Fusion Rings Related to Affine Weyl Groups

The construction of the fusion ring of a quasi-rational CFT based on $\hat{sl}(3)_k$ at generic level $k\not \in {\Bbb Q}$ is reviewed. It is a commutative ring generated by formal characters, elements in the group ring ${\Bbb Z}[\tilde{W}]$ of the extended affine Weyl group $\tilde{W}$ of $\hat{sl}(3)_k$. Some partial results towards the $\hat{sl}(4)_k$ generalisation of this character ring are presented.Comment: 13 pages; two figures. Talk at ``Lie Theory and Its Applications in Physics III'', Clausthal, 11-14 July, 1999, to appear in the Proceedings, eds. H.-D. Doebner et a

An Extension of the Character Ring of sl(3) and Its Quantisation

We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring $Z[\tilde{W}]$ of the extended affine Weyl group of $\hat{sl}(3)_k$ at $k\not \in Q$. The `quantised' version at rational level $k+3=3/p$ realises the fusion rules of a WZW conformal field theory based on admissible representations of $\hat{sl}(3)_k$.Comment: contains two TeX files: main file using harvmac.tex, amssym.def, amssym.tex, 35p.; file with figures using XY-pic package, 4p; v2: minor corrections, Note adde

Non-critical string pentagon equations and their solutions

We derive pentagon type relations for the 3-point boundary tachyon correlation functions in the non-critical open string theory with generic c_{matter} < 1 and study their solutions in the case of FZZ branes. A new general formula for the Liouville 3-point factor is derived.Comment: 18 pages, harvmac; misprints corrected, section 3.2 extended, a new general formula for the Liouville 3-point factor adde

Production of docosahexaenoic acid by Aurantiochytrium sp. ATCC PRA-276

The high costs and environmental concerns associated with using marine resources as sources of oils rich in polyunsaturated fatty acids have prompted searches for alternative sources of such oils. Some microorganisms, among them members of the genus Aurantiochytrium, can synthesize large amounts of these biocompounds. However, various parameters that affect the polyunsaturated fatty acids production of these organisms, such as the carbon and nitrogen sources supplied during their cultivation, require further elucidation. The objective of this investigation was to study the effect of different concentrations of carbon and total nitrogen on the production of polyunsaturated fatty acids, particularly docosahexaenoic acid, by Aurantiochytrium sp. ATCC PRA-276. We performed batch system experiments using an initial glucose concentration of 30 g/L and three different concentrations of total nitrogen, including 3.0, 0.44, and 0.22 g/L, and fed-batch system experiments in which 0.14 g/L of glucose and 0.0014 g/L of total nitrogen were supplied hourly. To assess the effects of these different treatments, we determined the biomass, glucose, total nitrogen and polyunsaturated fatty acids concentration. The maximum cell concentration (23.9 g/L) was obtained after 96 h of cultivation in the batch system using initial concentrations of 0.22 g/L total nitrogen and 30 g/L glucose. Under these conditions, we observed the highest level of polyunsaturated fatty acids production (3.6 g/L), with docosahexaenoic acid and docosapentaenoic acid ω6 concentrations reaching 2.54 and 0.80 g/L, respectively

Is depression a real risk factor for acute myocardial infarction mortality? A retrospective cohort study

Background: Depression has been associated with a higher risk of cardiovascular events and a higher mortality in patients with one or more comorbidities. This study investigated whether continuative use of antidepressants (ADs), considered as a proxy of a state of depression, prior to acute myocardial infarction (AMI) is associated with a higher mortality afterwards. The outcome to assess was mortality by AD use. Methods: A retrospective cohort study was conducted in the Veneto Region on hospital discharge records with a primary diagnosis of AMI in 2002-2015. Subsequent deaths were ascertained from mortality records. Drug purchases were used to identify AD users. A descriptive analysis was conducted on patients' demographics and clinical data. Survival after discharge was assessed with a Kaplan-Meier survival analysis and Cox's multiple regression model. Results: Among 3985 hospital discharge records considered, 349 (8.8%) patients were classified as AD users'. The mean AMI-related hospitalization rate was 164.8/100,000 population/year, and declined significantly from 204.9 in 2002 to 130.0 in 2015, but only for AD users (-40.4%). The mean overall follow-up was 4.64.1years. Overall, 523 patients (13.1%) died within 30days of their AMI. The remainder survived a mean 5.3 +/- 4.0years. After adjusting for potential confounders, use of antidepressants was independently associated with mortality (adj OR=1.75, 95% CI: 1.40-2.19). Conclusions: Our findings show that AD users hospitalized for AMI have a worse prognosis in terms of mortality. The use of routinely-available records can prove an efficient way to monitor trends in the state of health of specific subpopulations, enabling the early identification of AMI survivors with a history of antidepressant use

On sl^(3)\widehat{sl}(3) reduction, quantum gauge transformations, and W−{\cal W}- algebras singular vectors

The problem of describing the singular vectors of \cW_3 and \cW_3^{(2)} Verma modules is addressed, viewing these algebras as BRST quantized Drinfeld-Sokolov (DS) reductions of $A^{(1)}_2\,$. Singular vectors of an $A^{(1)}_2\,$ Verma module are mapped into \W algebra singular vectors and are shown to differ from the latter by terms trivial in the BRST cohomology. These maps are realized by quantum versions of the highest weight DS gauge transformations.Comment: 9 page