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.     

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.     

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.     

Studies on Mononuclear Chelates Derived from Substituted Schiff Base Ligands: Synthesis and Characterization of a New 5-Methoxysalicyliden-<Emphasis Type="Italic">p</Emphasis>-Aminoacetophenoneoxime and Its Complexes with Co(II), Ni(II), Cu(II), and Zn(II)

New complexes of Co(II), Ni(II), Cu(II), and Zn(II) with new Schiff bases derived by the condensation of p-aminoacetophenoneoxime with 5-methoxysalicylaldehyde are synthesized. The compounds are characterized by elemental analyses, magnetic susceptibility measurements, IR, ¹H and ¹³C NMR spectra, electronic spectral data, and molar conductivity. The thermal stabilities of the compounds are also reported. The Schiff base acts as bidentate O,N-donor atoms, and their metal complexes are supposed to possess a tetrahedral geometry with respect to the central metal ion. The general formula of the 5-methoxysalicyliden-p-aminoacetophenoneoxime Co(II), Ni(II), Cu(II), and Zn(II) complexes is Co(L)₂, Ni(L)₂, Cu(L)₂, and Zn(L)₂.     

Structures and stabilities of 3d-transition metal-benzene organometallic clusters

In the gas phase, we have successfully synthesized organometallic clusters, M_n(benzene)_m (M=3d transition metal atoms), by using a laser vaporization method. The measurements of mass spectra and ionization energies (E_i) have revealed that the organometallic clusters can take two types of structures; layered sandwich structures (m = n + 1) and metal clusters saturatedly covered with benzenes. For early transition metals of Sc, Ti, and V, only the multiple decker sandwich structure clusters were preferentially produced, in which benzene and metal atoms are alternately piled up. For late transition metals of Co and Ni, the metal clusters saturatedly surrounded by benzenes were also produced as well as the sandwich clusters. Furthermore, the E_is of M₁(benzene)₂ (M = Sc-Ni) were systematically measured and their electronic properties will be discussed.     

Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problem can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the v power of the monomer concentration C, in which the proportionality constant a = k_pR/k, where k_p and k_t are the propagation and termination rate constants, respectively, and R_i is the initiation rate. The values of v, w, and z depend on the particular reaction system. The results of our earlier work were generalized by allowing a non-Fickian diffusion rate, obtained from an extension of the Fujita free-volume theory, which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D₀ [exp(δC/M)], where M is the saturation concentration. It was shown that a reaction system is characterized by the three dimensionless parameters v, δ, and A = (L/2)[aM^(v?1)/D₀]^1/2, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of δ and v cause a reaction system to behave closer to the diffusion-free regime. The transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, v order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. The dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system.     

Iron speciation by solid phase extraction and flame atomic absorption spectrometry using N,N′-bis-(2-hydroxy-5-bromobenzyl)-2-hydroxy-1,3-diiminopropane

A new Schiff base, N,N′-bis-(2-hydroxy-5-bromobenzyl)-2-hydroxy-1,3-diiminopropane, has been synthesized for the very sensitive determination of iron(III) and iron(II) in natural water samples. It enabled a very selective and rapid method for iron determination to be developed. The method has also been applied to total iron determination in sediment samples. In the preconcentration system, the Schiff base reagent is mixed with the samples and chelates containing iron(III). The complexes are then adsorbed on silica gel within a column system. Elution of the adsorbed chelate from the silica gel was performed with a small volume of acetone containing 2.5% nitric acid. The iron is measured off-line by flame atomic absorption spectrometry. The method can be applied to the preconcentration, separation and speciation of iron. The effects of parameters such as pH, sample flow rate, eluent flow rate, foreign ions and ligand concentration have been investigated. The effect of humic acid that can produce complexes with metal ions in natural systems has also been investigated. The results obtained indicate that the method is not affected by the presence of up to 10 ppm humic acid, which would be a very high concentration to be present in natural systems. The solid phase extraction method developed has been applied to the determination of iron in both natural water samples and sediment samples. The LOD was found to be 0.17 mg L⁻¹ when no preconcentration was used, although preconcentration factors of 100 could be achieved. The recovery values for spiked samples were between 100 and 104%. The results were compared statistically with those from the standard 1,10 phenanthroline method used for iron speciation in water systems. A Student’s t-test indicated no significant difference between the two methods. In addition, this method was applied to the analysis of a certified sediment sample, LGC 6156. Generally, a 10-fold preconcentration factor was required for the analysis of natural water samples.     

Frequency and voltage-dependent electrical and dielectric properties of Al/Co-doped PVA/p-Si structures at room temperature

In order to investigate of cobalt-doped interracial polyvinyl alcohol （PVA） layer and interface trap （Dit） effects, A1/p- Si Schottky barrier diodes （SBDs） are fabricated, and their electrical and dielectric properties are investigated at room temperature. The forward and reverse admittance measurements are carded out in the frequency and voltage ranges of 30 kHz-300 kHz and -5 V-6 V, respectively. C-V or er-V plots exhibit two distinct peaks corresponding to inversion and accumulation regions. The first peak is attributed to the existence of Dit, the other to the series resistance （Rs）, and interfacial layer. Both the real and imaginary parts of dielectric constant （er and err） and electric modulus （Mr and Mrr）, loss tangent （tan~）, and AC electrical conductivity （aac） are investigated, each as a function of frequency and applied bias voltage. Each of the M~ versus V and Mrr versus V plots shows a peak and the magnitude of peak increases with the increasing of frequency. Especially due to the Dit and interfacial PVA layer, both capacitance （C） and conductance （G/w） values are strongly affected, which consequently contributes to deviation from both the electrical and dielectric properties of A1/Co-doped PVA/p-Si （MPS） type SBD. In addition, the voltage-dependent profile of Dit is obtained from the low-high frequency capacitance （CLF-CHF） method.     

Three-Phase Partitioning as a Rapid and Easy Method for the Purification and Recovery of Catalase from Sweet Potato Tubers (Solanum tuberosum)

Three-phase partitioning (TPP) was used to purify and recover catalase from potato crude extract. The method consists of ammonium sulfate saturation, t-butanol addition, and adjustment of pH, respectively. The best catalase recovery (262 %) and 14.1-fold purification were seen in the interfacial phase in the presence of 40 % (w/v) ammonium sulfate saturation with 1.0:1.0 crude extract/t-butanol ratio (v/v) at pH 7 in a single step. The sodium dodecyl sulfate–polyacrylamide gel electrophoresis (SDS-PAGE) analysis of the enzyme showed comparatively purification and protein molecular weight was nearly found to be 56 kDa. This study shows that TPP is a simple, economical, and quick method for the recovering of catalase and can be used for the purification process.