arXiv subjects

D. Chandra

Publications and source records attributed to D. Chandra.

4 recordsLinked to original sources

arXiv2024

Certain observations on selection principles related to bornological covers using ideals

We study selection principles related to bornological covers using the notion of ideals. We consider ideals $\mathcal I$ and $\mathcal J$ on $\omega$ and standard ideal orderings $KB, K$. Relations between cardinality of a base of a bornology with certain selection principles related to bornological covers are established using cardinal invariants such as modified pseudointersection number, the unbounding number and slaloms numbers. When $\mathcal I \leq_\square \mathcal J$ for ideals $\mathcal I, \mathcal J$ and $\square\in \{1\text{-}1,KB,K\}$, implications among various selection principles related to bornological covers are established. Under the assumption that ideal $\mathcal I$ has a pseudounion we show equivalences among certain selection principles related to bornological covers. Finally, the $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ is investigated. We prove that $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property of $X$ coincides with the $\mathfrak B^s$-Hurewicz property of $X$ if $\mathcal I$ has a pseudounion. Implications or equivalences among selection principles, games and $\mathcal I\text{-}\mathfrak B^s$-Hurewicz property which are obtained from our investigations are described in diagrams.

math.GN↗

arXiv2023

Two large-scale sloshing cold fronts in the outskirts of the galaxy cluster Abell 3558

Previous studies of the massive nearby galaxy cluster Abell 3558 reported a cold front around the cluster core, which is attributed to the sloshing of the core as it responds to the gravitational disturbance created by a past minor merger. Here, using XMM-Newton mosaic, we report the detection of two rare large-scale sloshing cold fronts far outside the cooling radius of Abell 3558. One of the detected cold fronts is located 600 kpc from the cluster core to the south-east, while the other is located 1.2 Mpc from the cluster core to the north-west. The latter cold front is one of the most distant cold fronts ever observed in a galaxy cluster. Our findings are in agreement with previous studies that sloshing can extend well beyond the cooling radius, on scales exceeding half the virial radius, suggesting that sloshing is a cluster-wide phenomenon and may affect the cluster's global properties.

astro-ph.CO↗

arXiv2021

On localization of the Menger property

In this paper we introduce and study the local version of the Menger property, namely locally Menger property (or, locally Menger space). We explore some preservation like properties in this space. We also discuss certain situations where this local property behaves somewhat differently from the classical Menger property. Some observations about the character of a point, network weight and weight in this space are also investigated carefully. We also introduce the notion of Menger generated space (in short, MG-space) and make certain investigations in this space. Several topological observations on the decomposition and the remainder of locally Menger spaces are also discussed.

math.GN↗

arXiv2018

A Quantum-Search-Aided Dynamic Programming Framework for Pareto Optimal Routing in Wireless Multihop Networks

Wireless Multihop Networks (WMHNs) have to strike a trade-off among diverse and often conflicting Quality-of-Service (QoS) requirements. The resultant solutions may be included by the Pareto Front under the concept of Pareto Optimality. However, the problem of finding all the Pareto-optimal routes in WMHNs is classified as NP-hard, since the number of legitimate routes increases exponentially, as the nodes proliferate. Quantum Computing offers an attractive framework of rendering the Pareto-optimal routing problem tractable. In this context, a pair of quantum-assisted algorithms have been proposed, namely the Non-Dominated Quantum Optimization (NDQO) and the Non-Dominated Quantum Iterative Optimization (NDQIO). However, their complexity is proportional to $\sqrt{N}$, where $N$ corresponds to the total number of legitimate routes, thus still failing to find the solutions in "polynomial time". As a remedy, we devise a dynamic programming framework and propose the so-called Evolutionary Quantum Pareto Optimization (EQPO) algorithm. We analytically characterize the complexity imposed by the EQPO algorithm and demonstrate that it succeeds in solving the Pareto-optimal routing problem in polynomial time. Finally, we demonstrate by simulations that the EQPO algorithm achieves a complexity reduction, which is at least an order of magnitude, when compared to its predecessors, albeit at the cost of a modest heuristic accuracy reduction.

quant-ph↗