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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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/271964 |
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| _version_ | 1841524512384876544 |
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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. |
| format | Article |
| id | doaj-art-14dd813f1bdf4a91a8487a498ebaaa87 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |