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DTSTART;TZID=America/Chicago:20241004T123000
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DTSTAMP:20260421T003917
CREATED:20240925T143928Z
LAST-MODIFIED:20240925T143928Z
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SUMMARY:Graduate Student Colloquium: Jillian Cervantes
DESCRIPTION:(t\,r) Broadcast Domination of the Truncated Square Tiling Graph\nJillian Cervantes\nGraduate Student\nUniversity of Wisconsin – Milwaukee \nThis talk will introduce graph domination theory and a generalization called (t\,r) broadcast domination. We study a family of graphs that arise as a finite subgraph of the truncated square tiling\, which utilizes regular squares and octagons to tile the Euclidean plane. For positive integers m and n\, we let Hm\,n be the graph consisting of m rows of n octagons (cycle graph on 8 vertices). For all t ≥ 2\, we provide lower and upper bounds for the (t\, 1) broadcast domination number for Hm\,n for all m\, n ≥ 1. We give exact (2\, 1) broadcast domination numbers for Hm\,n when (m\, n) ∈ {(1\, 1)\, (1\, 2)\, (1\, 3)\, (1\, 4)\, (2\, 2)}. We also consider the infinite truncated square tiling\, and we provide constructions of infinite (t\, r) broadcasts for (t\, r) ∈ {(2\, 1)\, (2\, 2)\, (3\, 1)\, (3\, 2)\, (3\, 3)\, (4\, 1)}. Using these constructions we give upper bounds on the density of these broadcasts i.e.\, the proportion of vertices needed to (t\, r) broadcast dominate this infinite graph. We end with some directions for future study
URL:/math/event/graduate-student-colloquium-jillian-cervantes/
LOCATION:EMS Building\, Room E495\, E495; 3200 N Cramer St.\, Milwaukee\, WI\, 53211\, United States
CATEGORIES:Graduate Student Colloquia
ORGANIZER;CN="The Department of Mathematical Sciences":MAILTO:math-staff@uwm.edu
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CREATED:20240826T192136Z
LAST-MODIFIED:20240828T152858Z
UID:10016168-1728050400-1728055800@uwm.edu
SUMMARY:Colloquium: Dr. Zhaosheng Feng
DESCRIPTION:Parabolic System of Aggregation Formation in Bacterial Colonies\nDr. Zhaosheng Feng\nEndowed Chair Professor of Mathematics\nUniversity of Texas Rio Grande Valley \nThe goal of this talk is to study a fourth-order nonlinear parabolic system with dispersion for describing bacterial aggregation. Analytical solution of traveling wave is found by taking into account the dispersion coefficient. Numerically\, we demonstrate that the initial concentration of bacteria in the form of a random distribution over time transforms into a periodic wave\, followed by a transition to a stationary solitary wave without dispersion.
URL:/math/event/colloquium-zhaosheng-feng/
LOCATION:EMS Building\, E495\, 3200 N Cramer St\, Milwaukee\, WI\, United States
CATEGORIES:Colloquia
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