On covers of cyclic acts over monoids

In (Bull. Lond. Math. Soc. 33:385–390, 2001) Bican, Bashir and Enochs finally solved a long standing conjecture in module theory that all modules over a unitary ring have a flat cover. The only substantial work on covers of acts over monoids seems to be that of Isbell (Semigroup Forum 2:95–118, 1971), Fountain (Proc. Edinb. Math. Soc. (2) 20:87–93, 1976) and Kilp (Semigroup Forum 53:225–229, 1996) who only consider projective covers. To our knowledge the situation for flat covers of acts has not been addressed and this paper is an attempt to initiate such a study. We consider almost exclusively covers of cyclic acts and restrict our attention to strongly flat and condition (P) covers. We give a necessary and sufficient condition for the existence of such covers and for a monoid to have the property that all its cyclic right acts have a strongly flat cover (resp. (P)-cover). We give numerous classes of monoids that satisfy these conditions and we also show that there are monoids that do not satisfy this condition in the strongly flat case. We give a new necessary and sufficient condition for a cyclic act to have a projective cover and provide a new proof of one of Isbell’s classic results concerning projective covers. We show also that condition (P) covers are not unique, unlike the situation for projective covers

Covers of acts over monoids II

In 1981 Edgar Enochs conjectured that every module has a flat cover and finally proved this in 2001. Since then a great deal of effort has been spent on studying different types of covers, for example injective and torsion free covers. In 2008, Mahmoudi and Renshaw initiated the study of flat covers of acts over monoids but their definition of cover was slightly different from that of Enochs. Recently, Bailey and Renshaw produced some preliminary results on the `other' type of cover and it is this work that is extended in this paper. We consider free, divisible, torsion free and injective covers and demonstrate that in some cases the results are quite different from the module case

Automatic structures for semigroup constructions

We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.Comment: 22 page

Standardized and reproducible methodology for the comprehensive and systematic assessment of surgical resection margins during breast-conserving surgery for invasive breast cancer

<p>Abstract</p> <p>Background</p> <p>The primary goal of breast-conserving surgery (BCS) is to completely excise the tumor and achieve "adequate" or "negative" surgical resection margins while maintaining an acceptable level of postoperative cosmetic outcome. Nevertheless, precise determination of the adequacy of BCS has long been debated. In this regard, the aim of the current paper was to describe a standardized and reproducible methodology for comprehensive and systematic assessment of surgical resection margins during BCS.</p> <p>Methods</p> <p>Retrospective analysis of 204 BCS procedures performed for invasive breast cancer from August 2003 to June 2007, in which patients underwent a standard BCS resection and systematic sampling of nine standardized re-resection margins (superior, superior-medial, superior-lateral, medial, lateral, inferior, inferior-medial, inferior-lateral, and deep-posterior). Multiple variables (including patient, tumor, specimen, and follow-up variables) were evaluated.</p> <p>Results</p> <p>6.4% (13/204) of patients had positive BCS specimen margins (defined as tumor at inked edge of BCS specimen) and 4.4% (9/204) of patients had close margins (defined as tumor within 1 mm or less of inked edge but not at inked edge of BCS specimen). 11.8% (24/204) of patients had at least one re-resection margin containing additional disease, independent of the status of the BCS specimen margins. 7.1% (13/182) of patients with negative BCS specimen margins (defined as no tumor cells seen within 1 mm or less of inked edge of BCS specimen) had at least one re-resection margin containing additional disease. Thus, 54.2% (13/24) of patients with additional disease in a re-resection margin would not have been recognized by a standard BCS procedure alone (P < 0.001). The nine standardized resection margins represented only 26.8% of the volume of the BCS specimen and 32.6% of the surface area of the BCS specimen.</p> <p>Conclusion</p> <p>Our methodology accurately assesses the adequacy of surgical resection margins for determination of which individuals may need further resection to the affected breast in order to minimize the potential risk of local recurrence while attempting to limit the volume of additional breast tissue excised, as well as to determine which individuals are not realistically amendable to BCS and instead need a completion mastectomy to successfully remove multifocal disease.</p

Modelling of the effect of ELMs on fuel retention at the bulk W divertor of JET

Effect of ELMs on fuel retention at the bulk W target of JET ITER-Like Wall was studied with multi-scale calculations. Plasma input parameters were taken from ELMy H-mode plasma experiment. The energetic intra-ELM fuel particles get implanted and create near-surface defects up to depths of few tens of nm, which act as the main fuel trapping sites during ELMs. Clustering of implantation-induced vacancies were found to take place. The incoming flux of inter-ELM plasma particles increases the different filling levels of trapped fuel in defects. The temperature increase of the W target during the pulse increases the fuel detrapping rate. The inter-ELM fuel particle flux refills the partially emptied trapping sites and fills new sites. This leads to a competing effect on the retention and release rates of the implanted particles. At high temperatures the main retention appeared in larger vacancy clusters due to increased clustering rate

Modelling of tungsten erosion and deposition in the divertor of JET-ILW in comparison to experimental findings

