Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of 1-methyl-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2]thiazin-4(3H)-one 2,2-dioxide

The reaction of methyl 2-bromo-6-(trifluoromethyl)-3-pyridinecarboxylate ( 1 ) with methanesulfonamide gave methyl 2-[(methylsulfonyl)amino]-6-(trifluoromethyl)-3-pyridine-carboxylate ( 2 ). Alkylation of compound 2 with methyl iodide followed by cyclization of the resulting methyl 2-[methyl(methylsulfonyl)amino]-6-(trifluoromethyl)-3-pyridinecarboxylate ( 3 ) yielded 1-methyl-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2]thiazin-4(3H)-one 2,2-dioxide ( 4 ). The reaction of compound 4 with α,2,4-trichlorotoluene, methyl bromopropionate, methyl iodide, 3-trifluoromethylphenyl isocyanate, phenyl isocyanate and 2,4-dichloro-5-(2-propynyloxy)phenyl isothiocyanate gave, respectively, 4-[(2,4-dichlorophenyl)methoxy]-1-methyl-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2]thiazine 2,2-dioxide ( 5 ), methyl 2-[[1-methyl-2,2-dioxido-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2]thiazin-4-yl]oxy]propanoate ( 6 ), 1,3,3-trimethyl-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2]thiazin-4(3H)-one 2,2-dioxide ( 7 ), 4-hydroxy-1-methyl-7-(trifluoromethyl)-N-[3-(trifluoromethyl)phenyl]-1H-pyrido[2,3-c][1,2]thiazine-3-carboxamide 2,2-dioxide ( 8 ), 4-hydroxy-1-methyl-7-(trifluoromethyl)-N-phenyl-1H-pyrido[2,3-c][1,2]thiazine-3-carboxamide 2,2-dioxide ( 9 ) and N-[2,4-dichloro-5-(2-propynyloxy)phenyl]-4-hydroxy-1-methyl-7-(trifluoromethyl)-1H-pyrido[2,3-c][1,2] thiazine-3-carboxamide 2,2-dioxide ( 10 ).     

On the preparation of substituted 4H- 1,3,4-thiadiazolo[2,3-c]-1,2,4-triazin-4-ones and 1,2,4-triazolo[3,4-b]-1,3,4-thiadiazoles

The reaction of benzoyl isothiocyanates and methoxycarbonyl isothiocyanate with 4-amino-4,5-dihydro-3-(methylthio)-1,2,4-triazin-5-ones in acetonitrile gave several substituted 4H-1,3,4-thiadiazolo[2,3-c]-1,2,4-triazin-4-ones VIa-h instead of the expected thioureas. In addition, benzoyl isothiocyanate reacted with 4-amino-3-(methylthio)-5-(trifluoromethyl)-4H-1,2,4-triazole to give the benzoyl thiourea IX and with 4-amino-3-mercapto-5-(trifluoromethyl)-4H-1,2,4-triazole to give the bicyclic compound N-[3-(trifluoromethyl)-1,2,4-triazolo[3,4-b]-1,3,4-thiadiazol-6-yl]benzamide IX .     

Characterizing Methyl‐Bearing Side Chain Contacts and Dynamics Mediating Amyloid β Protofibril Interactions Using 13Cmethyl‐DEST and Lifetime Line Broadening

Many details pertaining to the formation and interactions of protein aggregates associated with neurodegenerative diseases are invisible to conventional biophysical techniques. We recently introduced ¹⁵N dark‐state exchange saturation transfer (DEST) and ¹⁵N lifetime line‐broadening to study solution backbone dynamics and position‐specific binding probabilities for amyloid β (Aβ) monomers in exchange with large (2–80 MDa) protofibrillar Aβ aggregates. Here we use ¹³C_methyl DEST and lifetime line‐broadening to probe the interactions and dynamics of methyl‐bearing side chains in the Aβ‐protofibril‐bound state. We show that all methyl groups of Aβ40 populate direct‐contact bound states with a very fast effective transverse relaxation rate, indicative of side‐chain‐mediated direct binding to the protofibril surface. The data are consistent with position‐specific enhancements of ¹³C_methyl‐${R{{{\rm tethered}\hfill \atop 2\hfill}}}$ values in tethered states, providing further insights into the structural ensemble of the protofibril‐bound state.     

