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.     

Surface Characterization of Sepiolite by Inverse Gas Chromatography

Inverse gas chromatography (IGC) was applied to characterize the surface of sepiolite. The adsorption thermodynamic parameters (the standard enthalpy (ΔH ⁰), entropy (ΔS ⁰) and free energy of adsorption (ΔG ⁰)), the dispersive component of the surface energy (γ _S ^d ), and the acid/base character of sepiolite surface were estimated by using the retention time of different non-polar and polar probes at infinite dilution region. The specific free energy of adsorption (ΔG ^sp ), the specific enthalpy of adsorption (ΔH ^sp ), and the specific entropy of adsorption (ΔS ^sp ) of polar probes on sepiolite were determined. ΔH ^sp were correlated with the donor and modified acceptor numbers of the probes to quantify the acidic K _A and the basic K _D parameters of the sepiolite surface. The values obtained for the parameters K _A and K _D indicated an acidic character for sepiolite surface.     

Synthesis and Characterization of Mononuclear Cobalt(II), Nickel(II), Copper(II), Zinc(II), Cadmium(II) and Dinuclear Uranyl(VI) Complexes with N,N-bis(2-{[(2,2-dimethyl-1,3-dioxolan-4-yl)methyl]amino}butyl) N′,N′-dihydroxyethanediimidamide

In this study, the new vic-dioxime ligand (LH₂) and its complexes with Co^II, Ni^II, Cu^II, Zn^II, Cd^II and UO₂^VI are described. The structures of these complexes were characterized by elemental analyses, i.r., ¹H- and ¹³C-n.m.r. spectra, u.v.–vis. spectroscopy, magnetic susceptibility measurements, conductivity measurements and thermogravimetric analyses (t.g.a.).     

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 new formulation of some discrete-time stochastic-parameter state estimation problems

Linear unbiased full-order state estimation problem for discrete-time models with stochastic parameters and additive finite energy type disturbance signals is reformulated in terms of linear matrix inequalities. Two estimation problems that are considered are the design for mean-square bounded estimation error and the design for the mean-square stochastic version of the suboptimal H_∞ estimator. These two designs are shown to apply to both the estimation with random sensor delay and estimation under observation uncertainty.     

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.     

Thermodynamic interactions of water-soluble homopolymers and double-hydrophilic diblock copolymer

Thermodynamic interaction parameters of water-soluble poly[2-(dimethylamino)ethyl methacrylate] (DMA) and poly[2-(N-morpholino)ethyl methacrylate] (MEMA) homopolymers and their diblock copolymer (DMA–MEMA) were investigated at the temperatures above their glass-transition temperatures (T_g) by inverse gas chromatography (IGC) method. Sorption thermodynamic parameters of some aliphatic, alicyclic and aromatic hydrocarbons, weight fraction activity coefficients, Flory–Huggins interaction parameters, and solubility parameters for hydrocarbons and polymers were calculated. It was observed that sorption thermodynamic parameters on (co)polymers depend on the molecular structures of hydrocarbons. Evaluating both the calculated values of the weight fraction activity coefficients and Flory–Huggins interaction parameters, the solving ability of the hydrocarbons for DMA, MEMA homopolymers, and DMA–MEMA diblock copolymer decreased in the following sequence: Aromatic > alicyclic > aliphatic hydrocarbons.     

Determination of the ground- and excited-state dipole moments of 4’-(hexyloxy)-4-biphenylcarbonitrile and 4-isothiocyanatophenyl 4-pentylbicyclo [2,2,2] octane-1-carboxylate nematic liquid crystals and their mixtures

The dipole moments of the ground and excited states of 4′-(hexyloxy)-4-biphenylcarbonitrile and 4-isothiocyanatophenyl 4-pentylbicyclo [2.2.2] octane-1-carboxylate nematic liquid crystals and their mixtures prepared in chloroform and dichloromethane were studied at room temperature. The dipole moments of the ground states of the all samples were calculated according to the Guggenheim–Smith method. The dipole moments of their excited states were determined with the help of the Lippert equation by measuring the absorption and fluorescence spectra, solvent polarity and refractive index values. It was determined that dipole moments of the excited states were higher than those of the ground states. Moreover, the dipole moments of the ground and excited states of two nematic liquid crystals were also estimated by using molecular mechanic method (Gaussian09 program (DFT/B3LYP 6-31G(dp)). The results obtained are interpreted in detail.     

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.