Boundedness of Product Type Pseudodifferential Operators on Spaces of Besov Type

In this paper we consider pseudodifferential operators associated with symbols satisfying estimates of product type, and give some sufficient conditions for the operators to be bounded on BESOV spaces and on TRIEBEL —LIZORKIN spaces of product type corresponding to the above estimates. In the proof we use the characterization of these spaces by approximation by entire functions.     

NMR studies on polarized12B implanted in highly oriented pyrolytic graphite

NMR measurements on¹²B nuclei implanted in a thin sheet of highly oriented pyrolytic graphite (Grafoil) have been made to study the magnitude of the polarization of¹²B and its electric quadrupole coupling. The magnitude of the residual polarization of¹²B held in carbon material is of crucial importance to the experiment measuring the average polarization of¹²B produced in the muon capture by¹²C. It was found that the polarization of¹²B can be maintained at 101.0±2.2% in Grafoil under a magnetic field of 3 kG. The electric quadrupole coupling was determined to bee ² qQ/h=+1207.3±8.2 kHz. From the magnitude and the sign of the electric field gradienteq, the location of¹²B was found to be a substitutional site in the carbon lattice. The anomalous B-C bond involving thesp ₂ hybrid orbitals with partially filledp _z electrons is also discussed.     

Quantum statistical hierarchy equation in nonequilibrium systems

An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.