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.     

Visual detection of cysteine and homocysteine

The determination of cysteine and homocysteine levels is of great current interest for the monitoring of desease states. A new colorimetric method for the simultaneous detection of l-cysteine and l-homocysteine has been developed. A fluorescein derivative reacts with the above amino acids, producing their respective thiazolidines resulting in color changes. Interference from other amino acids and proteins is minimal.     

Spectroscopic studies of water-soluble sulfonated calix[6]arene

Fluorescence and absorption studies of water-soluble sulfonated calix[6]arene (SCX6) are reported. Water-soluble calixarenes are potentially useful as host molecules for luminophores, and studies of their spectroscopic characteristics are therefore crucial. The absorption and fluorescence spectra of these molecules in aqueous solution were collected, analyzed, and compared with 4-hydroxybenzene sulfonate at different pHs. A red shift in the absorption spectrum and a change in the fluorescence spectrum of the calixarenes are observed upon an increase in pH from 2.0 to 13.0. Some of these spectroscopic changes are attributed to intramolecular hydrogen bonding between adjacent hydroxyl groups of SCX6 after proton disassociation. The formation of excimers between phenolic groups in the calixarene molecule is proposed. In addition, inner-filter effects of SCX6 are discussed. These inner-filter effects prove to be a disadvantage for the use of SCX6 as a host molecule for complexation studies by use of fluorescence probes whose absorption spectra overlap with those of calixarenes.     

Influence of the polydispersity of polymeric surfactants on the enantioselectivity of chiral compounds in micellar electrokinetic chromatography

Poly(sodium undecenoyl-L-leucinate) (poly-L-SUL) was fractionated by the use of different molecular weight cutoff (MWCO) filters to narrow the polydispersity of the macromolecular sizes of the polymeric surfactant. The resulting polymeric surfactant fractions were characterized by the use of three techniques: (1) pulsed field gradient nuclear magnetic resonance (PFG-NMR) was used to determine the hydrodynamic radii, (2) analytical ultracentrifugation (AUC) was used to determine the molecular weights, and (3) steady-state fluorescence was used to determine the polarity of the nonfractionated and fractionated polymeric surfactants. From the data acquired from PFG-NMR, AUC, and fluorescence, it was noted that the hydrodynamic radii and molecular weight of the fractionated poly-L-SUL increased, while the polarity decreased with the increase in the size of the MWCO filter. However, a similarity in physical properties was observed between the nonfractionated and 10-30K fractionated poly-L-SUL except for the hydrodynamic radius and diffusion coefficients. The influence of different macromolecular sizes of poly-L-SUL on the chiral separation of phenylthiohydantion (PTH)-amino acids and coumarinic derivatives, as test analytes, was elucidated by the use of micellar electrokinetic chromatography (MEKC). The size of polymeric surfactants as a prerequisite for chiral separation was demonstrated by comparing the separation properties of fractionated versus nonfractionated polymeric surfactants. Fractionated poly-L-SUL resulted in enhanced resolution and separation efficiency of the test analytes as compared to the case of the nonfractionated poly-L-SUL. This observation indicates that minimizing polydispersity of polymeric surfactants may be important for some chiral separation applications.     

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.     

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.     

Bifunctional catalytic/magnetic Ni@Ru core-shell nanoparticles

Core-shell structured Ni@Ru bimetallic nanoparticles are demonstrated as a bifunctional nanoplatform system for the hydrolysis reaction of ammonia-borane and also for magnetic separation.     

Spectroscopic study of a representative polar cap of buckminsterfullerene: Cyclopentacorannulene

The spectroscopic properties of corannulene and cyclopentacorannulene are examined by use of absorption and steady-state fluorescence measurements. A red shift in the emission maxima of cyclopentacorannulene is noted with respect to the emission maxima in the corannulene spectrum. Similar differences in the absorption spectra of both molecules are also observed. Reasons for the dissimilarities in the absorption and emission spectra of these molecules are discussed. The fluorescence quantum yields and lifetimes of the molecules measured in organic solvents are reported. The fluorescence quantum yield and lifetime of cyclopentacorannulene are lower than those of corannulene. This difference is attributed to the highly strained and nonplanar structure of cyclopentacorannulene. The effectiveness of nitromethane as a quencher of corannulene and cyclopentacorannulene fluorescence is examined. In contrast to previously reported results, the fluorescence of these molecules is quenched by nitromethane. Fluorescence quenching of the molecules has been attributed to complex formation in the ground state, i.e., static quenching.