A note on log-convexity of q-Catalan numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q=1, to the Catalan numbers: 1, 1, 2, 5, 14,..., a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted

Unsung heroes: Constituency election agents in British general elections

Despite their central role in the electoral process, constituency agents have been largely overlooked by political scientists and this article seeks to rectify the omission. It sketches the origins and development of the role of agent from the late 19th century and suggests that a serious rethink of the role took place in the 1990s. Survey-based evidence about the social characteristics of agents is presented confirming that they are largely middle-aged, middle-class, well-educated men. They are also becoming more experienced, offer realistic assessments of the impact of constituency campaigning and, arguably, many take a long-term view of how their party's support can be maximised

Down-regulation of Fas gene expression in colon cancer is not a result of allelic loss or gene rearrangement.

Expression of Fas, an apoptosis-inducing receptor, in colonic epithelium is progressively reduced during malignant transformation. We have examined the human Fas gene for loss of heterozygosity (LOH) and gross rearrangements in colon tumours and matched normal mucosa. Polymerase chain reaction (PCR) primers were designed to span a DraI restriction fragment length polymorphic site in the gene. Heterozygosity was detected in normal DNA samples by PCR amplification of the polymorphic site and restriction enzyme digestion. Thirty-eight of 88 patients (43%) with colon carcinomas were informative for the assay, and LOH was detected in 6 of the 38 (16%) corresponding tumours. Tumours from three patients with LOH did not express detectable Fas mRNA, and Fas expression was reduced or absent in 7 of 11 tumours from informative patients without LOH. Southern blotting of tumour DNA samples was used to detect rearrangement of the Fas gene, but no altered hybridization patterns were observed in 64 tumours analysed. These findings indicate that disruption of the Fas gene is not primarily responsible for the loss of Fas protein expression reported in colon cancer. We have also shown that loss of Fas gene transcription is common in these tumours, which may be due to epigenetic gene silencing

UCET Discussion paper on effective Continuing Professional Development

This report is based on the wealth of experience and scholarship shared by UCET colleagues. It reflects on key aspects of CPD-related policy, practice and research over the past 50 years and highlights the following principles: - Education professionals require an expanding range of competences over their career; these are often context-specific, unforeseen and go beyond any single framework - As well as being research-informed, CPD should engage educators in theory so they can adapt their learning creatively to enrich their own setting - Reflective practitioners are best cultivated by supporting teachers’ in conducting their own research - Effective CPD is built on trusted relationships between deliverers and learners and include a strong element of coaching and/or mentoring often by peers - For sustained impact, CPD needs to be sustained over time (at least across two terms), making use of multiple formats - By engaging teachers in their wider social, economic and environmental contexts, CPD will ensure responsible professionals in the fullest sense - Developing teachers’ agency will enable them to consider their practice critically, lead their own learning and thus maximise the positive impact they have on their learners - All CPD should be subject to robust quality assurance mechanisms

Hairy Tongue

Hairy tongue (lingua villosa) is a commonly observed condition of defective desquamation of the filiform papillae that results from a variety of precipitating factors. [1] The condition is most frequently referred to as black hairy tongue (lingua villosa nigra); however, hairy tongue may also appear brown, white, green, pink, or any of a variety of hues depending on the specific etiology and secondary factors (eg, use of colored mouthwashes, breath mints, candies). [2, 3] See the images below

An Overview of the Groundwater Use and Capacity Use Program

2010 S.C. Water Resources Conference - Science and Policy Challenges for a Sustainable Futur

Testing the Integrity of Liquid Containing Hermetically Sealed Containers by the Use of Radioactive Markers

A method for detecting leaky ampules filled with a liquid such as a parenteral solution. The ampules to be tested are immersed in a solution containing a short-lived radionuclide, and a pressure differential is imposed between the solution containing the radionuclide and the parenteral solution or other liquid contained in the ampules. The ampules are then removed from solution, decontaminated to remove any solution adhering to the outer surface and pores thereof, dried, and finally examined for electromagnetic radiation, preferably gamma radiation, emanating from the interior of the ampules which would indicate a leaky condition thereof

Measuring surface-area-to-volume ratios in soft porous materials using laser-polarized xenon interphase exchange NMR

We demonstrate a minimally invasive nuclear magnetic resonance (NMR) technique that enables determination of the surface-area-to-volume ratio (S/V) of soft porous materials from measurements of the diffusive exchange of laser-polarized 129Xe between gas in the pore space and 129Xe dissolved in the solid phase. We apply this NMR technique to porous polymer samples and find approximate agreement with destructive stereological measurements of S/V obtained with optical confocal microscopy. Potential applications of laser-polarized xenon interphase exchange NMR include measurements of in vivo lung function in humans and characterization of gas chromatography columns.Comment: 14 pages of text, 4 figure