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The effective impedances of infinite ladder networks and Dirichlet problem on graphs (2004.09284v1)
Published 20 Apr 2020 in math.CO, math-ph, and math.MP
Abstract: We calculate effective impedances of infinite $LC$- and $CL$- ladder networks as limits of effective impedances of finite network approximations, using a new method, which involves precise mathematical concepts. These concepts are related to the classical differential operators on weighted graphs. As an auxiliary result, we solve a discrete boundary value Dirichlet problem on a finite ladder network.
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