Schur monotone increasing and decreasing sequences

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...

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Main Authors: Ganikhodzaev, Rasul, Saburov, Mansoor, Saburov, Khikmat
Format: Conference or Workshop Item
Language:English
English
Published: 2013
Subjects:
QA Mathematics
Online Access: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
id iium-28932
recordtype eprints
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 Conference or Workshop Item 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
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodzaev, Rasul
Saburov, Mansoor
Saburov, Khikmat
Schur monotone increasing and decreasing sequences
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.
format Conference or Workshop Item
author Ganikhodzaev, Rasul
Saburov, Mansoor
Saburov, Khikmat
author_facet Ganikhodzaev, Rasul
Saburov, Mansoor
Saburov, Khikmat
author_sort Ganikhodzaev, Rasul
title Schur monotone increasing and decreasing sequences
title_short 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_sort schur monotone increasing and decreasing sequences
publishDate 2013
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
first_indexed 2023-09-18T20:42:30Z
last_indexed 2023-09-18T20:42:30Z
_version_ 1777409458392006656

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