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.     

Highly selective PVC-membrane electrodes based on Co(II)-Salen for determination of nitrite ion.

A cobalt(II) derivative was used as a suitable ionophore for the preparation of a polymeric membrane nitrite-selective electrode. The electrode reveals a Nemstian behavior over a very wide NO2- ion concentration range (1.0 x 10(-6)-1.0 x 10(-1) M) and a very low detection limit (5.0 x 10(-7) M). The potentiometric response is independent of the pH of solution in the pH range 4.0-9.5. The electrode shows advantages such as low resistance, fast response and, most importantly, good selectivity relative to a wide variety of inorganic and organic anions. In fact, the selectivity behavior of the proposed NO2- ion-selective electrode shows great improvements compared to the previously reported electrodes for nitrite ion. The proposed electrodes could be used for at least 2 months without any significant changes in potentials. The electrode was successfully applied to the determination of nitrate ion concentrations in sausage and milk samples.     

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.     

Novel monohydrogenphosphate sensor based on vanadyl salophen

A novel PVC-based membrane sensor based on vanadyl salophen (VNSP) for determination of trace amounts of monohydrogenphosphate (MHP) ions is introduced. The electrode revealed Nernstian response towards monohydrogenphosphate over the wide concentration range from 1.0×10⁻¹ to 1.0×10⁻⁶ M at the pH of 8.2. The effect of solvent mediator, cationic additives and amount of ion-carrier on the behavior of the sensor was investigated. The sensor shows a short response time (<20 s) in the whole concentration ranges. The selectivity of the electrode is very high, and it can be used for detection of trace amounts of monohydrogenphosphate in the presence of large amounts of other anions. The detection limit of the electrode was 5.0×10⁻⁷ M (48 ng/ml) and it could be used for 14 weeks without any measurable changes in the slope. The potentiometric selectivity coefficients data revealed negligible interference from 16 common anions. It was successfully applied for the direct determination of monohydrogenphosphate in fertilizer samples and, as an indicator electrode, in potentiometric titration of HPO₄²⁻ ion with barium nitrate.     

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.