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.     

一些随机重合点定理

本文引入了一种满足更一般的收缩不等式的多重函数类,并证明了属于该类的可测多重函数对的一些随机重合点定理。     

Microbial Transformation of Sesquiterpenes, (−)‐Ambrox® and (+)‐Sclareolide

The microbial transformation of (?)‐Ambrox^® ( 1 ), a perfumery sesquiterpene, by a number of fungi, by means of standard two‐stage‐fermentation technique, afforded ambrox‐1α‐ol ( 2 ), ambrox‐1α,11α‐diol ( 3 ), ambrox‐1α,6α‐diol ( 4 ), ambrox‐1α,6α,11α‐triol ( 5 ), ambrox‐3‐one ( 6 ), ambrox‐3β‐ol ( 7 ), ambrox‐3β,6β‐diol ( 8 ), 13,14,15,16‐tetranorlabdane‐3,8,12‐triol ( 9 ), and sclareolide ( 10 ) (Schemes 1 and 2). Further incubation of compound 10 with Cunninghamella elegans afforded 3‐oxosclareolide ( 11 ), 3β‐hydroxysclareolide ( 12 ), 2α‐hydroxysclareolide ( 13 ), 2α,3β‐dihydroxysclareolide ( 14 ), 1α,3β‐dihydroxysclareolide ( 15 ), and 3β‐hydroxy‐8‐episclareolide ( 16 ) (Scheme 3). Metabolites 2 – 5, 12, 13 , and 16 were found to be new compounds. The major transformations include a reaction path involving hydroxylation, ether‐bond cleavage and inversion of configuration. Metabolites 11 – 16 of sclareolide showed significant phytotoxicity (Table 1). The structures of the metabolites were characterized on the basis of spectroscopic techniques.     

Microbial transformation of prednisone

The microbial transformation of prednisone (17alpha,21-dihydroxy-pregna-1,4-diene-3,11,20-trione) (1) by Cunninghamella elegans afforded two metabolites, 17alpha,21-dihydroxy-5alpha-pregn-1-ene-3,11,20-trione (2) and 17alpha,20S,21-trihydroxy-5alpha-pregn-1-ene-3,11-dione (3), while the fermentation of 1 with Fusarium lini, Rhizopus stolonifer and Curvularia lunata afforded a metabolite 1,4-pregnadiene-17alpha,20S,21-triol-3,11-dione (4). Compound 3 was found to be a new metabolite. Their structures were elucidated on the basis of spectroscopic techniques. Compound 3 showed inhibitory activity against lipoxygenase enzyme.     

An expedient esterification of aromatic carboxylic acids using sodium bromate and sodium hydrogen sulfite

Treatment of aromatic carboxylic acids and substituted toluenes with a mixture of sodium bromate and sodium hydrogen sulfite in a two-phase system gave the corresponding esters in good yield. The intermediate α-brominated toluene was formed by the in situ generated hypobromous acid. The α-bromotoluene underwent an intermolecular nucleophilic substitution reaction with aromatic carboxylic acids present in the reaction mixture to afford the corresponding esters.     

Validated TLC-densitometry method for the simultaneous analysis of pyrethroid insecticides in agricultural and domestic products

ABSTRACT: BACKGROUND: Pyrethroids are widely used for the control of pests and insects, as pyrethroids are believed to pose very little risk to human health and environment. However, exposure to the pyrethroids exceeding the label directions might adversely affect human health and environment. Hence a careful selection of environment friendly household product is required that must contain exactly the label claimed pyrethroids amount. RESULTS: A sensitive and robust TLC-densitometric method for simultaneous quantification of commonly used synthetic pyrethroids including esbiothrin, alpha-cypermethrin and cis/trans permethrin in agricultural and domestic products has been developed and validated. TLC aluminum plates, precoated with 0.2 mm thick layer of silica gel 60 F-254, were used for chromatographic process. Densitometric analysis of chromatoplates was carried out in absorbance mode at corresponding lamdamax of each pyrethroid. Equally valid common mobile phase for all pyrethroids consisted of hexane-dichloromethane-ethylacetate-formic acid (8:1.5:0.4:0.1 v/v/v/v) which provided sharp and symmetrical peaks of esbiothrin, alpha-cypermethrin, trans-permethrin and cis-permethrin, at Rf 0.31, 0.53, 0.6 and 0.65, respectively. Linear regression data for respective calibration curves showed a good linearity for all pyrethroids with r = 0.991-0.996. Limits of detection (LOD) and limits of quantification (LOQ) for all pyrethroids were found in the range of 1.6-2.8 and 4.9-8.5 ng/spot, respectively. CONCLUSIONS: The developed method is applicable for separating the mixture of pyrethroids and at the same time, it is also valid for separating their isomers. The method is reproducible, precise and accurate for the quantitative determination of pyrethroids in agricultural and domestic products.