Analytic regularity for a singularly perturbed fourth order reaction-diffusion boundary value problem

We consider a fourth order, reaction-diffusion type, singularly perturbed boundary value problem, and the regularity of its solution. Specifically, we provide estimates for arbitrary order derivatves, which are explicit in the singular perturbation parameter as well as the differentiation order. Such estimates are needed for the numerical analysis of high order methods, e.g.hp Finite Element Method (FEM).Comment: arXiv admin note: text overlap with arXiv:1901.0939

Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs

We consider a coupled system of two singularly perturbed reaction-diffusion equations, with two small parameters $0< \epsilon \le \mu \le 1$, each multiplying the highest derivative in the equations. The presence of these parameters causes the solution(s) to have \emph{boundary layers} which overlap and interact, based on the relative size of $\epsilon$ and $$. We construct full asymptotic expansions together with error bounds that cover the complete range $0 < \epsilon \leq \mu \leq 1$. For the present case of analytic input data, we derive derivative growth estimates for the terms of the asymptotic expansion that are explicit in the perturbation parameters and the expansion order

Analysis of the Singular Function Boundary Integral Method for a Biharmonic Problem with One Boundary Singularity

In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution, and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. By means of Green&apos;s theorem, the resulting discretized equations are posed and solved on the boundary of the domain, away from the point where the singularity arises. We analyze the convergence of the method and prove that the coefficients in the local asymptotic expansion, also referred to as stress intensity factors, are approximated at an exponential rate as the number of the employed expansion terms is increased. Our theoretical results are illustrated through a numerical experiment

Oceanic inside corner detachments of the Limassol Forest area, Troodos ophiolite, Cyprus

Flat-lying extensional detachment faults have been imaged in the inside corner regions of ridge-transform intersections on the Mid-Atlantic Ridge. Exposed detachment surfaces are 10 km or more across, and are corrugated in the direction of spreading, as are continental detachments. Beneath the detachments lie core complexes of peridotite and gabbro; these are overlain by blocks of crustal material. We argue here that similar detachments are an essential component of the Limassol Forest area of the Troodos ophiolite in Cyprus, which lies south of the Arakapas Fault zone, previously recognized as a palaco-transform fault, and here interpreted as a transform fault that evolved into a fracture zone. In the Limassol Forest, core complexes of mantle peridotite can be shown to have been exposed at the sea floor, or to have been covered by overlapping crustal blocks, separated from the peridotite core and from each other by low-angle extensional faults. The extension can be shown to have occured shortly after crustal construction, and the already extended terrain was then intruded by swarms of dykes and plutons. We interpret these relations as arising when crust is constructed in an inside corner area, extended by detachment faulting, deformed further during slip along the transform, and then intruded by new magma as it passes the second spreading centre. The structurally deeper parts of the crustal blocks that overlie the detachment lie broadly towards the west, indicating that the spreading axis lay in that direction. The ophiolite north of the transform is much less extended, and we interpret this as a section of outside corner crust. In this interpretation, the Troodos ophiolite formed to the east (in its current orientation) of a ridge-transform-ridge intersection, in which the transform had a dextral offset and sinistral slip. The part of the ophiolite that forms the Limassol Forest was produced at the western inside corner, and spread eastward until it passed the second spreading axis, at which point the ophiolite north of the Arakapas Fault was created and welded to the Limassol Forest when the transform became a fracture zone.published_or_final_versio

Twelve weeks of supervised exercise improves self-reported symptom burden and fatigue in chronic kidney disease : a secondary analysis of the ‘ExTra CKD’ trial

