On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

Polymeric sulfated surfactants with varied hydrocarbon tail: I. Synthesis, characterization, and application in micellar electrokinetic chromatography

The influence of surfactant hydrocarbon tail on the solute/pseudostationary phase interactions was examined. Four anionic sulfated surfactants with 8-, 9-, 10-, and 11-carbon chains having a polymerizable double bond at the end of the hydrocarbon chain were synthesized and characterized before and after polymerization. The critical micelle concentration (CMC), polarity, and aggregation number of the four sodium alkenyl sulfate (SAIS) surfactants were determined using fluorescence spectroscopy. The partial specific volume of the polymeric SAIS (poly-SAIS) surfactants was estimated by density measurements and capillary electrophoresis (CE) was employed for determination of methylene selectivity as well as for elution window. The CMC of the monomers of SAIS surfactants decrease with increase in chain length and correlated well when fluorescence method was compared to CE. The physicochemical properties (partial specific volume, methylene selectivity, electrophoretic mobility, and elution window) increased with an increase in chain length. However, no direct relationship was found between the aggregation number and the length of hydrophobic tail of poly-SAIS surfactants. These polymeric surfactants were then used as pseudostationary phases in micellar electrokinetic chromatography (MEKC) to study the retention behavior and selectivity factor of 36 benzene derivatives with different chemical characteristics. Although variation in chain length of the polymeric surfactants significantly affects the retention of nonhydrogen bonding (NHB) benzene derivatives, these effects were less pronounced for hydrogen bond acceptor (HBA) and hydrogen bond donor (HBD) benzene derivatives. Therefore, hydrophobicity of poly-SAIS surfactants was found to be a major driving force for retention of NHB derivatives. However, for several benzene derivatives (NHB, HBA, and HBD) significantly higher selectivity factor was observed with longest chain polymeric surfactant (e.g., poly(sodium 10-undecenyl sulfate), poly-SUS) compared to shorter chain polymeric surfactant (e.g., poly(sodium 7-octenyl sulfate), poly-SOcS). In addition, the effect of the surfactant hydrophobic chain was also found to have some impact on migration order of NHB, HBA, and HBD benzene derivatives.     

Binary mixed micelles of chiral sodium undecenyl leucinate and achiral sodium undecenyl sulfate: I. Characterization and application as pseudostationary phases in micellar electrokinetic chromatography

Sodium 10-undecenyl sulfate (SUS), sodium 10-undecenyl leucinate (SUL) and their five different mixed micelles at varied percent mole ratios were prepared. The critical micelle concentration (CMC), C₂₀, γ_CMC, partial specific volume, methylene group selectivity, mobilities and elution window were determined using a variety of analytical techniques. These surfactant systems were then evaluated as novel pseudostationary phases in micellar electrokinetic chromatography (MEKC). As a commonly used pseudostationary phase in MEKC, sodium dodecyl sulfate (SDS) was also evaluated. The CMC values of SUS and SUL were found to be 26 and 16 mM, respectively, whereas the CMC of mixed surfactants was found to be very similar to that of SUL. The C₂₀ values decreased dramatically as the concentration of SUL is increased in the mixed micelle. An increase in SUL content gradually increased the methylene group selectivity making the binary mixed surfactants more hydrophobic. Linear solvation energy relationships (LSERs) and free energy of transfer studies were also applied to predict the selectivity differences between the surfactant systems. The cohesiveness and the hydrogen bond acidic character of the surfactant systems were found to have the most significant influence on selectivity and MEKC retention. The SUS and SDS showed the strongest while SUL showed the weakest hydrogen bond donating capacity. The basicity, interaction with n and π-electrons of the solute and dipolarity/polarizability were the least significant factors in LSER model for the surfactant systems studied. Free energies of transfer of selected functional groups in each surfactant systems were also calculated and found to be in good agreement with the LSER data.     

Dendronized polymers via Diels–Alder “click” reaction

A modular approach toward the synthesis of polymers containing dendron groups as side chains is developed using the Diels–Alder “click” reaction. For this purpose, a styrene‐based polymer appended with anthracene groups as reactive side chains was synthesized. First through third‐generation polyester dendrons containing furan‐protected maleimide groups at their focal point were synthesized. Facile, reagent‐free, thermal Diels–Alder cycloaddition between the anthracene‐containing polymer and latent‐reactive dendrons leads to quantitative functionalization of the polymer chains to afford dendronized polymers. The efficiency of this functionalization step was monitored using ¹H and ¹³C NMR spectroscopy and FTIR and UV–vis spectrometry. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 410–416, 2010     

A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems.     

A generalization of a theorem of Arrow,Barankin and Blackwell to a nonconvex case

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a partially ordered reflexive Banach space.     

A General Approach for the Exact Solution of the Schrödinger Equation

The Schrödinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrödinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.     

Natural and artificial radioactivity levels of greenhouse soils and relations with soil properties

Journal of Radioanalytical and Nuclear Chemistry - In this study, natural (226Ra, 232Th, 40K) and artificial (137Cs) radionuclide activity concentration levels of 63 greenhouse soils collected from...     

Chiral separations in microemulsion electrokinetic chromatography. Use of micelle polymers and microemulsion polymers

In this study, microemulsions of the chiral surfactant polysodium N-undecenoyl-D-valinate (poly-D-SUV) was utilized for enantiomeric separation by investigating two approaches using polymeric chiral surfactant in microemulsion electrokinetic chromatography (MEEKC). In the first approach, poly-D-SUV was used as an emulsifier surfactant along with 1-butanol and n-heptane. Enantioseparation of anionic or partially anionic binaphthyl derivatives, anionic barbiturates, and cationic paveroline derivatives were achieved by varying the mass fraction of 1-butanol, n-heptane and poly-D-SUV. For anionic or partially anionic analytes, relatively lower mass fractions of n-heptane, and poly-D-SUV were found to give optimum chiral separations as compared to that for cationic solutes. In the second approach, the chiral microemulsion polymer was prepared by polymerizing mixtures of 3.50% (w/w) of sodium N-undecenoyl-D-valinate (D-SUV) and 0.82% (w/w) of n-heptane (core phase) at varying concentration of 1-butanol. After polymerization, the n-heptane and 1-butanol were removed to yield solvent free microemulsion polymers (MPs) which were then utilized for the separation of anionic binaphthyl derivatives and anionic barbiturates. When MPs of D-SUV were utilized for chiral separation, 1.00% (w/w) 1-butanol and 3.50% (w/w) 1-butanol was optimum for enantioseparation of (+/-)-BNP and (+/-)-BOH, respectively. On the other hand, for anionic (+/-)-barbiturates very low concentration of butanol (0.25%, w/w) provided optimum resolution. Compared with micellar electrokinetic chromatography (MEKC), the use of micelle polymers or microemulsion polymers in MEEKC showed dramatic enhancement for resolution of (+/-)-BNP, while this enhancement was less dramatic for other binaphthyls [(+/-)-BOH, (+/-)-BNA] as well as for (+/-)-barbiturates and (+/-)-paveroline derivatives. However, higher separation efficiency of the enantiomers was always observed with MEEKC than in MEKC.