Hierarchical subspace models for contingency tables

For the statistical analysis of multiway contingency tables, we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom than the usual hierarchical model, while preserving the localization property of the inference in the hierarchical model. This approach also enables us to evaluate the localization property of a given log-affine model. We discuss estimation and exact tests of the proposed model and illustrate the advantage of the proposed modeling with some data sets.     

Reaction and characterization of thioamide dianions derived from N-benzyl thioamides

Thioamide dianions were generated by the highly efficient reaction of N-benzyl thioamides with 2 equiv of BuLi. Alkylation, allylation, and silylation took place selectively at the carbon atom adjacent to the nitrogen atom of the thioamide dianions. Oxiranes and an aldehyde were also used as electrophiles in the reaction of thioamide dianions to form N-thioacyl 1,3- or 1,2-amino alcohols. The insertion reaction of elemental sulfur to a thioamide dianion and subsequent ethylation afforded a N-thioacyl hemithioaminal. NMR studies on the thioamide mono- and dianions derived from N-benzyl 2-methoxythiobenzamide showed a linear relationship between the chemical shifts of all carbon atoms of thioamide mono- and dianions. The results also suggested that the negative charge at the benzylic carbon atom of the dianion is not fully delocalized. The charge distribution patterns of the dianion are consistent with those of pi polarization.     

X-ray Structure of a 1:2 Complex of Hexakis (3-O-acetyl-2,6-di-O-methyl)-α-cyclodextrin with Butylacetate

Abstract

Crystal structure of a 1:2 complex of hexakis(3-O-acetyl-2,6-di-O-methyl)-α-cyclodextrin (ADMACD) with butylacetate was determined by the X-ray method. The space group of the crystal is P2₁2₁2₁ with Z = 4 and D _x = 1.293 g cm^?3, and the cell dimensions are a = 11.087(2), b = 23.543(3), and c = 31.739(6) Å. The structure was solved by the direct method and refined to the R-value of 0.123 for all the 4993 observed reflections with 1<0. The ADMACD molecule is in a round shape with the pseudo hexagonal symmetry. Methyl and acetyl groups point towards the outside of the molecule. Because of the acetyl groups attached to O3 and methyl groups attached to O6, the intramolecular cavity is ca. 3 Å deeper than the cavity of native α-CD. One butylacetate molecule is coaxially accommodated with its acetyl group at the O6 side in the host cavity while the other guest molecule is located in an intermolecular space between host molecules which are stacked to form a head-to-tail channel-type packing structure along the a axis.     

The design and characteristic features of a new time-of-flight mass spectrometer with a spiral ion trajectory

A new time-of-flight (TOF) mass spectrometer with a corkscrew ion trajectory was designed and constructed. The spiral trajectory was realized by using four toroidal electrostatic sectors. Each had fifteen-stories made of sixteen Matsuda plates piled up inside a cylindrical electrostatic sector. The ions passed the four toroidal electrostatic sectors sequentially and revolved along a figure-eight-shaped orbit on a certain projection plane. During the multiple revolutions, each ion trajectory was shifted by 50 mm per cycle on a direction perpendicular to the projection plane, thus generating a spiral trajectory. The flight path length of one cycle was 1.308 m so that the maximum flight path length became approximately 20 m. The mass resolution, mass accuracy, and ion transmission were tested by utilizing an orthogonally coupled electron ionization source. A mass resolution of 35,000 (FWHM) for m/z greater than 300 was achieved. Even in a lower mass region, mass resolutions of more than 20,000 (FWHM) were confirmed with a doublet of (12)C(5)(1)H(5)(14)N(+) and (13)C(12)C(5)(1)H(6)(+). The mass accuracy was also improved such that it was better than 1 ppm with only one internal standard peak. An ion transmission of approximately of 100% was observed for 15 cycles.     

Variation in the Isospecific Active Sites of Internal Donor‐Free MgCl2‐Supported Ziegler Catalysts: Effect of External Electron Donors

The stopped‐flow polymerization of propylene was carried out using an internal donor‐free MgCl₂‐supported Ziegler catalyst in the absence or presence of external electron donors. The variation in the isospecific active sites was investigated based on the isotacticity distribution of the poly(propylene) analyzed by the TREF method. Highly isospecific active sites derived from the highest isotactic fraction (elution temperature by TREF: >112 °C) exist in the electron donor‐free catalyst system. The addition of external electron donors converted parts of the aspecific into isospecific active sites, but showed no effects on the highest isospecific active sites. The external electron donor sterically affects a coordination vacancy of each aspecific titanium species and, consequently, transfers it into an isospecific active site of high, but not highest isospecificity.     

Kinetic evaluation of various isospecific active sites on MgCl2-supported Ziegler catalysts

The formation, variation and conversion of isospecific active sites were investigated, based on the isotacticity distribution of the polypropenes analyzed by the temperature rising elution fractionation (TREF) method. Stopped-flow polymerization of propene was carried out with a MgCl₂-supported Ziegler catalyst in the absence or presence of an internal or external electron donor so that the effects and roles of the electron donors could be clarified. The results showed that various kinds of active sites with different isospecificities, including the highest isospecific active sites responsible for producing the highest isotactic fraction (elution temperature: > 112°C) existed, even in the electron donor-free catalyst system. The isospecificity of the active sites in the donor-free catalyst might have originated from a surface monolayer multinuclear titanium species, namely an “island” of titanium species. The addition of the external electron donor converted a part of the aspecific and/or low isospecific active sites into the second highest isospecific active sites, but showed no effect on the formation of the highest isospecific active sites, whereas the addition of an internal donor played an important role in creating the highest isospecific active sites as well as suppressing the formation of the aspecific active sites.