NMR spectral analysis of strongly second-order 6-, 8-, 9- and 10- spin-systems (1H─19F, 19F─19F,and 13C─19F) in perfluorotoluyl- and tetrafluoro-pyridyl-aromatics using the lineshape method ANATOLIA

A simple to use nuclear magnetic resonance analysis method has been tested on complex ¹H, ¹⁹F, and ¹³C multiplets. This open-source line-shape analysis method analysis of total lineshape (ANATOLIA)¹ provides some significant advantages over traditional assign-iterate methods of NMR spectral analysis by avoiding false minima and progressing optimisation to the global minimum. The target molecules are 1-perfluorotol-4-yl-2-perfluorotol-4-yl-oxymethyl-1H-benzimidazole (molecule-I) and 1-tetrafluoropyrid-4-yl-2-tetrafluoropyrid-4-yl-thio-1H-benzimidazole (molecule-II) which were produced as part of a family of fluorinated drug scaffolds prepared for anticancer and antiparasitic screening. Spectra display significant second-order effects with ¹H Δδ = 3.68 and 4.67 Hz for the aromatic hydrogen “triplets”, with ¹⁹F ⁴J_AA', ⁴J_BB', ⁴J_XX', and ⁴J_YY' coupling constants range from +4.8 to −14.0 Hz and for ¹³C-isotopomers ¹⁹F Δδ of up to 111.56 Hz. A spin-system of six coupling nuclei (H_aH_bH_cH_d F_YF_Y') was analysed in 12 s, a spin-system of nine coupling fluorine nuclei (AA'BB'CCC-YY') was analysed within 2 min, and 10 coupling nuclei (XX'YY'ZZZ-BB'-H_d) was optimised in 6 min using a laptop computer. ANATOLIA was also robust enough to be able to yield accurate spectral values from inaccurate input values. In both compounds, a fluorine–fluorine coupling constant was identified between the two fluoro-aromatic rings (F_BB' and F_YY') of +4.05 and +4.67 Hz and attributed to a through-space interaction. Ab initio structure optimisations and coupling constant calculations provided useful input data for spectral analysis. A modern ¹⁹F nuclear magnetic resonance spectrum of perfluorotoluene (octafluorotoluene) and analysis from 1975 was used as a test data set to assess ANATOLIA.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Study of the charge-exchange reactions\pi ^ - p \to (\pi ^0 ,\eta ,\eta \prime )n at 63 GeV

Muon electron pairs were detected in an Al multiplate spark chamber, exposed to a neutrino beam from the CERN PS. The leptons were not accompanied by other particles, except occasionally by protons. The background came mainly from muon associated π⁰ production, with one decay gamma lost. It was determined empirically, together with the small contribution from υ _e reactions. For electron energies above 2 GeV the background is 5.7±1.5 events, whereas 18 (μe)-candidates have been observed. Hence the effect is established, with a rate of about 10^?4 as compared to the muonic reactions above 3 GeV. Charm creation as the origin of this (μe)-production process is excluded; heavy neutral lepton production does not fit the kinematics observed. Instead the events are compatible with the two-body decay of an object with variable invariant mass of order 1 GeV, possibly resulting from axion interactions.     

Cyclic permutations and evolutionary trees

Given a tree with leaf set X, there are certain ways of arranging the elements of X in a circular order so that can be embedded in the plane and ‘preserve’ this ordering. We investigate some new combinatorial properties of these ‘circular orderings.’ We then use these properties to establish two results concerning dissimilarity maps on X that are induced by edge-weighted trees with leaf set X.     

Die Bestimmung des Harzes in Seifen und Fetten

Ohne Zusammenfassung     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

Writhing instabilities of twisted rods: from infinite to finite length

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.     

Peeling phylogenetic ‘oranges’

We investigate the combinatorics of a topological space that is generated by the set of edge-weighted finite trees. This space arises by multiplying the weights of edges on paths in trees and is closely connected to tree reconstruction problems involving finite state Markov processes. We show that this space is a contractible finite CW-complex whose face poset can be described via a partial order on semilabelled forests. We then describe some combinatorial properties of this poset, showing that, for example, it is pure, thin and contractible.