An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.

Judging where a ball will go: the case of curved free kicks in football

This study examined whether adding spin to a ball in the free kick situation in football affects a professional footballer's perception of the ball's future arrival position. Using a virtual reality set-up, participants observed the flight paths of aerodynamically realistic free kicks with (+/- 600 rpm) and without sidespin. With the viewpoint being fixed in the centre of the goal, participants had to judge whether the ball would have ended up in the goal or not. Results show that trajectories influenced by the Magnus force caused by sidespin gave rise to a significant shift in the percentage of goal responses. The resulting acceleration that causes the ball to continually change its heading direction as the trajectory unfolds does not seem to be taken into account by the participants when making goal judgments. We conclude that the visual system is not attuned to such accelerated motion, which may explain why goalkeepers appear to misjudge the future arrival point of such curved free kicks.

Neuroprotective actions of a histidine analogue in models of ischemic stroke.

Histidine is a naturally occurring amino acid with antioxidant properties, which is present in low amounts in tissues throughout the body. We recently synthesized and characterized histidine analogues related to the natural dipeptide carnosine, which selectively scavenge the toxic lipid peroxidation product 4-hydroxynonenal (HNE). We now report that the histidine analogue histidyl hydrazide is effective in reducing brain damage and improving functional outcome in a mouse model of focal ischemic stroke when administered intravenously at a dose of 20 mg/kg, either 30 min before or 60 min and 3 h after the onset of middle cerebral artery occlusion. The histidine analogue also protected cultured rat primary neurons against death induced by HNE, chemical hypoxia, glucose deprivation, and combined oxygen and glucose deprivation. The histidine analogue prevented neuronal apoptosis as indicated by decreased production of cleaved caspase-3 protein. These findings suggest a therapeutic potential for HNE-scavenging histidine analogues in the treatment of stroke and related neurodegenerative conditions.

Cryptic species diversity in a widespread bumble bee complex revealed using mitochondrial DNA RFLPs

Cryptic species diversity is thought to be common within the class Insecta, posing problems for basic ecological and population genetic studies and conservation management. Within the temperate bumble bee (Bombus spp.) fauna, members of the subgenus Bombus sensu stricto are amongst the most abundant and widespread. However, their species diversity is controversial due to the extreme difficulty or inability morphologically to identify the majority of individuals to species. Our character-based phylogenetic analyses of partial CO1 (700 bp) from 39 individuals spread across their sympatric European ranges provided unequivocal support for five taxa (3-22 diagnostic DNA base pair sites per species). Inclusion of 20 Irish specimens to the dataset revealed >= 2.3% sequence divergence between taxa and 200 m) whilst B. cryptarum was relatively more abundant at higher altitudes. Bombus magnus was rarely encountered at urban sites. Both B. lucorum and B. terrestris are nowadays reared commercially for pollination and transported globally. Our RFLP approach to identify native fauna can underpin ecological studies of these important cryptic species as well as the impact of commercial bumble bees on them.

Vortex line and ring dynamics in trapped Bose-Einstein condensates

Vortex dynamics in inhomogeneous Bose-Einstein condensates are studied numerically in two and three dimensions. We simulate the precession of a single vortex around the center of a trapped condensate, and use the Magnus force to estimate the precession frequency. Vortex ring dynamics in a spherical trap are also simulated, and we discover that a ring undergoes oscillatory motion around a circle of maximum energy. The position of this locus is calculated as a function of the number of condensed atoms. In the presence of dissipation, the amplitude of the oscillation will increase, eventually resulting in self-annihilation of the ring.

Relationship between electrical resistivity and basic geotechnical parameters for marine clays

Recently, considerable efforts have been made in the attempt to map quick clay areas using electrical resistivity measurements. However there is a lack of understanding regarding which soil parameters control the measured resistivity values. To address this issue, inverted resistivity values from 15 marine clay sites in Norway have been compared with basic geotechnical index properties. It was found that the resistivity value is strongly controlled by the salt content of the pore fluid. Resistivity decreases rapidly with increasing salt content. There is also a relatively clear trend of decreasing resistivity with increasing clay content and plasticity index. Resistivity values become very low (˜5 O·m) for high clay content (>50%), medium- to high-plasticity (Ip ˜ 20%) materials with salt content values greater than about 8 g/L (or corresponding remoulded shear strength values greater than 4 kPa). For the range of values studied, there is poor correlation between resistivity and bulk density and between resistivity and water content. The data studied suggest that the range of resistivity values corresponding to quick clay is 10 to 100 O·m, which is consistent with other published limits. A comparison is made between two-dimensional electrical resistivity tomography (ERT) and resistivity cone penetration test (RCPTU) data for two of the sites and the two sets of data show similar trends and values irrespective of scale effect.

Platinum catalysed hydrosilylation of propargylic alcohols

A facile and user-friendly protocol has been developed for the selective synthesis of E-vinyl silanes derived from propargylic alcohols using a PtCl2/XPhos catalyst system. The reaction is generally high yielding and provides a single regioisomer at the ß-position with E-alkene geometry. The reaction is extremely tolerant of functionality and has a wide scope of reactivity both in terms of alkynes and silanes used. The catalyst loading has been investigated and it is found that good reactivity is observed at extremely low catalyst loadings. This methodology has also been extended to a one-pot hydrosilylation Denmark–Hiyama coupling.