Integrating factors for second order ODEs

A systematic algorithm for building integrating factors of the form mu(x,y), mu(x,y') or mu(y,y') for second order ODEs is presented. The algorithm can determine the existence and explicit form of the integrating factors themselves without solving any differential equations, except for a linear ODE in one subcase of the mu(x,y) problem. Examples of ODEs not having point symmetries are shown to be solvable using this algorithm. The scheme was implemented in Maple, in the framework of the "ODEtools" package and its ODE-solver. A comparison between this implementation and other computer algebra ODE-solvers in tackling non-linear examples from Kamke's book is shown.Comment: 21 pages - original version submitted Nov/1997. Related Maple programs for finding integrating factors together with the ODEtools package (versions for MapleV R4 and MapleV R5) are available at http://lie.uwaterloo.ca/odetools.ht

Multimorbidity in a large district hospital: A descriptive cross-sectional study

Background. There is substantial research documenting the burden of disease globally and in the South African (SA) primary care context. Few studies address the disease profile and its implications in the SA hospital setting.Objectives. To describe the disease profile in the internal medicine department of a large district hospital, using variables related to comorbidity and patient length of stay. The study included specific exploration into the HIV/tuberculosis (TB) syndemic, the acuity of HIV disease, and lifestyle risk factors.Methods. The sample population consisted of all consecutive admissions to the internal medicine department of a large district hospital in the Cape metropole during May 2015. A retrospective folder review and subsequent data analysis were completed.Results. Hypertension, HIV, type 2 diabetes mellitus, TB and cardiac failure were the five most prevalent diseases. Extensive multimorbidity was observed, with 86.0% of patients suffering from two or more diseases concurrently. The average number of comorbidities per patient was 3.4, although no clear relationship between the number of comorbidities and length of stay was found. Of the various diseases, only TB and HIV were associated with above-average length of stay, particularly among co-infected patients and those who had defaulted from or never received antiretroviral (ARV) treatment. Compared with patients currently receiving ARVs, much higher proportions of patients who had defaulted from or never received ARV treatment had CD4+ counts <200 cells/μL. Of the lifestyle risk factors investigated, a history of excessive alcohol use and/or drug use was associated with an increased length of stay. Most patients were discharged home, with 15.7% being referred to other institutions.Conclusions. Chronic conditions, particularly HIV, TB and non-communicable diseases, represented much of the disease profile in the internal medicine department. Of the comorbidities investigated, the greatest contributor to length of stay was HIV/TB co-infection. Factors such as HIV, TB and substance use that increase length of stay cannot be impacted upon by the district hospital staff in isolation. To improve the health of communities, we require partnerships between doctors, community health providers and patients with their families. Multimorbidity was widespread, suggesting the need to include an understanding of multimorbidity, including the patient perspective, in medical education and health system reform

Very low shot noise in carbon nanotubes

We have performed noise measurements on suspended ropes of single wall carbon nanotubes (SWNT) between 1 and 300 K for different values of dc current through the ropes. We find that the shot noise is suppressed by more than a factor 100 compared to the full shot noise 2eI. We have also measured an individual SWNT and found a level of noise which is smaller than the minimum expected. Another finding is the very low level of 1/f noise, which is significantly lower than previous observations. We propose two possible interpretations for this strong shot noise reduction: i) Transport within a rope takes place through a few nearly ballistic tubes within a rope and possibly involves non integer effective charges. ii) A substantial fraction of the tubes conduct with a strong reduction of effective charge (by more than a factor 50).Comment: Submitted to Eur. Phys. J. B (Jan. 2002) Higher resolution pictures are posted on http://www.lps.u-psud.fr/Collectif/gr_07/publications.htm

Mesoscale Equipartition of kinetic energy in Quantum Turbulence

The turbulence of superfluid helium is investigated numerically at finite temperature. Direct numerical simulations are performed with a "truncated HVBK" model, which combines the continuous description of the Hall-Vinen-Bekeravich-Khalatnikov equations with the additional constraint that this continuous description cannot extend beyond a quantum length scale associated with the mean spacing between individual superfluid vortices. A good agreement is found with experimental measurements of the vortex density. Besides, by varying the turbulence intensity only, it is observed that the inter-vortex spacing varies with the Reynolds number as $Re^{-3/4}$, like the viscous length scale in classical turbulence. In the high temperature limit, Kolmogorov's inertial cascade is recovered, as expected from previous numerical and experimental studies. As the temperature decreases, the inertial cascade remains present at large scales while, at small scales, the system evolves towards a statistical equipartition of kinetic energy among spectral modes, with a characteristic $k^2$ velocity spectrum. The accumulation of superfluid excitations on a range of mesoscales enables the superfluid to keep dissipating kinetic energy through mutual friction with the residual normal fluid, although the later becomes rare at low temperature. It is found that most of the superfluid vorticity can concentrate on these mesoscales at low temperature, while it is concentrated in the inertial range at higher temperature. This observation should have consequences on the interpretation of decaying turbulence experiments, which are often based on vortex line density measurements.Comment: 6 pages, 5 figure

