Induktive Limiten endlich erzeugter freier Moduln

If X is a set, R a ring and M an R-module, then it is shown that the R-module of all M-valued functions on X taking on X only finitely many values is free over R. This result is applied to show that inductive limits of finitely generated free R-modules are free over R, provided that the mappings of the inductive system are of a certain diagonal type. No restrictions are placed on the index set. There is a dual statement for projective limits. Among other applications it is shown that the -1^st Borel-Moore homology group (with values in any sheaf over an arbitrary integral domain and taken with respect to any paracompactifying family of supports) of a locally compact space vanishes.     

0-1-sequences of Toeplitz type

Summary 0-1-sequences are constructed by successive insertion of a periodic sequence of symbols 0, 1 and hole into the holes of the sequence already constructed. Assuming that finally all holes are filled with symbols 0, 1, an almost periodic point in shift space results. Under certain conditions, it is even strictly ergodic. It is proved that the attached invariant measure has pure point spectrum, and a rather explicit expression for eigenvectors is obtained.     

A novel azulene synthesis from the Ramirez ylide involving two different modes of its reaction with activated alkynes

The Ramirez ylide undergoes electrophilic substitution with acetylenedicarboxylates to form Z and E adducts. The latter can react by cycloaddition with another equivalent of the alkyne to provide a new route to novel tetra-substituted azulenes, which show interesting bond localisation and crystal packing effects.     

Synthesis of P-stereogenic BINAP bissulfide analogues

A synthetic route to BINAP disulfide analogues with chirality on one of the phosphorus atoms was developed. The synthesis of these ligands was achieved by step-wise palladium and nickel-catalysed coupling reactions of the precursor binaphthyl triflate with secondary phosphines and phosphine oxides, respectively. C2-Unsymmeric BINAP bissulfide analogues with the same aryl substituents were also synthesized for the sake of comparison. Preliminary studies of the reduction of these sulfides to the free phosphines are also described.     

Topological conjugacy to given constant length substitution minimal systems

We find necessary and sufficient conditions for a symbolic dynamical system to be topologically conjugate to any given constant length substitution minimal system, thus extending the results in Coven et al. (2008) for the Morse and Toeplitz substitutions.     

The influence of random interactions and decision heuristics on norm evolution in social networks

In this paper we explore the effect that random social interactions have on the emergence and evolution of social norms in a simulated population of agents. In our model agents observe the behaviour of others and update their norms based on these observations. An agent’s norm is influenced by both their own fixed social network plus a second random network that is composed of a subset of the remaining population. Random interactions are based on a weighted selection algorithm that uses an individual’s path distance on the network to determine their chance of meeting a stranger. This means that friends-of-friends are more likely to randomly interact with one another than agents with a higher degree of separation. We then contrast the cases where agents make highest utility based rational decisions about which norm to adopt versus using a Markov Decision process that associates a weight with the best choice. Finally we examine the effect that these random interactions have on the evolution of a more complex social norm as it propagates throughout the population. We discover that increasing the frequency and weighting of random interactions results in higher levels of norm convergence and in a quicker time when agents have the choice between two competing alternatives. This can be attributed to more information passing through the population thereby allowing for quicker convergence. When the norm is allowed to evolve we observe both global consensus formation and group splintering depending on the cognitive agent model used.     

Hair-based rapid analyses for multiple drugs in forensics and doping: application of dynamic multiple reaction monitoring with LC-MS/MS

Background

Considerable efforts are being extended to develop more effective methods to detect drugs in forensic science for applications such as preventing doping in sport. The aim of this study was to develop a sensitive and accurate method for analytes of forensic and toxicological nature in human hair at sub-pg levels.

Results

The hair test covers a range of different classes of drugs and metabolites of forensic and toxicological nature including selected anabolic steroids, cocaine, amphetamines, cannabinoids, opiates, bronchodilators, phencyclidine and ketamine. For extraction purposes, the hair samples were decontaminated using dichloromethane, ground and treated with 1 M sodium hydroxide and neutralised with hydrochloric acid and phosphate buffer and the homogenate was later extracted with hexane using liquid-liquid extraction (LLE). Following extraction from hair samples, drug-screening employed liquid chromatography coupled to tandem mass spectrometric (LC-MS/MS) analysis using dynamic multiple reaction monitoring (DYN-MRM) method using proprietary software. The screening method (for?>?200 drugs/metabolites) was calibrated with a tailored drug mixture and was validated for 20 selected drugs for this study. Using standard additions to hair sample extracts, validation was in line with FDA guidance. A Zorbax Eclipse plus C18 (2.1 mm internal diameter × 100 mm length × 1.8 μm particle size) column was used for analysis. Total instrument run time was 8 minutes with no noted matrix interferences. The LOD of compounds ranged between 0.05-0.5 pg/mg of hair. 233 human hair samples were screened using this new method and samples were confirmed positive for 20 different drugs, mainly steroids and drugs of abuse.

Conclusions

This is the first report of the application of this proprietary system to investigate the presence of drugs in human hair samples. The method is selective, sensitive and robust for the screening and confirmation of multiple drugs in a single analysis and has potential as a very useful tool for the analysis of large array of controlled substances and drugs of abuse.