Delta shock wave for a 3 × 3 hyperbolic system of conservation laws

We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. The system is a simplification of a recently proposed system of five conservations laws by Bouchut and Boyaval that models viscoelastic fluids. An important issue is that the considered 3×3 system is such that every characteristic field is linearly degenerate. We study theRiemann problemfor this system and under suitable generalized Rankine-Hugoniot relation and entropy condition, both existence and uniqueness of particular delta shock type solutions are established.     

The concept of proof in the light of mathematical work

ZDM – Mathematics Education - Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and...     

Absolute structure determination using CRYSTALS

A study of post‐refinement absolute structure determination using previously published data was carried out using the CRYSTALS software package. We show that absolute structure determination may be carried out optimally using the analyses available in CRYSTALS, and that it is not necessary to have the separate procedures absolute structure determination and no interest in absolute structure as proposed by Flack [Chimia (2014), 68 , 26–30].     

Dependence of collision‐induced dissociation energy on molecular degrees of freedom as a means to assess relative binding affinity in multivalent complexes

In collision‐induced dissociation mass spectrometry experiments, the collision energy required for dissociation linearly depends on the degrees of freedom in the precursor ion. The magnitude of the slope of this relationship previously has been shown to qualitatively correlate to the relative binding strength of a noncovalently bound, monovalent complex. The goal of the work presented here is to determine if a similar methodology can be applied for assessing relative binding strengths in multivalent species. We have tested the method on complexes formed from 18‐crown‐6 and a variety of protonated, primary alkylamines, [C_nH_2n+1NH₃]⁺ (n = 9, 12, 14, 16 and 18) and alkyldiamines, [H₃NC_nH_2nNH₃]²⁺ (n = 3, 5, 6, 9 and 12), and compared our results with dissociation energies calculated using density functional theory at the B3LYP/6‐31G* level. We found that the method correctly assessed the stronger crown ether/headgroup interaction in the two divalent species (1:1 and 2:1 complexes formed from the diaminoalkanes) compared with the weaker interaction in the monovalent species (1:1 complexes formed from mono‐aminoalkanes). However, the experimental method could not distinguish between the binding strengths of the two divalent complexes, perhaps because their calculated dissociation energies were quite similar. Our preliminary results suggest that this method could potentially be used for a quick and simple analysis of binding strengths in multivalent species if the binding strengths of the species are significantly different from one another. Copyright © 2011 John Wiley & Sons, Ltd.     

Annihilators for Harmonic Differential Forms Via Clifford Analysis

In this paper we describe completely the annihilators of harmonic differential forms into the Clifford analysis approach.     

Role of 2‐oxo and 2‐thioxo modifications on the proton affinity of histidine and fragmentation reactions of protonated histidine

A combination of electrospray ionisation (ESI), multistage and high‐resolution mass spectrometry experiments was used to compare the gas‐phase chemistry of the amino acids histidine (1), 2‐oxo‐histidine (2), and 2‐thioxo‐histidine (3). Collision‐induced dissociation (CID) of all three different proton‐bound heterodimers of these amino acids led to the relative gas‐phase proton affinity order of: histidine >2‐thioxo‐histidine >2‐oxo‐histidine. Density functional theory (DFT) calculations confirm this order, with the lower proton affinities of the oxidised histidine derivatives arising from their ability to adopt the more stable keto/thioketo tautomeric forms. All protonated amino acids predominately fragment via the combined loss of H₂O and CO to yield a₁ ions. Protonated 2 and 3 also undergo other small molecule losses including NH₃ and the imine HN=CHCO₂H. The observed differences in the fragmentation pathways are rationalised through DFT calculations, which reveal that while modification of histidine via the introduction of the oxygen atom in 2 or the sulfur atom in 3 does not affect the barriers against the loss of H₂O+CO, barriers against the losses of NH₃ and HN=CHCO₂H are lowered relative to protonated histidine. Copyright © 2010 John Wiley & Sons, Ltd.     

The electroneutrality approximation in electrochemistry

The electroneutrality approximation assumes that charge separation is impossible in electrolytic solutions. It has a long and successful history dating back to 1889 and may be justified because of the small absolute values for the permittivities of typical solvents. Dimensional analysis shows that the approximation becomes invalid only at nanosecond and nanometre scales. Recent work, however, has taken advantage of the capabilities of modern numerical simulation in order to relax this approximation, with concomitant advantages such as avoiding paradoxes and permitting a clear and consistent ??physical picture?? to describe charge dynamics in solution. These new theoretical techniques have been applied to liquid junction potentials and weakly supported voltammetry, with strong experimental corroboration for the latter. So long as dynamic processes are being studied, for which analytical solutions are unavailable in any case, numerical simulation is shown to render electroneutrality unnecessary as an a priori assumption.