η%-Superconvergence of Finite Element Solutions and Error Estimators

This paper is a summary of our study on the superconvergence of the finite element solutions and error estimators. We will persent the analysis of %-superconvergence for finite element solutions of the Poisson equation in the interior of meshes of triangles with straight edges, as well as the analysis at the boundary. The %-superconvergence via local averaging will also be presented, and the error estimators are compared in the sense of %-superconvergence.     

Optical absorption and photoluminescence studies of Eu-doped phosphate and fluorophosphate glasses

Phosphate (P₂O₅+K₂O+BaO+Al₂O₃+Eu₂O₃) and fluorophosphate (P₂O₅+K₂O+BaO+BaF₂+Al₂O₃+Eu₂O₃) glasses with different Eu³⁺ ion concentrations have been prepared and characterized through optical absorption, photoluminescence and decay times. An intense red luminescence is observed from the ⁵D₀ emitting level of Eu³⁺ ions in these glasses. The relative luminescence intensity ratio of ⁵D₀→⁷F₂→⁵D₀→⁷F₁ transitions has been evaluated to estimate the local site symmetry around the Eu³⁺ ions. The emission spectra of these glasses show a complete removal of degeneracy for the ⁵D₀→⁷F₁ and ⁵D₀→⁷F₂ transitions. Second and fourth rank crystal-field (CF) parameters have been calculated together with the CF strength parameter by assuming the C_2v symmetry for the Eu³⁺ ions in both the phosphate and fluorophosphate glasses. Judd-Ofelt parameters have been evaluated from the luminescence intensity ratios of ⁵D₀→⁷F_J (J=2, 4 and 6) to ⁵D₀→⁷F₁ transitions. These parameters have been used to derive radiative properties such as transition probabilities, branching ratios, radiative lifetimes and peak stimulated emission cross-sections for the ⁵D₀→⁷F_J transitions. Decay curves of the ⁵D₀ level of Eu³⁺ ions in these two Eu³⁺:glass systems have been measured by monitoring the ⁵D₀→⁷F₂ transition (611 nm) at room temperature. The experimental lifetime of the ⁵D₀ level in the title glasses is found to be higher than Eu³⁺-doped niobium phosphate glasses. The analysis indicates that the lifetime of the ⁵D₀ level is found to be less sensitive to the Eu³⁺ ion concentration and addition of BaF₂ has no significant effect on the optical properties of Eu³⁺-doped phosphate glasses.     

The finite element method with Lagrangian multipliers

Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.This paper was supported by the Atomic Energy Commission under Contract No. AEC AT (40-1) 3443/4.     

Flavonoids from Sedum japonicum subsp. oryzifolium (Crassulaceae)

Twenty-two flavonoids were isolated from the leaves and stems of Sedum japonicum subsp. oryzifolium (Crassulaceae). Of these compounds, five flavonoids were reported in nature for the first time, and identified as herbacetin 3-O-xyloside-8-O-glucoside, herbacetin 3-O-glucoside-8-O-(2′′′-acetylxyloside), gossypetin 3-O-glucoside-8-O-arabinoside, gossypetin 3-O-glucoside-8-O-(2′′′-acetylxyloside) and hibiscetin 3-O-glucoside-8-O-arabinoside via UV, HR-MS, LC-MS, acid hydrolysis and NMR. Other seventeen known flavonoids were identified as herbacetin 3-O-glucoside-8-O-arabinoside, herbacetin 3-O-glucoside-8-O-xyloside, gossypetin 3-O-glucoside-8-O-xyloside, quercetin, quercetin 3-O-glucoside, quercetin 3-O-xylosyl-(1→2)-rhamnoside-7-O-rhamnoside, quercetin 3-O-rhamnoside-7-O-glucoside, kaempferol, kaempferol 3-O-glucoside, kaempferol 7-O-rhamnoside, kaempferol 3,7-di-O-rhamnoside, kaempferol 3-O-glucoside-7-O-rhamnoside, kaempferol 3-O-glucosyl-(1→2)-rhamnoside-7-O-rhamnoside, kaempferol 3-O-xylosyl-(1→2)-rhamnoside, kaempferol 3-O-xylosyl-(1→2)-rhamnoside-7-O-rhamnoside, myricetin 3-O-glucoside and cyanidin 3-O-glucoside. Some flavonol 3,8-di-O-glycosides were found in Sedum japonicum subsp. oryzifolium as major flavonoids in this survey. They were presumed to be the diagnostic flavonoids in the species. Flavonoids were reported from S. japonicum for the first time.     

Synthesis of potential impurities of cloxacillin sodium drug substance

The present work describes the synthesis and characterization of six related compounds of cloxacillin sodium ( 1 ) viz penicilloic acid of cloxacillin (2) , (3-(2-chlorophenyl)-5-methylisoxazole-4-carbonyl) glycine (Glycine analogue of cloxacillin) (3), CMICAA adduct of cloxacillin (4) , (4S)-2-(carboxy(3-(2-chlorophenyl)-5-methylisoxazole-4-carboxamido) methyl)-3-(2-ethylhexanoyl)-5,5-dimethylthiazolidine-4-carboxylic acid (N-2-ethylhexanoyl penicilloic acid of cloxacillin) ( 5 ), N-Acetylated penicilloic acid of cloxacillin ( 6 ), and Cloxacillin Penicillamide (7) . These related compounds are very essential in the process development of cloxacillin sodium and are used as reference standards to determine the quality of the drug substance.     

Disperse dyes derived from 2-amino-5-mercapto-1,3,4-thiadiazole

Some novel heterocyclic monoazo dyes based on 2-amino-5-mercapto-1,3,4-thiadizole have been synthesized by coupling with various N-phenylacrylamide derivatives. The dyeing performance of these dyes was assessed on polyester fabrics. IR and visible spectra of the dyes were examined. The percentage dye bath exhaustion, fixation, and various fastness properties of the dyes were also determined. These dyes were found to give brownish-orange to reddish-pink shades on dyeing with good depth, levelness, and brightness on fabric. The dyed fabric showed a good to excellent fastness to washing, rubbing, perspiration, and sublimation.     

Locking effects in the finite element approximation of elasticity problems

Summary We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

Growth,electrical and optical behaviour of nanocrystalline Ag2Cu2O3 films produced by RF magnetron sputtering

Thin films of Ag₂Cu₂O₃ were formed on glass substrates by RF magnetron sputtering technique under different oxygen partial pressures in the range 5 × 10^‐3 – 8 × 10^‐2 Pa using mosaic target of Ag₇₀Cu₃₀. The influence of oxygen partial pressure on the core level binding energies, crystallographic structure, and electrical and optical properties of the deposited films was studied. The atomic ratio of copper to silver in the films was 0.302. The oxygen content was in correlation with the oxygen partial pressure maintained during the growth of the films. The films formed at oxygen partial pressures < 2 × 10^‐2 Pa was mixed phase of Ag₂Cu₂O₃ and Ag. The films deposited at 2 × 10^‐2 Pa were single phase of Ag₂Cu₂O₃. The crystallite size of the films formed at 2 × 10^‐2 Pa was 12 nm, while those films annealed at 473 K was 16 nm. The nanocrystalline Ag₂Cu₂O₃ films formed at oxygen partial pressure of 2 × 10^‐2 Pa showed electrical resistivity of 8.2 Ωcm and optical band gap of 1.95 eV. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)