Determination of nickel in standard rocks and glasses by photon activation analysis with 30-MeV bremsstrahlung

The determination of nickel in various silicate rocks and glasses by photon activation analysis with a linear electron accelerator is described. Simultaneous irradiation of the sample and comparative standards produces the ⁵⁸Ni(γ, n)⁵⁷Ni reaction, and a post-irradiation chemical separation is used in conjunction with Ge(Li) γ-spectrometry. Nickel abundances for ten standard silicate rocks and two elementally doped glasses are presented and compared with the data previously published. The method is quite simple and gives good reproducible results for nickel down to sub-p.p.m. levels.     

About a minimax theorem of Matthies,Strang and Christiansen

We give a new minisup theorem for noncompact strategy sets. Our result is of the type of the Matthies-Strang-Christiansen minimax theorem where the hyperplane should be replaced by any closed convex set. As an application, we derive a slight generalization of the Matthies-Strang-Christiansen minimax theorem.     

Evaluation of the use of consensus values in proficiency testing programmes

Proficiency testing (PT) is an essential tool used by laboratory accreditation bodies to assess the competency of laboratories. Because of limited resources of PT providers or for other reasons, the assigned reference value used in the calculation of z-score values has usually been derived from some sort of consensus value obtained by central tendency estimators such as the arithmetic mean or robust mean. However, if the assigned reference value deviates significantly from the ‘true value’ of the analyte in the test material, laboratories’ performance will be evaluated incorrectly. This paper evaluates the use of consensus values in proficiency testing programmes using the Monte Carlo simulation technique. The results indicated that the deviation of the assigned value from the true value could be as large as 40%, depending on the parameters of the proficiency testing programmes under investigation such as sample homogeneity, number of participant laboratories, concentration level, method precision and laboratory bias. To study how these parameters affect the degree of discrepancy between the consensus value and the true value, a fractional factorial design was also applied. The findings indicate that the number of participating laboratories and the distribution of laboratory bias were the prime two factors affecting the deviation of the consensus value from the true value.     

Limit of detection estimator for second-order bilinear calibration

A new approach is developed for estimating the limit of detection in second-order bilinear calibration with the generalized rank annihilation method (GRAM). The proposed estimator is based on recently derived expressions for prediction variance and bias. It follows the latest IUPAC recommendations in the sense that it concisely accounts for the probabilities of committing both types I and II errors, i.e. false positive and false negative declarations, respectively. The estimator has been extensively validated with simulated data, yielding promising results.     

Ruthenium(II) complexes with mono and ditertiary arsines and phosphines and their reaction with small molecules

Dichlorotetrakis(dimethylsulphoxide)ruthenium(II) reacts with AsPh₃ AsMePh₂, AsMe₂Ph and SbPh₃ in ethanolic hydrochloric acid solution to yield the complexes RuCl₂(DMSO)₂(AsPh₃)₂, RuCl₂(DMSO) L₂ (L = AsMePh₂, AsMe₂Ph, SbPh₃) respectively. The treatment of ruthenium(II) blue solution with AsMePh₂, AsMe₂Ph and SbPh₃ in alcohol resulted in the formation of the complexes; RuCl₂L₃ (L = AsMePh₂, AsMe₂Ph and SbPh₂), respectively. The reaction of RuCl₂(DMSO)₄ with the bidentate ligands 1,2 bis (diphenylarsino)methane (DPAM), 1,2 bis(diphenylarsino)ethane (DPAE) and 1,2 bis (diphenylphosphino)methane (DPPM). 1,2 bis(diphenylphosphino)ethane (DPPE), in ethanol gave the complexes RuCl₂(DPAM)₂, RuCl₂(DPAE)₂, RuCl₂ (DPPM)₂ RuCl₂(DPPE)₂, respectively. The complexes thus obtained undergo reaction with carbon monoxide, hydrogen, molecular nitrogen and nitric oxide to yield a variety of mixed ligand complexes.     

Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

On statistical properties of the lyapunov exponent of the generalized skew tent map

The statistical properties of the Lyapunov exponent of the chaotic generalized skew tent map is studied. Expressions of the mean and the variance of this Lyapunov exponent at each discrete time index are obtained. A sufficient condition for weakly mixing of the chaotic generalized skew tent map is derived, and the asymptotic distribution of its Lyapunov exponent is provided.     

Unscaled spatial branging process with interaction: macrospic equation and local equilibrium

For some spatial branching processes with interaction considered as measure–valued processes, convergence to solutions of non–linear macroscopic equation and local equilibrium are proved, without scaling but providing each particle with a small mass ε and assuming convergence of the initial distribution when ε goes to 0     

A note on commutators of Hardy operators

Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample.