Quasi-Cyclic Codes from a Finite Affine Plane

Finite geometry codes are defined as the null spaces of the incidence matrices of points and flats in finite geometries. In this paper, we investigate the incidence matrix of points other than the origin and lines not passing through the origin in the affine plane AG(2,2^s), and we present two classes of quasi-cyclic codes derived from submatrices of the point-line incidence matrix. We also investigate the 2-ranks of those submatrices. AMS Classification: 94B25, 94B05     

Williamson Ether Synthesis with Phenols at a Tertiary Stereogenic Carbon: Formal Enantioselective Phenoxylation of β‐Keto Esters

The enantioselective formation of α‐aryloxy‐β‐keto esters is described for the first time. Lewis acid catalyzed enantioselective chlorination of β‐keto esters and subsequent S_N2 reactions with phenols yielded α‐aryloxy‐β‐keto esters with up to 96 % ee. Favorskii rearrangement of α‐chloro‐β‐keto esters was also found to give 1,2‐diesters with slightly reduced enantiopurity.     

Thermodynamic interactions in rubbery polymer/gas systems

The Flory–Huggins interaction parameters χ for 23 gases (He, Ne, Ar, Kr, Xe, H₂, N₂, O₂, N₂O, CO₂, CH₄, C₂H₄, C₂H₆, C₃H₆, C₃H₈, 1,3-C₄H₆, four C₄H₈'s, n-C₄H₁₀, iso-C₄H₁₀, and n-C₅H₁₂) in five rubbery polymers (1,2-polybutadiene (PB), poly(ethylene-co-vinyl acetate)) (EVAc), polyethylene (PE), polypropylene (PP), and poly(dimethyl siloxane) (PDMS) were determined from either literature data on Henry's law coefficient and partial molar volume or those on sorptive dilation for each polymer/gas system. Values of χ for the gases increased in the order of PDMS < PP ≡ PB < EVAc ≡ PE. Among the gases except He and H₂ whose χ values are not reliable, Ne and Xe have respectively the highest and the lowest values of χ for the polyolefins. The χ values of the hydrocarbons were compared together with previously reported χ values of n-alkanes C₃-C₁₀. The dependencies of χ upon concentration and temperature were discussed on the basis of the literature data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1049–1053, 1997     

Solubilization of oligosaccharides into chloroform by their incorporation into polystyrene as pendant groups

Solubilization of hydrophilic saccharide chains into organic solvents has been attempted by incorporating saccharide-substituted styrene unit into polystyrene main chain. Lactose-, maltopentaose, and amylose-substituted styrene monomers were copolymerized with styrene. Resulting chloroform-soluble copolymers were characterized, and structural formation was investigated. Copolymers of lactose-substituted styrene and maltopentaose-substituted styrene with styrene were dissolved into chloroform. The chloroform-soluble polymers contained about 12 disaccharide lactose chains or 1.7 maltopentaose chains as the pendant groups in one polystyrene molecule. Chloroform-insoluble methyl orange was dissolved into chloroform with the help of chloroform-soluble polystyrene having some saccharide chains. On the other hand, when an amylose-substituted styrene unit was inserted in a polystyrene chain, the resulting polymer became insoluble into chloroform. Amylose polysaccharide of DP_n = ∼24 was not dissolved into chloroform by this method.     

A Class of Robust Principal Component Vectors

This paper is concerned with a study of robust estimation in principal component analysis. A class of robust estimators which are characterized as eigenvectors of weighted sample covariance matrices is proposed, where the weight functions recursively depend on the eigenvectors themselves. Also, a feasible algorithm based on iterative reweighting of the covariance matrices is suggested for obtaining these estimators in practice. Statistical properties of the proposed estimators are investigated in terms of sensitivity to outliers and relative efficiency via their influence functions, which are derived with the help of Stein's lemma. We give a simple condition on the weight functions which ensures robustness of the estimators. The class includes, as a typical example, a method by the self-organizing rule in the neural computation. A numerical experiment is conducted to confirm a rapid convergence of the suggested algorithm.     

Sorption and partial molar volumes of gases in poly(ethylene-co-vinyl acetate)

Sorption and dilation properties of polymer-gas systems involving poly(ethylene-co-vinyl acetate) and N₂, CH₄, or CO₂, have been investigated at pressures up to 50 atm at temperatures of 10–40°C. Sorption isotherms for low-solubility gases (i.e., CH₄ and N₂) can be described by Henry's law, and those for high-solubility gas (i.e., CO₂) by Flory-Huggins dissolution equation. Dilation isotherms are similar in contour to the corresponding sorption isotherms. From the obtained sorption and dilation data, partial molar volumes of the gases in the polymer were determined as a function of temperature. Thermal expansivity of dissolved CO₂ molecules was estimated at ca. 2.4 × 10^?3°C^?1 from the temperature dependence of partial molar volume. The expansivity is smaller than that of liquid CO₂ and larger than those of the polymer and organic liquids. © 1994 John Wiley & Sons, Inc.     

A resolvent expansion theorem for the Fourier transform of the retarded Green function and its application to the absorption bandshape of chromophore aggregates

A resolvent expansion theorem is developed for the Fourier transform of the retarded Green function. The resolvent expansion theorem coupled with a decorrelation approximation for a statistical average over the vibrational sublevels of the electronic ground state is applied to a theoretical formulation of the averaged Green function of chromophore aggregates. Consequently, thermal and static effects upon the aggregate's absorption bandshape are incorporated in terms of the correction shift of the individual chromophore's bandshapes. The utility of the theoretical formulation is shown by an illustrative calculation of the absorption bandshape of a model dimer.