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.     

Asymptotic discrimination between renewal processes

Limit theorems for the logarithm of the likelihood ratio are proven. With their help the rate of decrease in the probability of errors of the second kind in the Neumann-Pierson criterion is established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1382–1388, October, 1992.     

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.     

Synthesis of (1R,4R,7S)- and (1S,4S,7S)-2-(4-tolylsulfonyl)-5-phenyl-methyl-7-methyl-2,5-diazabicyclo[2.2.1]heptanes via regioselective opening of 3,4-epoxy-d-proline with lithium dimethyl cuprate

The synthesis of (1S,4S,7S)- and (1R,4R,7S)-2-(4-tolylsulfonyl>5-phenylmethyl-7-rnethyl-2,5-diazabicyclo-[2.2.1]heptanes ( 20 ) and ( 22 ) from trans 4-hydroxy-L-proline is described.     

Aminopropylcellulose,synthesis and derivatization

The preparation of 3-aminopropylcellulose from cyanoethylcellulose is readily achieved. Reduction of the cyano groups with borane-dimethyl sulfide in tetrahydrofuran or a borane-tetrahy-drofuran complex proceeds quantitatively in 3 h to a corresponding 3-aminopropylcellulose. The presence of primary amine functions is confirmed by spectroscopy and a positive ninhydrin test; the concentration of amino substituents, as ascertained by titration, ranged from 1.2 to 6.4 meq/g. Because the derivatives are neither soluble nor excessively swollen in water, applications as ion-exchange resins or chromatographic supports can be envisioned. Treatment of 3-aminopropyl-cellulose with acetyl chloride, phenyl isocyanate, or p-toluenesulfonyl isocyanate produced 3-acetamido-, 3-(N′-phenyluredo)-, or 3-(N′-p-toluenesulfonyluredo)-N-propylcellulose. Alkylation with methyl chloride yielded a water-soluble quaternary ammonium salt.     

Screening of urban aerosol particulate composites for selected metal distribution and their dependence on meteorological parameters

Local atmospheric aerosol particulate samples, collected as composites on daily 6-12 hour basis, at Quaid-i-Azam University campus, Islamabad, Pakistan, using high volume sampling technique, were analysed for Pb, Na, K, Fe, Mn, Cd, Cr, Ni, Zn and Co by FAAS method. The monitoring period ran from October, 2001 through March, 2002, with a total of 105 samples collected on cellulose filters, treated in part with the HNO3-based wet digestion method for metal quantification, and for particle size distribution separately. The metal content of the aerosols was examined in relation to dependence on meteorological parameters, such as temperature, relative humidity, wind speed, sun shine and pan evaporation. Statistical correlation analysis was conducted for multiple metal pairs in aerosols, and the data were examined in relation to meteorological parameters and relevant aerosol particle size fractions. The study revealed no viable strong correlation between the meteorological parameters and metal levels; in general, however, a significant positive correlation was found for temperature. A strong positive correlation was observed for PM<25 and PM2.5-10. For coarse particles (PM10-100 and PM>100), however, a negative correlation was observed. The levels of Na, K, Fe and Zn were found in the range of 1-5 microg/m3 while those for the rest of the metals in the sub microg/m3 range. Principal component analysis and cluster analysis were performed on dataset for source identification and appointment. Largest contribution (33%) was shown by the industrial emissions followed by traffic/road dust (16.7%).     

Retention, kinetics and thermodynamics profile of cadmium adsorption from iodide medium onto polyurethane foam and its separation from zinc bulk

The sorption behaviour of 2.5 × 10⁻⁵ M solution of Cd(II) on polyurethane foam (PUF) from iodide medium have been investigated. The conditions were optimized from aqueous solutions of different pH (1-10) and of acids of varied concentration (0.01-1.0 M). The maximum concentration of KI was found to be 0.24 M and equilibration time was established to be 20 min. The data successfully followed the Freundlich and Dubinin-Radushkevich (D-R) isotherms at low metal ion concentration while Langmuir isotherm followed at higher metal ion concentration. The Freundlich parameter 1/n = 0.66 ± 0.02 have been evaluated whereas D-R isotherm yields the sorption free energy E = 10.5 ± 0.1 kJ mol⁻¹ indicating ion exchange type chemisorption. The monolayer coverage (XL) constant of Langmuir isotherm was found to be 23.7 ± 0.4 mg g⁻¹. The numerical values of thermodynamics parameters enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) indicated the endothermic and spontaneous nature of sorption. The Scatchard plot analysis was tested to evaluate the binding sites of the PUF and stability constants of sorption were determined. On the basis of these parameters, the sorption mechanism was discussed. Among the foreign ions tested, Pb(II), Hg(II), cyanide and nitrite should be absent. The clean separation of Cd(II) from Zn(II) ions in the ratio 1:250, respectively, was achieved by column chromatography.     

Computer simulations of the solvation dynamics of Coumarin 153 in dimethylsulfoxide

We report molecular dynamics (MD) simulations of the solvation dynamics of Coumarin 153 in liquid dimethylsulfoxide using two distinct sets of partial charges for the coumarin probe. The excited state dipole moment of the coumarin and the dynamic Stokes shift in solution depend significantly on the type of charge distributions used. Nevertheless, the overall characteristics of the solvation responses obtained from both sets of charges are very similar and show good agreement with time-dependent Stokes shift experiments. Microscopic details of the solvent reorganization around the probe are discussed in light of the charge transfer upon photoexcitation.     

Synergic effect of triphenylphosphine oxide (TPPO) on the extraction of Hg(II), Se(IV), Co(II) and Mn(II) with fluorinated pyrazolone (HPMTFP)

Extraction of Hg(II), Se(IV), Mn(II) and Co(II) has been carried out with 1-phenyl-3-methyl-4-trifluoroacetyl-2-pyrazolin-5-one (HPMTFP) and triphenylphosphine oxide (TPPO) into chloroform from pH 1–10. Quantitative extraction of Hg(II), Mn(II) and Co(II) at pH 4 with equimolar 0.05M (PMTFP+TPPO) in chloroform was observed. Se(IV) remains unextracted at this pH range. The stoichiometric composition of the extracted complexes M(PMTFP)₂·nH₂O (M=Mn, Hg), M(PMTFP)₂·2TPPO (M=Mn and Co) and Co(PMTFP)₂·TPPO·H₂O at less than 0.1M TPPO has been established. The formation constantsK _m,0 andK _m,n and stability constants _m,n have been computed. The analytical method developed was applied to the IAEA standard reference material (SRM) potato fluor V-4 for the determination of these elements using NAA technique.     

Preparation,properties and x-ray crystal structure of a complex of bis(triphenylphosphoranylidene)ammonium iodide with 7,7,8,8-tetracyano-P-quinodimethane: (PPN)2(TCNQ)3(CH3CN)2

Bis(triphenylphosphoranylidene)ammonium iodide (PPN⁺I^?) forms a 2:3 complex with TCNQ [(PPN)₂(TCNQ)₃(CH₃CN)₂] that provides an example of a TCNQ complex containing acetonitrile in the crystal lattice; the material is a semi-conductor with trimerised TCNQ stacks.