Peculiar symmetry structure of some known discrete nonautonomous equations

Abstract The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we consider the $q$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $q$-P$\left (E_7^{(1)}/A_{1}^{(1)}\right )$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive symmetry structure.

Download Full-text

Isospin and Symmetry Structure in 36 Ar

Communications in Theoretical Physics ◽

10.1088/0253-6102/48/6/023 ◽

2007 ◽

Vol 48 (6) ◽

pp. 1067-1071 ◽

Cited By ~ 5

Author(s):

Bai Hong-Bo ◽

Zhang Jin-Fu ◽

Cao Wan-Cang ◽

Lü Li-Jun ◽

Zhaorigt ◽

...

Keyword(s):

Symmetry Structure

Download Full-text

Reconstructed Structure of SiO2/Si(111) Interface

MRS Proceedings ◽

10.1557/proc-208-309 ◽

1990 ◽

Vol 208 ◽

Author(s):

Ichiro Hirosawa ◽

Jun'ichiro Nizuki ◽

Toru Tatsumi ◽

Koichi Akimoto ◽

Junji Matsui

Keyword(s):

Molecular Beam ◽

Structural Model ◽

Oxidation Process ◽

Grazing Incidence ◽

Interface Structure ◽

X Ray Diffraction ◽

Initial Oxidation ◽

X Ray ◽

Diffraction Geometry ◽

Symmetry Structure

ABSTRACTIn order to investigate the initial oxidation process Qf the Si (111) surface, we have studied the molecular beam deposited Si0 2/Si(111)-7×7 interface structure using grazing incidence X-ray diffraction geometry. We suggest a three-fold symmetry structural model composed of stacking fault layer, dimer layer and additional ordered atoms. The three-fold symmetry structure comes from the preference for oxidation in the faulted half of the 7×7 structure.

Download Full-text

Temperature Dependent Raman Scattering in CsTiOAsO4 Single Crystal

MRS Proceedings ◽

10.1557/proc-398-661 ◽

1995 ◽

Vol 398 ◽

Author(s):

A.R. Guo ◽

C.-S. Tu ◽

Ruiwu Tao ◽

R.S. Katiyar ◽

Ruyan Guo ◽

...

Keyword(s):

Soft Mode ◽

Low Frequency ◽

High Mobility ◽

Vibrational Modes ◽

Frequency Range ◽

Temperature Dependent ◽

Higher Symmetry ◽

Phonon Spectra ◽

Symmetry Structure ◽

Increasing Temperature

ABSTRACTThe longitudinal (LO) and transverse (TO) A1 vibrational modes have been measured between 30-1200 cm−1 as a function of temperature (30–1240 K) for CsTiOAsO4 (CTA). The frequencies for all corresponding Raman components shifted to lower frequencies on increasing the temperature, however, there is no typical soft-mode like behavior observed in the measured frequency range. The relative intensities of the low frequency bands increase dramatically with increasing temperature due to high mobility of Cs+ ion. A higher symmetry structure taking place above 940K has been confirmed by changes in the phonon spectra.

Download Full-text