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.     

Silver(I)-selective coated-wire electrode based on an octahydroxycalix[4]arene derivative.

The performance of octahydroxycalix[4]arene derivative used as a neutral carrier for silver polymeric membrane electrode was studied. The sensor gave a good Nernstian response of 58 +/- 1 mV per decade for silver ion in the activity range 3.3 x 10(-6) to 3.3 x 10(-2) M Ag+. The limit of detection reached 2.1 x 10(-6) M Ag+ and exhibited high selectivity for silver ion against the alkali, alkaline earth and transition metal ions. The sensor can be used in wide pH range from 1.5 to 6.5. The response time of the sensor is less than 20 s. The potentiometric sensor was used as the indicator electrode in the titration of Ag+ ions by sodium chloride solution.     

Adsorption Behaviour of 134Cs and 22Na Ions on Tin and Titanium Ferrocyanides

Tin and titanium ferrocyanides were studied as adsorbents for alkali metal ions, viz., ¹³⁴Cs and ²²Na, which represent radioactive wastes. The ferrocyanides were prepared in granular form. The tin version contained 11.2% water, while the titanium version contained 17.7% water. The exchange capacities for Cs⁺ and Na⁺ in the hydrated tin version were about 1.5 and 0.7 meq/g, respectively, while those in the titanium version were 2.2 and 1.2 meq/g, respectively. Drying at 250°C decimated those capacities. The diffusional time constant of Cs⁺ at 25°C, determined via Fick's second law, was of order of magnitude 1 × 10^–3 s^–1, though there were minor differences due to particle size and the form of ferrocyanide. Similarly, the effective diffusivity was of order of magnitude 1 × 10^–8 cm²/s. The titanium version responded slightly faster than the tin version. Likewise, equilibrium measurements in mixtures with sodium nitrate, potassium nitrate, or uranium oxide, showed that the titanium version exhibited significantly greater selectivity for Cs⁺ than did the tin version. Unfortunately, tests of complete elution of the Cs⁺ from the ferrocyanides were mostly disappointing. Work continues on that subject.     

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.     

Selective extraction of iron(III) from aqueous nitrate solution in the presence of cobalt(II), copper(II) and nickel(II) ions using bis(delta2-2-imidazolinyl)-5,5'-dioxime.

The feasibility of using bis(delta2-2-imidazolinyl)-5,5'-dioxime (H2L) for the selective extraction of iron(III) from aqueous solutions was investigated by employing an solvent-extraction technique. The extraction of iron(III) from an aqueous nitrate solution in the presence of metal ions, such as cobalt(II), copper(II) and nickel(II), was carried out using H2L in binary and multicomponent mixtures. Iron(III) extraction has been studied as a function of the pH, equilibrium time and extractant concentration. From the extracted complex species in the organic phase, iron(III) was stripped with 2 M HNO3, and later determined using atomic-absorption spectrometry. The extraction was found to significantly depend on the aqueous solution pH. The extraction of iron(III) with H2L increases with the pH value, reaching a maximum in the zone of pH 2.0, remaining constant between 2 and 3.5 and subsequently decreasing. The quantitative extraction of iron(III) with 5 x 10(-30 M H2L in toluene is observed at pH 2.0. H2L was found to react with iron(III) to form ligand complex having a composition of 1:2 (Fe:H2L).     

Synthesis of New Dibenzosulfide and Dibenzosulfoxide Macrocyclic Compounds

Some new dibenzosulfo, dibenzosulfoxo macrocyclic diamides are synthesized.     

Spectrophotometric and AAS determination of trace amounts of cobalt after preconcentration by using alpha-benzilmonoxime-microcrystalline naphthalene.

The formed cobalt-a-benzilmonoxime complex was adsorbed onto microcrystalline naphthalene. Then it was determined by zero and first derivative spectrophotometry and by atomic absorption spectrophotometry (AAS) after dissolving into chloroform and methylisobutylketone (MIBK), respectively. Under optimum conditions, cobalt in the range of 1.0 - 20.0, 0.4 - 30.0 and 2.5 - 50.0 microg could be determined by spectrophotometry, first derivative spectrophotometry and AAS method, respectively. By the method, a preconcentration factor equal to approximately 30 for cobalt was obtained. The effect of diverse ions on the determination of 5.0 microg cobalt was also studied. The method was successfully applied to some pharmaceuticals and synthetic alloy samples.     

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.     

Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.