We describe a highly efficient numerical scheme for finding two‐sided bounds for the eigenvalues of the fractional Laplace operator (−Δ)α/2 in the unit ball D⊂Rd, with a Dirichlet condition in the ...complement of D. The standard Rayleigh–Ritz variational method is used for the upper bounds, while the lower bounds involve the lesser known Aronszajn method of intermediate problems. Both require explicit expressions for the fractional Laplace operator applied to a linearly dense set of functions in L2(D). We use appropriate Jacobi‐type orthogonal polynomials, which were studied in a companion paper (B. Dyda, A. Kuznetsov and M. Kwaśnicki, ‘Fractional Laplace operator and Meijer G‐function’, Constr. Approx., to appear, doi:10.1007/s00365‐016‐9336‐4). Our numerical scheme can be applied analytically when polynomials of degree two are involved. This is used to partially resolve the conjecture of Kulczycki, which claims that the second smallest eigenvalue corresponds to an antisymmetric function: we prove that this is the case when either d⩽2 and α∈(0,2, or d⩽9 and α=1, and we provide strong numerical evidence for d⩽9 and general α∈(0,2.
Abstract In disk-wind models for active galactic nuclei outflows, high-energy radiation poses a significant problem wherein the gas can become overionized, effectively disabling what is often ...inferred to be the largest force acting on the gas: the radiation force due to spectral line opacity. Calculations of this radiation force depend on the magnitude of ionizing radiation, which can strongly depend on the position above a disk where the radiation is anisotropic. As our first step to quantify the position and direction dependence of the radiation field, we assumed free streaming of photons and computed energy distributions of the mean intensity and components of flux as well as energy-integrated quantities such as mean photon energy. We find a significant dependence of radiation-field properties on position, but this dependence is not necessarily the same for different field quantities. A key example is that the mean intensity is much softer than the radial flux at many points near the disk. Because the mean intensity largely controls ionization, this softening decreases the severity of the overionization problem. The position dependence of mean intensity implies the position dependence of gas opacity, which we illustrate by computing the radiation force a fluid element feels in an accelerating wind. We find that in a vertical accelerating flow, the force due to radiation is not parallel to the radiation flux. This misalignment is due to the force’s geometric weighting by both the velocity field’s directionality and the position dependence of the mean intensity.
W artykule autor podejmuje refleksję nad zasadniczymi problemami stosowania prawa przez organy Państwa Miasta Watykańskiego, wynikającymi przede wszystkim z przyjętego w nim systemu źródeł prawa. ...Opiera się on w przeważającej mierze na normach kanonicznych – ustanowionych na potrzeby funkcjonowania Kościoła Katolickiego – oraz recypowanych przepisach prawa włoskiego. Tego typu połączenie powoduje szereg problemów praktycznych, zwłaszcza w sferze zastosowania zasady praworządności na gruncie watykańskiego prawa karnego, które dopuszcza karanie sprawcy bez wyraźnej podstawy prawnej. Jednocześnie kluczową rolę w stosowaniu prawa w Państwie Watykańskim odgrywają osądy moralne, wypracowywane na gruncie nauki Kościoła Katolickiego. W związku z tym autor stawia tezę, że analizy systemu źródeł prawa Państwa Miasta Watykańskiego dają także – unikatową – możliwość badania praktycznego zastosowania klasycznych dla Zachodniej tradycji prawniczej koncepcji, np. prawa naturalnego, bądź sprecyzowania istotnych zagadnień nauki prawa kanonicznego. Ponadto mogą się przyczynić do wyjaśnienia możliwości szerszego zastosowania zasad prawa na etapie jego stosowania, przy jednoczesnym minimum pozytywizacji.
The aim of this article is to provide an overview of peripheral nerve blocks, the use of peripheral nerve block within and outside interventional radiology, and the complications of peripheral nerve ...block.
Interventional radiologists are often responsible for sedation and pain management in the majority of interventional radiology procedures. Peripheral nerve block is increasingly being used in interventional radiology.
Acceptance of vaccines is an important predictor of vaccine uptake. This has public health implications as those who are not vaccinated are at a higher risk of infection from vaccine preventable ...diseases. We aimed to examine how parental attitudes and beliefs towards childhood vaccination were measured in questionnaires through a systematic review of the literature.
We systematically reviewed the literature to identify primary research studies using tools to measure vaccine attitudes and beliefs, published between January 2012 and May 2018. Studies were included if they involved a quantitative survey of the attitudes and beliefs of parents about vaccinations recommended for children. We undertook a synthesis of the results with a focus on evaluating the tools used to measure hesitancy.
A total of 116 studies met the inclusion criteria, 99 used a cross sectional study design, 5 used a case control study design, 4 used a pre-post study design and 8 used mixed methods study designs. Sample sizes of included studies ranged from 49 to 12,259. The most commonly used tool was the Parent Attitudes about Childhood Vaccines (PACV) Survey (n = 7). The most common theoretical framework used was the Health Belief Model (n = 25). Questions eliciting vaccination attitudes and beliefs varied widely.
There was heterogeneity in the types of questionnaires used in studies investigating attitudes and beliefs about vaccination in parents. Methods to measure parental attitudes and beliefs about vaccination could be improved with validated and standardised yet flexible instruments. The use of a standard set of questions should be encouraged in this area of study.
