A generalization of Lelieuvre’s formula to equiaffine immersions of general codimension

A non-degenerate equiaffine immersion of codimension one into an equiaffine space is locally expressed in terms of its conormal map and its affine fundamental form. The expression is called the Lelieuvre’s formula. We recently defined the notions of an equiaffine immersion of general codimension and its transversal volume element map. In this paper, we locally express a non-degenerate equiaffine immersion of general codimension into an equiaffine space in terms of its transversal volume element map and its affine fundamental form.     

Evaluating Optical Quality of a Bifocal Soft Contact Lens in Near Vision Using a Shack–Hartmann Wavefront Aberrometer

To assess optical characteristics of bifocal soft contact lenses (BCLs) in use, we measured wavefront aberrations of human eyes, of eyes with a monofocal soft contact lens (MCL), and of eyes with a BCL. Modulation transfer functions (MTFs), Strehl ratios, and simulated images for far and near vision were produced with the measured aberrations. High order aberrations of subject 1 were significantly smaller than those of subject 2 (t-test, P = 0.001). We found that wearing the BCL improved the optical quality of an eye in subject 1, expressed as the horizontal MTF from 2 to 48 cycles per degree (cpd) for near vision and the Strehl ratio (t-test, P = 0.009 for Strehl ratio). But we did not find the same effect in subject 2. This difference may be due to the difference in the aberrations of the eyes of the two subjects.     

Low-density attack revisited

The low-density attack proposed by Lagarias and Odlyzko is a powerful algorithm against the subset sum problem. The improvement algorithm due to Coster et al. would solve almost all the problems of density <0.9408... in the asymptotical sense. On the other hand, the subset sum problem itself is known as an NP-hard problem, and a lot of efforts have been paid to establish public-key cryptosystems based on the problem. In these cryptosystems, densities of the subset sum problems should be higher than 0.9408... in order to avoid the low-density attack. For example, the Chor-Rivest cryptosystem adopted subset sum problems with relatively high densities. In this paper, we further improve the low-density attack by incorporating an idea that integral lattice points can be covered with polynomially many spheres of shorter radius and of lower dimension. As a result, the success probability of our attack can be higher than that of Coster et al.’s attack for fixed dimensions. The density bound is also improved for fixed dimensions. Moreover, we numerically show that our improved low-density attack makes the success probability higher in case of low Hamming weight solution, such as the Chor-Rivest cryptosystem, if we assume SVP oracle calls.      

Investigations of morphology, purity and crystal defects of the InN pillar crystals prepared by means of halide chemical vapor deposition under atmospheric pressure

Indium nitride prepared under atmospheric pressure using a halide chemical vapor deposition method has been examined by means of a variety of analytical techniques. Scanning electron microscopic observations showed that the crystals deposited onto a Si(100) substrate have hexagonal pillar structure. Based on the X-ray diffraction and X-ray pole-figure analyses, it was deduced that each InN pillar crystal grows with a different rotation angle around the 〈001〉 axis. Transmission electron diffraction showed that they are of single-like form. This was also confirmed by the selected area electron diffraction image as well.     

Nondestructive discrimination of ivories and prediction of their specific gravity by Fourier-transform Raman spectroscopy and chemometrics

Fourier-transform (FF) Raman spectroscopy and chemometrics were used for nondestructive analysis of ivories. The discrimination of five kinds of ivories, two subspecies of African elephant, mammoth, hippopotamus, and sperm whale, was investigated, and a calibration model for predicting their specific gravity was developed. FT-Raman spectra were measured in situ for them and chemometrics analyses were carried out for the 3050-350 cm(-1) region. The five kinds of ivories were clearly discriminated from each other on the scores plots of two or three principal components (PCs) obtained by principal component analysis (PCA). The loadings plot for PC 1 shows that the discrimination relies on the content ratio of organic collagenous protein and inorganic hydroxyapatite of ivories. The loadings plot for PC 2 shows that bands due to the CH3 and CH2 stretching modes of the protein also play a role in the discrimination. Using partial least squares regression (PLSR), we developed a calibration model that predicts the specific gravity of the ivories from the FT-Raman spectra. The correlation coefficient and root mean square error of cross validation (RMSECV) of this model were 0.980 and 0.024, respectively.     

Asymmetric allylsilane-mediated carbocyclization: A highly enantiospecific synthesis of (1S, 2S)-(+)-2-methyl-3-cyclopenten-1-ol

An enantiospecific synthesis of the title compound is described which involves the TiCl₄-promoted cyclization of the chiral allylic silane having formyl group, which was obtained via the Claisen rearrangement of ($\text{R}$, $\text{E}$)-1-trimethylsilyl-1-buten-3-ol.     

Nitration of moderately deactivated arenes with nitrogen dioxide and molecular oxygen under neutral conditions. Zeolite-induced enhancement of regioselectivity and reversal of isomer ratios

In the presence of zeolites, moderately deactivated arenes such as 1-nitronaphthalene, naphthonitriles, and methylated benzonitriles can be smoothly nitrated at room temperature by the combined action of nitrogen dioxide and molecular oxygen. The regioselectivity is considerably improved as compared with the conventional nitration methodology based on nitric and sulfuric acids. In some cases, the minor isomer became favoured to a significant extent, resulting in the reversal of ordinary isomer ratios of nitration products.     

Isolation of the complex between acrylonitrile and trimethylaluminum

The complex of acrylonitrile (AN) with trimethylaluminum (AlMe₃) was successfully isolated as a white needlelike crystal with a melting point of 42.5°C. In this article the preparation of the complex is described in detail. Cryoscopic and spectral investigations indicated that the complex is formed by an equimolar ratio of AN and AlMe₃. From the measurement of the x-ray diffraction photograph of the crystal the repeat period was determined to be 9.47 ± 0.05 Å.