Show simple item record

dc.contributor.supervisor Prymak, Andriy (Mathematics) en_US
dc.contributor.author Radchenko, Danylo
dc.date.accessioned 2012-09-18T17:35:25Z
dc.date.available 2012-09-18T17:35:25Z
dc.date.issued 2012-09-18
dc.identifier.uri http://hdl.handle.net/1993/8871
dc.description.abstract In this work we study the following problem on constrained approximation. Let f be a continuous mapping defined on a bounded domain with piecewise smooth boundary in R^n and taking values in R^n. What are necessary and sufficient conditions for f to be uniformly approximable by C^1-smooth mappings with nonnegative Jacobian? When the dimension is equal to one, this is just approximation by monotone smooth functions. Hence, the necessary and sufficient condition is: the function is monotone. On the other hand, for higher dimensions the description is not as clear. We give a simple necessary condition in terms of the topological degree of continuous mapping. We also give some sufficient conditions for dimension 2. It also turns out that if the dimension is greater than one, then there exist real-analytic mappings with nonnegative Jacobian that cannot be approximated by smooth mappings with positive Jacobian. In our study of the above mentioned question we use topological degree theory, Schoenflies-type extension theorems, and Stoilow's topological characterization of complex analytic functions. en_US
dc.rights info:eu-repo/semantics/openAccess
dc.subject Approximation theory en_US
dc.subject Topological degree theory en_US
dc.title Orientation preserving approximation en_US
dc.type info:eu-repo/semantics/masterThesis
dc.degree.discipline Mathematics en_US
dc.contributor.examiningcommittee Kopotun, Kirill (Mathematics), Jafari Jozani, Mohammad (Statistics) en_US
dc.degree.level Master of Science (M.Sc.) en_US
dc.description.note October 2012 en_US


Files in this item

This item appears in the following Collection(s)

Show simple item record

View Statistics