Microlocal study of topological Radon transforms and real projective duality

Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.     

Structural determination of carvone, a component of spearmint, by means of gas electron diffraction augmented by theoretical calculations

The molecular structure and conformation of carvone, a compound with a minty odor, were investigated by means of gas electron diffraction supported by theoretical calculations. Electron diffraction patterns were recorded by heating the nozzle up to 128 °C to obtain enough scattering intensity. The infrared spectrum was also measured by using an absorption cell with a path length of 10 m. The obtained molecular scattering intensities were analyzed with the aid of theoretical calculations and infrared spectroscopy. It was revealed that the experimental data are well reproduced by assuming that carvone consists of a mixture of three conformers that have the isopropenyl group in the equatorial position and mutually differ in the torsional angle around the single bond connecting the ring and the isopropenyl group. It was also found that the puckering amplitude of the ring of carvone is close to those of menthol and isomenthol, a minty compound and its nonminty isomer. The determined structural parameters (r_g and ∠_α) of the most abundant conformer of carvone are as follows: 〈r(C-C)〉=1.520(3) Å; 〈r(CC)〉=1.360(5) Å; r(CO)=1.225(5) Å; 〈r(C-H)〉=1.104(4)Å; 〈∠CC-C〉=121.1(5)°; 〈∠C-C-C〉=110.4(5)°; ∠C-CO-C=117.1(14)°; 〈∠C-C-H〉=111.1(13)°. Angle brackets denote average values and parenthesized values are the estimated limits of error (3σ) referring to the last significant digit.     

Isolation of o-xylylene (o-quinodimethane) dirivatives. A strong through-bond interaction in 2,3-benzobicyclo[2.2.0]hexane system

Some o-xylylene (o-quinodimethane) derivatives were isolated as stable cyrstalline materials. A strong through-bond interaction in tetracyanoethylene addition product of tetraphenylbenzodicyclobutadiene ($\text{21}$ is suggested.     

Synthesis and cation-binding properties of poly-and bis(thiacrown ether)s

Poly- and bis(thiacrown ether) derivatives in which some oxygen atoms of benzocrown ether moiety are replaced by sulfur atoms have been synthesized. Their cation-binding abilities were investigated by using the solvent extraction method. The poly- and bis(benzothiacrown ether)s showed great affinity for silver ion, being more excellent in the affinity than the corresponding monocyclic analogs. They, however, possess very poor cation-binding ability for alkali and alkaline-earth metal ions. The poly- and bis(thiacrown ether)s also bind mercuric ions effectively, whereas the corresponding monomeric analogs do not at all.     

Novel synthesis of macrocycles with 1,1′-binaphthalene-2,2′-diol using intramolecular oxidative coupling

A new series of BINOL-based macrocycles with two phenolic protons have been synthesized via oxidative coupling reaction using CuCl(OH)-TMEDA.     

Laser spectroscopic investigation of salicylic acids hydrogen bonded with water in supersonic jets: Microsolvation effects for excited state proton dislocation

Geometric structures and excited-state proton dislocation of size-selected salicylic acid clusters (salicylic acid and 5-methoxysalicylic acid) with water were studied by using laser spectroscopic techniques. Fluorescence excitation, dispersed fluorescence, and infrared (IR) spectra of those clusters in supersonic jets were examined for both the electronic ground (S0) and first excited (S1) states. The geometric structures of the clusters were determined on the basis of the IR spectra of the OH stretch region with the help of quantum chemical calculations. The hydroxyl group of the water moiety in the clusters forms a ring involving the carboxylic group of the salicylic acid moiety. The IR spectra in S0 show that the intramolecular hydrogen bond in the salicylic acid moiety is still held upon cluster formation, but the phenolic OH stretch band intensity is remarkably weaken in the clusters. The IR spectra in the S1 state and dispersed fluorescence spectra indicated that the intramolecular excited state proton dislocation is hardly affected by the microsolvation with water, in contrast with the strong suppression of the dislocation in the self-solvation.