The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions

The analytic solutions of the one-dimensional Schroedinger equation for the trigonometric Rosen-Morse potential reported in the literature rely upon the Jacobi polynomials with complex indices and complex arguments. We first draw attention to the fact that the complex Jacobi polynomials have non-trivial orthogonality properties which make them uncomfortable for physics applications. Instead we here solve above equation in terms of real orthogonal polynomials. The new solutions are used in the construction of the quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl

Total positivity: tests and parametrizations

An introduction to total positivity (TP), with the emphasis on efficient TP criteria and parametrizations of TP matrices. Intended for general mathematical audience.Comment: 20 pages, with color figure

The practices of apartheid as a war crime: a critical analysis

The human suffering caused by the political ideology of apartheid in South Africa during the Apartheid era (1948-1994) prompted worldwide condemnation and a variety of diplomatic and legal responses. Amongst these responses was the attempt to have apartheid recognised both as a crime against humanity in the 1973 Apartheid Convention as well as a war crime in Article 85(4)(c) of Additional Protocol I. This article examines the origins, nature and current status of the practices of apartheid as a war crime and its possible application to the Israeli-Palestinian conflict

Hypoglycemia and Diabetes: A Report of a Workgroup of the American Diabetes Association and The Endocrine Society

OBJECTIVE To review the evidence about the impact of hypoglycemia on patients with diabetes that has become available since the past reviews of this subject by the American Diabetes Association and The Endocrine Society and to provide guidance about how this new information should be incorporated into clinical practice. PARTICIPANTS Five members of the American Diabetes Association and five members of The Endocrine Society with expertise in different aspects of hypoglycemia were invited by the Chair, who is a member of both, to participate in a planning conference call and a 2-day meeting that was also attended by staff from both organizations. Subsequent communications took place via e-mail and phone calls. The writing group consisted of those invitees who participated in the writing of the manuscript. The workgroup meeting was supported by educational grants to the American Diabetes Association from Lilly USA, LLC and Novo Nordisk and sponsorship to the American Diabetes Association from Sanofi. The sponsors had no input into the development of or content of the report. EVIDENCE The writing group considered data from recent clinical trials and other studies to update the prior workgroup report. Unpublished data were not used. Expert opinion was used to develop some conclusions. CONSENSUS PROCESS Consensus was achieved by group discussion during conference calls and face-to-face meetings, as well as by iterative revisions of the written document. The document was reviewed and approved by the American Diabetes Association’s Professional Practice Committee in October 2012 and approved by the Executive Committee of the Board of Directors in November 2012 and was reviewed and approved by The Endocrine Society’s Clinical Affairs Core Committee in October 2012 and by Council in November 2012. CONCLUSIONS The workgroup reconfirmed the previous definitions of hypoglycemia in diabetes, reviewed the implications of hypoglycemia on both short- and long-term outcomes, considered the implications of hypoglycemia on treatment outcomes, presented strategies to prevent hypoglycemia, and identified knowledge gaps that should be addressed by future research. In addition, tools for patients to report hypoglycemia at each visit and for clinicians to document counseling are provided

Exploiting unexpected situations in the mathematics classroom

The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement

Comparative Analyses of Two Methods of Backstroke Starting: Conventional and Whip

Generally, when a new skill, technique, or style is introduced into a sport, the first attempt to describe the change is by the coach or athlete. The biomechanist will then make a careful review of the mechanics involved, test the principles against the given theory, propose directions for future improvements, or reject the change. This procedure often occurs in the sport of swimming. During the last decade, techniques of competitive swimming have improved, resulting in several record-producing performances by the swimmers. This improvement may be attributed, in part, to coaches, researchers, and authors like Counsilman (1977) and Maglischo (1982), Hay (1985), Kreighbaum and Barthels (1985), among others. Backstroke swimming techniques have benefited from the investiveness of coaches, swimmers, and researchers. Probably much of the credit for initiating change in technique belongs to the backstrokers of the time. Two examples are Olympic champions John Naber in 1976 with his «headabove-water spin» turn and Rick Carey in 1984 with his «whip» start. These methods of turning and starting have been adopted by many coaches and swimmers. Even though the Naber turn and the Carey whip start have gained in popularity, little research has been conducted regarding the mechanics of such techniques. For instance, one of the few studies conducted was on the backstroke turns. Benson (1979) filmed two subjects: John Naber executing his unique turn and Peter Rocca (second to Naber in the 1976 Olympics) doing his standard backstroke turn. An elementary comparative eine analysis was made. Benson determined that the Naber turn was more efficient than the standard backstroke turn. Since scientific information about the backstroke whip start is limited. this study was conducted to fill that void and to serve as a basic for further research

