Unimodular integer circulants associated with trinomials

The n � n circulant matrix associated with the polynomial [image removed] (with d < n) is the one with first row (a0 ? ad 0 ? 0). The problem as to when such circulants are unimodular arises in the theory of cyclically presented groups and leads to the following question, previously studied by Odoni and Cremona: when is Res(f(t), tn-1) = �1? We give a complete answer to this question for trinomials f(t) = tm � tk � 1. Our main result was conjectured by the author in an earlier paper and (with two exceptions) implies the classification of the finite Cavicchioli?Hegenbarth?Repov? generalized Fibonacci groups, thus giving an almost complete answer to a question of Bardakov and Vesnin

Invariant sets of morphisms on projective and affine number spaces

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34172/1/0000461.pd

Humans don’t time sub-second intervals like a stopwatch

Many activities require the ability to estimate intervals of time in an accurate and flexible manner. A traditional and popular account suggests that humans possess a kind of internal stopwatch that can be started, paused and stopped at will. Here we test this idea by measuring variable performance errors in three experiments. Participants had to compare the total time accumulated during one to three short target intervals with a single standard interval. With two or more target intervals, participants had to pause, but not reset, their putative internal stopwatches. By establishing baseline performance at two different standard durations and extrapolating based on Weber’s law, we were able to estimate how much performance should have deteriorated when target segments contained breaks. The decrement in performance we observed far exceeded the stopwatch prediction, and also exceeded the simulated predictions of a modified stopwatch with a slowing pacemaker. The data thus favour either a counter that cannot be paused during sub-second durations or alternative models of sub-second interval duration discrimination which do not posit a count-based metric for time. We discuss several possible strategies which participants might have implemented in order to apply such clocks in the split-interval task

New constraints on the Middle Palaeozoic to enozoic burial and hermal history of the Holy ross Mts. (Central Poland) : results of numerical modelling

A 1-D burial-thermal modelling was performed using data from two borehole sections representative of the central part of the Holy Cross Mts. area. This area is located in the axial part of the Permian-Mesozoic Mid-Polish Trough that was inverted during the latest Cretaceous-Paleocene. The modelling involved different variants of restored stratigraphy of eroded Carboniferous to Cretaceous strata, whereas calibration was based on samples from cored Middle-Upper Devonian sediments. The modelling results are consistent with the assumption of a Variscan (Carboniferous-Early Permian) heat flow elevated up to 80 mWm-2, which is further confirmed by independent regional evidence. The zone of increased thermal maturity in the Devonian may be partly accounted for by a thicker Carboniferous section (by ca. 500 m) compared to previous estimates. Two variants of the post-Carboniferous geohistory were analysed. The variant of a thinner Permian-Mesozoic section, implying lower magnitude of the Late Cretaceous-Paleogene inversion, allows more realistic assumptions regarding heat flow distribution through time, including the possibility to incorporate an elevated Variscan heat flow. The alternative scenario, assuming deeper burial, generally lower heat flow and smaller Carboniferous thickness, is regarded as less probable. The accepted variant of the Permian-Mesozoic burial history implies that the total post-Carboniferous burial in the study area was on the order of 2000-2500 metres rather than 3000-3500 metres. The respective Upper Cretaceous thickness could have been 400 to 500 m instead of ca. 1000 m, whereas the Late Cretaceous Paleogene inversion more likely started in the Santonian than in the late Maastrichtian. Consequently, the preferred magnitude of total inversion was on the order of 2500 m

New constraints on the Middle Palaeozoic to Cenozoic burial and thermal history of the Holy Cross Mts. (Central Poland): results from numerical modelling

A 1-D burial-thermal modelling was performed using data from two borehole sections representative of the central part of the Holy Cross Mts. area. This area is located in the axial part of the Permian-Mesozoic Mid-Polish Trough that was inverted during the latest Cretaceous-Paleocene. The modelling involved different variants of restored stratigraphy of eroded Carboniferous to Cretaceous strata, whereas calibration was based on samples from cored Middle-Upper Devonian sediments. The modelling results are consistent with the assumption of a Variscan (Carboniferous-Early Permian) heat flow elevated up to 80 mWm-2, which is further confirmed by independent regional evidence. The zone of increased thermal maturity in the Devonian may be partly accounted for by a thicker Carboniferous section (by ca. 500 m) compared to previous estimates. Two variants of the post-Carboniferous geohistory were analysed. The variant of a thinner Permian-Mesozoic section, implying lower magnitude of the Late Cretaceous-Paleogene inversion, allows more realistic assumptions regarding heat flow distribution through time, including the possibility to incorporate an elevated Variscan heat flow. The alternative scenario, assuming deeper burial, generally lower heat flow and smaller Carboniferous thickness, is regarded as less probable. The accepted variant of the Permian-Mesozoic burial history implies that the total post-Carboniferous burial in the study area was on the order of 2000-2500 metres rather than 3000-3500 metres. The respective Upper Cretaceous thickness could have been 400 to 500 m instead of ca. 1000 m, whereas the Late Cretaceous-Paleogene inversion more likely started in the Santonian than in the late Maastrichtian. Consequently, the preferred magnitude of total inversion was on the order of 2500 m

Kidney function in the very elderly with hypertension: data from the hypertension in the very elderly (HYVET) trial.

BACKGROUND: numerous reports have linked impaired kidney function to a higher risk of cardiovascular events and mortality. There are relatively few data relating to kidney function in the very elderly. METHODS: the Hypertension in the Very Elderly Trial (HYVET) was a randomised placebo-controlled trial of indapamide slow release 1.5mg ± perindopril 2-4 mg in those aged ≥80 years with sitting systolic blood pressures of ≥160 mmHg and diastolic pressures of <110 mmHg. Kidney function was a secondary outcome. RESULTS: HYVET recruited 3,845 participants. The mean baseline estimated glomerular filtration rate (eGFR) was 61.7 ml/min/1.73 m(2). When categories of the eGFR were examined, there was a possible U-shaped relationship between eGFR, total mortality, cardiovascular mortality and events. The nadir of the U was the eGFR category ≥60 and <75 ml/min/1.73 m(2). Using this as a comparator, the U shape was clearest for cardiovascular mortality with the eGFR <45 ml/min/1.73 m(2) and ≥75 ml/min/1.73 m(2) showing hazard ratios of 1.88 (95% CI: 1.2-2.96) and 1.36 (0.94-1.98) by comparison. Proteinuria at baseline was also associated with an increased risk of later heart failure events and mortality. CONCLUSIONS: although these results should be interpreted with caution, it may be that in very elderly individuals with hypertension both low and high eGFR indicate increased risk