Contributions of non-extremum critical points to the semi-classical trace formula

We study the semi-classical trace formula at a critical energy level for a h-pseudo-differential operator on whose principal symbol has a totally degenerate critical point for that energy. We compute the contribution to the trace formula of isolated non-extremum critical points under a condition of “real principal type”. The new contribution to the trace formula is valid for all time in a compact subset of but the result is modest since we have restrictions on the dimension.     

Measurement of the total active 8B solar neutrino flux at the Sudbury Neutrino Observatory with enhanced neutral current sensitivity

The Sudbury Neutrino Observatory has precisely determined the total active (nu(x)) 8B solar neutrino flux without assumptions about the energy dependence of the nu(e) survival probability. The measurements were made with dissolved NaCl in heavy water to enhance the sensitivity and signature for neutral-current interactions. The flux is found to be 5.21 +/- 0.27(stat)+/-0.38(syst) x 10(6) cm(-2) s(-1), in agreement with previous measurements and standard solar models. A global analysis of these and other solar and reactor neutrino results yields Deltam(2)=7.1(+1.2)(-0.6) x 10(-5) eV(2) and theta=32.5(+2.4)(-2.3) degrees. Maximal mixing is rejected at the equivalent of 5.4 standard deviations.     

About the Decay of Vorticity in a Two-dimensional Incompressible Viscous Fluid

The main purpose of this article is to investigate the behavior of the vorticity in a two dimensional incompressible viscous medium. We give bounds for the maximal amount of vorticity which can be concentrated in a domain of a given size. In order to obtain bounds we compare the vorticity equation to the heat equation in ²     

Synthesis of vulpinic acids from dimethyl tartrate

A series of vulpinic acids differing by the aryl or heteroaryl groups placed in the ester α-position were prepared by Suzuki-Miyaura cross-coupling involving a common iodide and the corresponding aryl boronates. The preparation of the iodide precursor from (+)-dimethyl l-tartrate required four steps: the esterification of one hydroxyl group, a Dieckmann cyclization allowing the construction of the tetronic acid moiety, a dehydration leading to the installation of the exocyclic double bond and lastly, an N-iodosuccinimide-mediated iodation of the alkene obtained.     

High-frequency nanostructured magnetic materials for integrated inductors

Electroplating is compatible with the deposition of relatively thick layers i.e. several μm to 10s- of μm. However eddy current losses mean that thick layers will have an inferior frequency response. We have used a low content phosphorous bath together with pulse reverse plating to generate Co-rich and Co-deficient multi-nanolayers of CoP having improved saturation magnetisation and a better frequency response. The plating parameters have been optimised in order to produce a material with low loss, and a high permeability of around 700 retained up to 103 MHz for a sample with a thickness of 1.7 μm and a resistivity of 136 μΩ cm.     

Hybridization of Long Pyridine‐Dicarboxamide Oligomers into Multi‐Turn Double Helices: Slow Strand Association and Dissociation,Solvent Dependence,and Solid State Structures

Oligoamides of 2,6‐diaminopyridine and 2,6‐pyridinedicarboxylic acid comprised of 5, 7, 9, 11, or 13 units and bearing 4‐isobutoxychains on all pyridine rings and tert‐butyl‐carbamate terminal groups have been synthesized stepwise, along with an 11 mer having benzyl‐carbamate terminal groups. The crystal structure of all five Boc‐terminated compounds has been obtained and shows a highly regular and conserved double helical hybridization motif of up to 3 complete turns for the 13 mer. Four pyridine units span one helical turn and define a helix pitch of ca 7 Å. Solution studies in CDCl₃ demonstrated that the Boc‐terminated oligomers strongly hybridize in this solvent, and that K_dim values increase with oligomer length. The K_dim values are 31000 and 7×10⁵ L mol^?1 for the 7 mer and the 9 mer, respectively, and are too high to be measured by NMR for the 11 mer and the 13 mer. Hybridization and dissociation kinetics at 2 mM proceed at decreasing rates upon increasing oligomer length. The rate was faster than minutes for the 7 mer, of the order of hours for the 9 mer, and days for the 11 mer and 13 mer. The same trend was observed in [D₅]pyridine but with considerably lower K_dim values and faster kinetics. The benzylcarbamate 11 mer was also found to hybridize into a double helix but with reduced K_dim values and faster kinetics compared to its Boc‐terminated analogue. Combined with previous studies, the results presented here frame a global understanding of the hybridization of these pyridinecarboxamide oligomers and provide useful guidelines for the design of other artificial double helices.     

α‐Peptide–Oligourea Chimeras: Stabilization of Short α‐Helices by Non‐Peptide Helical Foldamers

Short α‐peptides with less than 10 residues generally display a low propensity to nucleate stable helical conformations. While various strategies to stabilize peptide helices have been previously reported, the ability of non‐peptide helical foldamers to stabilize α‐helices when fused to short α‐peptide segments has not been investigated. Towards this end, structural investigations into a series of chimeric oligomers obtained by joining aliphatic oligoureas to the C‐ or N‐termini of α‐peptides are described. All chimeras were found to be fully helical, with as few as 2 (or 3) urea units sufficient to propagate an α‐helical conformation in the fused peptide segment. The remarkable compatibility of α‐peptides with oligoureas described here, along with the simplicity of the approach, highlights the potential of interfacing natural and non‐peptide backbones as a means to further control the behavior of α‐peptides.