A system of evolution equations for non-isothermal phase transitions

We propose and study a system of evolution equations. This is an abstract formulation of problems arising in non-isothermal phase transitions. We consider time-dependent constraints on the unknown functions. Thus the problem yields a system of parabolic variational inequalities. We prove the existence of a solution in a general framework, and then apply the abstract result to some models of phase transitions.     

On Ocneanu's theory of double triangle algebras for subfactors and classification of irreducible connections on the Dynkin diagrams

We give an exposition of Ocneanu's theory of double triangle algebras for subfactors and its application to the classification of irreducible bi-unitary connections on the Dynkin diagrams _An$A_n$, _Dn$D_n$, _E6$E_6$, _E7$E_7$ and _E8$E_8$. More precisely, we give a detailed proof of the complete classification of irreducible K–L$K–L$ bi-unitary connections up to gauge choice, where K and L   represent the two horizontal graphs which are among the A–D–E$A–D–E$ Dynkin diagrams. The result also provides a simple proof of the flatness of _D2n$D_{2n}$, _E6$E_6$ and _E8$E_8$ connections as well as an easy computation of the flat part of _E7$E_7$ as an application.     

Assessment of the natural radioactivity using two techniques for the measurement of radionuclide concentration in building materials used in Japan

The specific activities of ²³⁸U, ²³²Th, and ⁴⁰K in selected building materials used in Japan were measured using a high-purity germanium detector. The uranium and thorium concentrations were determined from same samples using inductively coupled plasma mass spectrometry. There was a good agreement between the measurement of uranium and thorium with both methods (R ² = 0.94, and 0.97, respectively). Based on the specific activities, we have estimated some hazard indexes such as radium equivalent activities (Ra _eq), external hazard index (H _ex), internal hazard index (H _in), annual gonadal equivalent dose (AGED), internal alpha dose, mass exhalation rate and emanation coefficient of radon.     

Synthesis of pyridine-borane complexes via electrophilic aromatic borylation

Pyridine-borane complexes were synthesized from 2-arylpyridines through an electrophilic aromatic borylation reaction with BBr(3). The intermediate 2-(2-dibromoborylaryl)pyridines were stable enough to be handled in air and served as the synthetic platform for variously substituted pyridine-borane complexes. This facile method would be useful for the synthesis of aza-π-conjugated materials having boron-nitrogen coordination.     

Thermal carbosilylation of endohedral dimetallofullerene La(2)@I(h)-C(80) with silirane

Thermal carbosilylation of endohedral dimetallofullerene La(2)@I(h)-C(80) with silirane (silacyclopropane) is reported herein for the first time. Two diastereomers of the carbosilylated La(2)@I(h)-C(80) have been isolated and characterized. The fascinating molecular structure of one diastereomer of the carbosilylated derivatives has been determined unambiguously using X-ray crystallographic analysis. Detailed characteristics of the molecular structures including their metal atom movements have also been revealed using NMR spectroscopic studies and computational calculations. Results revealed that two La atoms move dynamically inside the carbon sphere. Furthermore, electrochemical study has demonstrated that carbosilylation is effective to fine-tune the La(2)@I(h)-C(80) electronic properties.     

Water-stable helical structure of tertiary amides of bicyclic β-amino acid bearing 7-azabicyclo[2.2.1]heptane. Full control of amide cis-trans equilibrium by bridgehead substitution

Helical structures of oligomers of non-natural β-amino acids are significantly stabilized by intramolecular hydrogen bonding between main-chain amide moieties in many cases, but the structures are generally susceptible to the environment; that is, helices may unfold in protic solvents such as water. For the generation of non-hydrogen-bonded ordered structures of amides (tertiary amides in most cases), control of cis-trans isomerization is crucial, even though there is only a small sterical difference with respect to cis and trans orientations. We have established methods for synthesis of conformationally constrained β-proline mimics, that is, bridgehead-substituted 7-azabicyclo[2.2.1]heptane-2-endo-carboxylic acids. Our crystallographic, 1D- and 2D-NMR, and CD spectroscopic studies in solution revealed that a bridgehead methoxymethyl substituent completely biased the cis-trans equilibrium to the cis-amide structure along the main chain, and helical structures based on the cis-amide linkage were generated independently of the number of residues, from the minimalist dimer through the tetramer, hexamer, and up to the octamer, and irrespective of the solvent (e.g., water, alcohol, halogenated solvents, and cyclohexane). Generality of the control of the amide equilibrium by bridgehead substitution was also examined.     

