Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces

We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest.     

Products, cones, and suspensions of spaces with the measure contraction property

This article concerns several geometric properties of metricmeasure spaces satisfying the measure contraction property (MCP),which can be considered as a generalized notion of lower Riccicurvature bounds. We prove that the MCP of spaces descends totheir products and Euclidean cones. We also show that a positivelycurved space in terms of the MCP with a maximal diameter canbe represented as the spherical suspension of some topologicalmeasure space.     

Synthesis of diazepinoquinoxalines and imidazolobenzopteridines

Diazepinoquinoxalines 3, 4 and imidazolobenzopteridines 5, 6a-d, 7a-d, 8, 9 were synthesized from 3-allylamino-6,7-dimethyl-2-quinoxalinecarboxamide ( 1 ) and 2-allylamino-6,7-dimethyl-3,4-dihydrobenzo[g]pteridin-4-one ( 2 ) by the intramolecular cyclization using phenylselenenyl chloride.     

Large-scale separation of metallic and semiconducting single-walled carbon nanotubes

In the applications of single-walled carbon nanotubes (SWNTs), it is extremely important to separate semiconducting and metallic SWNTs. Although several methods have been reported for the separation, only low yields have been achieved at great expense. We show a separation method involving a dispersion-centrifugation process in a tetrahydrofuran solution of amine, which makes metallic SWNTs highly concentrated to 87% in a simple way.     

Processing and characterization of Pb(Mg,Nb)O3-PbTiO3 thin films from metal alkoxide-derived gels

The sol-gel processing is one of promising methods to fabricate well-derived integrated thin films at relatively low temperature. Ferroelectric niobates films do afford the possibilities for adding the values by the hybridization with semiconductor and/or electro-optic systems. The molecular level designing of the precursor solution was stressed as well as the control of key processing factors. The advantages of this sol-gel have been extended to prepare the ferroelectric Pb(Mg, Nb)O₃-PbTiO₃ solid solution films integrated on Si wafers. The crystallization of the films with desired crystal structure could be promoted by the controlled partial hydrolysis of designed alkoxide solution in the intermediate state and the pre-heated treatment of alkoxide-derived films in flow of water vapor and oxygen gas mixture.     

Evidence of conformational equilibrium of 1-ethyl-3-methylimidazolium in its ionic liquid salts: Raman spectroscopic study and quantum chemical calculations

Raman spectra of liquid 1-ethyl-3-methylimidazolium (EMI+) salts, EMI(+)BF4-, EMI(+)PF6-, EMI(+)CF3SO3-, and EMI(+)N(CF3SO2)2-, were measured over the frequency range 200-1600 cm(-1). In the range 200-500 cm(-1), we found five bands originating from the EMI+ ion at 241, 297, 387, 430, and 448 cm(-1). However, the 448 cm(-1) band could hardly be reproduced by theoretical calculations in terms of a given EMI+ conformer, implying that the band originates from another conformer. This is expected because the EMI+ involves an ethyl group bound to the N atom of the imidazolium ring, and the ethyl group can rotate along the C-N bond to yield conformers. The torsion energy for the rotation was then theoretically calculated. Two local minima with an energy difference of ca. 2 kJ mol(-1) were found, suggesting that two conformers are present in equilibrium. Full geometry optimizations followed by normal frequency analyses indicate that the two conformers are those with planar and nonplanar ethyl groups against the imidazolium ring plane, and the nonplanar conformer is favorable. It elucidates that bands at 241, 297, 387, and 430 cm(-1) mainly originate from the nonplanar conformer, whereas the 448 cm(-1) band does originate from the planar conformer. Indeed, the enthalpy for conformational change from nonplanar to planar EMI+ experimentally obtained by analyzing band intensities of the conformers at varying temperatures is practically the same as that evaluated by theoretical calculations. We thus conclude that the EMI+ ion exists as either a nonplanar or planar conformer in equilibrium in its liquid salts.     

Conformational effects on the performance and selectivity of a polymeric pseudostationary phase in electrokinetic chromatography

The effect of the conformation of a polymeric pseudostationary phase on performance and selectivity in electrokinetic chromatography was studied using an amphiphilic pH-responsive polymer that forms compact intramolecular aggregates (unimer micelles) at low pH and a more open conformation at high pH. The change in conformation was found to affect the electrophoretic mobility, retention, selectivity, and separation efficiency. The low-pH conformer has higher electrophoretic mobility and greater affinity for most solutes. The unimer micelle conformation was also found to provide a solvation environment more like that of micelles and other amphiphilic self-associative polymers studied previously. It was not possible to fully characterize the effect of conformation on efficiency, but very hydrophobic solutes with long alkyl chains appeared to migrate with better efficiency when the unimer micelle conformation was employed. The results imply that polymers with a carefully optimized lipophilic-hydrophilic balance that allow self-association will perform better as pseudostationary phases. In addition, the results show that electrokinetic chromatography is a useful method for determining the changes in solvation environment provided by stimuli-responsive polymers with changes in the conditions.     

Oxytelluration of olefins to (β-alkoxy- and β-hydroxy-alkyl)aryltellurium dihalides and their reactions with reducing agents and aqueous NaOH

Treatment of olefinic hydrocarbons with phenyltellurium tribromide or a mixture of diphenylditelluride and bromine in alcohol affords (β-alkoxyalkyl)phenyltellurium dibromides in fair to good yield (alkoxytelluration of olefins). Various aryltellurium trichlorides, diphenylditelluride/CuCl₂, and phenyltellurocyanate/CuCl₂ can be used for the preparation of (β-alkoxyalkyl)aryltellurium dichlorides. Similar reactions in aqueous tetrahydrofuran or aqueous t-butyl alcohol result in the formation of the corresponding β-hydroxy compound (hydroxytelluration of olefins). The reaction is trans stereospecific in the cases of cis-2-butene and cis- and trans-4-octenes and regiospecific in the cases of all terminal olefins examined (1-hexene, 1-octene, 1-decene, styrene, α-methylstyrene, 2-methyl-1-pentene, and isobutylene), tellurium species attacking the terminal carbon solely. The diorganyltellurium dihalide produced is reduced to the corresponding diorganyltelluride by reducing agents such as N₂H₄, Na₂S, Na₂S₂O₃, and NaHSO₄ in aqueous solution. Treatment of the diorganyltellurium dibromide with aqueous NaOH affords either an allylic ether (by telluroxide elimination) or a telluroxide depending on the structure of the telluroxide.     

Single-bubble sonochemiluminescence in aqueous luminol solutions

Sonochemiluminescence (SCL) of luminol due to a single bubble is studied through spectral measurement. No SCL was observed from a stable single bubble that emitted high-intensity sonoluminescence (SL). In contrast, SCL was observed under conditions of an unstable dancing bubble, where a bubble grows and ejects tiny bubbles, making it "dance" by counteraction. Furthermore, SCL was observed from dancing bubbles even when SL was not observed, depending on the dissolved gas content. The instability of bubble collapse is the key parameter governing SCL.     

Application of infrared data analysis based on symbolic logic in automated structure elucidation by chemics

A computer program, IRASSL, is described for processing infrared (IR) data. The program, based on symbolic logic, is used to formulate complex relationships between substructures and their characteristic wavenumber regions. The program yields sets of substructures inferred from a correlation table prepared from accumulated IR data. The procedure is applied as an ancillary to the automated structure elucidation system CHEMICS. The introduction of the substructural information provided by IRASSL into CHEMICS as restrictions in the elucidation process produces a significant decrease in the number of candidate structures. Some examples of the application are given.