On Gouvêa's conjecture in the unobstructed case

In this article, for a residual modular representation defined over an arbitrary finite field, Gouvêa's conjecture which says that the universal deformation ring is isomorphic to a certain Hecke algebra is proven in the unobstructed case.     

Synthesis of well‐defined syndiotactic poly(methyl methacrylate) with low‐temperature atom transfer radical polymerization in fluoroalcohol

The copper‐mediated atom transfer radical polymerization of methyl methacrylate (MMA) in 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) was studied to simultaneously control the molecular weight and tacticity. The polymerization using tris[2‐(dimethylamino)ethyl]amine (Me₆TREN) as a ligand was performed even at ?78°C with a number‐average molecular weight (M_n) of 13,400 and a polydispersity (weight‐average molecular weight/number‐average molecular weight) of 1.31, although the measured M_n's were much higher than the theoretical ones. The addition of copper(II) bromide (CuBr₂) apparently affected the early stage of the polymerization; that is, the polymerization could proceed in a controlled manner under the condition of [MMA]₀/[methyl α‐bromoisobutyrate]₀/[CuBr]₀/[CuBr₂]₀/[Me₆TREN]₀ = 200/1/1/0.2/1.2 at ?20°C with an MMA/HFIP ratio of 1/4 (v/v). For the field desorption mass spectrum of Cu^IBr/Me₆TREN in HFIP, there were [Cu(Me₆TREN)Br]⁺ and [Cu(Me₆TREN)OCH(CF₃)₂]⁺, indicating that HFIP should coordinate to the Cu^I/Me₆TREN complex. The syndiotacticity of the obtained poly(methyl methacrylate)s increased with the decreasing polymerization temperature; the racemo content was 84% for ?78°C, 77% for ?30°C, 75% for ?20°C, and 63% for 30°C. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1436–1446, 2006     

Convergence of Riemannian Manifolds and Laplace Operators, II

We study spectral convergence of compact Riemannian manifolds or more generally certain Dirichlet spaces, obtaining some compactness results on harmonic functions and harmonic maps. Mathematics Subject Classifications (2000) 53C21, 58D17, 58J50. Atsushi Kasue: Partly supported by the Grant-in-Aid for Scientific Research (B) No. 15340053 of the Japan Society for the Promotion of Science.     

Host-guest complexation effect of 2,3,6-tri-O-methyl-β-cyclodextrin on a C60-porphyrin light-to-photocurrent conversion system

In a light-to-photocurrent conversion system based on a C₆₀-porphyrin bilayer prepared by electrostatic alternate adsorption, porphyrin units in a porphyrin polymer have been isolated by cyclodextrin utilizing the host-guest interaction. In this system, a high quantum yield was achieved by suppression of self-quenching of porphyrin units.     

Thermodynamic Insight into the Origin of a Calix[n]arene-[60]fullerene Interaction and its Application to a Porphyrin-[60]fullerene Energy Transfer System

The calixarene-fullerene interaction,which causes only a slight change in the absorptionspectra, has been substantiated by calorimetricmeasurements: the H° values arecomparable with those obtained from the associationconstants estimated by a spectroscopic method. Furthermore, we determined the association constantbetween homooxacalix[3]arene and [60]fullerenederivatives with a porphyrin moiety by fluorescencespectra.     

Polymerization of vinyl acetate in fatty acids and properties of poly (vinyl alcohols) derived from the poly (vinyl acetates)

Polymerization of vinyl acetate (VAc) in various fatty acids (carbon numbers 4–18) was carried out. Chain transfer constants to the acids were determined to be 20–35×10^–4, from which the constant to a methylene group was obtained to be 0.73×10^–4. Viscometry in aqueous solution of derived poly (vinyl alcohol) (PVA) showed the usual behavior in terms of Huggins constant obtained by the Schulz–Blaschkes equation for PVAs derived from fatty acid systems lower than hexadecanoic acid. PVA derived from octadecanoic acid system showed abnormality, indicating association of alkyl groups. Contact angles on surfaces of PVAs cast from aqueous solutions were measured. While those of PVA derived from lower acid systems were 62°, those of PVAs derived from higher aids were higher and increased to 92° with increase in carbon number to octadecanoic acid. Alkyl groups in the PVAs were estimated to appear on the surfaces. Surface tension of aqueous solution of the PVA derived from octadecanoic acid showed high surface activity, and depended on pH of the solution, indicating the presence and cleavage of lactone ring at the combined portion between PVA and the acid.     

