Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page

Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge

Nonlinear integral equations for the thermodynamics of the sl(4)-symmetric Uimin-Sutherland model

We derive a finite set of nonlinear integral equations (NLIE) for the thermodynamics of the one-dimensional sl(4)-symmetric Uimin-Sutherland model. Our NLIE can be evaluated numerically for arbitrary finite temperature and chemical potentials. We recover the NLIE for sl(3) as a limiting case. In comparison to other recently derived NLIE, the evaluation at low temperature poses no problem in our formulation. The model shows a rich ground-state phase diagram. We obtain the critical fields from the T to zero limit of our NLIE. As an example for the application of the NLIE, we give numerical results for the SU(4) spin-orbital model. The magnetic susceptibility shows divergences at critical fields in the low-temperature limit and logarithmic singularities for zero magnetic field.Comment: 32 pages, 7 figures; references added, minor corrections, final versio

Locally continuously perfect groups of homeomorphisms

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.Comment: 14 page

From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added; typos corrected; to appear in J. Phys. A: Math. Ge

Deep Near-Infrared Observations and Identifications of Chandra Sources in the Orion Molecular Cloud 2 and 3

We conducted deep NIR imaging observations of the Orion molecular cloud 2 and 3 using QUIRC on the 88-inch telescope of the University of Hawaii. Our purposes are 1) to generate a comprehensive NIR source catalog of these star forming clouds, and 2) to identify the NIR counterpart of the Chandra X-ray sources that have no counterpart in the 2MASS catalog. Our J-, H-, and K-band observations are about 2 mag deeper than those of 2MASS, and well match the current Chandra observation. We detected 1448 NIR sources, for which we derived the position, the J-, H-, and K-band magnitude, and the 2MASS counterpart. Using this catalog, we identified the NIR counterpart for about 42% of the 2MASS-unIDed Chandra sources. The nature of these Chandra sources are discussed using their NIR colors and spatial distributions, and a dozen protostar and brown dwarf candidates are identified.Comment: 39 pages, 9 postscript figures, accepted for publication in A

A simplification of boundary element model with rotational symmetry in electromagnetic field analysis

A simplification method for the boundary element model with rotational symmetry is described. When the boundary element model has a rotational symmetry, the region to be treated for boundary integrations can be reduced to the fundamental boundary surface. This reduction is possible because the coefficient matrix of the final simultaneous equations for the model can be transformed to a block diagonal matrix by a transformation matrix using spatial eigenmodes. The simplification reduces the computation time and storage capacity because the coefficient matrix of the final simultaneous equations of the boundary element method is dense. Computation results for a four-wire method demonstrate the applicability of the proposed simplification method </p