Background Chronic kidney disease (CKD) patients experience a high symptom burden including fatigue, sleep difficulties, muscle weakness and pain. These symptoms reduce levels of physical function (PF) and activity, and contribute to poor health-related quality of life (HRQoL). Despite the gathering evidence of positive physiological changes following exercise in CKD, there is limited evidence on its effect on self-reported symptom burden, fatigue, HRQoL and physical activity. Methods Thirty-six patients [mean ± SD 61.6 ± 11.8 years, 22 (61%) females, estimated glomerular filtration rate: 25.5 ± 7.8 mL/min/1.73 m2] not requiring renal replacement therapy underwent 12 weeks (3 times/week) of supervised aerobic exercise (AE), or a combination (CE) of AE plus resistance training. Outcomes included self-reported symptom burden, fatigue, HRQoL and physical activity. Results Exercise reduced the total number of symptoms reported by 17% and had favourable effects on fatigue in both groups. AE reduced the frequency of ‘itching’, ‘impotence’ and ‘shortness of breath’ symptoms, and the intrusiveness for symptoms of ‘sleep disturbance’, ‘loss of muscular strength/power’, ‘muscle spasm/stiffness’ and ‘restless legs’. The addition of resistance exercise in the CE group saw a reduction in ‘loss of muscular strength/power’. No changes were seen in subjective PF or physical activity levels. AE increased self-efficacy for physical activity. Conclusions Supervised exercise had favourable effects on symptom frequency and intrusiveness, including substantial improvements in fatigue. Although the intervention did not improve self-reported physical activity levels, AE increased patients’ self-efficacy for physical activity. These favourable changes in self-reported outcomes support the important role of exercise in CKD

The association of physical function and physical activity with all-cause mortality and adverse clinical outcomes in non-dialysis chronic kidney disease : a systematic review

Objective: People with nondialysis-dependent chronic kidney disease (CKD) and renal transplant recipients (RTRs) have compromised physical function and reduced physical activity (PA) levels. Whilst established in healthy older adults and other chronic diseases, this association remains underexplored in CKD. We aimed to review the existing research investigating poor physical function and PA with clinical outcome in nondialysis CKD. Data sources: Electronic databases (PubMed, MEDLINE, EMBASE, Web of Science, Cochrane Central Register of Controlled Trials) were searched until December 2017 for cohort studies reporting objective or subjective measures of PA and physical function and the associations with adverse clinical outcomes and all-cause mortality in patients with nondialysis CKD stages 1–5 and RTRs. The protocol was registered on the International Prospective Register of Systematic Reviews (PROSPERO) (CRD42016039060). Review methods: Study quality was assessed using the Newcastle-Ottawa Scale and the Agency for Healthcare and Research Quality (AHRQ) standards. Results: A total of 29 studies were included; 12 reporting on physical function and 17 on PA. Only eight studies were conducted with RTRs. The majority were classified as ‘good’ according to the AHRQ standards. Although not appropriate for meta-analysis due to variance in the outcome measures reported, a coherent pattern was seen with higher mortality rates or prevalence of adverse clinical events associated with lower PA and physical function levels, irrespective of the measurement tool used. Sources of bias included incomplete description of participant flow through the study and over reliance on self-report measures. Conclusions: In nondialysis CKD, survival rates correlate with greater PA and physical function levels. Further trials are required to investigate causality and the effectiveness of physical function and PA interventions in improving outcomes. Future work should identify standard assessment protocols for PA and physical function

Low HDL Cholesterol, Smoking and IL-13 R130Q Polymorphism are Associated with Myocardial Infarction in Greek Cypriot Males. A Pilot Study

This study was carried out in Greek Cypriot males to identify risk factors that predispose to myocardial infarction (MI). Genetic and lipid risk factors were investigated for the first time in a Greek Cypriot male case-control study.Contrary to other studies, mean low density lipoprotein cholesterol did not differ between cases and controls. High density lipoprotein cholesterol on the other hand, although within normal range in cases and controls, was significantly higher in the control population. In agreement with many other studies, smoking was significantly more prevalent in cases compared with controls. In pooled cases and controls, smokers had a significantly lower HDL-C level compared with non-smokers. The frequency of the IL-13 R130Q homozygotes for the mutation (QQ), as well as the mutant allele were significantly higher in cases compared with controls. The IL-13 R130Q variant, or another locus, linked to it, may increase the risk of MI