Host-guest interactions in the supramolecular incorporation of fullerenes into tailored holes on porphyrin-modified gold nanoparticles in molecular photovoltaics

Novel gold nanoparticles modified with a mixed self-assembled monolayer of porphyrin alkanethiol and short-chain alkanethiol were prepared (first step) to examine the size and shape effects of surface holes (host) on porphyrin-modified gold nanoparticles. The porphyrin-modified gold nanoparticles with a size of about 10 nm incorporated C60 molecules (guest) into the large, bucket-shaped holes, leading to the formation of a supramolecular complex of porphyrin-C60 composites (second step). Large composite clusters with a size of 200-400 nm were grown from the supramolecular complex of porphyrin-C60 composites in mixed solvents (third step) and deposited electrophoretically onto nanostructured SnO2 electrodes (fourth step). Differences in the porphyrin:C60 ratio were found to affect the structures and photoelectrochemical properties of the composite clusters in mixed solvents as well as on the SnO2 electrodes. The photoelectrochemical performance of a photoelectrochemical device consisting of SnO2 electrodes modified with the porphyrin-C60 composites was enhanced relative to a reference system with small, wedged-shaped surface holes on the gold nanoparticle. Time-resolved transient absorption spectroscopy with fluorescence lifetime measurements suggest the occurrence of ultrafast electron transfer from the porphyrin excited singlet states to C60 or the formation of a partial charge-transfer state in the composite clusters of supramolecular complexes formed between porphyrin and C60 leading to efficient photocurrent generation in the system. Elucidation of the relationship between host-guest interactions and photoelectrochemical function in the present system will provide valuable information on the design of molecular devices and machines including molecular photovoltaics.     

Amino acid end-group in commercial heparin. III. Determination of the number of amino groups of amino acid and hexosamine residues per heparin molecule

The reactions of heparin with 2,4,6-trinitrobenzenesulfonic acid (TNBS) were studied spectrometrically. Seven different commercial heparins were used in this study. The amino groups react with TNBS to form equimolar amounts of trinitrophenylated (TNP) amino groups and bisulfite ions. The TNP-amino groups further react with bisulfite ions to form the monosubstituted anionic sigma complex. The absorption spectrum with two maxima at approximately 350 nm and approximately 420 nm, characteristic of either the TNP-amino groups or the complex, was analyzed for the reaction of TNBS with heparin. It was shown that the reactivities of TNBS with amino groups from α-amino acid and hexosamine residues are greatly different. By combining the results of the reaction kinetics and the reaction of heparin with Sanger's reagent, the number of the α-amino groups and the free amino groups in hexosamine residues were determined. These data have been performed with a range of heparins from different commercial sources, of different activities and physical characteristics. No correlation was found between the free amino contents of these heparins and biological potency. © 1993 John Wiley & Sons, Inc.     

Rotational isomerism involving an acetylenic carbon. Part 5: Restricted rotation about acetylenic axis in sterically crowded bis(1-phenyl-9-anthryl)ethynes

The title sterically crowded di-9-anthrylethyne derivative with 3,5-ⁱPr₂-phenyl groups at 1-position showed a barrier to rotation about the acetylenic axis of 18.0 kcal mol⁻¹ based on a dynamic NMR study, which is an extremely high value for acyclic diarylethynes. The mechanism of the dynamic stereochemistry and the substituent effect on the rotational barrier are discussed.