A posteriori error bounds for discontinuous Galerkin methods for quasilinear parabolic problems

We derive a posteriori error bounds for a quasilinear parabolic problem, which is approximated by the $hp$-version interior penalty discontinuous Galerkin method (IPDG). The error is measured in the energy norm. The theory is developed for the semidiscrete case for simplicity, allowing to focus on the challenges of a posteriori error control of IPDG space-discretizations of strictly monotone quasilinear parabolic problems. The a posteriori bounds are derived using the elliptic reconstruction framework, utilizing available a posteriori error bounds for the corresponding steady-state elliptic problem.Comment: 8 pages, conference ENUMATH 200

The seasonal incidence of helminth parasites and of Oestrus ovis in Karakul sheep in the Kalahari region of South West Africa/Namibia.

The seasonal incidence of gastro-intestinal helminths and of Oestrus ovis was determined by slaughter of successive groups of 4 tracer lambs, each exposed on pasture for 33 days. Haemonchus contortus was present from March 1979 to early July 1979, with a generally increasing percentage of 4th stage larvae in each successive month. A "spring rise" in the egg count was seen in flock sheep in October 1978. Oesophagostomum columbianum was recovered from tracers slaughtered in March 1979. Apart from December and March, Moniezia spp. were present from November 1978 to early July 1979. Oestrus ovis was active from September 1978 to early June 1979, with peak larval burdens recorded from October to December and from April to early June.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format

A Compact High Order Finite Volume Scheme for Advection-Diffusion-Reaction Equations

We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying Gauss-Legendre quadrature rules to the integral representation gives the high order finite volume complete flux scheme, which is fourth order accurate for both diffusion dominated and advection dominated flow

Design of a freeform two-reflector system to collimate and shape a point source distribution

In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target. An important generalization in our approach compared to previous research is that the output beam can be in an arbitrary direction. The design problem is approached by using a generalized Monge-Amp\`ere equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. This algorithm calculates the optical map, from which we can then compute the surfaces. We test our algorithm on two cases. First we consider a uniform source and target distribution. Next, we use the model of a laser diode light source and a ring-shaped target distribution

Parasites of South African wildlife. II. Helminths of kudu, Tragelaphus strepsiceros, from South West Africa/Namibia

A total of 23 kudu, Tragelaphus strepsiceros, were shot at 2-month intervals from June 1983 to April 1984 in the Etosha Game Reserve in the north of South West Africa/Namibia. The parasite survey conducted on these animals yielded 2 cestode and 12 nematode species. Haemonchus vegliai and Cooperia neitzi were the most prevalent nematodes and occurred in 13 animals each, followed by Cooperia acutispiculum and an Onchocerca sp. (9 animals each). The remaining nematodes were present in 4 (17 %) or fewer of the antelope. C. neitzi was the most numerous nematode, a total of 3 564 being recovered from all the antelope, followed by C. acutispiculum (2 552) and H. vegliai (1 050). Individual total worm burdens varied from 4-1 326 with 2 kudu harbouring no worms. The mean burden of 399 worms was considered negligible. A single kudu was shot in the Namib-Naukluft Park in the south of the country. This animal harboured no parasites.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.lmchunu2014mn201

Design of two-dimensional reflective imaging systems: An approach based on inverse methods

Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively design reflectors using inverse methods from non-imaging optics and optimize them to obtain a system that produces minimal aberrations. This is done by minimizing a merit function that quantifies aberrations and is dependent on the energy distributions at the source and target of an optical system, which are input parameters essential for inverse freeform design. The proposed method is tested for two configurations: a single-reflector system and a double-reflector system. Classical designs consisting of aspheric elements are well-known for their ability to minimize aberrations. We compare the performance of our freeform optical elements with classical designs. The optimized freeform designs outperform the classical designs in both configurations

An Iterative Least-Squares Method for the Hyperbolic Monge-Amp\`ere Equation with Transport Boundary Condition

