Investigating the provenance of un-dyed spun cotton fibre using multi-isotope profiles and chemometric analysis

The analysis of un-dyed spun cotton fibres can be challenging within a forensic science context where discrimination of one fibre from another is of importance. Conventional microscopic and chemical analysis of these fibres is generally unsuccessful because of their similar morphology. In this work we have explored the potential of isotope ratio mass spectrometry (IRMS) as a tool for spun cotton fibre analysis in an attempt to reveal any discriminatory information available. Seven different batches of un-dyed spun cotton fibre from four different countries were analysed. A combination of the hydrogen and oxygen isotopic data facilitated the correct association of the samples, demonstrating, for the first time, the applicability of IRMS to fibre analysis in this way.     

Quasielastic small-angle neutron scattering from heavy water solutions of cyclodextrins

We present a model for quasielastic neutron scattering (QENS) by an aqueous solution of compact and inflexible molecules. This model accounts for time-dependent spatial pair correlations between the atoms of the same as well as of distinct molecules and includes all coherent and incoherent neutron scattering contributions. The extension of the static theory of the excluded volume effect [A. K. Soper, J. Phys.: Condens. Matter 9, 2399 (1997)] to the time-dependent (dynamic) case allows us to obtain simplified model expressions for QENS spectra in the low Q region in the uniform fluid approximation. The resulting expressions describe the quasielastic small-angle neutron scattering (QESANS) spectra of D(2)O solutions of native and methylated cyclodextrins well, yielding in particular translational and rotational diffusion coefficients of these compounds in aqueous solution. Finally, we discuss the full potential of the QESANS analysis (that is, beyond the uniform fluid approximation), in particular, the information on solute-solvent interactions (e.g., hydration shell properties) that such an analysis can provide, in principle.     

Strain effects in electron spin resonance spectroscopy of quintet 2,6-bis(4'-nitrenophenyl)-4-phenylpyridine

Photolysis of 2,6-bis(4'-azidophenyl)-4-phenylpyridine in 2-methyltetrahydrofuran (2MTHF) glass at 7 K leads to quintet 2,6-bis(4'-nitrenophenyl)-4-phenylpyridine as a mixture of rotational isomers. The electron spin resonance (ESR) spectrum of this mixture of rotamers shows a considerable broadening of many transitions in the range of 0-5000 G and cannot be reproduced by computer simulations solely based on the tuning of the spin Hamiltonian parameters g, D(Q), and E(Q) alone or on predictions of DFT calculations. The best modeling of the experimental ESR spectrum is obtained only when the large line-broadening parameter of Γ(E(Q)) = 1200 MHz along with the spin Hamiltonian g = 2.003, D(Q) = 0.154 cm(-1), and E(Q) = 0.050 cm(-1) is used in the spectral simulations. The most accurate theoretical estimations of the magnetic parameters of the dinitrene in a 2MTHF glass are obtained from the B3LYP/6-311+G(d,p)+PBE/DZ/COSMO calculations of the spin-spin coupling parameters D(SS) and E(SS). Such calculations overestimate the E(Q) and D(Q) values of the dinitrene just by 1% and 10%, respectively, demonstrating that contributions of the spin-orbit coupling parameters D(SOC) and E(SOC) to the total D(Q) and E(Q) values are negligibly small. The research shows that ESR studies of polynuclear high-spin nitrenes, obtained by photolysis of rotational isomers of the starting azides, can only be successful if large E(Q) strain effects are taken into account in the spectral simulations.     

Commuting Toeplitz operators on the Segal-Bargmann space

Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily.     

Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-Bargmann space

We study three different problems in the area of Toeplitz operators on the Segal-Bargmann space in Cn. Extending results obtained previously by the first author and Y.L. Lee, and by the second author, we first determine the commutant of a given Toeplitz operator with a radial symbol belonging to the class Sym_>0(Cn) of symbols having certain growth at infinity. We then provide explicit examples of zero-products of non-trivial Toeplitz operators. These examples show the essential difference between Toeplitz operators on the Segal-Bargmann space and on the Bergman space over the unit ball. Finally, we discuss the “finite rank problem”. We show that there are no non-trivial rank one Toeplitz operators Tf for f∈Sym_>0(Cn). In all these problems, the growth at infinity of the symbols plays a crucial role.     

Vibrational spectroscopic studies and DFT calculations on tribromoacetate and tribromoacetic acid in aqueous solution

Aqueous solutions of sodium tribromoacetate (NaCBr3CO2) and its corresponding acid (CBr3COOH) have been studied using Raman and infrared spectroscopy. The spectra of the species in solution were assigned according to symmetry Cs. Characteristic bands of CBr3CO2-(aq) and the tribromoacetic acid, CBr3COOH(aq), are discussed. For the hydrated anion, the CO2 group, the symmetric CO2 stretching mode at 1332 cm(-1) and the asymmetric stretching mode at 1651 cm(-1) are characteristic while the CO mode at 1730 cm(-1) is characteristic for the spectra of the acid. The stretching mode, νC-C at 912cm(-1) for CBr3CO2-(aq) is 10 cm(-1) lower in the anion compared with that of the acid. These characteristic modes are compared to those in acetate, CH3CO2-(aq). Coupling of the modes are fairly extensive and therefore DFT calculations have been carried out in order to compare the measured spectra with the calculated ones. The geometrical parameters such as bond length and bond angles of the tribromoacetate, and tribromoacetic acid have been obtained and may be compared with the ones published for other acetates and their conjugated acids. CBr3COOH(aq) is a moderately strong acid and the pKa value derived from quantitative Raman measurements is equal to -0.23 at 23°C. The deuterated acid CBr3COOD in heavy water has been measured as well and the assignments were given.     

Analytical Approach for Piecewise Linear Coupled Map Lattices

A simple construction is presented which generalizes piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. In particular, the spin Hamiltonian which is generated by the symbolic dynamics is accessible. As an example, a formal relation between a globally coupled system and an Ising mean-field model is established. The phase transition in the limit of infinite system size is analyzed and analytical results are compared with numerical simulations.     

The influence of the flexoelectric effect on the electrohydrodynamic instability in nematics

A rigorous three-dimensional linear analysis of the electrohydrodynamic instability in nematic liquid crystals including the flexoelectric effect is presented for the case of an applied d.c. voltage. The flexoelectric effect leads to an appreciable reduction of the threshold and to the appearance of oblique rolls at threshold for the standard material MBBA. We discuss the influence of a magnetic field and test several approximations against the rigorous results