Towards a splitter theorem for internally 4-connected binary matroids III

This paper proves a preliminary step towards a splitter theorem for internally 4-connected binary matroids. In particular, we show that, provided M   or M^?$M^{?}$ is not a cubic Möbius or planar ladder or a certain coextension thereof, an internally 4-connected binary matroid M with an internally 4-connected proper minor N   either has a proper internally 4-connected minor M^′$M^{\prime }$ with an N  -minor such that |E(M)−E(M^′)|?3$|E(M)-E(M^{\prime })|?3$ or has, up to duality, a triangle T and an element e of T   such that M\e$M\backslash e$ has an N-minor and has the property that one side of every 3-separation is a fan with at most four elements.     

Proton transfer reaction mass spectrometry for the sensitive and rapid real-time detection of solid high explosives in air and water

Relying on recent developments in proton transfer reaction mass spectrometry (PTR-MS), we demonstrate here the capability of detecting solid explosives in air and in water in real time. Two different proton transfer reaction mass spectrometers have been used in this study. One is the PTR-TOF 8000, which has an enhanced mass resolution (m/Δm up to 8,000) and high sensitivity (~50 cps/ppbv). The second is the high-sensitivity PTR-MS, which has an improved limit of detection of about several hundreds of parts per quadrillion by volume and is coupled with a direct aqueous injection device. These instruments have been successfully used to identify and monitor the solid explosive 2,4,6-trinitrotoluene (TNT) by analysing on the one hand the headspace above small quantities of samples at room temperature and from trace quantities not visible to the naked eye placed on surfaces (also demonstrating the usefulness of a simple pre-concentration and thermal desorption technique) and by analysing on the other hand trace compounds in water down to a level of about 100 pptw. The ability to identify even minute amounts of threat compounds, such as explosives, particularly within a complex chemical environment, is vital to the fight against crime and terrorism and is of paramount importance for the appraisal of the fate and harmful effects of TNT at marine ammunition dumping sites and the detection of buried antipersonnel and antitank landmines.

Wei-type duality theorems for matroids

We present several fundamental duality theorems for matroids and more general combinatorial structures. As a special case, these results show that the maximal cardinalities of fixed-ranked sets of a matroid determine the corresponding maximal cardinalities of the dual matroid. Our main results are applied to perfect matroid designs, graphs, transversals, and linear codes over division rings, in each case yielding a duality theorem for the respective class of objects.     

Isomeric effects in the gas-phase reactions of dichloroethene, C2H2CL2, with a series of cations

A study of the reactions of a series of gas-phase cations (NH(4)(+), H(3)O(+), SF(3)(+), CF(3)(+), CF(+), SF(5)(+), SF(2)(+), SF(+), CF(2)(+), SF(4)(+), O(2)(+), Xe(+), N(2)O(+), CO(2)(+), Kr(+), CO(+), N(+), N(2)(+), Ar(+), F(+), and Ne(+)) with the three structural isomers of dichloroethene, i.e., 1,1-C(2)H(2)Cl(2), cis-1,2-C(2)H(2)Cl(2), and trans-1,2-C(2)H(2)Cl(2) is reported. The recombination energy (RE) of these ions spans the range of 4.7-21.6 eV. Reaction rate coefficients and product branching ratios have been measured at 298 K in a selected ion flow tube (SIFT). Collisional rate coefficients are calculated by modified average dipole orientation (MADO) theory and compared with experimental data. Thermochemistry and mass balance have been used to predict the most feasible neutral products. Threshold photoelectron-photoion coincidence spectra have also been obtained for the three isomers of C(2)H(2)Cl(2) with photon energies in the range of 10-23 eV. The fragment ion branching ratios have been compared with those of the flow tube study to determine the importance of long-range charge transfer. A strong influence of the isomeric structure of dichloroethene on the products of ion-molecule reactions has been observed for H(3)O(+), CF(3)(+), and CF(+). For 1,1-C(2)H(2)Cl(2) the reaction with H(3)O(+) proceeds at the collisional rate with the only ionic product being 1,1-C(2)H(2)Cl(2)H(+). However, the same reaction yields two more ionic products in the case of cis-1,2- and trans-1,2-C(2)H(2)Cl(2), but only proceeds with 14% and 18% efficiency, respectively. The CF(3)(+) reaction proceeds with 56-80% efficiency, the only ionic product for 1,1-C(2)H(2)Cl(2) being C(2)H(2)Cl(+) formed via Cl(-) abstraction, whereas the only ionic product for both 1,2-isomers is CHCl(2)(+) corresponding to a breaking of the C=C double bond. Less profound isomeric effects, but still resulting in different products for 1,1- and 1,2-C(2)H(2)Cl(2) isomers, have been found in the reactions of SF(+), CO(2)(+), CO(+), N(2)(+), and Ar(+). Although these five ions have REs above the ionization energy (IE) of any of the C(2)H(2)Cl(2) isomers, and hence the threshold for long-range charge transfer, the results suggest that the formation of a collision complex at short range between these ions and C(2)H(2)Cl(2) is responsible for the observed effects.     

Use of proton transfer reaction time-of-flight mass spectrometry for the analytical detection of illicit and controlled prescription drugs at room temperature via direct headspace sampling

The first reported use of proton transfer reaction time-of-flight mass spectrometry (PTR-TOF-MS) for the detection of a range of illicit and prescribed drugs is presented here. We describe the capabilities of PTR-TOF-MS to detect the following commonly used narcotics—ecstasy (N-methyl-3,4-methylenedioxyamphetamine), morphine, codeine, cocaine and heroin—by the direct sampling of the headspace above small solid quantities (approximately 50 mg) of the drugs placed in glass vials at room temperature, i.e. with no heating of the sample and no pre-concentration. We demonstrate in this paper the ability to identify the drugs, both illicit and prescribed, using PTR-TOF-MS through the accurate m/z assignment of the protonated parent molecule to the second decimal place. We have also included in this study measurements with an impure sample of heroin, containing typical substances found in “street” heroin, to illustrate the use of the technology for more “real-world” samples. Therefore, in a real-world complex chemical environment, a high level of confidence can be placed on the detection of drugs. Although the protonated parent is observed for all drugs, the reactant channel leading to this species is not the only one observed and neither is it necessarily the most dominant. Details on the observed fragmentation behaviour are discussed and compared to electrospray ionisation MSⁿ studies available in the literature.     

Applications of proton transfer reaction time-of-flight mass spectrometry for the sensitive and rapid real-time detection of solid high explosives

Using recent developments in proton transfer reaction mass spectrometry, proof-of-principle investigations are reported here to illustrate the capabilities of detecting solid explosives in real-time. Two proton transfer reaction time-of-flight mass spectrometers (Ionicon Analytik) have been used in this study. One has an enhanced mass resolution (m/Δm up to 8000) and high sensitivity (～50 cps/ppbv). The second has enhanced sensitivity (～250 cps/ppbv) whilst still retaining high resolution capabilities (m/Δm up to 2000). Both of these instruments have been successfully used to identify solid explosives (RDX, TNT, HMX, PETN and Semtex A) by analyzing the headspace above small quantities of samples at room temperature and from trace quantities not visible to the naked eye placed on surfaces. For the trace measurements a simple pre-concentration and thermal desorption technique was devised and used. Importantly, we demonstrate the unambiguous identification of threat agents in complex chemical environments, where multiple threat agents and interferents may be present, thereby eliminating false positives. This is of considerable benefit to security and for the fight against terrorism.