The erosion, transport and deposition of tungsten in the outer divertor of JET-ILW has been studied for an HMode discharge with low frequency ELMs. For this specific case with an inter-ELM electron temperature at the strike point of about 20 eV, tungsten sputtering between ELMs is almost exclusively due to beryllium impurity and self-sputtering. However, during ELMs tungsten sputtering due to deuterium becomes important and even dominates. The amount of simulated local deposition of tungsten relative to the amount of sputtered tungsten in between ELMs is very high and reaches values of 99% for an electron density of 5E13 cm$^{-3}$ at the strike point and electron temperatures between 10 and 30 eV. Smaller deposition values are simulated with reduced electron density. The direction of the B-field significantly influences the local deposition and leads to a reduction if the E×B drift directs towards the scrape-off-layer. Also, the thermal force can reduce the tungsten deposition, however, an ion temperature gradient of about 0.1 eV/mm or larger is needed for a significant effect. The tungsten deposition simulated during ELMs reaches values of about 98% assuming ELM parameters according to free-streaming model. The measured WI emission profiles in between and within ELMs have been reproduced by the simulation. The contribution to the overall net tungsten erosion during ELMs is about 5 times larger than the one in between ELMs for the studied case. However, this is due to the rather low electron temperature in between ELMs, which leads to deuterium impact energies below the sputtering threshold for tungsten

Tritium distributions on W-coated divertor tiles used in the third JET ITER-like wall campaign

Tritium (T) distributions on tungsten (W)-coated plasma-facing tiles used in the third ITER-like wall campaign (2015–2016) of the Joint European Torus (JET) were examined by means of an imaging plate technique and β-ray induced x-ray spectrometry, and they were compared with the distributions after the second (2013–2014) campaign. Strong enrichment of T in beryllium (Be) deposition layers was observed after the second campaign. In contrast, T distributions after the third campaign was more uniform though Be deposition layers were visually recognized. The one of the possible explanations is enhanced desorption of T from Be deposition layers due to higher tile temperatures caused by higher energy input in the third campaign

The effect of beryllium oxide on retention in JET ITER-like wall tiles

Preliminary results investigating the microstructure, bonding and effect of beryllium oxide formation on retention in the JET ITER-like wall beryllium tiles, are presented. The tiles have been investigated by several techniques: Scanning Electron Microscopy (SEM) equipped with Energy Dispersive X-ray (EDX), Transmission Electron microscopy (TEM) equipped with EDX and Electron Energy Loss Spectroscopy (EELS), Raman Spectroscopy and Thermal Desorption Spectroscopy (TDS). This paper focuses on results from melted materials of the dump plate tiles in JET. From our results and the literature, it is concluded, beryllium can form micron deep oxide islands contrary to the nanometric oxides predicted under vacuum conditions. The deepest oxides analyzed were up to 2-micron thicknesses. The beryllium Deuteroxide (BeOxDy) bond was found with Raman Spectroscopy. Application of EELS confirmed the oxide presence and stoichiometry. Literature suggests these oxides form at temperatures greater than 700 °C where self-diffusion of beryllium ions through the surface oxide layer can occur. Further oxidation is made possible between oxygen plasma impurities and the beryllium ions now present at the wall surface. Under Ultra High Vacuum (UHV) nanometric Beryllium oxide layers are formed and passivate at room temperature. After continual cyclic heating (to the point of melt formation) in the presence of oxygen impurities from the plasma, oxide growth to the levels seen experimentally (approximately two microns) is proposed. This retention mechanism is not considered to contribute dramatically to overall retention in JET, due to low levels of melt formation. However, this mechanism, thought the result of operation environment and melt formation, could be of wider concern to ITER, dependent on wall temperatures

An assessment of nitrogen concentrations from spectroscopic measurements in the JET and ASDEX upgrade divertor

The impurity concentration in the tokamak divertor plasma is a necessary input for predictive scaling of divertor detachment, however direct measurements from existing tokamaks in different divertor plasma conditions are limited. To address this, we have applied a recently developed spectroscopic N II line ratio technique for measuring the N concentration in the divertor to a range of H-mode and L-mode plasma from the ASDEX Upgrade and JET tokamaks, respectively. The results from both devices show that as the power crossing the separatrix, P$_{sep}$, is increased under otherwise similar core conditions (e.g. density), a higher N concentration is required to achieve the same detachment state. For example, the N concentrations at the start of detachment increase from ≈2% to ≈9% as Psep is increased from ≈2.5 MW to ≈7 MW. These results tentatively agree with scaling law predictions (e.g. Goldston et al.) motivating a further study examining the parameters which affect the N concentration required to reach detachment. Finally, the N concentrations from spectroscopy and the ratio of D and N gas valve fluxes agree within experimental uncertainty only when the vessel surfaces are fully-loaded with N

Impact of fast ions on density peaking in JET : fluid and gyrokinetic modeling

The effect of fast ions on turbulent particle transport, driven by ion temperature gradient (ITG)/trapped electron mode turbulence, is studied. Two neutral beam injection (NBI) heated JET discharges in different regimes are analyzed at the radial position rho(t) = 0.6, one of them an L-mode and the other one an H-mode discharge. Results obtained from the computationally efficient fluid model EDWM and the gyro-fluid model TGLF are compared to linear and nonlinear gyrokinetic GENE simulations as well as the experimentally obtained density peaking. In these models, the fast ions are treated as a dynamic species with a Maxwellian background distribution. The dependence of the zero particle flux density gradient (peaking factor) on fast ion density, temperature and corresponding gradients, is investigated. The simulations show that the inclusion of a fast ion species has a stabilizing influence on the ITG mode and reduces the peaking of the main ion and electron density profiles in the absence of sources. The models mostly reproduce the experimentally obtained density peaking for the L-mode discharge whereas the H-mode density peaking is significantly underpredicted, indicating the importance of the NBI particle source for the H-mode density profile