Contribution to the certification of B,Cd, Cu,Mg and Pb in a synthetic water sample,by use of isotope-dilution ICP-MS,for Comparison 12 of the International Measurement Evaluation Programme

The contribution of the Institute for Reference Materials and Measurements to the certification of the B, Cd, Cu, Mg, and Pb content of a synthetic water sample used in Comparison 12 of the International Measurement Evaluation Programme (IMEP-12) is described. The aim of the IMEP programme is to demonstrate objectively the degree of equivalence and quality of chemical measurements of individual laboratories on the international scene by comparing them with reference ranges traceable to the SI (Système International d'Unités). IMEP is organized in support of European Union policies and helps to improve the traceability of values produced by field chemical measurement laboratories. The analytical procedure used to establish the reference values for the B, Cd, Cu, Mg, and Pb content of the IMEP-12 sample is based on inductively coupled plasma-isotope-dilution mass spectrometry (ICP-IDMS) applied as a primary method of measurement. The measurements performed for the IMEP-12 study are described in detail. Focus is on the element boron, which is particularly difficult to analyze by ICP-MS because of potential problems of low sensitivity, high mass discrimination, memory effects, and abundance sensitivity. For each of the certified amount contents presented here a total uncertainty budget was calculated using the method of propagation of uncertainties according to ISO (International Organization for Standardization) and Eurachem guidelines. For all investigated elements with concentrations in the low micro g kg(-1) and mg kg(-1) range (corresponding to pmol kg(-1) to the high micro mol kg(-1) level), SI-traceable reference values with relative expanded uncertainties ( k=2) of less than 2 % were obtained.     

Molecular dynamics study of gas hydrate formation

Long-time-scale molecular dynamics simulations are presented of the spontaneous formation of methane hydrate at a methane/liquid water interface. The water film was prepared at 300 K, 30 bar and showed no significant hydrate order. On crash cooling to 250 K, 300 bar (about 20 K subcooling), the system showed a rapid growth of hydrate clusters. Contrary to popular models for hydrate nucleation, the clusters formed first as two-dimensional arrangements and only later into three-dimensional cage structures; the results are, however, consistent with the local order model proposed recently. The hydrate clusters showed clear signatures of the type II hydrate structure even though the type I structure is the thermodynamically stable form for methane hydrate; this is in accord with the results of recent diffraction experiments.     

An ODE-based approach to nonlinearly constrained minimax problems

We consider the following problem: Choosex ₁, ...,x _n to wherem ₁,m ₂,m ₃ are integers with 0m ₁m ₂m ₃, thef _i are given real numbers, and theg _i are given smooth functions. Constraints of the formg _i (x ₁, ...,x _n )=0 can also be handled without problem. Each iteration of our algorithm involves approximately solving a certain non-linear system of first-order ordinary differential equations to get a search direction for a line search and using a Newton-like approach to correct back into the feasible region when necessary. The algorithm and our Fortran implementation of it will be discussed along with some examples. Our experience to date has been that the program is more robust than any of the library routines we have tried, although it generally requires more computer time. We have found this program to be an extremely useful tool in diverse areas, including polymer rheology, computer vision, and computation of convexity-preserving rational splines.     

Determination of the intrinsic site pK(a) value and cooperativity of the symmetrical hexadentate chelator N,N',N'-tris[2-(3-hydroxy-2-oxo-1,2-dihydropyridin-1-yl)acetamido]ethylamine

The three overlapping pK(a) values of N,N',N'-tris[2-(3-hydroxy-2-oxo-1,2-dihydropyridin-1-yl)acetamido]ethylamine, a tripodal hexadentate chelator formed from three 3-hydroxy-2(1H)-pyridinone moieties amide linked to tris-(2-aminoethyl)amine, were determined by simultaneous spectrophotometric and potentiometric titration. The data was analysed by non-linear regression with constraints to deal with (a) the highly correlated absorptivities and (b) the highly correlated pK(a) values. The three pK(a) values were optimized first from the spectrophotometric data (absorbance vs. pH) by non-linear regression to a model in which the molar absorptivity of the ith species ((i)) was constrained by the correlation equation (i) = epsilon (0) + (epsilon (3) - epsilon (0))i 3 with i = 0, 1, 2, 3, where (3) and (0) represent the molar absorptivities of the most protonated and least protonated species, respectively. The molar absorbitivity of the four species defined by three pK(a) values is, therefore, linearly related to proton stoichiometry. The pK(a) values were then optimized from the potentiometric data (pH vs. titrant volume) by non-linear regression to a model in which the three pK(a) values were constrained by the correlation equation pK(a(i)) = pK(a(int)) + b(i - 1) + (i - 2)log(3) where i = 1, 2 or 3. This expresses the three pK(a) values in terms of only two optimizable parameters, the intrinsic site pK(a) (pK(a(int))) and the interaction energy between sites (b). The fixed term (i - 2)log(3) accounts for the statistical effect on the pK(a) values of three equivalent ionizable sites. The modified analytical derivatives required for optimization of these parameters by the Gauss-Newton-Marquardt algorithm and the merits of optimizing pK(a) values with these two correlation equations are discussed. The optimized pK(a) values were 9.31 +/- 0.01, 8.75 +/- 0.01 and 8.19 +/- 0.01. The separation between pK(a) values is 0.58 comprising 0.477 for the statistical effect and 0.081 for the interaction energy while the intrinsic site pK(a) is 8.672 +/- 0.005. The tertiary amine at the centre of the tripodal backbone has a pK(a) of 5.88 +/- 0.03.     

A Popov-theory-based approach to digital H{infty} control with measurement feedback for Pritchard-Salamon systems

In this paper, we deal with the digital output-measurement-feedbackH control problem for Pritchard-Salamon infinite-dimensionalsystems with unbounded input and output operators. A discretePopov-theory-based solution is given in terms of the solvabilityof Kalman-Szegö-Popov-Yakubovitch systems associated withthe equivalent discrete-time time-invariant system obtainedby lifting the T-periodic continuous-time system.