A constructive study of the module structure of rings of partial differential operators

The purpose of this paper is to develop constructive versions of Stafford's theorems on the module structure of Weyl algebras A n (k) (i.e., the rings of partial differential operators with polynomial coefficients) over a base field k of characteristic zero. More generally, based on results of Stafford and Coutinho-Holland, we develop constructive versions of Stafford's theorems for very simple domains D. The algorithmization is based on the fact that certain inhomogeneous quadratic equations admit solutions in a very simple domain. We show how to explicitly compute a unimodular element of a finitely generated left D-module of rank at least two. This result is used to constructively decompose any finitely generated left D-module into a direct sum of a free left D-module and a left D-module of rank at most one. If the latter is torsion-free, then we explicitly show that it is isomorphic to a left ideal of D which can be generated by two elements. Then, we give an algorithm which reduces the number of generators of a finitely presented left D-module with module of relations of rank at least two. In particular, any finitely generated torsion left D-module can be generated by two elements and is the homomorphic image of a projective ideal whose construction is explicitly given. Moreover, a non-torsion but non-free left D-module of rank r can be generated by r+1 elements but no fewer. These results are implemented in the Stafford package for D=A n (k) and their system-theoretical interpretations are given within a D-module approach. Finally, we prove that the above results also hold for the ring of ordinary differential operators with either formal power series or locally convergent power series coefficients and, using a result of Caro-Levcovitz, also for the ring of partial differential operators with coefficients in the field of fractions of the ring of formal power series or of the ring of locally convergent power series. © 2014 Springer Science+Business Media

Identification of novel bacteriophages with therapeutic potential targeting Enterococcus faecalis

The Gram-positive opportunistic pathogen Enterococcus faecalis is frequently responsible for nosocomial infections in humans and represents one of the most common bacteria isolated from recalcitrant endodontic (root canal) infections. E. faecalis is intrinsically resistant to several antibiotics routinely used in clinical settings (such as cephalosporins and aminoglycosides) and can acquire resistance to vancomycin (vancomycin resistant enterococci, VRE). The resistance of E. faecalis to several classes of antibiotics and its capacity to form biofilms cause serious therapeutic problems. In this paper, we report the isolation of several bacteriophages that target E. faecalis strains isolated from the oral cavity of patients suffering root-canal infections. All phages isolated were Siphoviridae with similar tail lengths (200-250 nm) and icosahedral heads. The genome sequences of three isolated phages were highly conserved with the exception of predicted tail protein genes that diverge in sequence, potentially reflecting host range. The properties of the phage with the broadest host-range (SHEF2), was further characterised. We showed that this phage requires interaction with components of the major and variant region Enterococcal polysaccharide antigen (Epa) to engage in lytic infection. Finally, we explored the therapeutic potential of this phage and showed that it can eradicate E. faecalis biofilms formed in vitro on a standard polystyrene surface but also on a cross-sectional tooth-slice model of endodontic infection. We also show that SHEF2 cleared a lethal infection of zebrafish when applied in the circulation. We therefore propose that the phage described in this study could be used to treat a broad range of antibiotic resistant E. faecalis infections

The Influence of Dormitory Architecture On Resident Behavior

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66943/2/10.1177_001391657300500402.pd

The effect of autonomy, training opportunities, age and salaries on job satisfaction in the South East Asian retail petroleum industry

South East Asian petroleum retailers are under considerable pressure to improve service quality by reducing turnover. An empirical methodology from this industry determined the extent to which job characteristics, training opportunities, age and salary influenced the level of job satisfaction, an indicator of turnover. Responses are reported on a random sample of 165 site employees (a 68% response rate) of a Singaporean retail petroleum firm. A restricted multivariate regression model of autonomy and training opportunities explained the majority (35.4%) of the variability of job satisfaction. Age did not moderate these relationships, except for employees >21 years of age, who reported enhanced job satisfaction with additional salary. Human Capital theory, Life Cycle theory and Job Enrichment theory are invoked and explored in the context of these findings in the South East Asian retail petroleum industry. In the South East Asian retail petroleum industry, jobs providing employees with the opportunity to undertake a variety of tasks that enhanced the experienced meaningfulness of work are likely to promote job satisfaction, reduce turnover and increase the quality of service

New Blood Pressure-Associated Loci Identified in Meta-Analyses of 475,000 Individuals

Background - Genome-wide association studies have recently identified >400 loci that harbor DNA sequence variants that influence blood pressure (BP). Our earlier studies identified and validated 56 single nucleotide variants (SNVs) associated with BP from meta-analyses of exome chip genotype data. An additional 100 variants yielded suggestive evidence of association. Methods and Results - Here, we augment the sample with 140 886 European individuals from the UK Biobank, in whom 77 of the 100 suggestive SNVs were available for association analysis with systolic BP or diastolic BP or pulse pressure. We performed 2 meta-analyses, one in individuals of European, South Asian, African, and Hispanic descent (pan-ancestry, ≈475 000), and the other in the subset of individuals of European descent (≈423 000). Twenty-one SNVs were genome-wide significant (P<5×10-8) for BP, of which 4 are new BP loci: rs9678851 (missense, SLC4A1AP), rs7437940 (AFAP1), rs13303 (missense, STAB1), and rs1055144 (7p15.2). In addition, we identified a potentially independent novel BP-associated SNV, rs3416322 (missense, SYNPO2L) at a known locus, uncorrelated with the previously reported SNVs. Two SNVs are associated with expression levels of nearby genes, and SNVs at 3 loci are associated with other traits. One SNV with a minor allele frequency <0.01, (rs3025380 at DBH) was genome-wide significant. Conclusions - We report 4 novel loci associated with BP regulation, and 1 independent variant at an established BP locus. This analysis highlights several candidate genes with variation that alter protein function or gene expression for potential follow-up

On the design of broadband quasioptical systems for submillimeter-wave radio-astronomy receivers

In this paper, we summarize the issues that should be considered when designing broadband quasioptical systems for submillimetre-wave radioastronomy receivers. We cover topics such as bandwidth, cross-talk, truncation, and aberrations, and we argue that it should be possible to manufacture high-efficiency systems that have several octaves of bandwidth. A key feature of the paper is that we use the language of multimode Gaussian optics throughout, and in this way, we emphasize that a receiver is a diffraction-limited imaging system rather than just a collection of components for guiding Gaussian beams. The whole discussion is conducted in terms of a particular system we are constructing for the James Clerk Maxwell Telescope in Hawaii