regularity of averaging operators with higher fold singularities

In this paper, we give a sharp regularity result of averaging operators along curves in the plane with two-sided fold singularities.

     

Solution of the quadratically hyponormal completion problem

For , let be a collection of () positive weights. The Quadratically Hyponormal Completion Problem seeks necessary and sufficient conditions on to guarantee the existence of a quadratically hyponormal unilateral weighted shift with as the initial segment of weights. We prove that admits a quadratically hyponormal completion if and only if the self-adjoint matrix

is positive and invertible, where , , , , , and, for notational convenience, . As a particular case, this result shows that a collection of four positive numbers always admits a quadratically hyponormal completion. This provides a new qualitative criterion to distinguish quadratic hyponormality from 2-hyponormality.

     

A novel water-soluble and self-doped conducting polyaniline graft copolymer

A water-soluble and self-doped conducting polyaniline graft copolymer, poly(styrenesulfonic acid-g-aniline) (PSSA-g-PANI), was first synthesized and its electrical properties were investigated.     

Weyl's theorem for operator matrices

Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3.     

Glycine/Glycolic acid based copolymers

Glycine/glycolic acid based biodegradable copolymers have been prepared by ring-opening homopolymerization of morpholine-2,5-dione, and ring-opening copolymerization of morpholine-2,5-dione and glycolide. The homopolymerization of morpholine-2,5-dione was carried out in the melt at 200°C for 3 min using stannous octoate as an initiator, and continued at lower reaction temperatures (100–160°C) for 2–48 h. The highest yields (60%) and intrinsic viscosities ([η] = 0.50 dL/g; DMSO, 25°C) were obtained after 3 min reaction at 200°C and 17 h at 130°C using a molar ratio of monomer and initiator of 1000. The polymer prepared by homopolymerization of morpholine-2,5-dione was composed of alternating glycine and glycolic acid residues, and had a glass transition temperature of 67°C and a melting temperature of 199°C. Random copolymers of glycine and glycolic acid were synthesized by copolymerization of morpholine-2,5-dione and glycolide in the melt at 200°C, followed by 17 h reaction at 130°C using stannous octoate as an initiator. The morphology of the copolymers varied from semi-crystalline to amorphous, depending on the mole fraction of glycolic acid residues incorporated. © 1994 John Wiley & Sons, Inc.     

Thiocyanation of indoles

Treatment of indole, 2-phenylindole, 2-methylindole, and ethyl indole-2-carboxylate with thiocyanogen in acetic acid at 0° afforded the corresponding 3-thiocyanatoindoles in quantitative yields, whereas similar treatment of 3-methyl-2-phenylindoles and 2,3-diphenylindoles gave the corresponding 6-thiocyanatoindoles in high yields.     

Di-2-pyridyl carbonate: a new efficient coupling agent for the direct esterification of carboxylic acids

Reaction of carboxylic acids with equimolar amounts of di-2-pyridyl carbonate and alcohols or thiols in the presence of 4-dimethylamino pyridine as a catalyst in methylene chloride at room temperature affords the corresponding esters in high yields under mild conditions.     

Separation of racemic 2,4-dinitrophenyl amino acids on 9-O-(phenyloxycarbonyl)quinine-bonded carbon-clad zirconia in reversed-phase liquid chromatography

Zirconia is known to be one of the best materials for the chromatographic support due to its excellent chemical, thermal, and mechanical stability. In this work, we report preparation and use of 9-O-(phenyloxycarbonyl)quinine-bonded carbon-clad zirconia (QNCZ) as a chiral stationary phase (CSP) for separation of N-(2,4-dinitrophenyl) (DNP)-amino acids (AAs) enantiomers in reversed-phase liquid chromatography. Retention and enantioselectivity of the QNCZ CSP were compared with those of quinine 3-triethoxysilylpropylcarbamate-coated zirconia (QNZ) and quinine 3-triethoxysilylpropylcarbamate-bonded silica (QNS). The QNCZ CSP showed in general the better enantioselectivity for most of the amino acids studied.