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

Notes on highest weight modules of the elliptic algebra Aq,p(sl^2){\cal A}_{q,p}\left(\widehat{sl}_2\right)

We discuss a construction of highest weight modules for the recently defined elliptic algebra ${\cal A}_{q,p}(\widehat{sl}_2)$, and make several conjectures concerning them. The modules are generated by the action of the components of the operator $L$ on the highest weight vectors. We introduce the vertex operators $\Phi$ and $\Psi^*$ through their commutation relations with the $L$-operator. We present ordering rules for the $L$- and $\Phi$-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of $\widehat{sl}_2$-modules.Comment: Nonstandard macro package eliminate

Description of Pseudo-Newtonian Potential for the Relativistic Accretion Disk around Kerr Black Holes

We present a pseudo-Newtonian potential for accretion disk modeling around the rotating black holes. This potential can describe the general relativistic effects on accretion disk. As the inclusion of rotation in a proper way is very important at an inner edge of disk the potential is derived from the Kerr metric. This potential can reproduce all the essential properties of general relativity within 10% error even for rapidly rotating black holes.Comment: 5 Latex pages including 1 figure. Version to appear in Astrophysical Journal, V-581, N-1, December 10, 200

Fundamental Vibrational Transitions of HCl Detected in CRL 2136

We would like to understand the chemistry of dense clouds and their hot cores more quantitatively by obtaining more complete knowledge of the chemical species present in them. We have obtained high-resolution infrared absorption spectroscopy at 3-4 um toward the bright infrared source CRL 2136. The fundamental vibration-rotation band of HCl has been detected within a dense cloud for the first time. The HCl is probably located in the warm compact circumstellar envelope or disk of CRL 2136. The fractional abundance of HCl is (4.9-8.7)e-8, indicating that approximately 20 % of the elemental chlorine is in gaseous HCl. The kinetic temperature of the absorbing gas is 250 K, half the value determined from infrared spectroscopy of 13CO and water. The percentage of chlorine in HCl is approximately that expected for gas at this temperature. The reason for the difference in temperatures between the various molecular species is unknown.Comment: 6 pages, 3 figures, A&A in pres

RF amplification property of the MgO-based magnetic tunnel junction using field-induced ferromagnetic resonance

The radio-frequency (RF) voltage amplification property of a tunnel magnetoresistance device driven by an RF external-magnetic-field-induced ferromagnetic resonance was studied. The proposed device consists of a magnetic tunnel junction (MTJ) and an electrically isolated coplanar waveguide. The input RF voltage applied to the waveguide can excite the resonant dynamics in the free layer magnetization, leading to the generation of an output RF voltage under a DC bias current. The dependences of the RF voltage gain on the static external magnetic field strength and angle were systematically investigated. The design principles for the enhancement of the gain factor are also discussed.Comment: 12 pages, 3 figure

Terminal and bridging fluorine ligands in TiF₄ as studied by ¹⁹F NMR in solids

To examine bonding nature of fluorine ligands in a metal coordinated system, ¹⁹F high-resolution solid-state NMR has been applied to TiF₄, which bears both bridging and terminal fluorines. Observed 12 isotropic signals are assigned to 12 crystallographically different fluorines (6 terminal and 6 bridging fluorines) in TiF₄ by referring to the calculated isotropic shifts using density functional theory (DFT). The isotropic chemical shift (δiso) for terminal F (FT) appears at high frequency (420–480 ppm from δ(CCl3F) = 0 ppm) with large shielding anisotropy Δσ ∼ 850 ppm. Whereas the δiso and Δσ values for bridging F (FB) are moderate; δiso ∼ 0–25 ppm and Δσ ∼ 250 ppm. The origin of the observed high-frequency shift for FT is ascribed to the second-order paramagnetic shift with increased covalency, shorter Ti–F bonds, and smaller energy difference between the occupied and vacant orbitals. Examination of the orientation of the shielding tensor relative to the molecular structure shows that the most deshielded component of the shielding tensor is oriented along the Ti–F bond. The characteristic orientation is consistent with a Ti–F σ bond formed by dYZ of Ti and pz of F. Further, we show that the selectively observed spinning sideband patterns and the theoretical patterns with the calculated Δσ and η (shielding asymmetry) values are not consistent with each other for FB, indicating deficiency of the present DFT calculation in evaluating Δσ

Heat operator with pure soliton potential: properties of Jost and dual Jost solutions

Properties of Jost and dual Jost solutions of the heat equation, $\Phi(x,k)$ and $\Psi(x,k)$, in the case of a pure solitonic potential are studied in detail. We describe their analytical properties on the spectral parameter $k$ and their asymptotic behavior on the $x$-plane and we show that the values of $e^{-qx}\Phi(x,k)$ and the residua of $e^{qx}\Psi(x,k)$ at special discrete values of $k$ are bounded functions of $x$ in a polygonal region of the $q$-plane. Correspondingly, we deduce that the extended version $L(q)$ of the heat operator with a pure solitonic potential has left and right annihilators for $q$ belonging to these polygonal regions.Comment: 26 pages, 3 figure

Enhanced tunability of thermodynamic stability of complex hydrides by the incorporation of H- anions

First-principles calculations were employed to investigate hypothetical complex hydrides (M,M')4FeH8 (M = Na, Li; M'=Mg, Zn, Y, Al). Besides complex anion [FeH6]4-, these materials contain two H- anions, which raise the total anionic charge state from tetravalent to hexavalent, and thereby significantly increasing the number of combinations of countercations. We have determined that similar to complex hydrides (M,M')2FeH6 containing only [FeH6]4-, the thermodynamic stability is tuned by the average cation electronegativity. Thus, the chemical flexibility provided by incorporating H- enhances the tunability of thermodynamic stability, which will be beneficial in obtaining optimal stability for hydrogen storage materials