The relative Renyi dimensions. Относительные размерности Реньи
В работе вводятся понятия относительных размерностей Реньи для покрытий, упаковок и разбиений. а так же устанавливаются некоторые связи между ними.Recently, many authors are discussing the use of methods of fractal geometry [5] to compare the distributions of the various measures. However, in practi...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2012-01-01
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| Series: | Проблемы анализа |
| Subjects: | |
| Online Access: | http://issuesofanalysis.petrsu.ru/files/pdf/1741_en.pdf |
| _version_ | 1818620994593488896 |
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| author | Svetova N. Yu. |
| author_facet | Svetova N. Yu. |
| author_sort | Svetova N. Yu. |
| collection | DOAJ |
| description | В работе вводятся понятия относительных размерностей Реньи для покрытий, упаковок и разбиений. а так же устанавливаются некоторые связи между ними.Recently, many authors are discussing the use of methods of fractal geometry [5] to compare the distributions of the various measures. However, in practical applications, comparison of distributions by comparing the calculated multifractal spectra can be difficult. It often happens that a completely different distributions of measures can give very imperceptible differences in the spectra. To solve this problem, some authors [4,10] propose to use different methods of direct comparison of distributions. These methods are generalizations of the classical multifractal analysis developed in the works L. Olsen [9], K.-S. Lo and S.-M. Ngai [8] and others. Based on the idea of multifractal analysis [9] and the mutual multifractal analysis [1,2] we propose to introduce new concepts of relative Renyi dimensions for coverings, packings and partitions, as well as we establish some connection between them. It should be noted that these dimension proved mathematically rigorous new analogues "new relative multifractal spectrum of dimensions" proposed for purely practical purposes, R. Dansereau and W. Kinser [6]. |
| first_indexed | 2024-12-16T18:02:13Z |
| format | Article |
| id | doaj.art-383c6b750a0e431aa7bea7395031965c |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-16T18:02:13Z |
| publishDate | 2012-01-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-383c6b750a0e431aa7bea7395031965c2022-12-21T22:22:01ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322012-01-011 (19)11523The relative Renyi dimensions. Относительные размерности РеньиSvetova N. Yu.В работе вводятся понятия относительных размерностей Реньи для покрытий, упаковок и разбиений. а так же устанавливаются некоторые связи между ними.Recently, many authors are discussing the use of methods of fractal geometry [5] to compare the distributions of the various measures. However, in practical applications, comparison of distributions by comparing the calculated multifractal spectra can be difficult. It often happens that a completely different distributions of measures can give very imperceptible differences in the spectra. To solve this problem, some authors [4,10] propose to use different methods of direct comparison of distributions. These methods are generalizations of the classical multifractal analysis developed in the works L. Olsen [9], K.-S. Lo and S.-M. Ngai [8] and others. Based on the idea of multifractal analysis [9] and the mutual multifractal analysis [1,2] we propose to introduce new concepts of relative Renyi dimensions for coverings, packings and partitions, as well as we establish some connection between them. It should be noted that these dimension proved mathematically rigorous new analogues "new relative multifractal spectrum of dimensions" proposed for purely practical purposes, R. Dansereau and W. Kinser [6].http://issuesofanalysis.petrsu.ru/files/pdf/1741_en.pdfanalytic area Nevanlinnaclosed ideals |
| spellingShingle | Svetova N. Yu. The relative Renyi dimensions. Относительные размерности Реньи Проблемы анализа analytic area Nevanlinna closed ideals |
| title | The relative Renyi dimensions. Относительные размерности Реньи |
| title_full | The relative Renyi dimensions. Относительные размерности Реньи |
| title_fullStr | The relative Renyi dimensions. Относительные размерности Реньи |
| title_full_unstemmed | The relative Renyi dimensions. Относительные размерности Реньи |
| title_short | The relative Renyi dimensions. Относительные размерности Реньи |
| title_sort | relative renyi dimensions относительные размерности реньи |
| topic | analytic area Nevanlinna closed ideals |
| url | http://issuesofanalysis.petrsu.ru/files/pdf/1741_en.pdf |
| work_keys_str_mv | AT svetovanyu therelativerenyidimensionsotnositelʹnyerazmernostirenʹi AT svetovanyu relativerenyidimensionsotnositelʹnyerazmernostirenʹi |