Unitary representations of the quantum group SU q (1, 1): II — Matrix elements of unitary representations and the basic hypergoemetric functions

Some series of unitary representations of the quantum group SU _q (1, 1) are introduced. Their matrix elements are expressed in terms of the basic hypergeometric functions. Operator realization of the coordinate elements of SU _q (1, 1) and aq-analogue of some classical identities are discussed.     

A Short Note on the Lindelöf Hypothesis

We obtain a quantitative estimate for the measure of the set of large values of the zeta-function on the critical line which is related to the Lindelöf hypothesis and give its application to extreme values (-results). We also investigate the problem of small values.     

Superdiffusivity in first-passage percolation

Summary. In standard first-passage percolation on (with ), the time-minimizing paths from a point to a plane at distance are expected to have transverse fluctuations of order . It has been conjectured that with the inequality strict (superdiffusivity) at least for low and with . We prove (versions of) for all and . Received: 30 August 1995 / In revised form: 28 March 1996     

Synthesis of New Thiazoles from α-Halohetaryl Ketones

Reactions of -bromoacetylphenoxathiin, -bromoacetylphenoxathiin 10,10-dioxide, or -bromoacetylthianthrene with certain p-(arylsulfonyl)thiobenzamides lead to the formation of the corresponding 2,4-disubstituted thiazoles. The new compounds were characterized through elemental analysis and spectral data (IR, ¹H NMR, and ¹³C NMR).     

Synthesis of (22S,23S,24S)-3β,14α,22,23-Tetrahydroxy-5α-stigmast-7-en-6-one, a New Ecdysteroid Analog

A tetrahydroxyketone that is a structural analog of ecdysteroids is synthesized from stigmasterol     

The spectral property of dual matrix strings as a consequence of the existence of spectral matrix functions for canonical systems

The term dual string for scalar strings was introduced in [KK1], where some connections between the spectra of a string and its dual were studied. In [KK2] it was shown that if () is a spectral function of a scalar stringS ₁ with nonnegative spectrum (in the sense of [KK2]), then the function

24 h continuous observation of sodium layer over Wuhan by lidar

Based on the dual-wavelength lidar we have developed, the 24 h continuous ob- servation has been realized in its sodium channel by using Faraday atomic filter technology and other relevant technologies. This will facilitate the continuous ob- servation of the sodium layer and the relevant upper atmosphere over Wuhan. A result of about 50 h observation indicates that the daytime column density of so- dium layer over Wuhan is slightly increased compared to that during the nighttime, and the characteristics of the sporadic sodium layer occurring during the daytime are compared with that during the nighttime.     

Killing initial data on totally umbilical & compact hypersurfaces

In this note, we give a geometric characterization of the compact and totally umbilical hypersurfaces that carry non-trivial locally static Killing Initial Data (KID). More precisely, such compact hypersurfaces (Mⁿ,g,cg)$(M^n,g,cg)$ endowed with a Riemannian metric g$g$ and a second fundamental form cg$cg$ (where c∈C^∞(M)$c\in C^{\infty }\left(M\right)$ a priori) have constant mean curvature and are isometric to one of the following manifolds:

(i)

Sⁿ${\mathbb{S}}^n$ the standard sphere,     

On linear combinations of two idempotent matrices over an arbitrary field

Given an arbitrary field K and non-zero scalars α and β, we give necessary and sufficient conditions for a matrix A∈M_n(K) to be a linear combination of two idempotents with coefficients α and β. This extends results previously obtained by Hartwig and Putcha in two ways: the field K considered here is arbitrary (possibly of characteristic 2), and the case α≠±β is taken into account.