On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms

A wireless network system is a pair (U;B), where B is a family of some base stations and U is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of coverin...

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Main Author: Xun Ge
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2014/271964
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author Xun Ge
author_facet Xun Ge
author_sort Xun Ge
collection DOAJ
description A wireless network system is a pair (U;B), where B is a family of some base stations and U is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of covering approximation operators, this paper characterizes the connectivity of covering approximation spaces by their definable subsets. Furthermore, it is obtained that a wireless network system is connected if and only if the relevant covering approximation space has no nonempty definable proper subset. As an application of this result, the connectivity of a teacher-student interactive platform is discussed, which is established in the School of Mathematical Sciences of Soochow University. This application further demonstrates the usefulness of rough set theory in pedagogy and makes it possible to research education by logical methods and mathematical methods.
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series Journal of Applied Mathematics
spelling doaj-art-14dd813f1bdf4a91a8487a498ebaaa872025-02-03T05:53:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/271964271964On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive PlatformsXun Ge0School of Mathematical Sciences, Soochow University, Suzhou 215006, ChinaA wireless network system is a pair (U;B), where B is a family of some base stations and U is a set of their users. To investigate the connectivity of wireless network systems, this paper takes covering approximation spaces as mathematical models of wireless network systems. With the help of covering approximation operators, this paper characterizes the connectivity of covering approximation spaces by their definable subsets. Furthermore, it is obtained that a wireless network system is connected if and only if the relevant covering approximation space has no nonempty definable proper subset. As an application of this result, the connectivity of a teacher-student interactive platform is discussed, which is established in the School of Mathematical Sciences of Soochow University. This application further demonstrates the usefulness of rough set theory in pedagogy and makes it possible to research education by logical methods and mathematical methods.http://dx.doi.org/10.1155/2014/271964
spellingShingle Xun Ge
On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
Journal of Applied Mathematics
title On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
title_full On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
title_fullStr On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
title_full_unstemmed On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
title_short On the Connectivity of Wireless Network Systems and an Application in Teacher-Student Interactive Platforms
title_sort on the connectivity of wireless network systems and an application in teacher student interactive platforms
url http://dx.doi.org/10.1155/2014/271964
work_keys_str_mv AT xunge ontheconnectivityofwirelessnetworksystemsandanapplicationinteacherstudentinteractiveplatforms