On the origin of central abundance drops in the intracluster medium of galaxy groups and clusters

A central drop of ICM Fe abundance has been observed in several cool-core clusters. It has been proposed that this abundance drop may be due, at least partially, to the depletion of Fe into dust grains in the central, high-density regions. According to this scenario, noble gas elements such as Ar and Ne are not expected to be depleted into dust, and therefore should not show any drop, but follow the general increase of metal abundance toward the center. In this work, we test this scenario by measuring with {\sl Chandra} data the radial profiles of Ar and Ne in a sample of 12 groups and clusters where a central drop in Fe abundance has been detected. We confirm the presence of the Fe drop in 10 out of 12 clusters at more than 2$\sigma$ c.l., and 4 Ar drops with similar significance. We also find 4 Ne drops, with the caveat that Ne abundance measurement from CCD spectra suffers from systematics not completely under control. Our results are consistent with an abundance drop common to the three elements. When comparing the profiles, we find that, on average, the abundance profiles of Ar and Ne are significantly higher than Fe and steeper toward the center, while they all gradually become consistent with solar composition at $r\geq 0.05r_{500}$. We also check that Si and S profiles are mostly consistent with Fe. This result confirms a scenario in which some fraction of Fe is depleted into dust grains in the inner regions, although the global central abundance drop is mostly due to mechanical processes, like the displacement of metal-rich ICM from the very center to larger radii by AGN-driven feedback. Finally, we report the detection of an Fe drop in the cluster MACSJ1423.8+2404 at $z=0.543$, showing that this feature appears early on in cool-core clusters.Comment: To appear in MNRA

Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D

We consider the singularly perturbed fourth-order boundary value problem $\varepsilon ^{2}\Delta ^{2}u-\Delta u=f$ on the unit square $\Omega \subset \mathbb{R}^2$, with boundary conditions $u = \partial u / \partial n = 0$ on $\partial \Omega$, where $\varepsilon \in (0, 1)$ is a small parameter. The problem is solved numerically by means of a weak Galerkin(WG) finite element method, which is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on finite element partitions consisting of polygons of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter-free. Under reasonable assumptions on the structure of the boundary layers that appear in the solution, a family of suitable Shishkin meshes with $N^2$ elements is constructed ,convergence of the method is proved in a discrete $H^2$ norm for the corresponding WG finite element solutions and numerical results are presented

Tolerability and effectiveness of (S)-amlodipine compared with racemic amlodipine in hypertension: A systematic review and meta-analysis

AbstractBackground: Amlodipine is a calcium channel blocker prescribed for the management of angina and hypertension. As a racemic mixture, amlodipine contains (R)- and (S)-amlodipine isomers, but only (S)-amlodipine as the active moiety possesses therapeutic activity. Based on pharmacologic research, it remains uncertain if (S)-amlodipine alone has similar efficacy and fewer associated adverse events (AEs) compared with the racemic mixtures.Objective: The aim of this systematic review and meta-analysis was to determine the effectiveness and tolerability of (S)-amlodipine compared with that of racemic amlodipine.Methods: A systematic literature search was performed using MEDLINE (1966–2009), EMBASE (1966–2009), the Cochrane Central Register of Controlled Trials (issue 3, 2009), the Chinese Biomedical Database (1978–2009), and the China National Knowledge Internet (1980–2009). All randomized controlled trials (RCTs) comparing (S)-amlodipine 2.5 mg and racemic amlodipine 5.0 mg in the treatment of hypertension were included in the review. The outcome measures to be collected were cardiovascular events, systolic blood pressure (SBP), diastolic BP (DBP), and AEs. Quality assessments of clinical trials were conducted using a modified Jadad Scale, with trials being rated as low quality (score 0–3) or high quality (score 4–7). Meta-analysis of the included studies was performed using RevMan software.Results: Of the 229 references identified, 214 were excluded after screening the titles, abstracts, or full texts. Fifteen RCTs were included, of which 13 were in Chinese and 2 in English. Based on the Jadad Scale score, 3 of the RCTs were classified as high quality (score 5 or 6) and the remaining 12 as low quality (score 1–3). None of the trials evaluated cardiovascular events beyond 40 weeks. Meta-analysis of the 15 trials indicated that (S)-amlodipine was not significantly different from racemic amlodipine in the effect on BP. When only high-quality studies were included, after 4 weeks' treatment, the weighted mean difference (WMD) of SBP and DBP decrease (1 study) was −2.84 (95% CI, −6.42 to 0.74) with (S)-amlodipine and −1.71 (95% CI, −3.48 to 0.06) with racemic amlodipine. After 8 weeks' treatment, the WMD of SBP and DBP decrease (2 studies) was −1.13 (95% CI, −5.29 to 3.03) and −1.34 (95% CI, −2.67 to −0.01), respectively. The risk difference (RD) for the number of patients who experienced AEs with (S)-amlodipine and racemic amlodipine was found to be −0.04 (95% CI, −0.06 to −0.02). When all the trials were included, (S)-amlodipine treatment was associated with significantly less edema than racemic amlodipine (RD, −0.02; 95% CI, −0.03 to 0.00); however, when only high-quality studies (2 studies) were included, no difference was found between the 2 groups (RD, 0.01; 95% CI, −0.02 to 0.03). One high-quality study found significant differences in increases in aspartate and alanine aminotransferase activities in the 2 groups (RD, 0.08; 95% CI, 0.01 to 0.05). No significant differences between the 2 groups were found in the incidence of headache (RD, 0.00; 95% CI, −0.02 to 0.01) or flushing (RD, −0.01; 95% CI, −0.02 to 0.00).Conclusions: The majority of the clinical trials comparing (S)-amlodipine and racemic amlodipine treatment were low quality (12/15 [80%]). According to the limited evidence, there were no significant differences between (S)-amlodipine 2.5 mg and racemic amlodipine 5.0 mg in controlling BP. When all the trials were considered, (S)-amlodipine treatment was associated with significantly less edema than racemic amlodipine; however, when only high-quality trials were included, no significant difference was found. More long-term, high-quality RCTs with cardiovascular events as the primary outcome are needed to compare the safety and efficacy of (S)-amlodipine and racemic amlodipine

Optimal pricing strategy for green products under salience theory

Environmental pressures and people’s demands for green consumption have prompted manufacturers to engage in the research and development of green products. Manufacturers need to consider the price and greenness of products when making production decisions. This paper analyzes the level of greenness and price competition of duopoly manufacturers in the consumer market in which both green-sensitive consumers (salience to greenness) and price-sensitive consumers (salience to price) exist simultaneously according to salience theory. We find that the regular manufacturer will enter the green market when all consumers’ average degree of price responsiveness is small or in a moderate part of the region. In addition, this paper also discusses the influence of salience on manufacturers’ level of greenness and pricing strategy choice. We find that the degree of salient thinking of consumers influences optimal pricing, optimal greenness and profits under the uniform pricing and price discrimination mechanisms