Montgomery Multiplication in GF(2k)

We show that the multiplication operation c=a · b · r^-1 in the field GF(2^k can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform a thorough performance analysis, and compare the algorithm to the standard multiplication algorithm in GF(2^k. The Montgomery multiplication can be used to obtain fast software implementations of the discrete exponentiation operation, and is particularly suitable for cryptographic applications where k is large.     

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.     

Fluctuating energy level Landau-Teller theory: application to the vibrational energy relaxation of liquid methanol

State-to-state vibrational energy relaxation (VER) rates of the OH-stretch fundamental to select vibrational modes of liquid methanol are presented. The rates are calculated via a modified, fluctuating Landau-Teller (FLT) theory approach, which allow for dynamical vibrational energy level shifts. These rates are then compared to previously published results from Gulmen and Sibert [J. Phys. Chem. A 2004, 108, 2389] for the traditional Landau-Teller (LT) method as well as results calculated through time-dependent perturbation theory (TD), which naturally allow for the fluctuation. For the first time, this method is applied to a polyatomic molecular system, and the FLT theory greatly reduces the discrepancy between the LT and TD results or, at a minimum, is comparable to the LT approach with very little additional computational cost.     

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.     

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.     

New Copper（Ⅱ） and Nickel（Ⅱ） Complexes of 4-Morpholinoacetophenone Thiosemicarbazone： Structural, Electrochemical and Antimicrobial Studies

4-Morpholinoacetophenone thiosemicarbazone, MAPT, and its nickel（Ⅱ） and copper（Ⅱ） complexes have been prepared and characterized by elemental analysis, magnetic susceptibility, spectral methods （FT-IR, ^1H NMR） and cyclic voltammetry. Electrochemical behaviors of the complexes have been studied by cyclic voltammetry in DMF media showing metal centered reduction processes for both of them. The redox properties, nature of the electrode processes and the stability of the complexes were discussed. [Cu（MAPT）2]Cl2 complex shows Cu（Ⅱ）/Cu（Ⅰ） couple and quasi-reversible wave associated with the Cu（Ⅲ）/Cu（Ⅱ） process. The reduction/oxidation potential values depend on the structures of complexes. Also, the antimicrobial activities of these complexes were determined against S. aureus, E. coli and B. subtilis.