A least-squares method for solving the hyperbolic Monge-Amp\`ere equation with transport boundary condition is introduced. The method relies on an iterative procedure for the gradient of the solution, the so-called mapping. By formulating error functionals for the interior domain, the boundary, both separately and as linear combination, three minimization problems are solved iteratively to compute the mapping. After convergence, a fourth minimization problem, to compute the solution of the Monge-Amp\`ere equation, is solved. The approach is based on a least-squares method for the elliptic Monge-Amp\`ere equation by Prins et al., and is improved upon by the addition of analytical solutions for the minimization on the interior domain and by the introduction of two new boundary methods. Lastly, the iterative method is tested on a variety of examples. It is shown that, when the iterative method converges, second-order global convergence as function of the spatial discretization is obtained.Comment: 30 pages, 24 figure

Arthropod parasites of springbok, gemsbok, kudus, giraffes and Burchell's and Hartmann's zebras in the Etosha and Hardap Nature Reserves, Namibia

A total of 48 springbok, 48 gemsbok, 23 kudus and 6 giraffes were examined for ticks and lice, while 9 Burchell's zebras and 6 Hartmann's mountain zebras were examined only for ticks. Springbok and gemsbok were shot in both the Etosha National Park in the north and the Hardap Nature Reserve in the south of Namibia. All the other animals were shot in the Etosha National Park. A total of 7 ixodid tick species and 8 lice species were recovered. The springbok carried few ticks. The adults of a Rhipicephalus sp. (near R. oculatus) were most numerous on the gemsbok, especially during November. The kudus were the only animals harbouring Rhipicephalus zambeziensis. Adult Hyalomma truncatum, followed by adult Hyalomma marginatum rufipes, were most abundant on the giraffes and adult Rhipicephalus evertsi mimeticus were commonest on the zebras.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.Foundation for Research Development. University of Pretoria.mn201

Accuracy of magnetic resonance studies in the detection of chondral and labral lesions in femoroacetabular impingement : systematic review and meta-analysis

Background: Several types of Magnetic resonance imaging (MRI) are commonly used in imaging of femoroacetabular impingement (FAI), however till now there are no clear protocols and recommendations for each type. The aim of this meta-analysis is to detect the accuracy of conventional magnetic resonance imaging (cMRI), direct magnetic resonance arthrography (dMRA) and indirect magnetic resonance arthrography (iMRA) in the diagnosis of chondral and labral lesions in femoroacetabular impingement (FAI). Methods: A literature search was finalized on the 17th of May 2016 to collect all studies identifying the accuracy of cMRI, dMRA and iMRA in diagnosing chondral and labral lesions associated with FAI using surgical results (arthroscopic or open) as a reference test. Pooled sensitivity and specificity with 95% confidence intervals using a random-effects meta-analysis for MRI, dMRA and iMRA were calculated also area under receiver operating characteristic (ROC) curve (AUC) was retrieved whenever possible where AUC is equivocal to diagnostic accuracy. Results: The search yielded 192 publications which were reviewed according inclusion and exclusion criteria then 21 studies fulfilled the eligibility criteria for the qualitative analysis with a total number of 828 cases, lastly 12 studies were included in the quantitative meta-analysis. Meta-analysis showed that as regard labral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.864, 0.833 and 0.88 and for dMRA were 0.91, 0.58 and 0.92. While in chondral lesions the pooled sensitivity, specificity and AUC for cMRI were 0.76, 0.72 and 0.75 and for dMRA were 0.75, 0.79 and 0.83, while for iMRA were sensitivity of 0.722 and specificity of 0.917. Conclusions: The present meta-analysis showed that the diagnostic test accuracy was superior for dMRA when compared with cMRI for detection of labral and chondral lesions. The diagnostic test accuracy was superior for labral lesions when compared with chondral lesions in both cMRI and dMRA. Promising results are obtained concerning iMRA but further studies still needed to fully assess its diagnostic accuracy