Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families
Two-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex body K is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on K. These regio...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2016/4873276 |
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| author | Marco Longinetti Paolo Manselli Adriana Venturi |
| author_facet | Marco Longinetti Paolo Manselli Adriana Venturi |
| author_sort | Marco Longinetti |
| collection | DOAJ |
| description | Two-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex body K is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on K. These regions are bounded by arcs of involutes of ∂K and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self-contracting sets (with opposite orientation) are considered: necessary and/or sufficient conditions for them to be subsets of SDC are proved. |
| format | Article |
| id | doaj-art-186265bc24294aa6bdfa898cf93fb901 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-186265bc24294aa6bdfa898cf93fb9012025-02-03T05:51:39ZengWileyJournal of Applied Mathematics1110-757X1687-00422016-01-01201610.1155/2016/48732764873276Bounding Regions to Plane Steepest Descent Curves of Quasiconvex FamiliesMarco Longinetti0Paolo Manselli1Adriana Venturi2Dipartimento di Matematica e Informatica Ulisse Dini, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, ItalyDipartimento di Matematica e Informatica Ulisse Dini, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, ItalyDipartimento GESAAF, Università degli Studi di Firenze, Piazzale delle Cascine 15, 50144 Firenze, ItalyTwo-dimensional steepest descent curves (SDC) for a quasiconvex family are considered; the problem of their extensions (with constraints) outside of a convex body K is studied. It is shown that possible extensions are constrained to lie inside of suitable bounding regions depending on K. These regions are bounded by arcs of involutes of ∂K and satisfy many inclusions properties. The involutes of the boundary of an arbitrary plane convex body are defined and written by their support function. Extensions SDC of minimal length are constructed. Self-contracting sets (with opposite orientation) are considered: necessary and/or sufficient conditions for them to be subsets of SDC are proved.http://dx.doi.org/10.1155/2016/4873276 |
| spellingShingle | Marco Longinetti Paolo Manselli Adriana Venturi Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families Journal of Applied Mathematics |
| title | Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families |
| title_full | Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families |
| title_fullStr | Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families |
| title_full_unstemmed | Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families |
| title_short | Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families |
| title_sort | bounding regions to plane steepest descent curves of quasiconvex families |
| url | http://dx.doi.org/10.1155/2016/4873276 |
| work_keys_str_mv | AT marcolonginetti boundingregionstoplanesteepestdescentcurvesofquasiconvexfamilies AT paolomanselli boundingregionstoplanesteepestdescentcurvesofquasiconvexfamilies AT adrianaventuri boundingregionstoplanesteepestdescentcurvesofquasiconvexfamilies |