Convergence of a penalty-finite element approximation for an obstacle problem

Summary This study establishes an error estimate for a penalty-finite element approximation of the variational inequality obtained by a class of obstacle problems. By special identification of the penalty term, we first show that the penalty solution converges to the solution of a mixed formulation of the variational inequality. The rate of convergence of the penalization is where is the penalty parameter. To obtain the error of finite element approximation, we apply the results obtained by Brezzi, Hager and Raviart for the mixed finite element method to the variational inequality.     

Structural confirmation of oligosaccharides newly isolated from sugar beet molasses

ABSTRACT: BACKGROUND: Sugar beet molasses is a viscous by-product of the processing of sugar beets into sugar. The molasses is known to contain sucrose and raffinose, a typical trisaccharide, with a well-established structure. Although sugar beet molasses contains various other oligosaccharides as well, the structures of those oligosaccharides have not been examined in detail. The purpose of this study was isolation and structural confirmation of these other oligosaccharides found in sugar beet molasses. RESULTS: Four oligosaccharides were newly isolated from sugar beet molasses using high-performance liquid chromatography (HPLC) and carbon-Celite column chromatography. Structural confirmation of the saccharides was provided by methylation analysis, matrix-assisted laser desorption/ionaization time of flight mass spectrometry (MALDI-TOF-MS), and nuclear magnetic resonance (NMR) measurements. CONCLUSION: The following oligosaccharides were identified in sugar beet molasses: beta-D-galactopyranosyl-(1- > 6)-beta-D-fructofuranosyl-(2 <-> 1)-alpha-D-glucopyranoside (named beta-planteose), alpha-D-galactopyranosyl-(1- > 1)-beta-D-fructofuranosyl-(2 <-> 1)-alpha-D-glucopyranoside (named1-planteose), alpha-D-glucopyranosyl-(1- > 6)-alpha-D-glucopyranosyl-(1 <-> 2)-beta-D-fructofuranoside (theanderose), and beta-D-glucopyranosyl-(1- > 3)-alpha-D-glucopyranosyl-(1 <-> 2)-beta-D-fructofuranoside (laminaribiofructose). 1-planteose and laminaribiofructose were isolated from natural sources for the first time.     

Preliminary communication:Novel method for uniform orientation of liquid crystal molecules by a polyimide surface exposed to a water flow

A novel technique for surface-induced orientation of liquid crystal (LC) molecules is proposed, using a polyimide surface exposed to a unidirectional water flow. The LC molecules director was unidirectionally oriented along the water flow direction on the polyimide surface. The orientational state of the LC director was strongly dependent upon whether the water flow exposure was carried out before or after thermal curing for imidization, and also upon the temperature of water flow.     

Isolation of Biphenyl and Polychlorinated Biphenyl-Degrading Bacteria and Their Degradation Pathway

Four strains of biphenyl-degrading bacteria were isolated from a sewage and identified from the Rhodococcus genus (SK-1, SK-3, and SK-4) and Aquamicrobium genus (SK-2) by 16S rRNA sequence. Among these strains, strain SK-2 was most suitable for biphenyl degradation. When 0.65, 1.3, 2.6, or 3.9 mM of biphenyl was used, the biphenyl was completely degraded within 24 and 96 h of culture, respectively. However, in the case of 6.5 and 9.75 mM of biphenyl, the biphenyl degradation yields were about 80 % and 46.7 % after 120 h of culture, respectively. The isolated strains could degrade a broad spectrum of aromatic compounds including high-chlorinated polychlorinated biphenyl (PCB) congeners in the presence of biphenyl. In addition, strain SK-2 could utilize PCB congeners containing one to six chlorine substituents such as 2,2′,4,4′,5,5′-hexachlorobiphenyl. The PCB utilization rate by the strain SK-2 was increased compared to that of other PCB congener-utilizing bacteria. The four isolates metabolized 4-chlorobiphenyl to 4-chlorobenzoic acid and 2-hydroxy-6-oxo-6-(4′-chlorophenyl)-hexa-2,4-dienoic acid. These results suggest the isolated strains might be good candidates for the bioremediation of PCB-contaminated soil, especially high-saline soils.     

Ultraviolet Photoelectron Spectra of Potassium Dosed Higher Fullerenes

Abstract

Ultraviolet photoelectron spectra of potassium dosed higher fullerenes are measured with a synchrotron radiation light source. Potassium dosing to higher fullerenes brings a new structure between the spectral onset of pristine fullerenes and the Fermi level. As the spectral edge of the new structure does not cross the Fermi level, potassium dosed higher fullerenes are not metallic but semiconductive. When the potassium is excessively dosed to the fullerenes, the lower binding energy structures above 5 eV become faint. In contrast to this phenomenon, four distinct structures appear between 5 and 14 eV.     

One-Pot Synthesis of Enantioenriched β-Amino Secondary Amides via an Enantioselective [4+2] Cycloaddition Reaction of Vinyl Azides with N-Acyl Imines Catalyzed by a Chiral Brønsted Acid

A catalytic enantioselective synthesis of β-amino secondary amides was achieved using vinyl azides as the enamine-type nucleophile and chiral N-Tf phosphoramide as the chiral Brønsted acid catalyst through a five-step sequential transformation in one pot. The established sequential transformation involves an enantioselective [4+2] cycloaddition reaction of vinyl azides with N-acyl imines as the key stereo-determining step that is efficiently accelerated by a chiral N-Tf phosphoramide catalyst in a highly enantioselective manner in most cases. Further generation of the iminodiazonium ion intermediate through ring opening of the cycloaddition product and subsequent skeletal rearrangement involving Schmidt-type 1,2-aryl group migration followed by recyclization of the resulting nitrilium ion were also initiated by the same acid catalyst. Final acid hydrolysis of the recyclized products in the same pot gave rise to enantioenriched β-amino amides through C−C bond formation at the α-position of the secondary amides.     

Supramolecular system composed of B12 model complex and organic photosensitizer: impact of the corrin framework of B12 on the visible-light-driven dechlorination without the use of noble metals

The visible-light-driven dechlorination system without the use of a noble metal has been developed. We screened the combination of cobalt catalysts having square-planar monoanionic ligands (hydrophobic B₁₂ model complex 1/imine-oxime type complex 2) and typical red dyes (Rose Bengal 3/Rhodamine B 4/Nile Red 5) for the construction of a dehalogenation system via a noble-metal-free and visible-light-driven process. The combination of the hydrophobic B₁₂ model complex 1 and Rose Bengal 3 exhibited the highest catalytic activity to 1,1-bis(4-chlorophenyl)-2,2,2-trichloroethane (DDT) to form the monodechlorinated compound, 1,1-bis(4-chlorophenyl)-2,2-dichloroethane, as the major product. The prolonged photocatalysis of DDT by the B₁₂–Rose Bengal system afforded the tri-dechlorinated compound, trans-4,4′-dichlorostilbene, as the major product. Furthermore, we investigated the mechanism of the dehalogenation cycle using various methods such as UV–vis spectroscopy and laser flash photolysis. Finally, we clarified the advantage of using the hydrophobic B₁₂ model complex 1 as an electron acceptor as well as a cobalt catalyst in the organic dye-involved photocatalysis.