Schur monotone increasing and decreasing sequences
It is well known that on the one dimensional space, any bounded monotone increasing or monotone decreasing sequence converges to a unique limiting point. In order to generalize this result into the higher dimensional space, we should consider an appropriate order (or pre-order). A Majorization is a...
| Main Authors: | , , |
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| Format: | Proceeding Paper |
| Language: | English English |
| Published: |
2013
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| Online Access: | http://irep.iium.edu.my/28932/ http://irep.iium.edu.my/28932/1/Schur_Sequences--ICMSS2013.pdf http://irep.iium.edu.my/28932/4/schur_monotone.pdf |
| _version_ | 1848780036239261696 |
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| author | Ganikhodzaev, Rasul Saburov, Mansoor Saburov, Khikmat |
| author_facet | Ganikhodzaev, Rasul Saburov, Mansoor Saburov, Khikmat |
| author_sort | Ganikhodzaev, Rasul |
| building | IIUM Repository |
| collection | Online Access |
| description | It is well known that on the one dimensional space, any bounded monotone increasing or monotone decreasing sequence converges to a unique limiting point. In order to generalize this result into the higher dimensional space, we should consider an appropriate order (or pre-order). A Majorization is a partial ordering on vectors which determines the degree of similarity between vectors. The majorization plays a fundamental role in nearly all branches of mathematics. In this paper, we introduce Schur monotone increasing and decreasing sequences on an n-dimensional space based on the majorization pre-order. We proved that the Cesaro mean (or an arithmetic mean) of any bounded Schur increasing or decreasing sequences converges to a unique limiting point. As an application of our result, we show that the Cesaro mean of mixing enhancing states of the quantum system becomes more stable and mixing than given states. |
| first_indexed | 2025-11-14T15:27:17Z |
| format | Proceeding Paper |
| id | iium-28932 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-14T15:27:17Z |
| publishDate | 2013 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-289322013-10-11T03:46:59Z http://irep.iium.edu.my/28932/ Schur monotone increasing and decreasing sequences Ganikhodzaev, Rasul Saburov, Mansoor Saburov, Khikmat QA Mathematics It is well known that on the one dimensional space, any bounded monotone increasing or monotone decreasing sequence converges to a unique limiting point. In order to generalize this result into the higher dimensional space, we should consider an appropriate order (or pre-order). A Majorization is a partial ordering on vectors which determines the degree of similarity between vectors. The majorization plays a fundamental role in nearly all branches of mathematics. In this paper, we introduce Schur monotone increasing and decreasing sequences on an n-dimensional space based on the majorization pre-order. We proved that the Cesaro mean (or an arithmetic mean) of any bounded Schur increasing or decreasing sequences converges to a unique limiting point. As an application of our result, we show that the Cesaro mean of mixing enhancing states of the quantum system becomes more stable and mixing than given states. 2013-02-05 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/28932/1/Schur_Sequences--ICMSS2013.pdf application/pdf en http://irep.iium.edu.my/28932/4/schur_monotone.pdf Ganikhodzaev, Rasul and Saburov, Mansoor and Saburov, Khikmat (2013) Schur monotone increasing and decreasing sequences. In: International Conference On Mathematical Sciences And Statistics 2013 (ICMSS2013), 5–7 February 2013 , Kuala Lumpur, Malaysia . http://proceedings.aip.org/resource/2/apcpcs/1557/1/108_1?isAuthorized=no |
| spellingShingle | QA Mathematics Ganikhodzaev, Rasul Saburov, Mansoor Saburov, Khikmat Schur monotone increasing and decreasing sequences |
| title | Schur monotone increasing and decreasing sequences |
| title_full | Schur monotone increasing and decreasing sequences |
| title_fullStr | Schur monotone increasing and decreasing sequences |
| title_full_unstemmed | Schur monotone increasing and decreasing sequences |
| title_short | Schur monotone increasing and decreasing sequences |
| title_sort | schur monotone increasing and decreasing sequences |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/28932/ http://irep.iium.edu.my/28932/ http://irep.iium.edu.my/28932/1/Schur_Sequences--ICMSS2013.pdf http://irep.iium.edu.my/28932/4/schur_monotone.pdf |