Gaussian Estimates of Order α and L p -Spectral Independence of Generators of C 0-Semigroups

We prove L^p-spectral independence for generators of C₀-semigroups estimated by the positive C₀-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C₀-semigroup .     

Syntheses, structures, and coordination chemistry of phosphole-containing hybrid calixphyrins: promising macrocyclic P,N2,X-mixed donor ligands for designing reactive transition-metal complexes

The syntheses, structures, and coordination chemistry of phosphole-containing hybrid calixphyrins (P,N2,X-hybrid calixphyrins) and the catalytic activities of their transition-metal complexes are reported. The 5,10-porphodimethene type 14pi-P,(NH)2,X- and 16pi-P,N2,X-hybrid calixphyrins (X = O, S, NH) are prepared via acid-promoted dehydrative condensation between a sigma4-phosphatripyrrane and the corresponding 2,5-bis[hydroxy(phenyl)methyl]heteroles followed by DDQ oxidation. Both spectroscopic and crystallographic data of the hybrid calixphyrins have revealed that the conformation and size of the macrocyclic platforms as well as the oxidation state of the -conjugated pyrrole-heterole-pyrrole (N-X-N) units vary considerably depending on the combination of heteroles. The sigma3-P,(NH)2,S- and sigma3-P,N2,S-hybrids react with Pd(OAc)2 and Pd(dba)2, respectively, to afford the same Pd(II)-P,N2,S-hybrid complex, in which the calixphyrin platform is regarded as a dianionic ligand. In the complexation with [RhCl(CO)2]2 in dichloromethane, the sigma3-P,N2,S-hybrid behaves as a neutral ligand to afford an ionic Rh(I)-P,N2,S-hybrid complex, whereas the sigma3-P,N2,NH-hybrid behaves as an anionic ligand to produce Rh(III)-P,N3-hybrid complexes. In the latter reaction, it is likely that a neutral Rh(I)-P,N3-hybrid complex, generated as a highly nucleophilic intermediate, undergoes C-Cl bond activation of the solvent. The complexation of AuCl(SMe2) with the sigma3-P,N2,X-hybrids (X = S, NH) leads to the formation of the corresponding Au(I)-monophosphine complexes. The spectral data and crystal structures of these metal complexes exhibit the hemilabile nature of the phosphole-containing hybrid calixphyrin platforms derived from the flexible phosphole unit and the redox active N-X-N units. The hybrid calixphyrin-palladium and -rhodium complexes catalyze the Heck reaction and hydrosilylations, respectively, implying that the metal center in the core is capable of activating the substrates under appropriate reaction conditions. The present results demonstrate the potential utility of the phosphole-containing hybrid calixphyrins as a new class of macrocyclic P,N2,X-mixed donor ligands for designing highly reactive transition-metal complexes.     

A study on the reaction between chlorine trifluoride gas and glass-like carbon

The reaction between glass-like carbon (GC) and chlorine trifluoride (ClF₃) gas was investigated with weight measurements, surface analysis, and gas desorption measurements, where the ClF₃ gas is used for the in situ cleaning of tubes in silicon-related fabrication equipment. From Auger electron spectroscopy and X-ray photoelectron spectroscopy measurements, a carbon mono-fluoride, –(CF)_n–, film near the surface of GC is considered to be grown onto the GC surface above 400 °C by the chemical reaction with ClF₃, and this thickness of the fluoride film depends on the temperature. The grown fluoride film desorbs by annealing in a vacuum up to 600 °C. Although GC is apparently etched by ClF₃ over 600 °C, the etch rate of GC is much lower than that of SiC and quartz.     

Electro-optic response of cubic liquid crystal compounds in Kerr cell geometry

We present the results of our investigations on the electro-optic response of the cubic phase liquid crystal compounds 1,2-bis-[4-n-octyloxy-benzoyl]-hydrazine (BABH8) and 4'-n-hexadecyloxy-3'-nitrobiphenyl-4-carboxylic acid (ANBC16) in Kerr cell geometry. The AC electric field response in the BABH8 cubic phase was found to be as small as that of the isotropic phase, even though there was a response in the adjacent smectic C (SmC) phase. The response in the SmC phase means that the BABH8 molecule itself has an electric field coupling ability, but this ability is strongly inactivated in the cubic phase. This inactivity to the AC fields was also found in the cubic phase of ANBC16. This behaviour could be explained by the small structural unit size of the cubic phase.     

In situ monitoring of the H concentration change near an electrode surface through electrolysis using slab optical waveguide pH sensor

The H⁺ concentration change was monitored near an electrode surface through an electrolysis using a slab optical waveguide technique. Indium tin oxide transparent electrode modified by porous insulating polymer to which methyl red was covalently immobilized was used as a guiding layer, and the absorbance change of the polymer film was monitored. H⁺ generation at the vicinity of the electrode through the oxidation of ascorbic acid could be monitored by this technique.     

Existence test for solution of nonlinear systems applying affine arithmetic

A computational test is proposed for existence of solution in nonlinear systems. In this test, an interval inclusion of Newton mapping is estimated applying affine arithmetic. Numerical examples are presented to show the efficiency of this test.     

Rough set based rule induction from two decision tables

We study rule induction from two decision tables as a basis of rough set analysis of more than one decision tables. We regard the rule induction process as enumerating minimal conditions satisfied with positive examples but unsatisfied with negative examples and/or with negative decision rules. From this point of view, we show that seven kinds of rule induction are conceivable for a single decision table. We point out that the set of all decision rules from two decision tables can be split in two levels: a first level decision rule is positively supported by a decision table and does not have any conflict with the other decision table and a second level decision rule is positively supported by both decision tables. To each level, we propose rule induction methods based on decision matrices. Through the discussions, we demonstrate that many kinds of rule induction are conceivable.