Titlebook: Discrete and Continuous Models in the Theory of Networks; Fatihcan M. Atay,Pavel B. Kurasov,Delio Mugnolo Book 2020 Springer Nature Switze

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,Stability Matters for Reaction–Diffusion–Equations on Metric Graphs Under the Anti-Kirchhoff Vertexnearity leading to a unique stable nonconstant stationary solution, there are classes of reaction-terms allowing only stable stationary solutions that are constant on each edge. For example, odd nonlinearities allow only such stable stationary solutions, in particular they only allow the trivial solution as stable one on trees.

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TIA742

An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interactfor the considered operator. Then, we exploit that the resolvent may be obtained by a Laplace transformation of the heat semi-group, and an application of a suitable inverse Watson lemma eventually delivers the small-. asymptotic expansion of the heat-kernel trace.

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Spectral Zeta Functions,ies, the Langlands program, Verlinde formulas, Riemann hypotheses, Catalan numbers, Dedekind sums, and hypergeometric functions. Several open-ended problems are suggested with the hope of stimulating further research.