The Automorphism Group of a Finite p-Group is Almost Always a p-Group

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the third go to infinity: the lower p-length, the number of generators, and p. The proof of this theorem depends on a variety of topics: counting subgroups of a p-group; analyzing the lower p-series of a free group via its connection with the free Lie algebra; counting submodules of a module via Hall polynomials; and using numerical estimates on Gaussian coefficients.Comment: 38 pages, to appear in the Journal of Algebra; improved references, changes in terminolog

Attosecond Photoionization Dynamics: from Molecules over Clusters to the Liquid Phase

Photoionization is a process taking place on attosecond time scales. How its properties evolve from isolated particles to the condensed phase is an open question of both fundamental and practical relevance. Here, we review recent work that has advanced the study of photoionization dynamics from atoms to molecules, clusters and the liquid phase. The first measurements of molecular photoionization delays have revealed the attosecond dynamics of electron emission from a molecular shape resonance and their sensitivity to the molecular potential. Using electron-ion coincidence spectroscopy these measurements have been extended from isolated molecules to clusters. A continuous increase of the delays with the water-cluster size has been observed up to a size of 4-5 molecules, followed by a saturation towards larger clusters. Comparison with calculations has revealed a correlation of the time delay with the spatial extension of the created electron hole. Using cylindrical liquid-microjet techniques, these measurements have also been extended to liquid water, revealing a delay relative to isolated water molecules that was very similar to the largest water clusters studied. Detailed modeling based on Monte-Carlo simulations confirmed that these delays are dominated by the contributions of the first two solvation shells, which agrees with the results of the cluster measurements. These combined results open the perspective of experimentally characterizing the delocalization of electronic wave functions in complex systems and studying their evolution on attosecond time scales

On the representation ring of the polynomial algebra over a perfect field

We consider the tensor product of modules over the polynomial algebra corresponding to the usual tensor product of linear operators. We present a general description of the representation ring in case the ground field k is perfect. It is made explicit in the special cases when k is real closed respectively algebraically closed. Furthermore, we discuss the generalisation of this problem to representations of quivers. In particular the representation ring of quivers of extended Dynkin type A is provided.Comment: 17 page

Double-component convection due to different boundary conditions in an infinite slot diversely oriented to the gravity

Onset of small-amplitude oscillatory and both small- and finite-amplitude steady double-component convection arising due to component different boundary conditions in an infinite slot is studied for various slot orientations to the gravity. The main focus is on two compensating background gradients of the components. The physical mechanisms underlying steady and oscillatory convection are analyzed from the perspective of a universally consistent understanding of the effects of different boundary conditions.Comment: V2: Submitted to and published in Annals of Physics. 59 manuscript pages, 15 figures (occupying 21 pages). The full abstract is on the first page. Nonessential modifications/enhancements in the presentation (more compact presentation of the text and figure data, some style improvements, etc.

Spin-orbit delays in photoemission

Attosecond delays between photoelectron wave packets emitted from different electronic shells are now well established. Is there any delay between electrons originating from the same electronic shell but leaving the cation in different fine-structure states? This question is relevant for all attosecond photoemission studies involving heavy elements, be it atoms, molecules or solids. We answer this fundamental question by measuring energy-dependent delays between photoelectron wave packets associated with the P3/22 and P1/22 components of the electronic ground states of Xe+ and Kr+. We observe delays reaching up to 33±6 as in the case of Xe. Our results are compared with two state-of-the-art theories. Whereas both theories quantitatively agree with the results obtained for Kr, neither of them fully reproduces the experimental results in Xe. Performing delay measurements very close to the ionization thresholds, we compare the agreement of several analytical formulas for the continuum-continuum delays with experimental data. Our results show an important influence of spin-orbit coupling on attosecond photoionization delays, highlight the requirement for additional theory development, and offer a precision benchmark for such workWe gratefully acknowledge funding from an ERC Starting Grant (Contract No. 307270-ATTOSCOPE) and the NCCR-MUST, a funding instrument of the Swiss National Science Foundation. S.P. is funded by the Alexander von Humboldt Foundation and by the NSF through a grant to ITAMP. A.S.K. acknowledges support from the Australian Research Council under Discovery Grant No. DP120101805. I.J. and M.H. contributed equally to this work

Hypertension and happiness across nations

In surveys of well-being, countries such as Denmark and the Netherlands emerge as particularly happy while nations like Germany and Italy report lower levels of happiness. But are these kinds of findings credible? This paper provides some evidence that the answer is yes. Using data on 16 countries, it shows that happier nations report systematically lower levels of hypertension. As well as potentially validating the differences in measured happiness across nations, this suggests that blood-pressure readings might be valuable as part of a national well-being index. A new ranking of European nations’ GHQ-N6 mental health scores is also given