Comparison of OH reactivity measurements in the atmospheric simulation chamber SAPHIR

Hydroxyl (OH) radical reactivity (kOH) has been measured for 18 years with different measurement techniques. In order to compare the performances of instruments deployed in the field, two campaigns were conducted performing experiments in the atmospheric simulation chamber SAPHIR at Forschungszentrum Jülich in October 2015 and April 2016. Chemical conditions were chosen either to be representative of the atmosphere or to test potential limitations of instruments. All types of instruments that are currently used for atmospheric measurements were used in one of the two campaigns. The results of these campaigns demonstrate that OH reactivity can be accurately measured for a wide range of atmospherically relevant chemical conditions (e.g. water vapour, nitrogen oxides, various organic compounds) by all instruments. The precision of the measurements (limit of detection  < 1 s−1 at a time resolution of 30 s to a few minutes) is higher for instruments directly detecting hydroxyl radicals, whereas the indirect comparative reactivity method (CRM) has a higher limit of detection of 2 s−1 at a time resolution of 10 to 15 min. The performances of the instruments were systematically tested by stepwise increasing, for example, the concentrations of carbon monoxide (CO), water vapour or nitric oxide (NO). In further experiments, mixtures of organic reactants were injected into the chamber to simulate urban and forested environments. Overall, the results show that the instruments are capable of measuring OH reactivity in the presence of CO, alkanes, alkenes and aromatic compounds. The transmission efficiency in Teflon inlet lines could have introduced systematic errors in measurements for low-volatile organic compounds in some instruments. CRM instruments exhibited a larger scatter in the data compared to the other instruments. The largest differences to reference measurements or to calculated reactivity were observed by CRM instruments in the presence of terpenes and oxygenated organic compounds (mixing ratio of OH reactants were up to 10 ppbv). In some of these experiments, only a small fraction of the reactivity is detected. The accuracy of CRM measurements is most likely limited by the corrections that need to be applied to account for known effects of, for example, deviations from pseudo first-order conditions, nitrogen oxides or water vapour on the measurement. Methods used to derive these corrections vary among the different CRM instruments. Measurements taken with a flow-tube instrument combined with the direct detection of OH by chemical ionisation mass spectrometry (CIMS) show limitations in cases of high reactivity and high NO concentrations but were accurate for low reactivity (< 15 s−1) and low NO (< 5 ppbv) conditions

Fenamate NSAIDs inhibit the NLRP3 inflammasome and protect against Alzheimer's disease in rodent models.

Non-steroidal anti-inflammatory drugs (NSAIDs) inhibit cyclooxygenase-1 (COX-1) and COX-2 enzymes. The NLRP3 inflammasome is a multi-protein complex responsible for the processing of the proinflammatory cytokine interleukin-1β and is implicated in many inflammatory diseases. Here we show that several clinically approved and widely used NSAIDs of the fenamate class are effective and selective inhibitors of the NLRP3 inflammasome via inhibition of the volume-regulated anion channel in macrophages, independently of COX enzymes. Flufenamic acid and mefenamic acid are efficacious in NLRP3-dependent rodent models of inflammation in air pouch and peritoneum. We also show therapeutic effects of fenamates using a model of amyloid beta induced memory loss and a transgenic mouse model of Alzheimer's disease. These data suggest that fenamate NSAIDs could be repurposed as NLRP3 inflammasome inhibitors and Alzheimer's disease therapeutics

Analysis of the capacity of google trends to measure interest in conservation topics and the role of online news

With the continuous growth of internet usage, Google Trends has emerged as a source of information to investigate how social trends evolve over time. Knowing how the level of interest in conservation topics--approximated using Google search volume--varies over time can help support targeted conservation science communication. However, the evolution of search volume over time and the mechanisms that drive peaks in searches are poorly understood. We conducted time series analyses on Google search data from 2004 to 2013 to investigate: (i) whether interests in selected conservation topics have declined and (ii) the effect of news reporting and academic publishing on search volume. Although trends were sensitive to the term used as benchmark, we did not find that public interest towards conservation topics such as climate change, ecosystem services, deforestation, orangutan, invasive species and habitat loss was declining. We found, however, a robust downward trend for endangered species and an upward trend for ecosystem services. The quantity of news articles was related to patterns in Google search volume, whereas the number of research articles was not a good predictor but lagged behind Google search volume, indicating the role of news in the transfer of conservation science to the public