Numerical approach to the Schrodinger equation in momentum space

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schrodinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound-states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio

On the exact electric and magnetic fields of an electric dipole

We derive from Jefimenko's equations a multipole expansion in order to obtain the exact expressions for the electric and magnetic fields of an electric dipole with an arbitrary time dependence. A few comments are also made about the usual expositions found in most common undergraduate and graduate textbooks as well as in the literature on this topic

Cholesterolomics: An update

Cholesterolomics can be regarded as the identification and quantification of cholesterol, its precursors post squalene, and metabolites of cholesterol and of its precursors, in a biological sample. These molecules include 1,25-dihydroxyvitamin D3, steroid hormones and bile acids and intermediates in their respective biosynthetic pathways. In this short article we will concentrate our attention on intermediates in bile acid biosynthesis pathways, in particular oxysterols and cholestenoic acids. These molecular classes are implicated in the aetiology of a diverse array of diseases including autoimmune disease, Parkinson's disease, motor neuron disease, breast cancer, the lysosomal storage disease Niemann-Pick type C and the autosomal recessive disorder Smith-Lemli-Opitz syndrome. Mass spectrometry (MS) is the dominant technology for sterol analysis including both gas-chromatography (GC)-MS and liquid chromatography (LC)-MS and more recently matrix-assisted laser desorption/ionisation (MALDI)-MS for tissue imaging studies. Here we will discuss exciting biological findings and recent analytical improvements

Randomised trial of glutamine and selenium supplemented parenteral nutrition for critically ill patients

Background: Mortality rates in the Intensive Care Unit and subsequent hospital mortality rates in the UK remain high. Infections in Intensive Care are associated with a 2–3 times increased risk of death. It is thought that under conditions of severe metabolic stress glutamine becomes "conditionally essential". Selenium is an essential trace element that has antioxidant and anti-inflammatory properties. Approximately 23% of patients in Intensive Care require parenteral nutrition and glutamine and selenium are either absent or present in low amounts. Both glutamine and selenium have the potential to influence the immune system through independent biochemical pathways. Systematic reviews suggest that supplementing parenteral nutrition in critical illness with glutamine or selenium may reduce infections and mortality. Pilot data has shown that more than 50% of participants developed infections, typically resistant organisms. We are powered to show definitively whether supplementation of PN with either glutamine or selenium is effective at reducing new infections in critically ill patients. Methods/design: 2 × 2 factorial, pragmatic, multicentre, double-blind, randomised controlled trial. The trial has an enrolment target of 500 patients. Inclusion criteria include: expected to be in critical care for at least 48 hours, aged 16 years or over, patients who require parenteral nutrition and are expected to have at least half their daily nutritional requirements given by that route. Allocation is to one of four iso-caloric, iso-nitrogenous groups: glutamine, selenium, both glutamine & selenium or no additional glutamine or selenium. Trial supplementation is given for up to seven days on the Intensive Care Unit and subsequent wards if practicable. The primary outcomes are episodes of infection in the 14 days after starting trial nutrition and mortality. Secondary outcomes include antibiotic usage, length of hospital stay, quality of life and cost-effectiveness. Discussion: To date more than 285 patients have been recruited to the trial from 10 sites in Scotland. Recruitment is due to finish in August 2008 with a further six months follow up. We expect to report the results of the trial in summer 2009. Trial registration: This trial is registered with the International Standard Randomised Controlled Trial Number system. ISRCTN87144826Not peer reviewedPublisher PD

Sterols and oxysterols in plasma from Smith-Lemli-Opitz syndrome patients

Smith-Lemli-Opitz syndrome (SLOS) is a severe autosomal recessive disorder resulting from defects in the cholesterol synthesising enzyme 7-dehydrocholesterol reductase (Δ7-sterol reductase, DHCR7, EC 1.3.1.21) leading to a build-up of the cholesterol precursor 7-dehydrocholesterol (7-DHC) in tissues and blood plasma. Although the underling enzyme deficiency associated with SLOS is clear there are likely to be multiple mechanisms responsible for SLOS pathology. In an effort to learn more of the aetiology of SLOS we have analysed plasma from SLOS patients to search for metabolites derived from 7-DHC which may be responsible for some of the pathology. We have identified a novel hydroxy-8-dehydrocholesterol, which is either 24- or 25-hydroxy-8-dehydrocholesterol and also the known metabolites 26-hydroxy-8-dehydrocholesterol, 4-hydroxy-7-dehydrocholesterol, 3β,5α-dihydroxycholest-7-en-6-one and 7α,8α-epoxycholesterol. None of these metabolites are detected in control plasma at quantifiable levels (0.5 ng/mL)

Update on LIPID MAPS classification, nomenclature, and shorthand notation for MS-derived lipid structures

