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.     

Polymeric Three-Dimensional Crystal Structure of a Tributyltin(IV) Derivative with Acetylene Dicarboxylic Acid

Abstract

A novel polymeric complex has been synthesized by refluxing disodium acetylene dicarboxylate with tributyltin chloride in dry methanol. The solid-state structure of the complex has been determined by single-crystal X-ray analysis. The tin(IV) metal exhibits distorted trigonal bipyramidal geometry. Each carboxylate group of the ligand acts in a bidentate fashion, linking adjacent metal atoms to produce polymeric chains, which are cross-linked into a three-dimensional network.     

Synthesis,Characterization, and Semi-Empirical Study of Organotin(IV) Complexes with 4-(Hydroxymethyl)piperidine-1-carbodithioic Acid: X-Ray Structure of Chlorodimethyl-(4-hydroxymethyl piperidine-1-carbodithioato-S,S′)tin(IV)

Abstract

Organotin complexes with the general formulae R₂SnL₂, R₂Sn(Cl)L, and R₃SnL have been synthesized where R = CH₃, n-C₄H₆, C₆H₅, C₆H₁₁, and L = 4-(hydroxy methyl)piperidine-1-carbodithioic acid. The newly synthesized complexes have been characterized by elemental analysis, IR, NMR (¹H, ¹³C and ¹¹⁹Sn), and, for one example, a single crystal x-ray structure. The FT-IR data shows the bidentate nature of the ligand. This coordination behavior is also confirmed by semi-empirical study. In the solid state, diorganotin complexes exhibit the penta/hexacoordinated geometry, whereas the triorganotin(IV) complexes show the five coordinated geometry. ¹¹⁹Sn NMR data reveal that triorganotin(IV) complexes exhibit the four coordinated geometry in solution, whereas the diorganotin(IV) compounds show the higher coordination, probably five or six. X-ray diffraction analysis of complex (2) shows a square pyramidal geometry around the tin atom on the basis of τ value.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.

GRAPHICAL ABSTRACT      

Ornamental Plant Efficiency for Heavy Metals Phytoextraction from Contaminated Soils Amended with Organic Materials

Accumulation of heavy metals (HMs) by ornamental plants (OPs) from contaminated agriculture soils is a unique technique that can efficiently reduce the metal load in the food chain. Amaranthus tricolor L. has attractive characteristics acquiring a higher growth rate and large biomass when grown at heavy metal contaminated soils. Site-specific detailed information is not available on the use of A. tricolor plant in metal phytoremediation from the polluted sites. The study aimed to enhance the uptake of HMs (Pb, Zn, and Cu) via amending poultry litter extract (PLE), vinasse sugarcane (VSC), and humic acid (HA) as natural mobilized organic materials compared to ethylene diamine tetraacetic acid (EDTA), as a common mobilized chemical agent by A. tricolor plant. The studied soils collected from Helwan, El-Gabal El-Asfar (Cairo Governorate), Arab El-Madabeg (Assiut Governorate), Egypt, and study have been conducted under pot condition. Our results revealed all organic materials in all studied soils, except EDTA in EL-Gabal El-Asfar soil, significantly increased the dry weight of the A. tricolor plant compared to the control treatment. The uptake of Pb and Zn significantly (p > 0.05) increased due to applying all organic materials to the studied soils. HA application caused the highest uptake as shown in Pb concentration by more than 5 times in Helwan soil and EDTA by 65% in El-Gabal El-Asfar soil while VSC increased it by 110% in El-Madabeg soil. Also, an increase in Zn concentration due to EDTA application was 58, 42, and 56% for Helwan, El-Gabal El-Asfar, and El-Madabeg soil, respectively. In all studied soils, the application of organic materials increased the remediation factor (RF) than the control. El-Madabeg soil treated with vinasse sugarcane gave the highest RF values; 6.40, 3.26, and 4.02% for Pb, Zn, and Cu, respectively, than the control. Thus, we identified A. tricolor as a successful ornamental candidate that, along with organic mobilization amendments, most efficiently develop soil health, reduce metal toxicity, and recommend remediation of heavy metal-contaminated soils. Additionally, long-term application of organic mobilization amendments and continued growth of A. tricolor under field conditions could be recommended for future directions to confirm the results.     

