Mirror symmetry,mirror map and applications to Calabi-Yau hypersurfaces

Mirror Symmetry, Picard-Fuchs equations and instanton corrected Yukawa couplings are discussed within the framework of toric geometry. It allows to establish mirror symmetry of Calabi-Yau spaces for which the mirror manifold had been unavailable in previous constructions. Mirror maps and Yukawa couplings are explicitly given for several examples with two and three moduli.On leave of absence from Dept. of Math., Toyama Univ., Toyama 930, Japan (address after Sept. 1, 1993)Address after Oct. 1, 1993: Dept. of Math., Harvard Univ., Cambridge, MA 02138, USA. after April 1, 1994: CERN, Theory Division, CH-1211 Geneva 23, Switzerland     

Observation of phase transition of cesium manganese hexacyanoferrates by X-ray absorption spectroscopy

Cesium manganese hexacyanoferrates exhibit an interesting phenomenon of temperature-induced phase transition accompanied by a variation in the magnetic susceptibility. We observed the variation in the electronic state of Mn during the phase transition by using X-ray absorption spectroscopy. The results of the analyses showed that the content ratio of Fe^II-CN-Mn^III and Fe^III-CN-Mn^II systematically varied during the phase transition. However, the ratio of Fe^II-CN-Mn^II remained constant at almost all temperatures. These results suggest that the charge transfer between Fe and Mn ions in the Fe^III-CN-Mn^II or the Fe^II-CN-Mn^III bond produces the phase transition.     

On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition

Summary We consider the stationary Navier-Stokes equations in a certain type of semi-infinite channel under the general outflow condition. Assuming that the domain and the data are symmetric with respect to a straight line, the axis of symmetry, and that the axis intersects every component of the boundary, we show the existence of solutions and certain regularity properties of the solutions.

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Sunto In questo lavoro consideriamo le equazioni di Navier-Stokes stazionarie in un certo tipo di canali semi-infiniti sotto la condizione generale di outflow. Assumendo che sia il dominio sia i dati siano simmetrici rispetto ad una retta, l’asse di simmetria, e che questa retta intersechi ogni componente del bordo, mostriamo esistenza di soluzioni ed alcune proprietà di regolarità delle stesse.

     

Development of heterodyne detection of dynamic light scattering enhanced by the Talbot effect for the size measurement of nanoparticles.

A new type of dynamic light scattering method for the size measurement of nanoparticles was developed using a transmission grating. A sample cell was located behind the grating, and light was incident from the grating side. The scattered light by a solution with nanopariticles was mixed with diffracted light by the grating, and the mixed signal was detected; namely, the diffracted light was used as reference light for heterodyne detection. It was confirmed that the S/N ratio of the autocorrelation curve was 26-times improved by heterodyne detection. Furthermore, the S/N ratio was improved by setting the sample cell at the sample grating distance where the electromagnetic field is maximum due to the Talbot effect. Size measurements for several kinds of nanoparticles were demonstrated by this new method.     

The stress concentration in keyways when torque is transmitted through keys

The stress-concentration factor for keyways is obtained by the electroplating method of strain analysis which was recently developed in Japan. The stresses in keyways are examined under most practical conditions. The shaft to be examined is set in a boss and fixed with a key so that the torque is wholly transmitted to the test piece through the key. To obtain the limit value for a shaft twisted only through a key, the fitting is devised so as to minimize the surface friction at the fitted portion. The results are compared to those reported previously by other authors in which local effects of the key are ignored.     

Application of self-consistent HMO theory to heteroconjugated molecules

Substantial improvement of the self-consistent HMO theory, as recently developed by one of us, is made in the parametrization for heterobonds. The theory is extensively applied to a large scale of heteroconjugated molecules including rather complicated ones which are biologically important. The calculated molecular geometries and the wavelengths of optical absorption spectra are found to be in good agreement with experimental values. Examining the effect of inclusion of the -technique to this theory, we find that the calculated values of molecular geometries, electronic spectra and ionization potentials are little affected for most molecules. Dependences of the absorption wavelength and the adiabatic potential on the molecular geometry are also investigated.     

Synthesis of optically active alkynyl alcohols and α-hydroxy esters by microbial asymmetric hydrolysis of the corresponding acetates

Asymmetric hydrolysis of the acetates of racemic alkynyl alcohols and α-hydroxy esters by Bacillus subtilis var. Niger afforded optically active acetates and alcohols in 7–90% optical purities. The both enantiomers of optically pure mandelie acid were prepared by this microbial method.