| 研究実績の概要 |
The research activities have been adapted to the COVID-19 context, and have been centered on the following 3 topics:
1) With N. Tsuzu, we investigated the spectral and scattering theory of operators acting on topological crystals perturbed by infinitely many new edges. The setting of topological crystals corresponds to the most general framework for studying discrete periodic structures and their perturbations. The results have already been published.
2) With R. Tiedra de Aldecoa we have introduced a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. The framework is general enough for accommodating evolution groups generated by self-adjoin operators or dynamical systems generated by iteration of a fixed unitary operator. The result of these investigations have been submitted for publication.
3) With T. Miyoshi, Q. Sun, C. Sun, and N. Tsuzu, we have completed the investigations on a new approach for computing the effective reproduction number based on data assimilation. This reproduction number plays a key role in the propagation of epidemics, and our results have directly been applied to the current COVID-19 epidemic. Two papers have been submitted for publication, and one has already been accepted.
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