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     

Triphase catalysis. I. Kinetics and mechanism of alkylation of phenylacetonitrile with alkyl halides catalyzed by aqueous naoh and polymer-supported benzyltriethylammonium chloride

The alkylation and cycloalkylation of phenylacetonitrile (PAN) with excess of 1-bromobutane and 1,4-dibromobutane respectively catalyzed by aqueous NaOH and insoluble polystyrene-bound benzyltriethylammonium chloride were studied and the rates depend upon several experimental parameters. The rate of cycloalkylation of PAN is five times faster than the alkylation and the former proceeds even in the absence of the solid catalyst. Both alkylation and cycloalkylation gave higher rates in reverse addition method than in direct addition. Deprotonation of PAN by hydroxide ion takes place without participation of the polymeric catalyst. The electrostatic force between the positive charge on the nitrogen atom of catalyst and carbanion is responsible for alkylation of active nitrile with polystyrene-bound phase-transfer catalyst. The rates of both the reactions increase with increased stirring speed, ring substitution, hydroxide ion concentration and catalyst amount and decrease with increased particle size and the degree of cross-linking of the polymer. Apparent activation energies for the reactions were calculated. The kinetic results are discussed in terms of mass transfer and a combination of intraparticle diffusion and intrinsic reactivity limitations of the rates.     

Cationic carbohydroxylation of alkenes and alkynes using the cation pool method

The reactions of an N-acyliminium ion pool with alkenes and alkynes gave gamma-amino alcohols and beta-amino carbonyl compounds, respectively, after treatment with H(2)O/Et(3)N. The present reaction serves as an efficient method for cationic carbohydroxylation of alkenes and alkynes. When vinyltrimethylsilane was used as an alkene, the reaction was highly diastereoselective and served as an access to an enantiomerically pure alpha-silyl-gamma-amino alcohol. [reaction: see text]     

A Highly stereospecific and efficient synthesis of homopentafluoro- phenylalanine

A short and efficient synthesis of homopentafluorophenylalanine (6) from oxazolidine aldehyde 1 in 57% overall yield and in > 98% ee is described. The enantiomeric excess of the product was determined by 19F NMR analysis of the coupling product derived from 5 and L-Ser(O-t-Bu)-OCH3, by comparison to a dipeptide obtained from racemic 5.     

Facile Synthesis of Pyrazolo[3,4‐d]pyrimidines and Pyrimido[4,5‐d]pyrimidin‐4‐one Derivatives

Pyrazolopyrimidine and pyrimidopyrimidine derivatives have shown a wide range of biological activities such as acting as A₁ adenosine receptors, kinase insert domain receptor (KDR), Rous sarcoma oncogene (Src), epidermal growth factor receptor (EGFR), antiproliferative, dihydrofolate reductase (DHFR), antimicrobial, antifungal, and lipid peroxidation. Because of this wide range of activities, we have synthesized pyrazolo[3,4‐d]pyrimidines and pyrimido[4,5‐d]pyrimidin‐4‐one derivatives.     

Thermoelectric properties of n-type Bi2Te3 alloys produced by a combined process of magnetic pulsed compaction (MPC) and spark plasma sintering (SPS)

In this study, n-type 95 %Bi₂Te₃-5 %Bi₂Se₃ thermoelectric materials have been produced by a combined process of gas atomization with subsequent magnetic pulsed compaction and spark plasma sintering, and then we investigated the behavior of transport properties with sintering temperature. The microstructural observation was performed by optical microscopy and scanning electron microscopy. The crystal structures were analyzed by X-ray diffractometer. The mechanical properties were calculated by measuring the density and micro-Vickers hardness of the samples. It was found that with increasing sintering temperature the gaps between powder particles decreases and the grain sizes were coarsened. The mechanical properties shows higher values along the parallel direction compared to the perpendicular direction to the pressing. The transport properties of the thermoelectric material were investigated with variation of the sintering temperatures. The maximum power factor 1.7 × 10^?3 Wm^?1 K^?2 was measured at the sintering temperature of 450 °C.     

Development and validation of LC‐MS/MS method for the estimation of β‐hydroxy‐β‐methylbutyrate in rat plasma and its application to pharmacokinetic studies

A simple, sensitive and specific high‐performance liquid chromatography mass spectrometry (LC‐MS/MS) method was developed and validated for the quantification of β‐hydroxy‐β‐methyl butyrate (HMB) in small volumes of rat plasma using warfarin as an internal standard (IS). The API‐4000 LC‐MS/MS was operated under the multiple reaction‐monitoring mode using the electrospray ionization technique. A simple liquid–liquid extraction process was used to extract HMB and IS from rat plasma. The total run time was 3 min and the elution of HMB and IS occurred at 1.48 and 1.75 min respectively; this was achieved with a mobile phase consisting of 0.1% formic acid in a water–acetonitrile mixture (15:85, v/v) at a flow rate of 1.0 mL/min on a Agilent Eclipse XDB C₈ (150 × 4.6, 5 µm) column. The developed method was validated in rat plasma with a lower limit of quantitation of 30.0 ng/mL for HMB. A linear response function was established for the range of concentrations 30–4600 ng/mL (r > 0.998) for HMB. The intra‐ and inter‐day precision values for HMB were acceptable as per Food and Drug Administration guidelines. HMB was stable in the battery of stability studies, viz. bench‐top, autosampler freeze–thaw cycles and long‐term stability for 30 days in plasma. The developed assay method was applied to a bioavailability study in rats. Copyright © 2012 John Wiley & Sons, Ltd.