sample of known SiO maser sources covering a wide dust-temperature range. A cold part of the sample was selected from the SiO maser sources found in our recent SiO maser survey of cold dusty objects. The aim of the present research is to investigate the causes of the correlation between infrared colors and SiO maser intensity ratios among different transition lines. In particular, the correlation between infrared colors and SiO maser intensity ratio among the J=1-0 v=1, 2, and 3 lines are mainly concerned in this paper. We observed in total 75 SiO maser sources with the Nobeyama 45m telescope quasi-simultaneously in the SiO J=1-0 v=0, 1, 2, 3, 4 and J=2-1 v=1, 2 lines. We also observed the sample in the 29SiO J=1-0 v=0 and J=2-1 v=0, and 30SiO J=1-0 v=0 lines, and the H2O 6(1,6)-5(2,3) line. As reported in previous papers, we confirmed that the intensity ratios of the SiO J=1-0 v=2 to v=1 lines clearly correlate with infrared colors. In addition, we found possible correlation between infrared colors and the intensity ratios of the SiO J=1-0 v=3 to v=1&2 lines. Two overlap lines of H2O (i.e., 11(6,6) nu_2=1 -> 12(7,5) nu_2=0 and 5(0,5) nu_2=2 -> 6(3,4) nu_2=1) might explain these correlation if these overlap lines become stronger with increase of infrared colors, although the phenomena also might be explained by more fundamental ways if we take into account the variation of opacity from object to object.Comment: 49 pages, 7 figures, 3 tables, accepted for publication in ApJ. Full resolution version available at http://www.asiaa.sinica.edu.tw/~junichi/paper

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure