2026-09-22T08:53:56Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/72793 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Baryshnikov, Yuliy Schenck, Hal Baryshnikov, Yuliy Hirani, Anil Zharnitsky, Vadim Wang, Han 2015-01-21T19:48:15Z 2015-01-21T19:48:15Z 2014-12 2015-01-21 2014-12 The spaces of coverings (SoC) arise from various configuration spaces of the covering problems. We study the topology of these spaces for different domains and covering agents. In particular, we study the SoCs for grid domains and metric trees covered by balls. Characterizations of their topology are given for analysis of the topological complexities (the Betti numbers in all dimensions). We also study the spaces of fort coverings, a topological approximation of the SoCs capturing some essential features of the SoCs. The applications of the SoCs abound, in the end we present the feedback control on the SoC for metric tree coverage as a case study. Item withdrawn by Laura Spradlin (lspradl2@illinois.edu) on 2014-12-04T20:23:29Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Wang_Han.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5) Made available in DSpace on 2015-01-21T19:48:15Z (GMT). No. of bitstreams: 1 Han_Wang.pdf: 20911608 bytes, checksum: 8b1d6939749948747120b634f473fdab (MD5) http://hdl.handle.net/2142/72793 en Copyright 2014 Han Wang Covering Topology Configuration space Feedback Control On the topology of the spaces of coverings text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD