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.     

Preparation of a novel molecularly imprinted polymer using a water-soluble crosslinking agent

A molecularly imprinted polymer was prepared using a water-soluble crosslinking agent. An ionic complex was utilized as the assembly for the template molecule and the functional monomer, and water as porogenic solvent during preparation of the imprinted polymer. The results of chromatographic evaluations for the prepared polymer suggested that the polymer had much lower hydrophobicity compared with usual octadecyl group bonded silica or the usual molecular imprinted polymer prepared from ethyleneglycol dimethacrylate, and the selective recognition ability for template molecule in the completely aqueous condition.     

Synthesis and characterization of oligo-4-[(pyridin-3-ylimino)methyl]phenol

The oxidative polycondensation of 4-[(pyridin-3-ylimino)methyl]phenol (4-PIMP) with O₂, H₂O₂, and NaOCl was studied in an aqueous alkaline medium between 50°C and 90°C. Oligo-4-[(pyridin-3-ylimino)methyl]phenol (O-4-PIMP) prepared was characterized by ¹H-NMR, ¹³C-NMR, FT-IR, UV-VIS, size-exclusion chromatography, and elemental and thermal analyses techniques. At the optimum reaction conditions, the yield of O-4-PIMP was 18.9%, 39.4%, and 46.8% using H₂O₂, O₂, and NaOCl oxidant, respectively. According to the TG analysis, the initial degradation temperature of O-4-PIMP was 218°C, which was by 50°C higher than that of 4-PIMP. Thermal analyses of 4-PIMP and O-4-PIMP were carried out in N₂ atmosphere at 15–1000°C. The highest occupied molecular orbital, the lowest unoccupied molecular orbital, and electrochemical energy gaps of 4-PIMP and O-4-PIMP were determined from the onset potentials for n-doping and p-doping, respectively. Also, optical band gaps of 4-PIMP and O-4-PIMP were determined according to UV-VIS measurements.     

Reaction of Aln clusters with oxygen and ammonia

Aluminum clusters were generated by a laser vaporization method. Ionization potential of Al₂ was found to be lower than that of Al. In the reaction with oxygen at high concentration, the mixed cluster Al₉O₇ survives predominantly as a stable cluster. Ammonia was found to be adsorbed weakly on the Al_n surface.     

Vibronic coupling and Raman intensities of pyrazine

The fluorescence spectrum of pyrazine vapour and the Raman spectra of liquid pyrazine excited at various wavelengths were observed. The appearance of the long progression of the hydrogen bending vibration ν₅ (b_2g) in the fluorescence spectrum and a remarkable preresonance effect of the Raman line of the same vibration confirm the theoretical prediction given by Albrecht.     

Sodium p‐nitro­benzoxasulfamate monohydrate

The title compound, alternatively named sodium 6‐nitro‐3H‐1,2,3‐benzoxa­thia­zole 2,2‐dioxide monohydrate, Na⁺·C₆H₃­N₂O₅S^?·H₂O, consists of chains of NaO₇ units, with the seven donor‐O atoms coming from two water mol­ecules and five p‐­nitro­benzoxasulfamate anions. The seven‐coordinate geometry around the Na⁺ ion is described as monocapped trigonal prismatic, but with a large distortion from ideal geometry. Each triangular face is defined by one O atom each from a water mol­ecule, a nitro group and a sulfonyl group. An O atom from a sulfonyl group caps one of the square faces of the trigonal prism in an unsymmetrical fashion. The water mol­ecules and one sulfonyl O atom are involved in bridging adjacent units, as is the nitro group of the anion. The sulfamate ions adopt an antiparallel alignment between the NaO₇ units and are connected to each other by C—H?O and π–π interactions. The three‐dimensional crystal structure is stabilized by a network of strong O—H?N hydrogen bonds.     

Catalytic air oxidation of manganese in synthetic waters

An attempt was made to study the oxidation of manganese by air in synthetic waters. A series of batch experments were performed at differnet values of concentration, temperature and pH. Unoxidized manganese in the solution was determined by formaldoxime spectrometric method. Results of these studies indicated that the air oxidation of manganese soluble in water can be effectively performed in basic media and that oxidation yield increasedwith an increase in pH and concentration. The yield was very high in the presence of manganese dioxide, sepiolite or clinoptilolite in solution and, the oxidation was almost completed especially at high values of pH and concentration. The reaction was found to be first order with respect to Mn²⁺ with a very low activation energy. A yield of 62% was obtained for the air oxidation of wastewater taken from the treatment plant of Corum Municipality.     

Chromatographic molecular recognition for catechol-related compounds using thiacalix[4]arene as an effective selector

Thiacalix[4]arene (5,11,17,23-tetra-tert-butyl-25,26,27,28-tetrahydroxy-2,8,14,20-tetrathiacalix[4]arene) is an amphiphilic molecule comprising four p-tert-butylphenol-like groups ortho-linked by single sulfur atoms. This molecule has a high electron density area owing to the close proximity of the hydroxyl groups and sulfur atoms. We studied the applicability of this interesting compound as a selector for high-performance liquid chromatography (HPLC) thereby presumably exploiting this feature. Firstly, uniformly sized polymer particles were prepared by using a multi-step swelling and polymerization method with ethylene glycol dimethacrylate (EDMA) as a cross-linker. Methacrylic acid (MAA) was introduced onto the surface of the resulting polymer particles through a new modification method. Thiacalix[4]arene was chemically bonded through the MAA group by using 1,4-dibromobutane as a spacer to reduce steric hindrance around the MAA and the polymer particle itself. The performance of the prepared polymer-based thiacalix[4]arene-modified stationary phase was evaluated with HPLC. Specific chromatographic retention behavior was observed for catechol relative to positional isomers of xylene, cresol, and benzene-diol. Catecholamine and catechol showed specific chromatographic retention behavior.