Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Let be a surjective mapping from a uniform algebra on a compact Hausdorff space onto a uniform algebra on a compact Hausdorff space . Suppose that holds for every . Then we have that is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).

     

Double affine Hecke algebras,conformal coinvariants and Kostka polynomials

We study a class of representations called ‘calibrated representations’ of the rational and trigonometric double affine Hecke algebras of type ${\mathit{GL}}_n$. We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra ${\stackrel{?}{\mathfrak{gl}}}_m$. We also give a character formula of these irreducible modules in terms of a generalization of Kostka polynomials. These results are conjectured by Arakawa, Suzuki and Tsuchiya based on the conformal field theory. The proofs using recent results on the representation theory of the double affine Hecke algebras will be presented in the forthcoming papers. To cite this article: T. Suzuki, C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Enhanced photoluminescence from very thin double-wall carbon nanotubes synthesized by the zeolite-CCVD method

Photoluminescence (PL) from purified (>90%) double-wall carbon nanotubes (DWNTs), which have been synthesized by zeolite catalyst-supported chemical vapor deposition (zeolite-CCVD), of very small diameters (0.8-nm average inner tube) is reported. The PL contour mappings for various ratios (1-90%) of double- versus single-wall carbon nanotubes by thermal oxidation have enabled us to unambiguously identify the chirality of inner tubes for the DWNTs synthesized. After the extensive high-temperature oxidation at 700 degrees C, high-purity (>90%) DWNTs of approximately 0.8 nm inner diameter are obtained, and most of these correspond to the DWNTs having inner tubes with chiralities of (7,5), (7,6), and (9,4).     

Solvation and dynamic behavior of cyclodextrins in dimethyl sulfoxide solution

High-frequency dielectric relaxation behavior up to 20 GHz was investigated for plain (alpha, beta, gamma) and (62 and 100%) methylated cyclodextrins, CDs, in dimethyl sulfoxide, DMSO, solution. Each hydrogen atom of OH groups of the CDs solvated a DMSO molecule for a residence time of 130-180 ps due to the hydrogen bond formation to an oxygen atom of DMSO, and a few DMSO molecules were included in cavities of the CDs for a while similar to the residence time. The overall rotational relaxation modes of solvated CDs were also observed depending on the effective sizes of the solvated CDs.     

Selective extraction and purification of endohedral metallofullerene from carbon soot

A preferential extraction of endohedral metallofullerenes (EMFs) from carbon soot through the use of reduction in the extraction process and a convenient isolation of endohedral metallofullerene anions (EMFs(-)) and empty fullerenes utilizing their difference in solubility are accomplished. EMFs are easily isolated by one-stage high-performance liquid chromatography after chemical oxidation of the extracted endohedral EMFs(-).     

Soft-landing isolation of vanadium-benzene sandwich clusters on a room-temperature substrate using n-alkanethiolate self-assembled monolayer matrixes

Gas-phase synthesized vanadium-benzene 1:2 (VBz(2)) sandwich clusters were size-selectively deposited onto bare gold and long-chain n-alkanethiolate [-S-(CH(2))(n-1)-CH(3); n = 16, 18, and 22] self-assembled monolayer (SAM)-coated gold substrates under ultrahigh vacuum (UHV) conditions. Investigation of the resulting deposited clusters was performed by infrared reflection absorption spectroscopy (IRAS) and thermal desorption spectroscopy (TDS). The IR frequencies of the soft-landed VBz(2) clusters show excellent agreement with the fundamentals reported in IR data of VBz(2) in an argon matrix. The analysis of IRAS spectra reveals that while there was no orientational preference of the VBz(2) clusters on a bare gold substrate, the VBz(2) clusters deposited onto the SAM substrates were highly oriented with the molecular axis 70-80 degrees tilted off the surface normal. In addition, analysis of TDS spectra revealed unusually large adsorption heats of the physisorbed VBz(2) clusters. The present results are explained by cluster penetration into the long-chain alkanethiolate SAM and for the first time demonstrate the matrix isolation of gas-phase organometallic clusters around room temperature.     

A perturbation of ring derivations on Banach algebras

Suppose A is a Banach algebra and suppose is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation.     

Synthesis of bis(azafulvene)s by dehydration of hydroxymethylpyrrole derivatives

Bis(azafulvene) was isolated in 55% yield by the reaction of 4 equivalents of phenyllithium with 5,5'-diformyl-3,3',4,4'-tetraethyl-2,2'-bipyrrole followed by quenching with acetic anhydride. Unstable bis(azafulvene)s were obtained in much higher yields by dehydrating 5,5'-bis(hydroxymethyl) derivatives of 2,2'-bipyrrole and gem-dimethyl-2,2'-dipyrrylmethane with (Boc)2O-DMAP at room temperature. X-Ray crystallography of two bis(azafulvene)s is reported.     

Molecular design of novel non-planar heteropolycyclic fluorophores with bulky substituents: convenient synthesis and solid-state fluorescence characterization

Novel indeno[1,2-b]benzo[4,5-e]pyran-11-one-type fluorophores exhibiting intense solid-state fluorescence were conveniently synthesized and the relation between their solid-state photophysical properties and the X-ray crystal structures were investigated, which demonstrates that non-planar structures with sterical hindered substituents prevent the fluorophores from forming short pi-pi contacts causing fluorescence quenching in the solid state.     

Lithium secondary batteries using modified-imidazolium room-temperature ionic liquid

Highly reversible, safe lithium secondary batteries that use imidazolium-cation-based room-temperature ionic liquid as an electrolyte and lithium metal as an anode material were realized by the molecular design. To achieve higher reduction stability, an electron-donating substituent was introduced to promote charge delocalization in the imidazolium cation of room-temperature ionic liquids.