Commuting difference operators arising from the elliptic C_2^{(1)}-face model

We study a pair of commuting difference operators arising from the elliptic C_2^{(1)}-face model. The operators, whose coefficients are expressed in terms of the Jacobi's elliptic theta function, act on the space of meromorphic functions on the weight space of the C_2 type simple Lie algebra. We show that the space of functions spanned by the level one characters of the affine Lie algebra sp(4,C) is invariant under the action of the difference operators.Comment: latex2e file, 19 pages, no figures; added reference

Discharge Patterns of Single Fibers in the Cat's Auditory Nerve

Discharge patterns of single fibers in cat auditory nerve in response to controlled acoustic stimul

First-principles accurate total-energy surfaces for polar structural distortions of BaTiO3, PbTiO3, and SrTiO3: consequences to structural transition temperatures

Specific forms of the exchange correlation energy functionals in first-principles density functional theory-based calculations, such as the local density approximation (LDA) and generalized-gradient approximations (GGA), give rise to structural lattice parameters with typical errors of -2% and 2%. Due to a strong coupling between structure and polarization, the order parameter of ferroelectric transitions, they result in large errors in estimation of temperature dependent ferroelectric structural transition properties. Here, we employ a recently developed GGA functional of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] and determine total-energy surfaces for zone-center distortions of BaTiO3, PbTiO3, and SrTiO3, and compare them with the ones obtained with calculations based on standard LDA and GGA. Confirming that the Wu and Cohen functional allows better estimation of structural properties at 0 K, we determine a new set of parameters defining the effective Hamiltonian for ferroelectric transition in BaTiO3. Using the new set of parameters, we perform molecular-dynamics (MD) simulations under effective pressures p=0.0 GPa, p=-2.0 GPa, and p=-0.005T GPa. The simulations under p=-0.005T GPa, which is for simulating thermal expansion, show a clear improvement in the cubic to tetragonal transition temperature and c/a parameter of its ferroelectric tetragonal phase, while the description of transitions at lower temperatures to orthorhombic and rhombohedral phases is marginally improved. Our findings augur well for use of Wu-Cohen functional in studies of ferroelectrics at nano-scale, particularly in the form of epitaxial films where the properties depend crucially on the lattice mismatch.Comment: 10 pages, 7 figures, 3 tables, resubmitted to PR

A Molecular Line Observation toward Massive Clumps Associated with Infrared Dark Clouds

We have surveyed the N2H+ J=1-0, HC3N J=5-4, CCS J_N=4_3-3_2, NH3 (J, K) = (1, 1), (2, 2), (3, 3), and CH3OH J=7-6 lines toward the 55 massive clumps associated with infrared dark clouds by using the Nobeyama Radio Observatory 45 m telescope and the Atacama Submillimeter Telescope Experiment 10 m telescope. The N2H+, HC3N, and NH3 lines are detected toward most of the objects. On the other hand, the CCS emission is detected toward none of the objects. The [CCS]/[N2H+] ratios are found to be mostly lower than unity even in the Spitzer 24 micron dark objects. This suggests that most of the massive clumps are chemically more evolved than the low-mass starless cores. The CH3OH emission is detected toward 18 out of 55 objects. All the CH3OH-detected objects are associated with the Spitzer 24 micron sources, suggesting that star formation has already started in all the CH3OH-detected objects. The velocity widths of the CH3OH J_K=7_0-6_0 A+ and 7_{-1}-6_{-1} E lines are broader than those of N2H+ J=1-0. The CH3OH J_K=7_0-6_0 A+ and 7_{-1}-6_{-1} E lines tend to have broader linewidth in the MSX dark objects than in the others, the former being younger or less luminous than the latter. The origin of the broad emission is discussed in terms of the interaction between an outflow and an ambient cloud.Comment: Accepted to Ap

Fast Molecular-Dynamics Simulation for Ferroelectric Thin-Film Capacitors Using a First-Principles Effective Hamiltonian

A newly developed fast molecular-dynamics method is applied to BaTiO3 ferroelectric thin-film capacitors with short-circuited electrodes or under applied voltage. The molecular-dynamics simulations based on a first-principles effective Hamiltonian clarify that dead layers (or passive layers) between ferroelectrics and electrodes markedly affect the properties of capacitors, and predict that the system is unable to hop between a uniformly polarized ferroelectric structure and a striped ferroelectric domain structure at low temperatures. Simulations of hysteresis loops of thin-film capacitors are also performed, and their dependence on film thickness, epitaxial constraints, and electrodes are discussed.Comment: 12 figures, 1 table. Submitted to PRB v2->v3: Major changes are underlined in the manuscript. Added new reference

Zone Diagrams in Euclidean Spaces and in Other Normed Spaces

Zone diagram is a variation on the classical concept of a Voronoi diagram. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain "dominance" map. Asano, Matousek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano et al. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) norm.Comment: Title page + 16 pages, 20 figure

24(S)-Hydroxycholesterol protects the ex vivo rat retina from injury by elevated hydrostatic pressure

In the central nervous system, 24(S)-hydroxycholesterol (24(S)-HC) is an oxysterol synthesized from cholesterol by cholesterol 24-hydroxylase (CYP46A1) encoded by the cyp46a1 gene. In the present study using a rat ex vivo glaucoma model, we found that retinal 24(S)-HC synthesis is facilitated by pressure elevation. Moreover, we found that 24(S)-HC is neuroprotective against pressure mediated retinal degeneration. Quantitative real-time RT-PCR, ELISA, and immunohistochemistry revealed that elevated pressure facilitated the expression of cyp46a1 and CYP46A1. Immunohistochemically, the enhanced expression of CYP46A1 was mainly observed in retinal ganglion cells (RGC). LC-MS/MS revealed that 24(S)-HC levels increased in a pressure-dependent manner. Axonal injury and apoptotic RGC death induced by 75 mmHg high pressure was ameliorated by exogenously administered 1 μM 24(S)-HC. In contrast, voriconazole, a CYP46A1 inhibitor, was severely toxic even at normobaric pressure. Under normobaric conditions, 30 μM 24(S)-HC was required to prevent the voriconazole-mediated retinal damage. Taken together, our findings indicate that 24(S)-HC is facilitated by elevated pressure and plays a neuroprotective role under glaucomatous conditions, while voriconazole, an antifungal drug, is retinotoxic. 24(S)-HC and related compounds may serve as potential therapeutic targets for protecting glaucomatous eyes from pressure-induced injuries