A comprehensive and standardized system to report lipid structures analyzed by mass spectrometry is essentialfor the communication and storage of lipidomics data. Herein, an update on both the LIPID MAPSclassification system and shorthand notation of lipid structures is presented for lipid categories Fatty Acyls(FA), Glycerolipids (GL), Glycerophospholipids (GP), Sphingolipids (SP), and Sterols (ST). With its majorchanges, i.e. annotation of ring double bond equivalents and number of oxygens, the updated shorthandnotation facilitates reporting of newly delineated oxygenated lipid species as well. For standardized reportingin lipidomics, the hierarchical architecture of shorthand notation reflects the diverse structural resolutionpowers provided by mass spectrometric assays. Moreover, shorthand notation is expanded beyond mammalianphyla to lipids from plant and yeast phyla. Finally, annotation of atoms is included for the use of stableisotope-labelled compounds in metabolic labelling experiments or as internal standards

Bile acid biosynthesis in Smith-Lemli-Opitz syndrome bypassing cholesterol: Potential importance of pathway intermediates

Bile acids are the end products of cholesterol metabolism secreted into bile. They are essential for the absorption of lipids and lipid soluble compounds from the intestine. Here we have identified a series of unusual Δ5-unsaturated bile acids in plasma and urine of patients with Smith-Lemli-Opitz syndrome (SLOS), a defect in cholesterol biosynthesis resulting in elevated levels of 7-dehydrocholesterol (7-DHC), an immediate precursor of cholesterol. Using liquid chromatography – mass spectrometry (LC-MS) we have uncovered a pathway of bile acid biosynthesis in SLOS avoiding cholesterol starting with 7-DHC and proceeding through 7-oxo and 7β-hydroxy intermediates. This pathway also occurs to a minor extent in healthy humans, but elevated levels of pathway intermediates could be responsible for some of the features SLOS. The pathway is also active in SLOS affected pregnancies as revealed by analysis of amniotic fluid. Importantly, intermediates in the pathway, 25-hydroxy-7-oxocholesterol, (25R)26-hydroxy-7-oxocholesterol, 3β-hydroxy-7-oxocholest-5-en-(25R)26-oic acid and the analogous 7β-hydroxysterols are modulators of the activity of Smoothened (Smo), an oncoprotein that mediates Hedgehog (Hh) signalling across membranes during embryogenesis and in the regeneration of postembryonic tissue. Computational docking of the 7-oxo and 7β-hydroxy compounds to the extracellular cysteine rich domain of Smo reveals that they bind in the same groove as both 20S-hydroxycholesterol and cholesterol, known activators of the Hh pathway

Help-Seeking Behavior during Elevated Temperature in Chinese Population

The negative impact of extreme temperatures on health is well-established. Individual help-seeking behavior, however, may mitigate the extent of morbidity and mortality during elevated temperatures. This study examines individual help-seeking behavior during periods of elevated temperatures among a Chinese population. Help-seeking patterns and factors that influence behavior will be identified so that vulnerable subgroups may be targeted for health protection during heat crises. A retrospective time-series Poisson generalized additive model analysis, using meteorological data of Hong Kong Observatory and routine emergency help call data from The Hong Kong Senior Citizen Home Safety Association during warm seasons (June–September) 1998–2007, was conducted. A “U”-shaped association was found between daily emergency calls and daily temperature. About 49% of calls were for explicit health-related reasons including dizziness, shortness of breath, and general pain. The associate with maximum temperature was statistically significant (p = 0.034) with the threshold temperature at which the frequency of health-related calls started to increase being around 30–32°C. Mean daily relative humidity (RH) also had a significant U-shaped association with daily emergency health-related calls with call frequency beginning to increase with RH greater than 70–74% (10–25% of the RH distribution). Call frequency among females appeared to be more sensitive to high temperatures, with a threshold between 28.5°C and 30.5°C while calls among males were more sensitive to cold temperatures (threshold 31.5–33.5°C). Results indicate differences in community help-seeking behavior at elevated temperatures. Potential programs or community outreach services might be developed to protect vulnerable subgroups from the adverse impact of elevated temperatures

The Early Royal Society and Visual Culture

Recent studies have fruitfully examined the intersection between early modern science and visual culture by elucidating the functions of images in shaping and disseminating scientific knowledge. Given its rich archival sources, it is possible to extend this line of research in the case of the Royal Society to an examination of attitudes towards images as artefacts –manufactured objects worth commissioning, collecting and studying. Drawing on existing scholarship and material from the Royal Society Archives, I discuss Fellows’ interests in prints, drawings, varnishes, colorants, images made out of unusual materials, and methods of identifying the painter from a painting. Knowledge of production processes of images was important to members of the Royal Society, not only as connoisseurs and collectors, but also as those interested in a Baconian mastery of material processes, including a “history of trades”. Their antiquarian interests led to discussion of painters’ styles, and they gradually developed a visual memorial to an institution through portraits and other visual records.AH/M001938/1 (AHRC