The quality of consensus values

The definition of a metrological term “quality” is discussed in relation to a series of consensus values pertaining to a set of measurement results from an actual PT exercise. It was concluded that the definition used by ISO in quality management systems could be readily interpreted in the metrological sphere.     

Systems of variational inequalities in the context of optimal switching problems and operators of Kolmogorov type

In this paper we study the system $$\begin{aligned}&\min \biggl \{-\mathcal H u_i(x,t)-\psi _i(x,t),u_i(x,t)-\max _{j\ne i}(-c_{i,j}(x,t)+u_j(x,t))\biggr \}=0,\\&u_i(x,T)=g_i(x),\ i\in \{1,\ldots ,d\}, \end{aligned}$$ where \((x,t)\in \mathbb R ^{N}\times [0,T]\) . A special case of this type of system of variational inequalities with terminal data occurs in the context of optimal switching problems. We establish a general comparison principle for viscosity sub- and supersolutions to the system under mild regularity, growth, and structural assumptions on the data, i.e., on the operator \(\mathcal H \) and on continuous functions \(\psi _i\) , \(c_{i,j}\) , and \(g_i\) . A key aspect is that we make no sign assumption on the switching costs \(\{c_{i,j}\}\) and that \(c_{i,j}\) is allowed to depend on \(x\) as well as \(t\) . Using the comparison principle, the existence of a unique viscosity solution \((u_1,\ldots ,u_d)\) to the system is constructed as the limit of an increasing sequence of solutions to associated obstacle problems. Having settled the existence and uniqueness, we subsequently focus on regularity of \((u_1,\ldots ,u_d)\) beyond continuity. In this context, in particular, we assume that \(\mathcal H \) belongs to a class of second-order differential operators of Kolmogorov type of the form: $$\begin{aligned} \mathcal H =\sum _{i,j=1}^m a_{i,j}(x,t)\partial _{x_i x_j}+\sum _{i=1}^m a_i(x,t)\partial _{x_i} +\sum _{i,j=1}^N b_{i,j}x_i\partial _{x_j}+\partial _t, \end{aligned}$$ where \(1\le m\le N\) . The matrix \(\{a_{i,j}(x,t)\}_{i,j=1,\ldots ,m}\) is assumed to be symmetric and uniformly positive definite in \(\mathbb R ^m\) . In particular, uniform ellipticity is only assumed in the first \(m\) coordinate directions, and hence, \(\mathcal H \) may be degenerate.     

Determination of xylo-oligosaccharides in enzymatically hydrolysed pulp by liquid chromatography and capillary electrophoresis

Three different commercial β-1,4-endoxylanase preparations were used to hydrolyze bleached kraft pulp. Xylo-oligosaccharides in the produced filtrates were separated and quantified using both high performance liquid chromatography (HPLC) and capillary electrophoresis (CE). All the determinations were performed without sample derivatization. The analytical methods were used to highlight the differences between the enzymes behaviour in terms of hydrolysates, but also to estimate the productivity of xylo-oligosaccharides from kraft pulp when the bleached material would be used in biorefining industry. The research showed that the glycosyl hydrolase family 10 enzyme produced by Aspergillus oryzae released xylobiose and xylotriose from the pulp material. The major oligosaccharides released by the family 11 enzyme produced by Bacillus sp. were xylotriose, xylobiose and xylotetraose. On the contrary, another family 11 enzyme produced by A. oryzae produced also xylose. The HPLC results agreed well with the xylose concentrations obtained after acid hydrolysis. The CE data showed the same trend, but much lower concentrations were identified than with HPLC. At the same time the HPLC method was able to separate only small oligosaccharides, whereas CE could be used for separation of all the xylo-oligosaccharides from xylobiose to xylohexaose. The highest xylo-oligosaccharide yield was achieved with Shearzyme at pH 5 corresponding to 22 % of total xylan from bleached birch kraft pulp.     

Combined lp and quasi-Newton methods for minimax optimization

We present an algorithm for minimax optimization that combines LP methods and quasi-Newton methods. The quasi-Newton algorithm is used only if an irregular solution is detected, in which case second-order derivative information is needed in order to obtain a fast final rate of convergence. We prove that the algorithm can converge only to a stationary point and that normally the final rate of convergence will be either quadratic or superlinear. The performance is illustrated through some numerical examples.     

Evaluation of sample fractionation using micro-scale liquid-phase isoelectric focusing on mass spectrometric identification and quantitation of proteins in a SILAC experiment

Mass spectrometric methods based on stable isotopes have shown great promise for identification and quantitation of complex mixtures. Stable isotope labelling by amino acids in cell culture (SILAC) is a straightforward and accurate procedure for quantitation of proteins from cell lines, that are cultured in media containing the natural amino acid or its isotopically labelled analogue, giving rise to either 'light' or 'heavy' proteins. The two cell populations are pooled and treated as a single sample, which allows the use of various protein purification methods without introducing errors into the quantitative analysis. The quantitation of the proteins is based on the intensities of the light and heavy peptides. The increased number of peptides in a quantitative experiment arising from peptide pairs implies that prefractionation is critical prior to liquid chromatography/mass spectrometric (LC/MS) analysis to minimise signal suppression effects and errors in measurements of the intensity ratios. In this study, the effect of a prefractionation step on identification and quantitation of proteins in a SILAC experiment was evaluated. We show that micro-scale liquid-phase isoelectric focusing in the Micro Rotofor separates proteins into well-defined fractions and reduces the sample complexity. Furthermore, the fractionation enhanced the number of identified proteins and improved their quantitation.     

Cluster glass magnetism in the phase-separated Nd2/3Ca1/3MnO3 perovskite

A detailed study of the low-temperature magnetic state and the relaxation in the phase-separated colossal magnetoresistance Nd_2/3Ca_1/3MnO₃ perovskite has been carried out. Clear experimental evidence of the cluster-glass magnetic behavior of this compound has been revealed. Well defined maxima in the in-phase linear ac susceptibility χ′(T) were observed, indicative of the magnetic glass transition at T_g∼60 K. Strongly divergent zero-field-cooled and field-cooled static magnetizations and frequency dependent ac susceptibility are evident of the glassy-like magnetic state of the compound at low temperatures. The frequency dependence of the cusp temperature T_max of the χ′(T) susceptibility was found to follow the critical slowing down mechanism. The Cole–Cole analysis of the dynamic susceptibility at low temperature has shown extremely broad distribution of relaxation times, indicating that spins are frozen at “macroscopic” time scale. Slow relaxation in the zero-field-cooled magnetization has been experimentally revealed. The obtained results do not agree with a canonical spin-glass state and indicate a cluster glass magnetic state of the compound below T_g, associated with its antiferromagnetic–ferromagnetic nano-phase segregated state. It was found that the relaxation mechanisms below the cluster glass freezing temperature T_g and above it are strongly different. Magnetic field up to about μ₀H∼0.4 T suppresses the glassy magnetic state of the compound.