Ideal extensions of free commutative monoids

We introduce a new family of monoids, which we call gap absorbing monoids. Every gap absorbing monoid is an ideal extension of a free commutative monoid. For a gap absorbing monoid $S$ we study its set of atoms and Betti elements, which allows us to show that the catenary degree of $S$ is at most four and that the set of lengths of any element in $S$ is an interval. We also give bounds for the $\omega$-primality of any ideal extension of a free commutative monoid. For ideal extensions $S$ of $\mathbb{N}^d$, with $d$ a positive integer, we show that $\omega(S)$ is finite if and only if $S$ has finitely many gaps

Calcium phosphate nanoparticles as intrinsic inorganic antimicrobials: In search of the key particle property

One of the main goals of materials science in the 21st century is the development of materials with rationally designed properties as substitutes for traditional pharmacotherapies. At the same time, there is a lack of understanding of the exact material properties that induce therapeutic effects in biological systems, which limits their rational optimization for the related medical applications. This study sets the foundation for a general approach for elucidating nanoparticle properties as determinants of antibacterial activity, with a particular focus on calcium phosphate nanoparticles. To that end, nine physicochemical effects were studied and a number of them were refuted, thus putting an end to frequently erred hypotheses in the literature. Rather than having one key particle property responsible for eliciting the antibacterial effect, a complex synergy of factors is shown to be at work, including (a) nanoscopic size; (b) elevated intracellular free calcium levels due to nanoparticle solubility; (c) diffusivity and favorable electrostatic properties of the nanoparticle surface, primarily low net charge and high charge density; and (d) the dynamics of perpetual exchange of ultrafine clusters across the particle/solution interface. On the positive side, this multifaceted mechanism is less prone to induce bacterial resistance to the therapy and can be a gateway to the sphere of personalized medicine. On a more problematic side, it implies a less intense effect compared to single-target molecular therapies and a difficulty of elucidating the exact mechanisms of action, while also making the rational design of theirs for this type of medical application a challenge

Associations between tooth wear and dental sleep disorders : A narrative overview

Objectives Tooth wear is a common finding in adult patients with dental sleep disorders. The aim of this paper was to review the literature on the possible associations between tooth wear and the following dental sleep disorders: sleep-related oro-facial pain, oral moistening disorders, gastroesophageal reflux disease (GERD), obstructive sleep apnoea syndrome (OSAS) and sleep bruxism. Methods A PubMed search was performed on 1 June 2018 using MeSH terms in the following query: Tooth Wear AND (Facial Pain OR Temporomandibular Joint Disorders OR Xerostomia OR Sialorrhea OR Gastroesophageal Reflux OR Sleep Apnea Syndrome OR Sleep Bruxism). Results The query yielded 706 reports on tooth wear and the mentioned dental sleep disorders. Several associations between tooth wear and the dental sleep disorders were suggested in the literature. It could be concluded that: (a) tooth wear is associated with dental pain and/or hypersensitivity; (b) oral dryness is associated with tooth wear, oro-facial pain and sleep bruxism; (c) GERD is associated with tooth wear, oro-facial pain, oral dryness, OSAS and sleep bruxism; (d) OSAS is associated with oral dryness, GERD and sleep bruxism; and (e) sleep bruxism is associated with tooth wear. Conclusions Tooth wear is associated with the dental sleep disorders oro-facial pain, oral dryness, GERD and sleep bruxism. The dental sleep disorders are interlinked with each other, which leads to indirect associations as well, and makes the consequences of each single condition difficult to disentangle. Knowledge of these associations is clinically relevant, but more research is needed to confirm their validity.Peer reviewe

Caries associated with orthodontic care part 2: management

It is recognized that wearing an orthodontic appliance increases the caries risk of the individual. The prevalence of demineralization has been reported to be as high as 73%. When demineralization occurs a number of treatments exist: fluoride application, acid microabrasion, casein phosphopeptide-amorphous calcium phosphate (CCP-ACP), resin infiltration and self-assembling peptides. Of these, topical fluoride has the most evidence to support its use. CPD/Clinical Relevance: Demineralization is the most common complication of orthodontic care. The clinician should understand how to manage this when it occurs

Fermi-LAT observations of the exceptional gamma-ray outbursts of 3C 273 in September 2009

We present the light curves and spectral data of two exceptionally luminous gamma-ray outburts observed by the Large Area Telescope (LAT) experiment on board Fermi Gamma-ray Space Telescope from 3C 273 in September 2009. During these flares, having a duration of a few days, the source reached its highest gamma-ray flux ever measured. This allowed us to study in some details their spectral and temporal structures. The rise and decay are asymmetric on timescales of 6 hours, and the spectral index was significantly harder during the flares than during the preceding 11 months. We also found that short, very intense flares put out the same time-integrated energy as long, less intense flares like that observed in August 2009.Comment: Corresponding authors: E. Massaro, [email protected]; G. Tosti, [email protected]. 15 pages, 4 figures, published in The Astrophysical Journal Letters, Volume 714, Issue 1, pp. L73-L78 (2010

Oral health promotion: the economic benefits to the NHS of increased use of sugarfree gum in the UK.

