Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

Air Quality Considerations for Stormwater Green Street Design

Green streets are increasingly being used as a stormwater management strategy to mitigate stormwater runoff at its source while providing other environmental and societal benefits, including connecting pedestrians to the street. Simultaneously, human exposure to particulate matter from urban transportation is of major concern worldwide due to the proximity of pedestrians, drivers, and cyclists to the emission sources. Vegetation used for stormwater treatment can help designers limit the exposure of people to air pollutants. This goal can be achieved through the deliberate placement of green streets, along with strategic planting schemes that maximize pollutant dispersion. This communication presents general design considerations for green streets that combine stormwater management and air quality goals. There is currently limited guidance on designing green streets for air quality considerations; this is the first communication to offer suggestions and advice for the design of green stormwater streets in regards to their effects on air quality. Street characteristics including (1) the width to height ratio of the street to the buildings, (2) the type of trees and their location, and (3) any prevailing winds can have an impact on pollutant concentrations within the street and along sidewalks. Vegetation within stormwater control measures has the ability to reduce particulate matter concentrations; however, it must be carefully selected and placed within the green street to promote the dispersion of air flow

Software to compute infinitesimal symmetries of exterior differenial systems, with applications

A description is given of a software package to compute symmetries of partial differential equations, using computer algebra. As an application, the computation of higher-order symmetries of the classical Boussinesq equation is given leading to the recursion operator for symmetries in a straightforward way. Nonlocal symmetries for the Federbush model are obtained yielding the linearization of the model

Alpha-particle-induced complex chromosome exchanges transmitted through extra-thymic lymphopoiesis in vitro show evidence of emerging genomic instability

Human exposure to high-linear energy transfer α-particles includes environmental (e.g. radon gas and its decay progeny), medical (e.g. radiopharmaceuticals) and occupational (nuclear industry) sources. The associated health risks of α-particle exposure for lung cancer are well documented however the risk estimates for leukaemia remain uncertain. To further our understanding of α-particle effects in target cells for leukaemogenesis and also to seek general markers of individual exposure to α-particles, this study assessed the transmission of chromosomal damage initially-induced in human haemopoietic stem and progenitor cells after exposure to high-LET α-particles. Cells surviving exposure were differentiated into mature T-cells by extra-thymic T-cell differentiation in vitro. Multiplex fluorescence in situ hybridisation (M-FISH) analysis of naïve T-cell populations showed the occurrence of stable (clonal) complex chromosome aberrations consistent with those that are characteristically induced in spherical cells by the traversal of a single α-particle track. Additionally, complex chromosome exchanges were observed in the progeny of irradiated mature T-cell populations. In addition to this, newly arising de novo chromosome aberrations were detected in cells which possessed clonal markers of α-particle exposure and also in cells which did not show any evidence of previous exposure, suggesting ongoing genomic instability in these populations. Our findings support the usefulness and reliability of employing complex chromosome exchanges as indicators of past or ongoing exposure to high-LET radiation and demonstrate the potential applicability to evaluate health risks associated with α-particle exposure.This work was supported by the Department of Health, UK. Contract RRX95 (RMA NSDTG)

Matched-pair analysis of patients with female and male breast cancer: a comparative analysis

<p>Abstract</p> <p>Background</p> <p>Male breast cancer (MBC) is a rare disease accounting for approximately 1% of all breast carcinomas. Presently treatment recommendations are derived from the standards for female breast cancer. However, those approaches might be inadequate because of distinct gender specific differences in tumor biology of breast cancer. This study was planned in order to contrast potential differences between female and male breast cancer in both tumor biological behavior and clinical management.</p> <p>Methods</p> <p>MBC diagnosed between 1995-2007 (region Chemnitz/Zwickau, Saxony, Germany) was retrospectively analyzed. Tumor characteristics, treatment and follow-up of the patients were documented. In order to highlight potential differences each MBC was matched with a female counterpart (FBC) that showed accordance in at least eight tumor characteristics (year of diagnosis, age, tumor stage, nodal status, grade, estrogen- and progesterone receptors, HER2 status).</p> <p>Results</p> <p>108 male/female matched-pairs were available for survival analyses. In our study men and women with breast cancer had similar disease-free (DFS) and overall (OS) survival. The 5-years DFS was 53.4% (95% CI, range 54.1-66.3) in men respectively 62.6% (95% CI, 63.5-75.3) in women (p > 0.05). The 5-years OS was 71.4% (95% CI, 62.1-72.7%) and 70.3% (95% CI, 32.6-49.6) in women (p > 0.05). In males DFS analyses revealed progesterone receptor expression as the only prognostic relevant factor (p = 0.006). In multivariate analyses for OS both advanced tumor size (p = 0.01) and a lack of progesterone receptor expression were correlated (p = 0.01) with poor patients outcome in MBC.</p> <p>Conclusion</p> <p>Our comparative study revealed no survival differences between male and female breast cancer patients and gives evidence that gender is no predictor for survival in breast cancer. This was shown despite of significant gender specific differences in terms of frequency and intensity of systemic therapy in favor to female breast cancer.</p

