Duality and multiplication operators

We describe a space of functions contained inxxLx (D)C(D G) but not necessarily inU. We give a representation of these functions as bounded multiplication operators on the Bergman spacexxLx _a ² and identify the subspace consisting of functions which induce compact multiplication operators. We also describe a newC ^*-subalgebra ofxxLx (D) which we conjecture to be a proper super-set ofU.Most of this research was done while the second author was visiting Cleveland State University. He would like to thank the Mathematics Department for its hospitality. He would also like to thank the NNSFC for partial support.     

Levels in182W populated in the decay of182Ta

Theγ-rays emitted in theβ-decay of¹⁸²Ta have been reinvestigated with improved statistics in attempting to clarify the reported new levels at 1460.41, 1592.98, 1620.36, 1712.29 and 1762.91 keV in¹⁸²W observed in theβ-decay of¹⁸²Ta. The present study demonstrated that the fifteen newγ-rays, which were used to support the existence of the five new levels, are not relevant to theγ-decay of¹⁸²Ta. Therefore the five new levels are not populated in this decay. Additionally, theγ-ray with an energy of 1035.6 keV (0 ₂ ⁺ →2 ₁ ⁺ ) deexciting theβ-band head in¹⁸²W is observed for the first time in the present decay study and the previous tentative placement of the 351.0 keVγ-ray in the level scheme is confirmed by the present coincidence measurements.     

Large third-order nonlinear optical properties of C70 fullerene in the infrared regime

The nonlinear third-order optical susceptibility of C₇₀ in a toluene solution is measured for the first time by the method of degenerate four-wave mixing using 10 ns laser pulses at 1.06 m. The third-order susceptibility X _in ⁽³⁾ is 5.6×10^–12 esu for a C₇₀ toluene solution at a concentration of 0.476 g/l. The correspondent magnitude of the hyperpolarizability ₁₁₁₁ of the C₇₀ molecule is 1.2×10^–30 esu which is in a good agreement with the prediction given by the model of a free electron in a spherical box.