Sampling with a String

Kramer's sampling theorem forms a bridge between the Whittaker-Shannon-Kotel'nikov sampling theorem and boundary-value problems. It has been shown that sampling expansions associated with Sturm-Liouville boundary-value problems are Lagrange-type sampling series, i.e., Lagrange series with infinitely many terms converging to entire functions. String theory as developed by Feller, Kac, and Krein, is a generalization of the Sturm-Liouville theory. We investigate sampling series associated with strings and compare them with those associated with Sturm-Liouville problems. We show that unlike sampling series associated with Sturm-Liouville problems, those associated with strings include not only Lagrange-type sampling series, but also Lagrange polynomial interpolation.     

Growth of InP/InGaAs multiple quantum well structures by chemical beam epitaxy

InP/InGaAs multiple quantum well structures with up to 200 periods have been grown by CBE. These structures exhibit exceptional lateral uniformity, measured as ±1 Å in period, ±13 ppm in lattice mismatch and ±0.5 nm in wavelength across a 2 inch wafer. Good surface morphology, sharp interfaces and excellent growth control have all been demonstrated.     

Symmetrical and Asymmetrical Bisphosphonate Esters. Synthesis, Selective Hydrolysis, and Isomerization

Two simple and efficient one-pot procedures for the synthesis of a series of α-branched N-heterocycle-substituted methane-1,1-bisphosphonates are outlined. In the first method, the parent halosubstrates were reacted with cyanomethylphosphonate followed by reaction with dialkyl phosphonates to give asymmetrical or symmetrical bisphosphonates (BPs). In the second approach, the same halocompounds were reacted with tetraethyl methyl-1,1-bisphosphonate to give the requisite BPs. Partial and complete hydrolysis of the prepared BPs were also investigated. The products contain functional groups advantageous for further synthetic modification as structural units for coupling with the drug.     

Efficient Oxidation of Alcohols to Carbonyl Compounds by N,N‐Dichloro‐4‐Methylbenzenesulfonamide under Mild Conditions

A number of aldehydes and ketones were prepared by oxidation of alcohol by N,N‐dichloro‐4‐methylbenzenesulfonamide under mild and neutral conditions in good to high yield in dichloromethane at room temperature.     

Titrimetric microdetermination of salicylic, acetylsalicylic, and p-hydroxybenzoic acids by amplification reactions

A novel titrimetric method with amplification has been developed for the determination of 0.05–2.0 mg of salicylic, acetylsalicylic, or p-hydroxybenzoic acid. It depends on bromination of these compounds by bromine to tribromophenylhypobromite, which liberates iodine when treated with iodide. The liberated iodine is extracted with chloroform, reduced to iodide, oxidation of the resulting iodide with bromine, and iodometric titration of the iodate produced gives the sixfold amplification method. The coefficient of variation does not exceed 1% for above 0.5 mg of the studied compounds, but increases to 2.8% at the 0.05-mg level.     

Characterization of a Novel Tellurite Selective Electrode

Tellurium was determined by introducing a solid membrane for the selective determination of tellurite ion. An electrode composed of a compressed disk containing a mixture of HgTeO₃and Hg₂Cl₂was found to give a typical Nernstian response of 29 mV/concentration decade for the concentration range 10⁻⁵to 10⁻¹M). The connection was made by Hg metal instead of aqueous inner filling. The optimum pH was 3.5–10.5. The selectivity of the electrode toward several inorganic and organic anions was estimated. The electrode was applied to the determination of tellurium in binary mixtures with a mean recovery of 98.99% and relative standard deviation range of 0.19–0.51%.     

Spectrophotometric assay of cephalosporins in pharmaceutical products,using chromotrope 2B and chromotrope 2R

A simple, rapid and sensitive Spectrophotometric method is proposed for the determination of cephadroxil (I), cephalexin (II) and cephradine (III). The method is based on ion-pair complex formation between these derivatives and Chromotrope 2B (C2B) or Chromotrope 2R (C2R), to give a highly coloured radical anion. The coloured products are quantified spectrophotometrically at 542 and 564 nm for C2B and C2R, respectively. The optimization of the experimental conditions is described. The method has been used for the determination of 0.4–15, 0.4–14 and 0.4–18 g/ml of drugs I, II and III, respectively. The accuracy of the method is indicated by the excellent recovery (100.0±1.7%) and the precision is supported by the low relative standard deviations 1.5%. The sensitivity of the method is discussed and the results are compared with the official method. The interference from common degradation products and excipients was also studied. The proposed method was applied successfully to the determination of the different cephalosporins in dosage forms, with good precision and accuracy. The results were compared with those given by the official B.P. 1993 method.