INTRODUCTION: The effect of sugarfree gum (SFG) on the prevention of dental caries has been established for some time. With increased constraints placed on healthcare budgets, the importance of economic considerations in decision-making about oral health interventions has increased. The aim of this study was to demonstrate the potential cost savings in dental care associated with increased levels of SFG usage. METHODS: The analysis examined the amount of money which would hypothetically be saved if the UK 12-year-old population chewed more SFG. The number of sticks chewed per year and the caries risk reduction were modelled to create a dose response curve. The costs of tooth restoration, tooth extraction in primary care settings and under general anaesthetic were considered, and the effects of caries reduction on these costs calculated. RESULTS: If all members of the UK 12-year-old population chewed SFG frequently (twice a day), the potential cost savings for the cohort over the course of one year were estimated to range from £1.2 to £3.3 million and if they chewed three times a day, £8.2 million could be saved each year. Sensitivity analyses of the key parameters demonstrated that cost savings would still be likely to be observed even in scenarios with less significant increases in SFG use. CONCLUSION: This study shows that if levels of SFG usage in the teenage population in the UK could be increased, substantial cost savings might be achieved

Discovery of Pulsed γ\gamma-rays from PSR J0034-0534 with the Fermi LAT: A Case for Co-located Radio and γ\gamma-ray Emission Regions

Millisecond pulsars (MSPs) have been firmly established as a class of gamma-ray emitters via the detection of pulsations above 0.1 GeV from eight MSPs by the Fermi Large Area Telescope (LAT). Using thirteen months of LAT data significant gamma-ray pulsations at the radio period have been detected from the MSP PSR J0034-0534, making it the ninth clear MSP detection by the LAT. The gamma-ray light curve shows two peaks separated by 0.274$\pm$0.015 in phase which are very nearly aligned with the radio peaks, a phenomenon seen only in the Crab pulsar until now. The $\geq$0.1 GeV spectrum of this pulsar is well fit by an exponentially cutoff power law with a cutoff energy of 1.8$\pm 0.6\pm$0.1 GeV and a photon index of 1.5$\pm 0.2\pm$0.1, first errors are statistical and second are systematic. The near-alignment of the radio and gamma-ray peaks strongly suggests that the radio and gamma-ray emission regions are co-located and both are the result of caustic formation.Comment: 20 pages, 3 figures, 2 tables. Accepted for publication in Ap

Fermi Gamma-ray Space Telescope Observations of Recent Gamma-ray Outbursts from 3C 454.3

The flat spectrum radio quasar 3C~454.3 underwent an extraordinary outburst in December 2009 when it became the brightest gamma-ray source in the sky for over one week. Its daily flux measured with the Fermi Large Area Telescope at photon energies E>100 MeV reached F = 22+/-1 x 10^-6 ph cm^-2 s^-1, representing the highest daily flux of any blazar ever recorded in high-energy gamma-rays. It again became the brightest source in the sky in 2010 April, triggering a pointed-mode observation by Fermi. The correlated gamma-ray temporal and spectral properties during these exceptional events are presented and discussed. The main results show flux variability over time scales less than 3 h and very mild spectral variability with an indication of gradual hardening preceding major flares. No consistent loop pattern emerged in the gamma-ray spectral index vs flux plane. A minimum Doppler factor of ~ 15 is derived, and the maximum energy of a photon from 3C 454.3 is ~ 20 GeV. The spectral break at a few GeV is inconsistent with Klein-Nishina softening from power-law electrons scattering Ly_alpha line radiation, and a break in the underlying electron spectrum in blazar leptonic models is implied.Comment: submitted to the Astrophysical Journa

Fermi observations of high-energy gamma-ray emission from GRB 090217A

The Fermi observatory is advancing our knowledge of Gamma-Ray Bursts (GRBs) through pioneering observations at high energies, covering more than 7 decades in energy with the two on-board detectors, the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM). Here we report on the observation of the long GRB 090217A which triggered the GBM and has been detected by the LAT with a significance greater than 9 sigma. We present the GBM and LAT observations and on-ground analyses, including the time-resolved spectra and the study of the temporal profile from 8 keV up to 1 GeV. All spectra are well reproduced by a Band model. We compare these observations to the first two LAT-detected, long bursts GRB 080825C and GRB 080916C. These bursts were found to have time-dependent spectra and exhibited a delayed onset of the high-energy emission, which are not observed in the case of GRB 090217A. We discuss some theoretical implications for the high-energy emission of GRBs.Comment: 17 pages, 4 figures. Contact Authors: Fred, Piron; Sara, Cutini; Andreas, von Kienli