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

Soil humic substances hinder the propagation of prions

Prions are infectious pathogens causing fatal neurodegenerative disorders, known as transmissible spongiform encephalopathies (TSEs), or prion diseases, which affect different mammalian species. TSEs include scrapie in sheep, bovine spongiform encephalopathy (BSE) in cattle, chronic wasting disease (CWD) in mule deer, elk, and moose (cervids), and Creutzfeldt-Jakob disease (CJD) in humans. The prominent, if not only, component of prions is a misfolded conformer (PrPSc) of a constitutive sialoglycoprotein, the cellular prion protein (PrPC). A notable feature of prion diseases is horizontal transmission between grazing animals, implying that contaminated soil may serve to propagate the disease. In this respect, it has been reported that grazing animals ingest from tens to hundreds grams of soil per day, either incidentally through the diet, or deliberately in answering salt needs, and that mule deer can develop CWD after grazing in locations that previously housed infected \u202

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

The Increase of the Micoporosity and CO2 Adsorption Capacity of the Commercial Activated Carbon CWZ-22 by KOH Treatment

The chemical modification of CWZ-22—commercial activated carbon (AC) with KOH‐ to enhance CO2 adsorption was examined. The effect of different impregnation ratios KOH:CWZ-22 from 1 to 4 was studied. The ACs were characterized by CO2 and N2 sorption, Fourier transform infrared (FTIR), SEM, and XRD methods

Epilepsy and hypertension: The possible link for sudden unexpected death in epilepsy?

Epilepsy affects about 50 million people worldwide. Sudden unexpected death in epilepsy (SUDEP) is the main cause of death in epilepsy accounting for up to 17% of all deaths in epileptic patients, and therefore remains a major public health problem. SUDEP likely arises from a combination and interaction of multiple risk factors (such as being male, drug resistance, frequent generalized tonic-clonic seizures) making risk prediction and mitigation challenging. While there is a general understanding of the physiopathology of SUDEP, mechanistic hypotheses linking risk factors with a risk of SUDEP are still lacking. Identifying cross-talk between biological systems implicated in SUDEP may facilitate the development of improved models for SUDEP risk assessment, treatment and clinical management. In this review, the aim was to explore an overlap between the pathophysiology of hypertension, cardiovascular disease and epilepsy, and discuss its implication for SUDEP. Presented herein, evidence in literature in support of a cross-talk between the renin–angiotensin system (RAS) and sympathetic nervous system, both known to be involved in the development of hypertension and cardiovascular disease, and as one of the underlying mechanisms of SUDEP. This article also provides a brief description of local RAS in brain neuroinflammation and the role of centrally acting RAS inhibitors in epileptic seizure alleviation

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

On certain infinite extensions of the rationals with Northcott property

A set of algebraic numbers has the Northcott property if each of its subsets of bounded Weil height is finite. Northcott's Theorem, which has many Diophantine applications, states that sets of bounded degree have the Northcott property. Bombieri, Dvornicich and Zannier raised the problem of finding fields of infinite degree with this property. Bombieri and Zannier have shown that \IQ_{ab}^{(d)}, the maximal abelian subfield of the field generated by all algebraic numbers of degree at most $d$, is such a field. In this note we give a simple criterion for the Northcott property and, as an application, we deduce several new examples, e.g. \IQ(2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...) has the Northcott property if and only if $2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...$ tends to infinity

Apoptosis in the course of experimetal intracerebral haemorrhage in the rat

Intracerebral haematoma was produced in 25 adult rats by infusion of 100 µl of autologous blood into the striatum. The animals’ brains were removed at 1, 3, 7, 14 and 21 days after production of the haematoma. The TUNEL method was used to detect DNA fragmentation and TUNEL-positive cells were qualified. TUNEL-positive cells were already found on the first day of observation and were present for three weeks after haematoma production. These results provide evidence that programmed cell death is associated with intracerebral haemorrhage

In Vitro Aggregation Assays for the Characterization of \u3b1-synuclein Prion-Like Properties

Aggregation of \u3b1-synuclein plays a crucial role in the pathogenesis of synucleinopathies, a group of neurodegenerative diseases including Parkinson disease (PD), dementia with Lewy bodies (DLB), diffuse Lewy body disease (DLBD) and multiple system atrophy (MSA). The common feature of these diseases is a pathological deposition of protein aggregates, known as Lewy bodies (LBs) in the central nervous system. The major component of these aggregates is \u3b1-synuclein, a natively unfolded protein, which may undergo dramatic structural changes resulting in the formation of \u3b2-sheet rich assemblies. In vitro studies have shown that recombinant \u3b1-synuclein protein may polymerize into amyloidogenic fibrils resembling those found in LBs. These aggregates may be uptaken and propagated between cells in a prion-like manner. Here we present the mechanisms and kinetics of \u3b1-synuclein aggregation in vitro, as well as crucial factors affecting this process. We also describe how PD-linked \u3b1-synuclein mutations and some exogenous factors modulate in vitro aggregation. Furthermore, we present a current knowledge on the mechanisms by which extracellular aggregates may be internalized and propagated between cells, as well as the mechanisms of their toxicity. \ua9 2014 Landes Bioscience