Krein's strings with singular left boundary

M. G. Krein established a one-to-one correspondence between strings with regular left boundary and their spectral measures. In this note we treat strings with a certain class of singular left boundary and obtain a condition that the spectral measure grows polynomially.     

Time-resolved optical transmission during pulsed-laser annealing of ion-implanted amorphous silicon-on-sapphire

Time-resolved optical transmission of annealing dye laser pulse (wavelength : 590 nm and pulse width : 250 nsec) itself has been measured in thin layers of Si⁺-implanted amorphized silicon-on-sapphire (SOS) with several energy densities in the range of 0.02 to 2.64 J/cm². At the energy densities where the amorphized SOS is recrystallized, the transmission exhibits a sudden drop and subsequently remains at a detectable level. This laser-induced absorption is inconsistent with the presence of ordinary molten silicon but suggests an electronic structural-change from amorphous to crystalline state.     

The stereochemistry of 4-methyl-6-phenyl-5,6,7,8-tetrahydro-4H-1,3,2,6-dioxathiazocine 2-oxides using NMR

Two isomeric 4-methyl-6-phenyl-5,6,7,8-tetrahydro-4H-1,3,2,6-dioxathiazocine 2-oxides were prepared, and their pmr and cmr spectra were examined. From the aromatic solvent shielding values and the magnitudes of the γ shifts, the title compounds are found to exist in the trans and cis forms in solution.     

Theory of core photoemission spectra in CeO2

By using the Anderson model with a filled valence band, we calculate the core photoemission spectra of CeO₂, and compare them with experimental results. It is shown that in the ground state of CeO₂ the 4?⁰ and 4?¹ configurations are mixed strongly due to the large hybridization between the 4? states and the valence band. In the final state of the photoemission, the 4?¹ and 4?² configurations are also mixed strongly due to the final state interaction coming from a core hole potential and the large hybridization. The fractional intensity of the 4?⁰ photoemission peak is considerably different from the weight of the 4?⁰ configuration in the ground state because of the strong final state interaction.     

Time-resolved spectrum for resonant light scattering in an exciton-phonon system

A formula is given for the time-resolved spectrum of the resonantly- scattered radiation from an exciton-phonon system, and it is applied to the calculation of two-LO-phonon assisted spectrum. Both the Raman component associated with virtual intermediate states and the luminescence with real intermediate states are obtained. A Raman-like component with an oscillatory behavior can be seen, when the exciton relaxation time is shorter than the excitation pulse duration. It is proposed that the energy dependence of exciton relaxation rate can be directly measured from the time decay of a hot luminescence spectrum.     

Support theorems for random Schrödinger operators

In the multi-dimensional case it is shown that the increase of the topological support of the probability measure describing the randomness of potentials implies the increase of the spectrum. In the one-dimensional case the converse statement for the absolutely continuous spectrum is valid. Especially the spectrum (in general dimension) and the absolutely continuous spectrum (in one-dimension) are determined only by the topological support of the random potentials.Research partially supported by the USNSF under grant MCS-81-20833     

Anomalous behavior of the surface state in ferromagnetic superconductors

The effect of the electromagnetic interaction between the persistent current and the magnetic moments to the surface state in ferromagnetic superconductors is studied theoretically. This interaction causes an oscillatory decay of the penetrated magnetic field near the magnetic phase transition temperature. Below a critical temperature, the spontaneous surface magnetization is stabilized by the magnetic field induced by the surface persistent current.