Age determines the prognostic role of the cancer stem cell marker aldehyde dehydrogenase-1 in breast cancer

<p>Abstract</p> <p>Background</p> <p>The purpose of this study was to compare the expression and the prognostic effect of the breast cancer stem cell marker aldehyde dehydrogenase-1 (ALDH1) in young and elderly breast cancer patients.</p> <p>Methods</p> <p>The study population (N = 574) consisted of all early breast cancer patients primarily treated with surgery in our center between 1985 and 1994. Median follow-up was 17.9 years (range: 0.1 to 23.5). Tissue microarray slides were immunohistochemically stained for ALDH1 expression and quantified by two independent observers who were blinded to clinical outcome. Assessment of the prognostic effect of ALDH1 expression was stratified according to age and systemic treatment.</p> <p>Results</p> <p>Complete lack of expression of ALDH1 was found in 40% of tumors. With increasing age more tumors showed complete absence of ALDH1 expression (<it>P </it>< .001). In patients aged > 65 years, ALDH1 status was not associated with any clinical outcome. Conversely, in patients aged < 65 years, ALDH1 positivity was an independent risk factor of worse outcome for relapse free period (hazard ratio = 1.71 (95% CI, 1.09 to 2.68); <it>P </it>= .021) and relative survival (relative excess risks of death = 2.36 (95% CI, 1.22 to 3.68); <it>P </it>= .016). Ten-year relative survival risk was 57% in ALDH1-positive patients compared to 83% in ALDH1-negative patients.</p> <p>Conclusion</p> <p>ALDH1 expression and its prognostic effect are age-dependent. Our results support the hypothesis that breast cancer biology is different in elderly patients compared to their younger counterparts and emphasizes the importance of taking into consideration age-specific interactions in breast cancer research.</p

Exploring differential item functioning in the SF-36 by demographic, clinical, psychological and social factors in an osteoarthritis population

The SF-36 is a very commonly used generic measure of health outcome in osteoarthritis (OA). An important, but frequently overlooked, aspect of validating health outcome measures is to establish if items work in the same way across subgroup of a population. That is, if respondents have the same 'true' level of outcome, does the item give the same score in different subgroups or is it biased towards one subgroup or another. Differential item functioning (DIF) can identify items that may be biased for one group or another and has been applied to measuring patient reported outcomes. Items may show DIF for different conditions and between cultures, however the SF-36 has not been specifically examined in an osteoarthritis population nor in a UK population. Hence, the aim of the study was to apply the DIF method to the SF-36 for a UK OA population. The sample comprised a community sample of 763 people with OA who participated in the Somerset and Avon Survey of Health. The SF-36 was explored for DIF with respect to demographic, social, clinical and psychological factors. Well developed ordinal regression models were used to identify DIF items. Results: DIF items were found by age (6 items), employment status (6 items), social class (2 items), mood (2 items), hip v knee (2 items), social deprivation (1 item) and body mass index (1 item). Although the impact of the DIF items rarely had a significant effect on the conclusions of group comparisons, in most cases there was a significant change in effect size. Overall, the SF-36 performed well with only a small number of DIF items identified, a reassuring finding in view of the frequent use of the SF-36 in OA. Nevertheless, where DIF items were identified it would be advisable to analyse data taking account of DIF items, especially when age effects are the focus of interest