On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras

A molecule is a nonzero non-unit element of an integral domain (resp., commutative cancellative monoid) having a unique factorization into irreducibles (resp., atoms). Here we study the molecules of Puiseux monoids as well as the molecules of their corresponding semigroup algebras, which we call Puiseux algebras. We begin by presenting, in the context of numerical semigroups, some results on the possible cardinalities of the sets of molecules and the sets of reducible molecules (i.e., molecules that are not irreducibles/atoms). Then we study the molecules in the more general context of Puiseux monoids. We construct infinitely many non-isomorphic atomic Puiseux monoids all whose molecules are atoms. In addition, we characterize the molecules of Puiseux monoids generated by rationals with prime denominators. Finally, we turn to investigate the molecules of Puiseux algebras. We provide a characterization of the molecules of the Puiseux algebras corresponding to root-closed Puiseux monoids. Then we use such a characterization to find an infinite class of Puiseux algebras with infinitely many non-associated reducible molecules.Comment: 21 pages, 2 figure

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

On the probabilities of local behaviors in abelian field extensions

For a number field K and a finite abelian group G, we determine the probabilities of various local completions of a random G-extension of K when extensions are ordered by conductor. In particular, for a fixed prime p of K, we determine the probability that p splits into r primes in a random G-extension of K that is unramified at p. We find that these probabilities are nicely behaved and mostly independent. This is in analogy to Chebotarev's density theorem, which gives the probability that in a fixed extension a random prime of K splits into r primes in the extension. We also give the asymptotics for the number of G-extensions with bounded conductor. In fact, we give a class of extension invariants, including conductor, for which we obtain the same counting and probabilistic results. In contrast, we prove that that neither the analogy with the Chebotarev probabilities nor the independence of probabilities holds when extensions are ordered by discriminant.Comment: 28 pages, submitte

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

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 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

Ground states for a class of deterministic spin models with glassy behaviour

We consider the deterministic model with glassy behaviour, recently introduced by Marinari, Parisi and Ritort, with \ha\ $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the discrete sine Fourier transform. The ground state found by these authors for $N$ odd and $2N+1$ prime is shown to become asymptotically dege\-ne\-ra\-te when $2N+1$ is a product of odd primes, and to disappear for $N$ even. This last result is based on the explicit construction of a set of eigenvectors for $J$, obtained through its formal identity with the imaginary part of the propagator of the quantized unit symplectic matrix over the $2$-torus.Comment: 15 pages, plain LaTe

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

Two-way FSI modelling of blood flow through CCA accounting on-line medical diagnostics in hypertension

Flow parameters can induce pathological changes in the arteries. We propose a method to asses those parameters using a 3D computer model of the flow in the Common Carotid Artery. Input data was acquired using an automatic 2D ultrasound wall tracking system. This data has been used to generate a 3D geometry of the artery. The diameter and wall thickness have been assessed individually for every patient, but the artery has been taken as a 75mm straight tube. The Young’s modulus for the arterial walls was calculated using the pulse pressure, diastolic (minimal) diameter and wall thickness (IMT). Blood flow was derived from the pressure waveform using a 2-parameter Windkessel model. The blood is assumed to be non-Newtonian. The computational models were generated and calculated using commercial code. The coupling method required the use of Arbitrary Lagrangian-Euler formulation to solve Navier-Stokes and Navier-Lamè equations in a moving domain. The calculations showed that the distention of the walls in the model is not significantly different from the measurements. Results from the model have been used to locate additional risk factors, such as wall shear stress or circumferential stress, that may predict adverse hypertension complications

Opposite Structural Effects of Epigallocatechin-3-gallate and Dopamine Binding to α-Synuclein

The intrinsically disordered and amyloidogenic protein α-synuclein (AS) has been linked to several neurodegenerative states, including Parkinson's disease. Here, nanoelectrospray-ionization mass spectrometry (nano-ESI-MS), ion mobility (IM), and native top-down electron transfer dissociation (ETD) techniques are employed to study AS interaction with small molecules known to modulate its aggregation, such as epigallocatechin-3-gallate (EGCG) and dopamine (DA). The complexes formed by the two ligands under identical conditions reveal peculiar differences. While EGCG engages AS in compact conformations, DA preferentially binds to the protein in partially extended conformations. The two ligands also have different effects on AS structure as assessed by IM, with EGCG leading to protein compaction and DA to its extension. Native top-down ETD on the protein-ligand complexes shows how the different observed modes of binding of the two ligands could be related to their known opposite effects on AS aggregation. The results also show that the protein can bind either ligand in the absence of any covalent modifications, such as oxidation