Shear-induced pressure changes and seepage phenomena in a deforming porous layer-I

We present a model for flow and seepage in a deforming, shear-dilatant sensitive porous layer that enables estimates of the excess pore fluid pressures and flow rates in both the melt and solid phase to be captured simultaneously as a function of stress rate. Calculations are relevant to crystallizing magma in the solidosity range 0.5–0.8 (50–20 per cent melt), corresponding to a dense region within the solidification front of a crystallizing magma chamber. Composition is expressed only through the viscosity of the fluid phase, making the model generally applicable to a wide range of magma types. A natural scaling emerges that allows results to be presented in non-dimensional form. We show that all length-scales can be expressed as fractions of the layer height H, timescales as fractions of H2(nβ'θ+ 1)/(θk) and pressures as fractions of . Taking as an example the permeability k in the mush of the order of magnitude 1015 m2 Pa1 s1, a layer thickness of tens of metres and a mush strength (θ) in the range 108–1012 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 105–109 s. Using mush permeability as a proxy, we show that the greatest maximum excess pore pressures develop consistently in rhyolitic (high-viscosity) magmas at high rates of shear ( , implying that during deformation, the mechanical behaviour of basaltic and rhyolitic magmas will differ. Transport parameters of the granular framework including tortuosity and the ratio of grain size to layer thickness (a/H) will also exert a strong effect on the mechanical behaviour of the layer at a given rate of strain. For dilatant materials under shear, flow of melt into the granular layer is implied. Reduction in excess pore pressure sucks melt into the solidification front at a velocity proportional to the strain rate. For tectonic rates (generally 1014 s1), melt upwelling (or downwelling, if the layer is on the floor of the chamber) is of the order of cm yr1. At higher rates of loading comparable with emplacement of some magmatic intrusions (1010 s1), melt velocities may exceed effects due to instabilities resulting from local changes in density and composition. Such a flow carries particulates with it, and we speculate that these may become trapped in the granular layer depending on their sizes. If on further solidification the segregated grain size distribution of the particulates is frozen in the granular layer, structure formation including layering and grading may result. Finally, as the process settles down to a steady state, the pressure does not continue to decrease. We find no evidence for critical rheological thresholds, and the process is stable until so much shear has been applied that the granular medium fails, but there is no hydraulic failure

Altered gene expression in the Werner and Bloom syndromes is associated with sequences having G-quadruplex forming potential

The human Werner and Bloom syndromes (WS and BS) are caused by deficiencies in the WRN and BLM RecQ helicases, respectively. WRN, BLM and their Saccharomyces cerevisiae homologue Sgs1, are particularly active in vitro in unwinding G-quadruplex DNA (G4-DNA), a family of non-canonical nucleic acid structures formed by certain G-rich sequences. Recently, mRNA levels from loci containing potential G-quadruplex-forming sequences (PQS) were found to be preferentially altered in sgs1Δ mutants, suggesting that G4-DNA targeting by Sgs1 directly affects gene expression. Here, we extend these findings to human cells. Using microarrays to measure mRNAs obtained from human fibroblasts deficient for various RecQ family helicases, we observe significant associations between loci that are upregulated in WS or BS cells and loci that have PQS. No such PQS associations were observed for control expression datasets, however. Furthermore, upregulated genes in WS and BS showed no or dramatically reduced associations with sequences similar to PQS but that have considerably reduced potential to form intramolecular G4-DNA. These findings indicate that, like Sgs1, WRN and BLM can regulate transcription globally by targeting G4-DNA

Wind-driven upwelling around grounded tabular icebergs

Funding was provided by NSF Polar Programs - Grant Number: ARC-1304137.Temperature and salinity data collected around grounded tabular icebergs in Baffin Bay in 2011, 2012 and 2013 indicate wind-induced upwelling at certain locations around the icebergs. These data suggest that along one side of the iceberg, wind forcing leads to Ekman transport away from the iceberg, which causes upwelling of the cool saline water from below. The upwelling water mixes with the water in the thermocline, causing the mixed layer to become cooler and more saline. Along the opposite side of the iceberg, the surface Ekman transport moves towards the iceberg, which causes a sharpening of the thermocline as warm fresh water is trapped near the surface. This results in higher mixed layer temperatures and lower mixed layer salinities on this side of the iceberg. Based on these in situ measurements, we hypothesize that the asymmetries in water properties around the iceberg, caused by the opposing effects of upwelling and sharpening of the thermocline, lead to differential deterioration around the iceberg. Analysis of satellite imagery around iceberg PII-B-1 over a six month monitoring period reveals differential decay around the iceberg, in agreement with this mechanism.Publisher PDFPeer reviewe