New Cepheid variables in the young open clusters Berkeley 51 and Berkeley 55

As part of a wider investigation of evolved massive stars in Galactic open clusters, we have spectroscopically identified three candidate classical Cepheids in the little-studied clusters Berkeley 51, Berkeley 55 and NGC 6603. Using new multi-epoch photometry, we confirm that Be 51 #162 and Be 55 #107 are bona fide Cepheids, with pulsation periods of 9.83±0.01 d and 5.850±0.005 d respectively, while NGC 6603 star W2249 does not show significant photometric variability. Using the period-luminosity relationship for Cepheid variables, we determine a distance to Be 51 of 5.3 +1.0 −0.8 kpc and an age of 44 +9 −8 Myr, placing it in a sparsely-attested region of the Perseus arm. For Be 55, we find a distance of 2.2±0.3 kpc and age of 63 +12 −11 Myr, locating the cluster in the Local arm. Taken together with our recent discovery of a long-period Cepheid in the starburst cluster VdBH222, these represent an important increase in the number of young, massive Cepheids known in Galactic open clusters. We also consider new Gaia (data release 2) parallaxes and proper motions for members of Be 51 and Be 55; the uncertainties on the parallaxes do not allow us to refine our distance estimates to these clusters, but the well-constrained proper motion measurements furnish further confirmation of cluster membership. However, future final Gaia parallaxes for such objects should provide valuable independent distance measurements, improving the calibration of the period-luminosity relationship, with implications for the distance ladder out to cosmological scales

Galaxy Clustering Evolution in the UH8K Weak Lensing Fields

We present measurements of the two-point galaxy angular correlation function as a function of apparent magnitude, color, and morphology. We present new galaxy number counts to limiting magnitudes of I=24.0 and V=25.0. We find $\omega(\theta)$ to be well described by a power-law of slope -0.8. We find the amplitude of the correlation function to decrease monotonically with increasingly faint apparent magnitude. We compare with predictions utilizing redshift distributions based on deep spectroscopic observations. We conclude that simple redshift-dependent models which characterize evolution by means of the epsilon parameter inadequately describe the observations. We find a strong clustering dependence on V-I color because galaxies of extreme color lie at similar redshifts and the angular correlation functions for these samples are minimally diluted by chance projections. We then present the first attempt to investigate the redshift evolution of clustering, utilizing a population of galaxies of the same morphological type and absolute luminosity. We study the dependence of $\omega(\theta)$ on redshift for Lstar early-type galaxies in the redshift range 0.2<z<0.9. Although uncertainties are large, we find the evolution in the clustering of these galaxies to be consistent with stable clustering [epsilon=0]. We find Lstar early-type galaxies to cluster slightly more strongly (rnought = 5.25\pm0.28 \hMpc assuming epsilon=0) than the local full field population. This is in good agreement with the 2dFGRS value for Lstar early-type galaxies in the local universe (abridged).Comment: 41 pages, including 12 figs, 10 tables, to appear in Ap

Electronic transport properties of quasicrystals: a Review

We present a review of some results concerning electronic transport properties of quasicrystals. After a short introduction to the basic concepts of quasiperiodicity, we consider the experimental transport properties of electrical conductivity with particular focus on the effect of temperature, magnetic field and defects. Then, we present some heuristic approaches that tend to give a coherent view of different, and to some extent complementary, transport mechanisms in quasicrystals. Numerical results are also presented and in particular the evaluation of the linear response Kubo-Greenwood formula of conductivity in quasiperiodic systems in presence of disorder.Comment: Latex, 28 pages, Journ. of Math. Phys., Vol38 April 199

Plebanski Theory and Covariant Canonical Formulation

We establish an equivalence between the Hamiltonian formulation of the Plebanski action for general relativity and the covariant canonical formulation of the Hilbert-Palatini action. This is done by comparing the symplectic structures of the two theories through the computation of Dirac brackets. We also construct a shifted connection with simplified Dirac brackets, playing an important role in the covariant loop quantization program, in the Plebanski framework. Implications for spin foam models are also discussed.Comment: 18 page