On the surjectivity of quadratic stochastic operators acting on the simplex
It is well-known that a linear stochastic operator (a Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hy...
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| Language: | English English English |
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Pleiades Publishing
2016
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| Online Access: | http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf |
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iium-51164 |
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eprints |
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iium-511642016-12-22T06:42:54Z http://irep.iium.edu.my/51164/ On the surjectivity of quadratic stochastic operators acting on the simplex Saburov, Mansoor QA Mathematics It is well-known that a linear stochastic operator (a Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hyper-matrices (higher dimensional matrices). In this paper, we solved this problem for quadratic stochastic operators acting on the simplex. Namely, we showed that a quadratic stochastic operator associated with a cubic stochastic matrix is a surjection of the simplex if and only if it is bijective. Moreover, we also described all surjective quadratic stochastic operators of the simplex. Pleiades Publishing 2016-03 Article PeerReviewed application/pdf en http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf application/pdf en http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf Saburov, Mansoor (2016) On the surjectivity of quadratic stochastic operators acting on the simplex. Mathematical Notes, 99 (3-4). pp. 623-627. ISSN 0001-4346 E-ISSN 1573-8876 http://link.springer.com/article/10.1134/S0001434616030391 10.1134/S0001434616030391 |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English English English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Saburov, Mansoor On the surjectivity of quadratic stochastic operators acting on the simplex |
| description |
It is well-known that a linear stochastic operator (a
Markov operator) associated with a square stochastic matrix is a surjection of the simplex if and only if it is bijective. The similar problem was open for nonlinear stochastic operators (nonlinear Markov operators) associated with stochastic hyper-matrices (higher dimensional matrices). In this paper, we solved this problem for quadratic stochastic operators acting on the simplex. Namely, we showed that a quadratic stochastic operator associated with a cubic stochastic matrix is a surjection of the simplex if and only if
it is bijective. Moreover, we also described all surjective quadratic stochastic operators of the simplex. |
| format |
Article |
| author |
Saburov, Mansoor |
| author_facet |
Saburov, Mansoor |
| author_sort |
Saburov, Mansoor |
| title |
On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_short |
On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_full |
On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_fullStr |
On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_full_unstemmed |
On the surjectivity of quadratic stochastic operators
acting on the simplex |
| title_sort |
on the surjectivity of quadratic stochastic operators
acting on the simplex |
| publisher |
Pleiades Publishing |
| publishDate |
2016 |
| url |
http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/ http://irep.iium.edu.my/51164/1/Surjective_QSO_---_MN_%28Eng%29.pdf http://irep.iium.edu.my/51164/4/51164-On_the_surjectivity_of_quadratic_stochastic_operators_SCOPUS.pdf http://irep.iium.edu.my/51164/5/51164-On_the_surjectivity_of_quadratic_stochastic_operators_WOS.pdf |
| first_indexed |
2023-09-18T21:12:24Z |
| last_indexed |
2023-09-18T21:12:24Z |
| _version_ |
1777411339967266816 |