Abstract
Acceleration can change the ionization of X-ray irradiated gas to the point that the gas becomes thermally unstable. Cloud formation, the expected outcome of thermal instability (TI), will ...be suppressed in a dynamic flow, however, due to the stretching of fluid elements that accompanies acceleration. It is therefore unlikely that cloud formation occurs during the launching phase of a supersonic outflow. In this paper, we show that the most favorable conditions for dynamical TI in highly supersonic outflows are found at radii beyond the acceleration zone, where the growth rate of entropy modes is set by the linear theory rate for a static plasma. This finding implies that even mildly relativistic outflows can become clumpy, and we explicitly demonstrate this using hydrodynamical simulations of ultrafast outflows. We describe how the continuity and heat equations can be used to appreciate another impediment (beside mode disruption due to the stretching) to making an outflow clumpy: background flow conditions may not allow the plasma to enter a TI zone in the first place. The continuity equation reveals that both impediments are in fact tightly coupled, yet one is easy to overcome. Namely, time variability in the radiation field is found to be a robust means of placing gas in a TI zone. We further show how the ratio of the dynamical and thermal timescales enters linear theory; the heat equation reveals how this ratio depends on the two processes that tend to remove gas from a TI zone: adiabatic cooling and heat advection.
Binding to minerals is one mechanism crucial toward the accumulation and stabilization of organic matter (OM) in soils. Of the various biochemicals produced by plants, lignin-derived phenols are ...among the most surface-reactive compounds. However, it is not known to what extent mineral-bound lignin-derived phenols can be analytically assessed by alkaline CuO oxidation. We tested the potential irreversible binding of lignin from three litters (blue oak, foothill pine, annual grasses) to five minerals (ferrihydrite, goethite, kaolinite, illite, montmorillonite) using the CuO-oxidation technique, along with bulk organic carbon (OC) sorption. Up to 56% of sorbed lignin could not be extracted from the minerals with the CuO-oxidation technique. The composition of the irreversibly bound lignin component differed markedly between minerals and from that of the parent litter leachates, indicating different bonding strengths related to individual monomers and conformations. The difference in extractability of individual phenols suggests that abiotic processes, such as sorption/desorption, should be taken into account when using CuO oxidation data for assessing lignin turnover in mineral matrixes. However, given the apparent relationship between aromaticity as indicated by carbon-specific UV absorbance (SUVA) and bulk OC sorption, it is likely that irreversible sorption is a concern for any technique that addresses the broad class of aromatic/phenolic compounds in soils and sediments.
Vitamin D is essential for maintaining optimal bone health. The prevalence of vitamin D inadequacy in athletes is currently unclear.
The objective of this study is to determine the prevalence of ...vitamin D inadequacy in athletes.
We conducted a systematic review and meta-analysis. Multiple databases were searched and studies assessing serum 25-hydroxyvitamin D 25(OH)D status in athletes were identified. Serum 25(OH)D is measured to clinically determine vitamin D status. Reviewers independently selected the eligible articles, assessed the methodological quality, and extracted data. Disagreements were resolved by consensus. Weighted proportions of vitamin D inadequacy serum 25(OH)D <32 ng/mL were calculated (DerSimonian-Laird random-effects model) and compared using Chi-squared (χ (2)) test. Subgroup analyses were conducted and risk ratios (RRs) with 95 % confidence intervals (CIs) were reported.
Twenty-three studies with 2,313 athletes mean (standard deviation) age 22.5 (5.0) years, 76 % male were included. Of 2,313 athletes, 56 % (44-67 %) had vitamin D inadequacy that significantly varied by geographical location (p < 0.001). It was significantly higher in the UK and in the Middle East. The risk significantly increased for winter and spring seasons (RR 1.85; 95 % CI 1.27-2.70), indoor sport activities (RR 1.19; 95 % CI 1.09-1.30), and mixed sport activities (RR 2.54; 95 % CI 1.03-6.26). The risk was slightly higher for >40°N latitude RR 1.14 (95 % CI 0.91-1.44) but it increased significantly RR 1.85 (1.35-2.53) after excluding the Middle East as an outlier. Seven studies with 359 athletes reported injuries. The prevalence of injuries in athletes was 43 % (95 % CI 20-68) bone related = 19 % (95 % CI 7-36); muscle and soft-tissue = 37.5 % (95 % CI 11.5-68.5).
Despite the limitations of the current evidence, the prevalence of vitamin D inadequacy in athletes is prominent. The risk significantly increases in higher latitudes, in winter and early spring seasons, and for indoor sport activities. Regular investigation of vitamin D status using reliable assays and supplementation is essential to ensure healthy athletes. The prevalence of injuries in athletes is notable but its association with vitamin D status is unclear. A well-designed longitudinal study is needed to answer this possible association.
HUH endonucleases are numerous and widespread in all three domains of life. The major function of these enzymes is processing a range of mobile genetic elements by catalysing cleavage and rejoining ...of single-stranded DNA using an active-site Tyr residue to make a transient 5'-phosphotyrosine bond with the DNA substrate. These enzymes have a key role in rolling-circle replication of plasmids and bacteriophages, in plasmid transfer, in the replication of several eukaryotic viruses and in various types of transposition. They have also been appropriated for cellular processes such as intron homing and the processing of bacterial repeated extragenic palindromes. Here, we provide an overview of these fascinating enzymes and their functions, using well-characterized examples of Rep proteins, relaxases and transposases, and we explore the molecular mechanisms used in their diverse activities.
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