Wellposedness of abstract Cauchy problems for second order differential equations

This paper concerns the abstract Cauchy problem (ACP) for an evolution equation of second order in time. LetA be a closed linear operator with domainD(A) dense in a Banach spaceX. We first characterize the exponential wellposedness of ACP onD(A ^k+1),k teN. Next let {C(t);t teR} be a family of generalized solution operators, on [D(A ^k)] toX, associated with an exponentially wellposed ACP onD(A ^k+1). Then we define a new family {T(t); Ret>0} by the abstract Weierstrass formula. We show that {T(t)} forms a holomorphic semigroup of class (H _k) onX. Research of the second-named author was partially supported by Grant-in-Aid for Scientific Research (No. 63540139), Ministry of Education, Science and Culture.     

Measurement of the g-Factor of the 27− High-Spin Isomer State of 152Dy

The g-factor of the 27⁻ isomer state of ¹⁵²Dy has been measured using the Time-Integral Perturbed Angular Distribution (TIPAD) method. The high-spin states of ¹⁵²Dy have been populated by ¹⁴¹Pr(¹⁶O,p4n)¹⁵²Dy reaction at E = 115 MeV from the AVF cyclotron at CYRIC. The paramagnetic correction factor of Dy ions in Pr has been determined to be 4.2(5) by the Time-Differential Perturbed Angular Distribution (TDPAD) measurement of the 21⁻ state of ¹⁵²Dy. As a result, the g-factor of the 27⁻ isomer state of ¹⁵²Dy has been obtained to be +0.09(5). This shows the smaller value than the expected one of +0.39 deduced from a fully aligned configuration of π(h _11/2 ²) ⊗ ν(f _7/2 ² h _9/2 i _13/2).     

Molecular probe for a fluorous medium: long-lived phosphorescence of alpha-diketones in perfluoromethylcyclohexane at room temperature.

We found that alpha-diketones (2,3-butanedione (BD) and 1-phenyl-1,2-propanedione (PPD)) were very suitable luminescence probes for studying the properties of a perfluorinated solvent (i.e., fluorous solvent; perfluoromethylcyclohexane (PFMC)), since these compounds were soluble in PFMC and showed long-lived phosphorescence even at room temperature. The phosphorescence lifetime (tau(p)) of BD in PFMC (650 micros) was much longer than that in cyclohexane (CH, 270 micros). The longer tau(p) value of BD in PFMC was ascribed to the variation of the intersystem crossing rate constant (k(isc)) from the excited triplet state (T1) to the ground state (S0) with the solvent. Some possible reasons for the change in k(isc) were discussed in terms of solute-solvent interactions. Furthermore, by utilizing phosphorescence quenching of BD by pyrene, we, determined a rate constant of the diffusion-controlled reaction in PFMC. Characteristic behaviors of mixing/separation processes between PFMC and a common organic solvent observed by Schlieren photographs were also reported.     

Synthesis and Optical Properties of SiO2-Coated CeO2 Nanoparticles

Silica (SiO₂)-coated ceria (CeO₂) nanoparticles were prepared using water-in-oil microemulsion. Polyoxyethylene (15) cetylether and cyclohexane were used as a surfactant and organic solvent. SiO₂-coated CeO₂ nanoparticles were obtained by hydrolysis of metal alkoxide (tetraethylorthosilicate, TEOS) in the solution containing CeO₂ precursor nanoparticles. The effects of CeO₂ sources (Ce metal salt) and CeO₂ particle-forming agents on the morphology of SiO₂–CeO₂ particles were investigated. Observation via transmission electron microscopy revealed that the type of particle-forming agent affected the nanoparticles' morphology and that CeO₂ nanoparticles were spherically coated with SiO₂ when using oxalic acid ((COOH)₂) as a particle-forming agent of CeO₂. Furthermore, the transmittance of the particles was high in the visible region (above 400 nm) and decreased in the ultraviolet region.     

A new synthesis of 7-substituted 2,3-bis(alkylthio)naphth[1,8-bc]-azepines using the tris(alkylthio)cyclopropenyl cation

7-Substituted 2,3-bis(isopropylthio)naphth[1,8-bc]azepines 3a-c were synthesized in good yields by the reactions of 5-substituted 1-naphthylamines 2a-c with tris(isopropylthio)cyclopropenylium perchlorate ( 1 ) in acetonitrile under reflux. This reaction proceeds through the facile ring opening of 1 , followed by the intermediary formation of iminium salts 5a-c and then intramolecular cyclization.     

Quantitative analysis of original and powdered rocks and mineral inclusions by laser ablation inductively coupled plasma mass spectrometry

Direct analysis of rocks by laser ablation inductively coupled plasma mass spectrometry is described. Both powdered standard rocks and the original rocks were analysed and the results agreed with each other in spite of the difference in the surface states. Microprobe analysis of biotite in granite JG1 was also done directly with a focused laser beam and the results obtained were very close to the solution values given by the conventional aqueous method using biotite separated from an original rock. For quantitative analysis, the measured signal intensity was normalized either by the ablated weight or the barium signal intensity. Forty-two major and minor elements (two of them being used as internal standards) in twelve standard rocks fromt the igneous rock series of the Geological Survey of Japan were determined successfully.     

Novel enhancement of the reducing ability of ytterbium diiodide by irradiation with near-UV light

Irradiation with near-UV light, dramatically enhances the reducing ability of ytterbium diiodide (YbI₂). Organic bromides, iodides, tosylates, and tellurides are reduced efficiently by a YbI₂-hv system, while these can not be reduced with YbI₂ in the dark.     

Exciton and magneto-absorption in tellurium

Infrared magneto-absorption has been investigated in tellurium crystals in magnetic fields up to 45 koe at liquid helium temperatures. When the magnetic field was applied parallel or perpendicular to the c-axis, oscillatory absorptions with many transmission minima involving the exciton absorption were observed. The results were analysed taking into account the complicated structure of the valence band.