Practical heavy fluorous tag for carbohydrate synthesis with minimal chromatographic purification

A practical heavy fluorous tag 5 bound to a benzylic linker was prepared and applied to carbohydrate synthesis. The fluorous tag 5 was readily introduced to the desired hydroxyl group and carboxyl group by using various methods. Synthesis of the oligosaccharide, which included the terminal structure of class III mucin, was achieved with single-column chromatographic purification. In addition, because of the symmetrical structure of 5, each fluorous synthetic intermediate could be analyzed much easier by NMR spectroscopy than in the case of the fluorous compounds connecting our previous fluorous tags.     

Structural characterization of mono-ruthenium substituted Keggin-type silicotungstates

We have synthesized the mono-ruthenium substituted Keggin-type silicotungstate [SiW(11)O(39)Ru(III)(H(2)O)](5-) (1a) by reaction of the mono-lacunary silicotungstate precursor [SiW(11)O(39)](8-) with Ru(acac)(3) under hydrothermal conditions and isolated as the caesium salt Cs(5)[SiW(11)O(39)Ru(III)(H(2)O)] (1). The DMSO-coordinated complex [SiW(11)O(39)Ru(III)(DMSO)](5-) (2a) was prepared by reaction of 1a with DMSO in aqueous solution at 353 K and isolated as the caesium-potassium mixed salt Cs(4.9)K(0.1)[SiW(11)O(39)Ru(III)(DMSO)] (2). Both compounds 1 and 2 were characterized by single-crystal X-ray structure analysis, powder X-ray structure analysis, UV-Vis spectroscopy, cyclic voltammetry, IR-spectroscopy and elemental analysis. 1 crystallized in the tetragonal space group P4(2)/ncm with a = 20.9299(4), c = 10.3603(4) Angstrom, Z = 4. The ruthenium atom in the Keggin unit could not be distinguished from the tungsten due to disorder. The structural analysis of 2 (monoclinic, P2(1)/c, a = 13.5850(4), b = 20.2764(7), c = 18.1326(4) Angstrom, beta = 90.8730(10) degrees , Z = 4) successfully revealed that the incorporated ruthenium atom is coordinated by DMSO through a Ru-S bond. Polyanion 2a represents the first mono-substituted Keggin ion in which the ruthenium center is not crystallographically disordered. UV-Vis spectroscopy combined with controlled potential electrolysis confirmed that the incorporated rutheniums in 1 and 2 have a valence state of +3. The IR spectra of both 1 and 2 were very similar. All these data indicate that 1 synthesized by reaction of the mono-lacunary silicotungstate K(8)[SiW(11)O(39)] with Ru(acac)(3) under hydrothermal conditions is truly the mono-ruthenium substituted Keggin-type silicotungstate.     

Interstitial OH radicals in F2-laser-irradiated bulk amorphous SiO2

An interstitial hydroxyl radical (HO*) has been generated in bulk amorphous SiO2 (a-SiO2) loaded with interstitial H2O molecules and exposed to F2 laser light (hnu = 7.9 eV, lambda = 157 nm) at 77 K. F2 laser light dissociates an O-H bond of interstitial H2O into a pair of hydrogen atom (H0) and HO*. The resultant H0 disappears below 150 K, whereas HO* is detectable after thermal annealing at 200 K. The electron paramagnetic resonance (EPR) signal of the interstitial HO* recorded at 77 K is similar to that formed in amorphous ice, indicating that HO* is confined in an orthorhombic field by hydrogen bonding, probably with adjacent H2O molecules, silanol (SiOH) groups, and bridging oxygen atoms in the a-SiO2 network.     

Elucidation of codoping effects on the solubility enhancement of Er3+ in SiO2 glass: striking difference between Al and P codoping

The codoping effect mechanism of Al and P on the solubility enhancement of Er(3+) ion in SiO(2) glass was clarified by electron spin-echo envelope modulation spectroscopy. It turned out that doped P ions preferentially coordinate to the Er(3+) ion to form a "solvation shell structure", and the environment is similar to that in phosphate glass, while doped Al ions do not form such a selective solvation structure, taking octahedral coordination. This striking difference indicates that the primary roles of the P-doping and the Al-doping are attributed to "enthalpy of mixing" and to "entropy of mixing", respectively.