A Joint Chandra and XMM-Newton View of Abell 3158: Massive Off-Centre Cool Gas Clump As A Robust Diagnostic of Merger Stage

By analysing the Chandra and XMM-Newton archived data of the nearby galaxy cluster Abell 3158, which was reported to possess a relatively regular, relaxed morphology in the X-ray band in previous works, we identify a bow edge-shaped discontinuity in the X-ray surface brightness distribution at about $120h_{71}^{-1}$ kpc west of the X-ray peak. This feature is found to be associated with a massive, off-centre cool gas clump, and actually forms the west boundary of the cool clump. We find that the cool gas clump is moving at a subsonic velocity of ~700 km/s toward west on the sky plane. We exclude the possibility that this cool clump was formed by local inhomogeneous radiative cooling in the intra-cluster medium, due to the effectiveness of the thermal conduction on the time-scale of $\sim 0.3$ Gyr. Since no evidence for central AGN activity has been found in Abell 3158, and this cool clump bears many similarities to the off-centre cool gas clumps detected in other merging clusters in terms of their mass, size, location, and thermal properties (e.g. lower temperature and higher abundance as compared with the environment), we speculate that the cool clump in Abell 3158 was caused by a merger event, and is the remnant of the original central cool-core of the main cluster or the infalling sub-cluster. This idea is supported not only by the study of line-of-sight velocity distribution of the cluster member galaxies, but also by the study of gas entropy-temperature correlation. This example shows that the appearance of such massive, off-centre cool gas clumps can be used to diagnose the dynamical state of a cluster, especially when prominent shocks and cold fronts are absent.Comment: Accepted by MNRAS; 12 pages, 6 figure

Controllability of Hilfer fractional Langevin evolution equations

The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo fractional derivative. Exact controllability is one of the fundamental issues in control theory: under some admissible control input, a system can be steered from an arbitrary given initial state to an arbitrary desired final state. In this article, using the (α, β) resolvent operator and three different fixed point theorems, we discuss the control problem for a class of Hilfer fractional Langevin evolution equations. The exact controllability of Hilfer fractional Langevin systems is established. An example is also discussed to illustrate the results

An Ensemble Framework of Evolutionary Algorithm for Constrained Multi-Objective Optimization

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances