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.     

Diversified synthetic approaches to the carbapenem antibiotics based on symmetrization-asymmetrization concept

cis-Fused bicyclic β-lactam compound 9, a key intermediate to cis-substituted carbapenem antibiotics, has been synthesized in optically pure form based on symmetrization-asymmetrization concept.     

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.     

Structural change in a series of protonated layered perovskite compounds, HLnTiO4 (Ln=La, Nd and Y)

A deuterated n=1 Ruddlesden-Popper compound, DLnTiO₄ (HLnTiO₄, Ln=La, Nd and Y), was prepared by an ion-exchange reaction of Na⁺ ions in NaLnTiO₄ with D⁺ ions, and its structure was analyzed by Rietveld method using powder neutron diffraction data. The structure analyses showed that DLaTiO₄ and DNdTiO₄ crystallized in the space group P4/nmm with a=3.7232(1) and c=12.3088(1) Å, and a=3.7039(1) and c=12.0883(1) Å, respectively. On the other hand, DYTiO₄ crystallized in the space group P2₁/c with a=11.460(1), b=5.2920(4), c=5.3628(5) Å and β=90.441(9)°. The loaded protons were found to statistically occupy the sites around an apical oxygen of TiO₆ octahedron in the interlayer of these compounds, rather than Na atom sites in NaLnTiO₄.     

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.     

Ordered mesoporous silica with large cage-like pores: structural identification and pore connectivity design by controlling the synthesis temperature and time

FDU-1 silicas with large cage-like pores (diameter about 10 nm) were synthesized under acidic conditions from tetraethyl orthosilicate in the presence of a poly(ethylene oxide)-poly(butylene oxide)-poly(ethylene oxide) triblock copolymer template B50-6600 (EO(39)BO(47)EO(39)). High-resolution transmission electron microscopy and small-angle X-ray scattering provided strong evidence that FDU-1 silica synthesized under typical conditions is a face-centered cubic Fm3m structure with 3-dimensional hexagonal intergrowth and is not a body-centered cubic Im3m structure, as originally reported. Samples synthesized in a wide range of conditions (initial temperatures from 298 to 353 K; hydrothermal treatment at 333-393 K) exhibited similar XRD patterns and their nitrogen adsorption isotherms indicated a good-quality cage-like pore structure. The examination of low-pressure nitrogen adsorption isotherms for FDU-1 samples, whose pore entrance diameters were evaluated using an independent method, allowed us to conclude that low-pressure adsorption was appreciably stronger for samples with smaller pore entrance sizes. This prompted us to examine low-pressure adsorption isotherms for a wide range of samples and led us to a conclusion that the FDU-1 pore entrance size can be systematically enlarged from about 1.3 nm (perhaps even lower) to at least 2.4 nm without an appreciable loss of uniformity by increasing the temperature of the hydrothermal treatment or the initial synthesis. Further enlargement of pore entrance size was achieved for sufficiently long hydrothermal treatment times at temperatures of 373 K or higher, as seen from the shape of nitrogen desorption isotherms. This allowed us to obtain samples with uniform pore sizes, high adsorption capacity, and with pore entrances enlarged so much that their size was similar to the size of the pore itself, resulting in a highly open porous structure. However, in the latter case, there was evidence that the pore entrance size distribution was quite broad.     

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.     

Ammonothermal Synthesis,X-Ray and Time-of-Flight Neutron Crystal-Structure Determination,and Vibrational Properties of Barium Guanidinate,Ba(CN3H4)2

We report the crystal structure of Ba(CN₃H₄)₂ as synthesized from liquid ammonia. Structure solution based on X-ray diffraction data suffers from a severe pseudo-tetragonal problem due to extreme scattering contrast, so the true monoclinic symmetry is detectable only from neutron powder diffraction patterns, and structure solution and refinement was greatly aided by density-functional theory. The symmetry lowering is due to slight deviations of the guanidinate anion from the mirror plane in space group P b2, a necessity of hydrogen bonding. At 300 K, barium guanidinate crystallizes in P2₁/c with a=6.26439(2) Å, b=16.58527(5) Å, c=6.25960(2) Å, and a monoclinic angle of β=90.000(1)°. To improve the data-to-parameter ratio, anisotropic displacement parameters from first-principles theory were incorporated in the neutron refinement. Given the correct structural model, the positional parameters of the heavy atoms were also refinable from X-ray diffraction of a twinned crystal. The two independent guanidinate anions adopt the all-trans- and the anti-shape. The Ba cation is coordinated by eight imino nitrogens in a square antiprism with Ba−N contacts between 2.81 and 3.04 Å. The IR and Raman spectra of barium guanidinate were compared with DFT-calculated phonon spectra to identify the vibrational modes.     

The Structure of the Polycyclic Nonadecapeptide Ro 09-0198

The conventional determination of the amino-acid sequence of the peptide antibiotic Ro 09-0198 was prevented by four cyclizations via side chains. The joint application of NMR spectroscopy at highest field and automated Edman degradation yielded a complete determination of the connectivity pattern. The three-dimensional structure derived from NOE data exhibits an interesting separation of amino acids with hydrophilic and hydrophobic side chains.