Comparison of Two Stability-Indicating Chromatographic Methods for the Determination of Mirabegron in Presence of Its Degradation Product

Mirabegron is a novel β₃-adrenoceptor agonist containing an amide group. It was subjected to stress conditions of acidic and alkaline hydrolyses. The hydrolytic degradation product was isolated and its structure was confirmed using mass and IR spectrometry. Two stability-indicating chromatographic methods have been proposed for the determination of mirabegron. TLC method was applied using silica gel as stationary phase and chloroform–methanol–ammonia (9.0:1.0:0.1 by volume) as the mobile phase, and chromatograms were scanned at 250 nm. Accurate determination of the drug was achieved over the concentration range of 2–12 μg per band. In addition, an isocratic HPLC method was developed on Agilent C18 column (150 mm × 4.5 mm I.D., particle size 5 µm) using ethanol-phosphate buffer pH 2.5 (30:70, by volume) as a mobile phase with flow rate of 1 mL min^?1.The intact drug was detected at 250 nm with running time less than 5 min. Mirabegron was determined accurately in a concentration range of 1–25 µg mL^?1. The proposed chromatographic methods were applied successfully for the assay of mirabegron in pharmaceutical dosage form and both methods were validated as per the International Conference on Harmonization guidelines and statistically compared with a reported gradient HPLC method.     

Perfect extinction in subwavelength dual metallic transmitting gratings

We investigate the strong electromagnetic coupling that settles in dual metallic grating structures. This coupling is evidenced to lead to a perfect optical extinction in the transmission spectrum. The behavior of this perfect extinction that strongly depends on the longitudinal space and the lateral displacement between the two gratings can be explained by a simple model that describes the interference between a propagating mode and a couple of evanescent modes. The results show that the electromagnetic transmission of the structure can be tuned by controlling the position of this perfect transmission extinction and thus pave the way to new types of infrared tunable filters.     

Microstructure-property relationship in magnetoelectric bulk composites

We present systematic studies that comprise phase connectivity and dielectric, multiferroic (MF) and magnetoelectric (ME) properties of (x) Ni_0.8Co_0.2Fe₂O₄+(1−x) Pb(Mg_1/3Nb_2/3)_0.67Ti_0.33O₃ [where x=0.15, 0.30 and 0.45] ME composites prepared by conventional solid-state reaction method. Scanning electron microscopic images of the composites predict different types of connectivity schemes viz 3-0, 3-1 and 3-3. The phase transition temperature of PMN-PT is independent of Ni_0.8Co_0.2Fe₂O₄ content. Room temperature P-E and M-H loops indicate the simultaneous existence of ferroelectric/magnetic ordering. In order to study the possibility of monitoring electrical ordering by means of a magnetic field, ME measurements were carried out. The composition-dependent phase connectivity was well co-related to formation of percolation path and inturn magnetoelectric output.     

Multiple Dedekind zeta functions and evaluations of extended multiple zeta values

We define the number field analog of the zeta function of d-complex variables studied by Zagier in (First European Congress of Mathematics, vol. II (Paris, 1992), Progress in Mathematics, vol. 120, Birkhauser, Basel, 1994, pp. 497-512). We prove that in certain cases this function has a meromorphic continuation to C^d, and we identify the linear subvarieties comprising its singularities. We use our approach to meromorphic continuation to prove that there exist infinitely many values of these functions at regular points in their extended domains which can be expressed as a rational linear combination of values of the Dedekind zeta function.     

Physics at the linear collider

The physics at the plannede ⁺ e ^- colliders is discussed around three main topics corresponding to different manifestations of symmetry breaking:W physics in the no Higgs scenario, studies of the properties of the Higgs and precision tests of SUSY. A comparison with the LHC is made for all these cases. The γγ mode of the linear collider will also be reviewed.