Extraction-ability and -selectivity of tetra-aza-crown ethers for transition metal cations

In order to investigate the relative effects of the differences between the structures and lipophilicities of 1, 10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TA-18-crown-6) and the tetrabenzyl derivative of 1,10-dioxa-4, 7, 13, 16-tetra-azacyclo-octadecane (TBTA-18-crown-6) on their extraction-abilities and -selectivities for transition metal cations, constants of the overall extraction (logK _ex) of 1:1 (M:L) complexes, the distribution (K _D) for two diluents (CH₂Cl₂ and CHCl₃) with different dielectric constants have been determined at 25 ± 0.1 °C. The magnitude of logK _ex is largely determined by that of K _D. The equilibrium constants of TA-18-crown-6 have been compared with those of TBTA-18-crown-6. It is found that:(i) logK _ex sequences of TA-18-crown-6 and TBTA-18-crown-6 for transition metals in CH₂Cl₂ lie in order: Fe³⁺ > Cu²⁺ > Mn²⁺ > Co²⁺ > Cd²⁺ > Ni²⁺ > Zn²⁺ and Fe³⁺ > Cu²⁺ > Co²⁺ > Mn²⁺ > Ni²⁺ > Cd²⁺ > Zn²⁺ respectively; (ii) the stability sequences of two types of tetra-aza-crown ethers with the transition metal cations in CHCl₃ are the same as follows: Fe³⁺ > Ni²⁺ > Cu²⁺ > Co²⁺ > Zn²⁺ > Cd²⁺ > Mn²⁺, and (iii) unusual selectivities are observed for transition metal-tetra-aza-crowns, e.g. the high Fe³⁺/M ⁿ⁺ selectivity factors (S_f) of TA-18-crown-6, except for the competitive-extractions for the special case in CHCl₃ of TBTA-18-crown-6, it was found that the Mn²⁺/M ⁿ⁺ values were relatively higher according to the other transition metal cations. A systematic sequence in these two types of solvents is not found for a given transition metal cation in terms of the variation of selectivity with the tetra-aza-crown ethers. The results provide alternatives for the rational design of other specific ligands on the transition metal cations.     

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.     

Erratum: Synthesis and characterization of diorganotin(IV) complexes of Schiff bases with ONO‐type donors and crystal structure of [N‐(2‐hydroxy‐4‐nitrophenyl)‐3‐ethoxysalicylideneiminato]diphenyltin(IV)

The article referenced above was first published online on 30 August 2007 with incorrect pagination; the pagination has now been corrected online and in print. Copyright © 2007 John Wiley & Sons, Ltd.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

A locally computed suboptimal control strategy for a class of interconnected systems

In this paper, a locally computed suboptimal control strategy for a class of interconnected systems is introduced. First, optimal statefeedback control equations are derived for a finite-horizon quadratic cost. Then, the control for each subsystem is separated into two portions. The first portion stabilizes the isolated subsystem, and the second portion corresponds to the interactions. To achieve a locally calculable control, an approximation to the optimal control equations is introduced, and two iterative suboptimal control algorithms are developed. In the first algorithm, the initial conditions of subsystems are assumed to be known; in the second algorithm, this information is replaced by statistical distributions. The orders of errors in the iterations of the algorithm and in the suboptimality are given in terms of interconnections. An example with comparisons is also included to show the performance of the approach.     

Eigenvalues of Two Parameter Polynomial Operator Pencils of Waveguide Type

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1–3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.     

Levels of natural and artifical radioactivity in sediments in the Eastern Black Sea of Turkey

Sediment samples collected from the Eastern Black Sea in 1993 from 15 sampling stations of different depths have been analyzed. Natural and artifical radionuclide activity levels in offshore sediment samples from the Eastern Black Sea in Turkey are reported about seven years after the Chernobyl accident. The purpose of this paper is to follow up the earlier study and present results for the distributions of radionuclides in sediments of the Black Sea.     

Determination of bismuth, indium and lead in geological samples by electrothermal AAS Part 2. Comparative study of palladium and molybdenum containing chemical modifiers*

A comparative and systematic study has been carried out of the effects of palladium and molybdenum containing chemical modifiers, such as Pd + Rh, Pd + Pt, Pd + Ru, Pd + Rh + Pt, Pd + Rh + Ru, Mo + Pd, Mo + Rh, Mo + Ru and Mo + Pt and additionally tartaric acid (TA) as a reducing agent together with mixed modifiers for the thermal stabilization of Bi, In and Pb in a Zeeman electrothermal atomic absorption spectrometer (ETAAS). The effect of the mass ratios of the mixed modifier components on the maximum pretreatment temperature for the analytes has been determined. The modifier mixtures of Pd + Rh + Pt, Mo + Pd + TA and Mo + Pt + TA were found to be especially powerful for the determination of Bi, In and Pb. These mixed modifiers could increase the ashing temperatures of the analytes up to 1250–1400° C. They were applied to the determination of Bi and Pb in dissolved geological reference samples and accuracy and precision of the method were thereby enhanced. The percent relative error was decreased from 20.0 to 0.4 for Bi and from 10.5 to 0.3 for Pb, depending on the sample type. Received: 9 May 1997 / Revised: 19 August 1997 / Accepted: 20 August 1997     

Optimization Strategy for Isocratic Separation of α-Aspartame and Its Breakdown Products by Reversed Phase Liquid Chromatography

α-Aspartame (L-α-aspartyl-L-phenylalanine methyl ester) is increasingly being used in wide variety of commonly consumed food products. This structure contains ester and peptide bonds. The ester linkage may hydrolyze to produce L-α-aspartyl-L-phenylalanine or cyclohydrolyze to produce the corresponding diketopiperazine ring. This ring can open to form L-α-aspartyl-L-phenylalanine and ultimately this compound can hydrolyze to L-phenylalanine and L-aspartic acid. The pH, buffer type, concentration, the presence of water and temperature are other important factors affecting its stability. Because α-aspartame can lose its sweetness under these conditions determination of aspartame and its breakdown products is extremely important for diet foods quality. The optimum mobile phase for the chromatographic separation was found to be acetonitrile-water (20:80, ν/ν) with 5.10^?3 M hexanesulfonic acid and a pH of 2.6.