A note on natural risk statistics

Recently Heyde, Kou and Peng [C.C. Heyde, S.G. Kou, X.H. Peng, What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, 2007, preprint.] proposed the notion of a natural risk statistic associated with a finite sample that relaxes the subadditivity assumption in the classical coherent risk statistics. In this note we use convex analysis to provide alternate proofs of the representation results regarding natural risk statistics.     

Synthesis,characterization and biological properties of novel ON donor bidentate Schiff bases and their copper(II) complexes

Four novel ON donor Schiff bases (E)-3-((4-phenoxyphenylimino)methyl)benzene-1,2-diol (HL₁),(E)-3-((4-(4-biphenyloxy)phenyliminomethyl)benzene-1,2-diol (HL₂), (E)-3-((4-naphthoxyphenylimino)methyl)benzene-1,2-diol (HL₃), (E)-3-((4-(2-naphthoxy)phenylimino)methyl)benzene-1,2-diol (HL₄) and their copper(II) complexes bis((E)-3-((4-phenoxyphenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₁)₂) bis((E)-3-((4-(4-biphenyloxy)phenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₂)₂), bis((E)-3-((4-naphthoxyphenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₃)₂), bis((E)-3-((4-(2-naphthoxy)phenylimino)methyl)benzene-1,2-diol) copper(II) (Cu(L₄)₂) have been synthesized and characterized by spectroscopic (FTIR, NMR, UV–visible) and elemental analysis. The crystal structures of HL₁, HL₂, HL_3, and HL₄ have been determined, which reveal intramolecular N-H?O (HL₁, HL₂, HL_3, and HL₄) hydrogen bonds in the solid state. Keto-amine and enol-imine tautomerism is exhibited by the Schiff bases in solid and solution states. The Schiff bases and their copper(II) complexes have been screened for their biological activities. In antimicrobial assays (antibacterial and antifungal), HL₄ showed promising results against all strains through dual inhibition property while the rest of the compounds showed activity against selective strains. On the other hand, in cytotoxic, DPPH, and inhibition of hydroxyl (OH) free radical-induced DNA damage assays, the results were found significantly correlated with each other, i.e. the ligands HL₁ and HL₂ showed moderate activity while their complexes Cu(L₁)₂ and Cu(L₂)₂ exhibited prominent increase in activity. As the results of these assays are supporting each other, it represents the strong positive correlation and antioxidant nature of investigated compounds.     

Multinuclear (Sn/Pd) complexes with disodium 2,2′-(dithiocarboxyazanediyl)diacetate hydrate; Synthesis,characterization and biological activities

Bimetallic chlorodi-/triorganotin(IV) derivatives of general formulas R₂(H₂O)SnLCSSSn(Cl)R₂ (R=Me: 1; Ph: 2) and R₃Sn(Na)LCSSSnR₃·H₂O (R=Bu: 3; Ph: 4) were prepared by reaction of iminodiacetic acid disodium salt hydrate (Na₂LH) with CS₂ and R₂SnCl₂/R₃SnCl in methanol. The reaction between Na₂LH, CS₂, and PdCl₂ produced [Na₂LCSS]₂Pd·2H₂O (5) which was treated with R₃SnCl to synthesize the heterobimetallic derivatives [R₃Sn(Na)LCSS]₂Pd·2H₂O (R=Me: 6; Ph: 7). The complexes were characterized by microanalysis, spectroscopic, and thermogravimetric analyses. Elemental analysis data, mass fragmentation, and thermal degradation patterns supported the molecular composition of the complexes. FT-IR data indicated monodentate binding of carboxylate while a chelating coordination mode of the dithiocarboxylate was verified in the solid state. A five-coordinate tin(IV) was demonstrated in the solid state. In solution, a tetrahedral/trigonal bipyramidal configuration around Sn(IV) and a square planar geometry of Pd(II) was indicated by multinuclear NMR (¹H and ¹³C) and UV-visible studies. The Pd(II) derivatives showed interaction with salmon sperm-DNA and caused an inhibition of alkaline phosphatase (ALPs). The antibacterial/antifungal potential of the coordination products varied with the nature of incorporated metal and a substitution pattern at tin(IV); the palladium metallation decreased the antimicrobial activities. The triorganotin(IV) products exhibited more powerful action against bacteria/fungi as compared to their diorganotin(IV) counterparts. The complexes displayed sufficiently lower hemolytic effects in vitro as compared to triton X-100 and slightly higher than PBS.