On parabolic Whittaker functions

We derive a Mellin-Barnes integral representation for solution to generalized (parabolic) quantum Toda lattice introduced in \cite{GLO}, which presumably describes the $(S^1\times U_N)$-equivariant Gromov-Witten invariants of Grassmann variety.Comment: 14 page

Critical densities for the Skyrme type effective interactions

We use the stability conditions of the Landau parameters for the symmetric nuclear matter and pure neutron matter to calculate the critical densities for the Skyrme type effective nucleon-nucleon interactions. We find that the critical density can be maximized by adjusting appropriately the values of the enhancement factor $\kappa$ associated with isovector giant dipole resonance, the quantity $L$ which is directly related to the slope of the symmetry energy and the Landau parameter $G_0^\prime$. However, restricting $\kappa$, $L$ and $G_0^\prime$ to vary within acceptable limits reduces the maximum value for the critical density $\tilde\rho_{cr}$ by $\sim 25$. We also show that among the various quantities characterizing the symmetric nuclear matter, $\tilde\rho_{cr}$ depends strongly on the isoscalar effective mass $m^*/m$ and surface energy coefficient $E_s$. For realistic values of $m^*/m$ and $E_s$ we get $\tilde\rho_{cr} = 2\rho_0$ to $3\rho_0$ ($\rho_0 = 0.16$fm$^{-3}$).Comment: 10 pages, 3 figures. Physicsl Review C (in press

Correlation Assisted Phonon Softenings and the Mott-Peierls Transition in VO2_{2}

To explore the driving mechanisms of the metal-insulator transition (MIT) and the structural transition in VO2, we have investigated phonon dispersions of rutile VO2 (R-VO2) in the DFT and the DFT+U (U : Coulomb correlation) band calculations. We have found that the phonon softening instabilities occur in both cases, but the softened phonon mode only in the DFT+U describes properly both the MIT and the structural transition from R-VO2 to monoclinic VO2 (M1-VO2). This feature demonstrates that the Coulomb correlation effect plays an essential role of assisting the Peierls transition in R-VO2. We have also found from the phonon dispersion of M1-VO2 that M1 structure becomes unstable under high pressure. We have predicted a new phase of VO2 at high pressure that has a monoclinic CaCl2-type structure with metallic nature

Multivariate p-dic L-function

We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.Comment: 9 page

Type Ia supernova diversity: Standardizing the candles

Future use of type Ia supernovae for cosmology aims not only to determine the equation of state of dark energy, but also to constrain possible variations in its value. To achieve this goal, supernovae need to become better calibrated standard candles - not only to improve the precision of the measurement, but more importantly to gain better control over systematic uncertainties in order to ensure the accuracy of the result. Here we report on a project to quantify the diversity in type Ia supernovae, and to look for trends and/or sub-types that can be used to improve their calibration as standard candles. We implement a version of principal component analysis on type Ia supernova spectra. Although the quantity of data is not sufficient to draw any firm conclusions we show that this method holds promise for, at the very least, effectively separating peculiar supernovae. Whether it can be further used to improve the calibration of normal type Ia's remains a project for future study.Comment: Conference Proceedings. Cefalu 2006, The multicoloured landscape of compact objects and their explosive origins. Six pages, three figure