The detection of nicotine in e-liquids using ion mobility spectrometry

Ion mobility spectrometry (IMS) is a well known field technique for the detection of various materials such as explosives and narcotics. IMS has been used for the detection and identification of nicotine, and this paper describes a simple preparation method and analysis using an Ionscan 500DT which could be used in a field environment for the detection of nicotine in e-liquids. E-liquids containing nicotine are presently a topic of much debate in many countries and their shipment across the Canadian border is prohibited. The method described here would allow border officers or any other operators of IMS instruments to use this technique to correctly determine the presence or absence of nicotine in the e-liquid; this would allow the timely importation of the e-liquids with no nicotine and restrict the laboratory analysis only to those liquids containing nicotine. The IMS method has been used on a number of samples received from manufacturers of e-liquids as well as samples seized at the border. The results of the IMS analysis correspond well with those obtained using a Gas Chromatograph – Mass Spectrometer (GC-MS) method of analysis for nicotine.     

On a Constant Related to the Prime Counting Function

Let \({\pi(x)}\) be the number of primes not exceeding x. We produce new explicit bounds for \({\pi(x)}\) and we use them to obtain a fine frame for the remainder term in the asymptotic formula of the sum \({\sum_{2\leq n\leq x}1/\pi(n)}\).     

Courant-Sharp Eigenvalues for the Equilateral Torus,and for the Equilateral Triangle

We address the question of determining the eigenvalues \({\lambda_{n}}\) (listed in nondecreasing order, with multiplicities) for which Courant’s nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with \({n}\) nodal domains (Courant-sharp eigenvalues). Following ideas going back to Pleijel (1956), we prove that the only Courant-sharp eigenvalues of the flat equilateral torus are the first and second, and that the only Courant-sharp Dirichlet eigenvalues of the equilateral triangle are the first, second, and fourth eigenvalues. In the last section we sketch similar results for the right-angled isosceles triangle and for the hemiequilateral triangle.     

Pulsed lasers versus continuous light sources in capillary electrophoresis and fluorescence detection studies: Photodegradation pathways and models

Pulsed lasers are widely used in capillary electrophoresis (CE) studies to provide laser induced fluorescence (LIF) detection. Unfortunately pulsed lasers do not give linear calibration curves over a wide range of concentrations. While this does not prevent their use in CE/LIF studies, the non-linear behavior must be understood. Using 7-hydroxycoumarin (7-HC) (10–5000 nM), Tamra (10–5000 nM) and tryptophan (1–200 μM) as dyes, we observe that continuous lasers and LEDs result in linear calibration curves, while pulsed lasers give polynomial ones. The effect is seen with both visible light (530 nm) and with UV light (355 nm, 266 nm). In this work we point out the formation of byproducts induced by pulsed laser upon irradiation of 7-HC. Their separation by CE using two Zeta LIF detectors clearly shows that this process is related to the first laser detection. All of these photodegradation products can be identified by an ESI-/MS investigation and correspond to at least two 7HC dimers. By using the photodegradation model proposed by Heywood and Farnsworth (2010) and by taking into account the 7-HC results and the fact that in our system we do not have a constant concentration of fluorophore, it is possible to propose a new photochemical model of fluorescence in LIF detection. The model, like the experiment, shows that it is difficult to obtain linear quantitation curves with pulsed lasers while UV-LEDs used in continuous mode have this advantage. They are a good alternative to UV pulsed lasers. An application involving the separation and linear quantification of oligosaccharides labeled with 2-aminobezoic acid is presented using HILIC and LED (365 nm) induced fluorescence.     

Inverting Ray-Knight identity

We provide a short proof of the Ray-Knight second generalized Theorem, using a martingale which can be seen (on the positive quadrant) as the Radon–Nikodym derivative of the reversed vertex-reinforced jump process measure with respect to the Markov jump process with the same conductances. Next we show that a variant of this process provides an inversion of that Ray-Knight identity. We give a similar result for the Ray-Knight first generalized Theorem.     

Bilayer splitting versus Fermi-surface warping as an origin of slow oscillations of in-plane magnetoresistance in rare-earth tritellurides

Slow oscillations (SlO) of the in-plane magnetoresistance with a frequency less than 4 T are observed in the rare-earth tritellurides and proposed as an effective tool to explore the electronic structure in various strongly anisotropic quasi-two-dimensional compounds. Contrary to the usual Shubnikov-de-Haas oscillations, SlO originate not from small Fermi-surface pockets, but from the entanglement of close frequencies due to a finite interlayer transfer integral, either between the two Te planes forming a bilayer or between two adjacent bilayers. From the observed angular dependence of the frequency and the phase of SlO we argue that they originate from the bilayer splitting rather than from the Fermi-surface warping. The SlO frequency gives the value of the interlayer transfer integral ≈1 meV for TbTe₃ and GdTe₃.     

Lossless compression of chemical fingerprints using integer entropy codes improves storage and retrieval

Many modern chemoinformatics systems for small molecules rely on large fingerprint vector representations, where the components of the vector record the presence or number of occurrences in the molecular graphs of particular combinatorial features, such as labeled paths or labeled trees. These large fingerprint vectors are often compressed to much shorter fingerprint vectors using a lossy compression scheme based on a simple modulo procedure. Here, we combine statistical models of fingerprints with integer entropy codes, such as Golomb and Elias codes, to encode the indices or the run lengths of the fingerprints. After reordering the fingerprint components by decreasing frequency order, the indices are monotone-increasing and the run lengths are quasi-monotone-increasing, and both exhibit power-law distribution trends. We take advantage of these statistical properties to derive new efficient, lossless, compression algorithms for monotone integer sequences: monotone value (MOV) coding and monotone length (MOL) coding. In contrast to lossy systems that use 1024 or more bits of storage per molecule, we can achieve lossless compression of long chemical fingerprints based on circular substructures in slightly over 300 bits per molecule, close to the Shannon entropy limit, using a MOL Elias Gamma code for run lengths. The improvement in storage comes at a modest computational cost. Furthermore, because the compression is lossless, uncompressed similarity (e.g., Tanimoto) between molecules can be computed exactly from their compressed representations, leading to significant improvements in retrival performance, as shown on six benchmark data sets of druglike molecules.     

Asymmetric synthesis of the epimeric (3S)-3-((E)-hex-1-enyl)-2-methylcyclohexanones

The asymmetric rhodium-catalysed 1,4-addition of alkenylzirconium reagents to 2-cyclohexenone can be useful in the synthesis of 3-alkenyl-2-methylcyclohexanones, provided that formaldehyde is used in trapping the intermediate zirconium enolates. In this manner a four-step sequence leading to the two epimeric 3-hexenyl-2-methylcyclohexanones in enantiomeric form was developed.     

Synthesis of 3,4,7,8-tetrahydronaphthalene-1,5(2H,6H)-dione

A short and high yielding route for the preparation of the title compound, starting from commercially available 1,5-dihydroxynaphthalene, is described. The key step in the sequence is the air oxidation of a bis(trimethylsilyloxy)diene precursor.