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.     

On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

Synthèse de nouveaux dérivés tétrahydroquinoléines et quinoléines via la réaction d'aza-Diels-Alder suivie d'aromatisation

The Aza-Diels-Alder reaction of aldimines with isoeugenol is described. New 1,2,3,4-tetrahydroquinoline and quinoline structures are reported. The stereo- and regioselectivities of the [4+2] cycloaddition are discussed.     

The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Homogeneous liquid-liquid extraction of uranium(VI) using tri-n-octylphosphine oxide.

A simple and efficient method for the selective separation and preconcentration of uranium(VI) using homogeneous liquid-liquid extraction was developed. Tri-n-octylphosphine oxide (TOPO) and tri-n-butylphosphate (TBP) were investigated as complexing ligands, and perfluorooctanoate ion (PFOA-) was applied as a phase separator agent under strongly acidic conditions. Under the optimal conditions ([PFOA-] = 1.7 x 10(-3) M, [TOPO] = 5.4 x 10(-4) M, [HNO3] = 0.3 M, [acetone] = 3.2% v/v) 10 microg of uranium in 40 ml aqueous phase could be extracted quantitatively into 8 microl of the sedimented phase. The maximum concentration factor was 5000-fold. However, an effort for the quantitative extraction using TBP was inefficient and the percent recovery was at most 56.7. The influence of the type and concentration of acid solution, optimum amount of the ligand, type and volume of the organic solvent, concentration of PFOA, volume of the aqueous sample and effect of different diverse ions on the extraction and determination of uranium(VI) were investigated. The proposed method was applied to the extraction and determination of uranium(VI) in natural water samples.     

Kinetic determination of silver ion by its perturbation on Belousov-Zhabotinskii oscillating chemical reaction using potentiometric method.

Silver ion can perturb the Belousov-Zhabotinskii (B-Z) oscillating chemical reaction. Therefore, the B-Z oscillating system was applied in the determination of silver ion by using a platinum wire as an indicator electrode in the potentiometric method. The amplitude of the potentiometric oscillation increased linearly in proportion to [Ag+] in the range of 9.42 x 10(-6) M to 2.54 x 10(-4) M, with a correlation coefficient of 0.999 under the optimum conditions. The obtained LOD (2sigma) was 8.85 x 10(-6) M and the relative standard deviation (RSD) for five measurements of 1 x 10(-4) M silver ion was 5%. The influence of some potentially interference was also investigated.     

Simultaneous kinetic-spectrophotometric determination of hydrazine and acetylhydrazine in micellar media using the H-point standard addition method.

The H-point standard addition method (HPSAM), based on a spectrophotometric measurement for the simultaneous determination of hydrazine and acetylhydrazine, is described. This method is based on the difference between the rates of their reactions with N,N-dimethylaminobenzaldehyde (DAB) in the presence of sodium dodecyl sulfate (SDS) in acidic media. The results showed that hydrazine and acetylhydrazine could be determined simultaneously in the range of 0.020 - 0.70 and 0.20 - 5.0 mg L(-1), respectively. Under the working conditions, the proposed method was successfully applied to the simultaneous determination of hydrazine and acetylhydrazine in several synthetic mixtures and plasma and water samples.