Limit theorems for triangular urn schemes

We study a generalized Pólya urn with balls of two colours and a triangular replacement matrix; the urn is not required to be balanced. We prove limit theorems describing the asymptotic distribution of the composition of the urn after a long time. Several different types of asymptotics appear, depending on the ratio of the diagonal elements in the replacement matrix; the limit laws include normal, stable and Mittag-Leffler distributions as well as some less familiar ones. The results are in some cases similar to, but in other cases strikingly different from, the results for irreducible replacement matrices.     

Coupling and Poisson approximation

We give an overview of the Stein-Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other applications it suffices to show the existence of couplings with certain monotonicity properties.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

Study of DNA coated nanoparticles as possible programmable self-assembly building blocks

Nanoparticles coated with single stranded DNA have been shown to efficiently hybridize to targets of complementary DNA. This property might be used to implement programmable (or algorithmic) self-assembly to build nanoparticle structures. However, we argue that a DNA coated nanoparticle by itself cannot be used as a programmable self-assembly building block since it does not have directed bonds. A general scheme for assembling and purifying nanoparticle eight-mers with eight geometrically well-directed bonds is presented together with some preliminary experimental work.     

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.     

N-Vinyl as N-H protecting group. Synthesis of cyclic imines from N-vinyllactams and organolithium reagents

On reaction with organolithium reagents followed by hydrolysis and distillation, N-vinylpyrrolidone ( 1 ) gives five-membered ring imines 3-8 , whereas N-vinylcaprolactam ( 2 ) gives mixtures of seven-membered ring imines and the corresponding ∈-amino ketones.     

Novel rapid liquid chromatography tandem masspectrometry method for vemurafenib and metabolites in human plasma,including metabolite concentrations at steady state

A novel, rapid and sensitive liquid chromatography tandem–mass spectrometry method for quantification of vemurafenib in human plasma, that also for the first time allows for metabolite semi‐quantification, was developed and validated to support clinical trials and therapeutic drug monitoring. Vemurafenib was analysed by precipitation with methanol followed by a 1.9 min isocratic liquid chromatography tandem masspectrometry analysis using an Acquity BEH C₁₈ column with methanol and formic acid using isotope labelled internal standards. Analytes were detected in multireaction monitoring mode on a Xevo TQ. Semi‐quantification of vemurafenib metabolites was performed using the same analytical system and sample preparation with gradient elution. The vemurafenib method was successfully validated in the range 0.5–100 μg/mL according to international guidelines. The metabolite method was partially validated owing to the lack of commercially available reference materials. For the first time concentration levels at steady state for melanoma patients treated with vemurafenib is presented. The low abundance of vemurafenib metabolites suggests that they lack clinical significance. Copyright © 2016 John Wiley & Sons, Ltd.     

Digestion method for silver accumulated in micro-organisms

Silver is accumulated to high concentrations in certain microbial strains. Here a bomb digestion method is proposed, using HNO3 and HCl, for the extraction and digestion of silver and silver compounds from the organic matrix. The method is applicable for the quantitative determination of silver by inductively coupled plasma atomic emission spectroscopy.     

Search for localized phonon modes inlead-based alloys by superconducting tunneling

To investigate the appearance of localized phonon modes, superconductive tunneling was performed into films of Pb_0·9M_0·1 (M = Ag, Cd, Ga, Ge, In, Mg, Mg, Sb, Sn, Te, Zn) and Pb_0·97Sn_0·03. The films were quench-condensed and later annealed at 30, 100 and 300°K. Structure in tunneling curves resulting from localized phonons was observed only for a well annealed In alloy film. For most of the impurities an absence of observable local phonon modes could be explained as due to a lack of solid solubility or of sufficient structural order in the film. For Na and Sn alloys, however, these arguments cannot be used. No modes could be seen for such alloys even in films condensed at room temperature, heat-treated slightly, and quenched directly into liquid helium.     

Superconductivity in ultrathin films I. Transition temperatures of amorphous Bi and Ga

Superconducting transition temperatures (T _c) and electron tunneling characteristics have been measured on amorphous, vapour quenched films of Ga and Bi in the thickness range 3 to 50 nm. TheT _c's are depressed and the tunnel densities of states are smeared as compared to bulk superconductors. A model considering the proximity effect between an extremely thin non-superconducting sheath (presumably due to the decrease of electron concentration at the surfaces) and a remaining bulk superconducting part gives good agreement withT _c measurements, while the predicted tunnel density of states is only in qualitative correspondence with experiments.