Asymptotic Distribution of Nodes for Near-Optimal Polynomial Interpolation on Certain Curves in R 2

Let E\subset \Bbb R ^s be compact and let d _n ^E denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ _n ={ \bf x _k,n } _k=1 ^dnE , n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R ² . It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore, for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes. November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001.     

Size exclusion chromatographic determination of hydroxypropyl methyl cellulose and polyethylene glycol 400 in an ophthalmic solution

Summary Hydroxypropyl methyl cellulose (HPMC) and polyethylene glycol 400 (PEG 400) content in HypoTears™ Daily Dose ophthalmic solution are determined simultaneously by size exclusion chromatography. The retention times of HPMC and PEG 400 are 10.6 and 15.4 minutes, respectively. The method requires minimal sample pretreatment and is accurate and reproducible. The peak area response from a refractive index detector versus HPMC and PEG 400 concentration is linear over the range of 50–150 % of their label claims of 2.5 mg/mL and 10 mg/mL, respectively. The mean absolute recoveries of HPMC and PEG 400 at their label claim using the described method are 98.9±1.3 % and 100.4±1.2 % (mean±SD, n=12), respectively.     

Investigation of the stability of metal species with respect to liquid chromatographic separations

Summary For accurate speciation analyses it is important to know the stability of the respective species, especially in the case of metal complexes. Factors affecting the chromatographic stability of such metal species are investigated. By using thermodynamic models for complex formation and chromatographic retention equilibria the influence of species concentration, stoichiometry and excess of ligand is calculated and compared with experimental results for iron complexes (lactate, gluconate and citrate species). Iron citrate is the only species, that is chromatographed as 1:2 complex (metal: ligand), while iron lactate and gluconate are transformed to 1:1 species. Problems resulting from the coelution of different species are discussed.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Diastereoselective formation of 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines: An X-ray crystallographic and H NMR study

N-Arylsulfonamides of (R)- and (S)-2-amino-1-butanol, on condensation with aromatic aldehydes produced diastereomerically pure 2-aryl-3-arenesulfonyl 4-ethyl-1,3-oxazolidines. The absolute configurations of one enantiomeric pair have been determined from two fully refined X-ray structures, supplemented by nmr data.     

Regioorientation in the reaction of side chain activated alkylpyridines with electrophiles

X-ray structural data has shown that condensation of sym-3-nitrocollidine with benzaldehyde occurs at the 6-methyl group. The presence of an acceptor group in the side chain of 2,6-dimethyl-4-cyanomethyl-3-nitropyridine causes condensation to occur at the activated methylene group in the 4-position.M. V. Lomonosov State University, Moscow 119899. A. N. Nesmeyanov Institute of Organoelemental Compounds, Moscow 117813. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11. pp. 1543–1550, November, 1995. Original article submitted June 10, 1995.     

TLC-screening of important pharmaceutical substances using fluorescence detection

Summary Observation of fluorescence reactions on TLC plates is a valuable additional tool within the scope of screening procedures for many toxicologically relevant substances commonly encountered in clinical- and forensic-toxicological analysis. The reactions are based on native fluorescence without any treatment and on reactions obtained with an approved derivatization procedure. Due to the enormous sensitivity of the fluorescence detection, the method is also applicable to very low concentrations and small amounts of biological materials. The procedures described in this article have proven their high pragmatic usefulness in many practical cases.Dedicated to Professor Dr. Wilhelm Fresenius on the occasion of his 80th birthday     

Structure of thin block copolymer films studied by X-ray reflectivity

Summary X-ray reflectivity may be used to determine the internal structure of thin polymer films. An electron density difference of 10% for polystyrene and polyisoprene is sufficient to distinguish between a random distribution of lamellae, complete orientation parallel to the substrate surface and a surface induced formation of lamellae. The disappearance of the lamellar Bragg-peaks, with heating of the film, shows the transition into the disordered state.     

Crossing of shears bands in196Pb

High-spin states in¹⁹⁶Pb have been populated using the reaction¹⁷⁰Er(³⁰Si,4n). The previously observed shears bands in this nucleus have been extended and some of their transitions have been reordered. They now form regular bands with band crossings. One of the bands splits into two pathways at high spin.     

Use of spheron for separating flavonoids

Institute of Biology, Ufa Scientific Center, Russian Academy of Sciences, Ufa, fax (3472) 35 6103. Translated from Khimiya Prirodnykh Soedinenii, No. 5, pp. 755-756, September-October, 1995. Original article submitted September 6, 1994.