Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families
Joint Authors
Longinetti, Marco
Manselli, Paolo
Venturi, Adriana
Source
Journal of Applied Mathematics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-07-27
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Longinetti, Marco& Manselli, Paolo& Venturi, Adriana. 2016. Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families. Journal of Applied Mathematics،Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1107204
Modern Language Association (MLA)
Longinetti, Marco…[et al.]. Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families. Journal of Applied Mathematics No. 2016 (2016), pp.1-17.
https://search.emarefa.net/detail/BIM-1107204
American Medical Association (AMA)
Longinetti, Marco& Manselli, Paolo& Venturi, Adriana. Bounding Regions to Plane Steepest Descent Curves of Quasiconvex Families. Journal of Applied Mathematics. 2016. Vol. 2016, no. 2016, pp.1-17.
https://search.emarefa.net/detail/BIM-1107204
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1107204