Three-electron two-centred bonds and the stabilisation of cationic sulfur radicals

Electronic communication in biological systems is fundamental to understanding protein signalling and electron hopping pathways. Frequently studied examples are cationic radical methionine and its functional derivatives. These systems are understood to be stabilised by a direct ‘three-electron two-centred’ bond. We demonstrate for methionine and a series of cationic radical methionine analogues that long-range multi-centred indirect stabilisation occurs, which cannot be attributed to three-electron two-centred interactions. A revised description of the radical stabilisation process is presented, which includes contributions from all atoms with accessible p-orbitals, independent of the distance to the sulfur radical

Singular Oscillatory Integrals on R^n

Let Pd,n denote the space of all real polynomials of degree at most d on R^n. We prove a new estimate for the logarithmic measure of the sublevel set of a polynomial P in Pd,1. Using this estimate, we prove a sharp estimate for a singular oscillatory integral on R^n.Comment: final version, 10 pages, small typos corrected, one reference added. To appear in Math.

Pregnancy and inflammatory bowel disease: Do we provide enough patient education? A British study of 1324 women

AIM: To examine patient knowledge and factors influencing knowledge about pregnancy in British women with inflammatory bowel disease (IBD). METHODS: This is a post hoc analysis of a study of female members of Crohn’s and Colitis United Kingdom, aged 18-45 years who were sent an online questionnaire recording patient demographics, education, employment, marital status, and disease characteristics. Disease related pregnancy knowledge was recorded using Crohn’s and colitis pregnancy knowledge score (CCPKnow). RESULTS: Of 1324 responders, 776 (59%) suffered from Crohn’s disease, 496 (38%) from ulcerative colitis and 52 (4%) from IBD-uncategorised. CCPKnow scores were poor (0-7) in 50.8%, adequate (8-10) in 23.6%, good (11-13) in 17.7% and very good (≥ 14) in 7.8%. Multiple linear regression analysis revealed that higher CCPKnow scores were independently associated with higher educational achievement (P < 0.001), younger age at diagnosis (P = 0.003) and having consulted a health care professional about pregnancy and IBD (P = 0.001). CONCLUSION: Knowledge was poor in 50%. Speaking with health-care professionals was a modifiable factor associated with better knowledge. This illustrates the importance of disease related pregnancy educatio

Helical frontier orbitals of conjugated linear molecules

Compounds containing allenes, cumulenes and oligoynes (polyalkynes) have attracted attention for both their conformation and reactivity. Whilst the textbook molecular orbital description explains the general electronic and molecular structure of the cumulenes, there are anomalies in both the crystal structures and cycloaddition products involving oligoynes and allenes; the understanding of these molecules is incomplete. Through a computational study we elucidate that the frontier orbitals of the allene and oligoyne families are extended helices. These orbitals are the linear analogue to the Möbius aromatic systems, which also display non-linear π interactions. The axial chirality found in allenes and oligoynes is intimately related to the topology of the frontier orbitals, and has implications for predictions of cycloaddition pathways, structure stability and spectroscopy

A Note on Weighted Estimates for the Schrödinger Operator

We study two problems closely related to each other. The first one is concerned with some smoothing weighted estimates with weights in a certain Morrey- Campanato spaces, for the solution of the free Schrödinger equation. The second one is a weighed trace inequality.We study two problems closely related to each other. The first one is concerned with some smoothing weighted estimates with weights in a certain Morrey- Campanato spaces, for the solution of the free Schrödinger equation. The second one is a weighed trace inequality

Weights and L log L

Let ω(x) be positive locally integrable weight on [0,1]. Discussed are conditions on ω necessary and sufficient for the (dyadic) Hardy-Littlewood maximal function to map L log L(w dx) into L1(ω dx) or into weak L1