Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications
We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which ne...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/4030658 |
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| author | Soo Hwan Kim |
| author_facet | Soo Hwan Kim |
| author_sort | Soo Hwan Kim |
| collection | DOAJ |
| description | We introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space. |
| format | Article |
| id | doaj-art-5a363a76a79c4b0d97530dd3294e31f2 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-5a363a76a79c4b0d97530dd3294e31f22025-02-03T00:58:53ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/40306584030658Stability of the Cauchy Additive Functional Equation on Tangle Space and ApplicationsSoo Hwan Kim0Department of Mathematics, Dong-eui University, Busan 614-714, Republic of KoreaWe introduce real tangle and its operations, as a generalization of rational tangle and its operations, to enumerating tangles by using the calculus of continued fraction and moreover we study the analytical structure of tangles, knots, and links by using new operations between real tangles which need not have the topological structure. As applications of the analytical structure, we prove the generalized Hyers-Ulam stability of the Cauchy additive functional equation fx⊕y=fx⊕fy in tangle space which is a set of real tangles with analytic structure and describe the DNA recombination as the action of some enzymes on tangle space.http://dx.doi.org/10.1155/2016/4030658 |
| spellingShingle | Soo Hwan Kim Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications Advances in Mathematical Physics |
| title | Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications |
| title_full | Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications |
| title_fullStr | Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications |
| title_full_unstemmed | Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications |
| title_short | Stability of the Cauchy Additive Functional Equation on Tangle Space and Applications |
| title_sort | stability of the cauchy additive functional equation on tangle space and applications |
| url | http://dx.doi.org/10.1155/2016/4030658 |
| work_keys_str_mv | AT soohwankim stabilityofthecauchyadditivefunctionalequationontanglespaceandapplications |