Lower bounds for the distributions of certain multivariate test statistics

A lower (upper) bound is given for the distribution of each d_j, j = k + 1, …, p (j = 1, …, s), the jth latent root of AB^?1, where A and B are independent noncentral and central Wishart matrices having $\text{W}{}_{\mathrm{p}}\text{(q, Σ; Ω)}$ with rank $\text{(Ω) ≤ k = p ? s}$ and W_p(n, Σ), respectively. Similar bound are also given for the distributions of noncentral means and canonical correlations. The results are applied to obtain lower bounds for the null distributions of some multivariate test statistics in Tintner's model, MANOVA and canonical analysis.     

Living ethylene/norbornene copolymerisation catalyzed by titanium complexes having two pyrrolide-imine chelate ligands

Ethylene/norbornene copolymerisation behaviour of titanium complexes with two pyrrolide-imine chelate ligands is described.     

Transformations with Improved Chi-Squared Approximations

Suppose that a nonnegative statistic T is asymptotically distributed as a chi-squared distribution with f degrees of freedom, χ²_f, as a positive number n tends to infinity. Bartlett correction T was originally proposed so that its mean is coincident with the one of χ²_f up to the order O(n⁻¹). For log-likelihood ratio statistics, many authors have shown that the Bartlett corrections are asymptotically distributed as χ²_f up to O(n⁻¹), or with errors of terms of O(n⁻²). Bartlett-type corrections are an extension of Bartlett corrections to other statistics than log-likelihood ratio statistics. These corrections have been constructed by using their asymptotic expansions up to O(n⁻¹). The purpose of the present paper is to propose some monotone transformations so that the first two moments of transformed statistics are coincident with the ones of χ²_f up to O(n⁻¹). It may be noted that the proposed transformations can be applied to a wide class of statistics whether their asymptotic expansions are available or not. A numerical study of some test statistics that are not a log-likelihood ratio statistic is discribed. It is shown that the proposed transformations of these statistics give a larger improvement to the chi-squared approximation than do the Bartlett corrections. Further, it is seen that the proposed approximations are comparable with the approximation based on an Edgeworth expansion.     

Clarithromycin form I determined by synchrotron X‐ray powder diffraction

The structure of the metastable form I polymorph of the macrolide antibiotic clarithromycin, C₃₈H₆₉NO₁₃, was determined by a powder diffraction method using synchrotron radiation. The space group of form I is P2₁2₁2. The initial model was determined by a molecular replacement method using the structure of clarithromycin form 0 as a search model, and the final structure was obtained through Rietveld refinements. In the form I crystal structure, the clarithromycin molecules are aligned parallel along the a axis in a head‐to‐tail manner with intermolecular hydrogen bonds between the hydroxy O atoms. The dimethylamine groups of the clarithromycin molecule interdigitate between neighbouring head‐to‐tail clarithromycin alignments. The novel crystal packing found in form I provides a mechanism that describes the transformation of form 0 to form I.     

Metal-binding ability of human prion protein fragment peptides analyzed by column switch HPLC

The structural conversion of the prion protein (PrP) from the normal cellular isoform (PrP(C)) to the posttranslationally modified form (PrP(Sc)) is thought to relate to Cu2? binding to histidine (H) residues. Traditionally, the binding of metals to PrP has been investigated by monitoring the conformational conversion using circular dichroism (CD). In this study, the metal-binding ability of 21 synthetic peptides representing regions of human PrP(C) was investigated by column switch high-performance liquid chromatography (CS-HPLC). The CS-HPLC system is composed of a metal chelate affinity column and an octadecylsilica (ODS) reversed-phase column that together enable the identification of metal-binding regardless of conformational conversion. Synthetic peptides were designed with respect to the position of H residues as well as the secondary structure of human PrP (hPrP). The ability of the octapeptide (PHGGGWGQ)-repeating region (OP-repeat) to bind metals was analyzed by CS-HPLC and supported by CD analysis, and indicated that CS-HPLC is a reliable and useful method for measuring peptide metal-binding. Peptides from the middle region of hPrP showed a high affinity for Cu2?, but binding to Zn2?, Ni2?, and Co2? was dependent on peptide length. C-Terminal peptides had a lower affinity for Cu2?, Zn2?, Ni2?, and Co2? than OP-repeat region peptides. Interestingly, hPrP193-230, which contained no H residues, also bound to Cu2?, Zn2?, Ni2?, and Co2?, indicating that this region is a novel metal-binding site in the C-terminal region of PrP(C). The CS-HPLC method described in this study is useful and convenient for assessing metal-binding affinity and characterizing metal-binding peptides or proteins.     

Stereoselective Isomerization of Unsymmetrical Diallyl Ethers to Allyl (E)-Vinyl Ethers by a Cationic Iridium Catalyst

The stereoselective isomerization of unsymmetrical diallyl ethers to allyl (E)-vinyl ethers was carried out in the presence of a cationic iridium(I) catalyst. The catalyst prepared in situ by treating [Ir(cod)(PPh₂Me)₂]PF₆ with hydrogen was found to be an excellent catalyst to selectively isomerize the less substituted allyl group to an (E)-vinyl ether.