Arithmetic-Analytic Representation of Peano Curve
In this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a un...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/6745202 |
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| _version_ | 1832561989550866432 |
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| author | Guangjun Yang Xiaoling Yang Ping Wang |
| author_facet | Guangjun Yang Xiaoling Yang Ping Wang |
| author_sort | Guangjun Yang |
| collection | DOAJ |
| description | In this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a unit square and that the coordinate functions satisfy a Hölder inequality with index α=1/2, which implies that the curve is everywhere continuous and nowhere differentiable. |
| format | Article |
| id | doaj-art-89ef01d0d250464dad62d17b5578b872 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-89ef01d0d250464dad62d17b5578b8722025-02-03T01:23:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/67452026745202Arithmetic-Analytic Representation of Peano CurveGuangjun Yang0Xiaoling Yang1Ping Wang2College of Mathematics and Statistics, Yunnan University, Kunming 650091, ChinaCollege of Mathematics and Statistics, Yunnan University of Finance and Economy, Kunming 650221, ChinaDepartment of Mathematics, Penn State University, Schuylkill Haven, PA 17972, USAIn this work, we obtained a nonmatrix analytic expression for the generator of the Peano curve. Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. We proved that the curve passes each point in a unit square and that the coordinate functions satisfy a Hölder inequality with index α=1/2, which implies that the curve is everywhere continuous and nowhere differentiable.http://dx.doi.org/10.1155/2019/6745202 |
| spellingShingle | Guangjun Yang Xiaoling Yang Ping Wang Arithmetic-Analytic Representation of Peano Curve International Journal of Mathematics and Mathematical Sciences |
| title | Arithmetic-Analytic Representation of Peano Curve |
| title_full | Arithmetic-Analytic Representation of Peano Curve |
| title_fullStr | Arithmetic-Analytic Representation of Peano Curve |
| title_full_unstemmed | Arithmetic-Analytic Representation of Peano Curve |
| title_short | Arithmetic-Analytic Representation of Peano Curve |
| title_sort | arithmetic analytic representation of peano curve |
| url | http://dx.doi.org/10.1155/2019/6745202 |
| work_keys_str_mv | AT guangjunyang arithmeticanalyticrepresentationofpeanocurve AT xiaolingyang arithmeticanalyticrepresentationofpeanocurve AT pingwang arithmeticanalyticrepresentationofpeanocurve |