A long ℂ<Superscript>2</Superscript> which is not Stein

We construct a 2-dimensional complex manifold X which is the increasing union of proper subdomains that are biholomorphic to ℂ², but X is not Stein.     

Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Exposing Points on the Boundary of a Strictly Pseudoconvex or a Locally Convexifiable Domain of Finite 1-Type

We show that for any bounded domain \(\varOmega\subset\mathbb{C} ^{n}\) of 1-type 2k which is locally convexifiable at p∈bΩ, having a Stein neighborhood basis, there is a biholomorphic map \(f:\bar{\varOmega}\rightarrow\mathbb{C} ^{n} \) such that f(p) is a global extreme point of type 2k for \(f{(\overline{\varOmega})}\) .     

Four levels of pattern recognition

Problems of pattern recognition in chemistry and other subjects can be divided conveniently into four different types depending on the level of scope of the problem.(1) Classification into one of a number of defined classes. As an example blood samples taken from persons known to be either controls or welders are considered. The problem is whether trace element concentrations in these samples contain information on whether or not a person is a welder.(2) Level 1 plus the possibility that an object is an outlier, i.e. does not belong to any of the defined classes. As an example, the üse of ¹³C-n.m.r. data to decide whether 2-substituted norbornanes have the exo or endo structure is discussed. (2A) Level 2, asymmetric. This situation occurs when one class does not have a systematic structure, but another class is homogeneous and can be described by a level 2 model. This occurs in the classification of materials or compounds as good or bad, active or inactive, and in binary classifications. As an example the use of trace element data to classify steel samples as having good or poor properties of strength is discussed.(3) Level 2 plus the ability to relate the variables measured to external properties of continuous character. As an example, the classification of a series of chemical compounds as β -receptor blockers, β -receptor stimulants, or neither, on the basis of their structural variables is discussed. In addition, relations between these structural variables and the measured biological activity are sought within each of the two classes.(4) Level 3 with the difference that several external property variables in the objects are measured. It may be desirable to use variables of the objects both for classification and for relations to several property variables: such examples are numerous in analytical chemistry.     

The potential of Raman spectroscopy for characterisation of the fatty acid unsaturation of salmon

Raman spectroscopy has been evaluated for characterisation of the degree of fatty acid unsaturation (iodine value) of salmon (Salmo salar). The Norwegian Quality Cuts from 50 salmon samples were obtained, and the samples provided an iodine value range of 147.8-170.0 g I₂/100 g fat, reflecting a normal variation of farmed salmon. Raman measurements were performed both on different spots of the intact salmon muscle, on ground salmon samples as well as on oil extracts, and partial least squares regression (PLSR) was utilised for calibration. The oil spectra provided better iodine value predictions than the other data sets, and a correlation coefficient of 0.87 with a root mean square error of cross-validation of 2.5 g I₂/100 g fat was achieved using only one PLSR component. The ground samples provided comparable results, but at least two PLSR components were needed. Higher prediction errors were obtained from Raman spectra of intact salmon muscle, and this may partly be explained by sampling uncertainties in the relation between Raman measurements and reference analysis. All PLSR models obtained were based on chemically sound regression coefficients, and thus information regarding fatty acid unsaturation is readily available from Raman spectra even in systems with high contents of protein and water. The accuracy, the robustness and the low complexity of the PLSR models obtained suggest Raman spectroscopy as a promising method for rapid in-process control of the degree of unsaturation in salmon samples.     

Preparation and properties of two indium antimony selenides

Crystals of antimony-doped In₂Se₃ were grown by the Bridgeman method. This compound, whose composition is In_1.8Sb_0.2Se₃, appears to be isostructural with In_1.9As_0.1Se₃. The refined unit cell parameters are a = 3.97(1), c = 18.87(1) Å. Orthorhombic crystals of InSbSe₃ were grown from an isothermal melt. The refined unit cell parameters are a = 9.43(1), b = 14.02(5), and c = 3.96(1) Å. These parameters agree with those determined for α-InSbSe₃ by other studies. The observed densities measured by a hydrostatic technique are 5.98(3) g/cm³ for In_1.8Sb_0.2Se₃ and 6.07(2) g/cm³ for InSbSe₃. The room temperature dc resistivity for In_1.8Sb_0.2Se₃ has been found to be 4.4 × 10⁴ Ω-cm, whereas that of InSbSe₃ has been found to be 15.2(1) Ω-cm. A resistivity versus temperature study has beenn carried out for InSbSe₃ between 230 and 400°K. Optical studies indicate that In_1.8Sb_0.2Se₃ is an n-type semiconductor with a band gap of 1.1 eV and InSbSe₃ is a p-type semiconductor with a band gap of 0.92 eV.     

The centrifugal stretching model and the deviation from the L(L+1) rule for rare-earth nuclei

The deviation from the L(L+1) rule for the deformed rare-earth nuclei is formulated in terms of the centrifugal stretching model of Sood. A two-parameter formula is presented which reproduces the general experimental trend. The result is discussed and compared with the results of Sood and Holmberg.