Zapraszamy na seminarium „Informatyka Stosowana i Modelowanie Matematyczne”, które odbędzie się w czwartek 12 czerwca 2022 w godzinach 13:15–14:45.

Seminarium odbędzie się wyłącznie w trybie stacjonarnym w sali E1/10.

Prelegentka: Anna Muranova, UWM.

Referat: Weighted graphs with edge weights from an ordered field

Streszczenie:

A weighted graph is a graph, whose each edge is given a positive weight. In classical theory of weighted graphs, this weight is a positive real number. We consider a more general weights, namely, we allow weights to be positive elements of arbitrary ordered field. We prove the existence and uniqueness of the solution of a Dirichlet problem on finite graphs and investigate some properties of infinite graphs. Classical weighted graphs are related to electrical networks with resistors. In the similar way, one can relate the weighted graphs over field of rational functions to electrical networks with coils, capacitors and resistors. The ordered field of rational functions is the most known non-Archimedean field. Its Cauchy completion is a Levi-Civita field R. Therefore, as an application, we consider some known infinite electrical networks (e.g. Feynman ladder) over R. 

No pre-knowledge on ordered fields is assumed in this talk. 

References: 
[1] Anna Muranova. On the notion of effective impedance. Operators and Matrices. Volume 14, Number 3 (2020), 723–741. 
[2] Anna Muranova. Effective impedance over ordered fields. J. Math. Phys. 62, 033502 (2021).

Serdecznie zapraszamy,
Mariusz Bodzioch, Aleksander Denisiuk, Mikhail Kolev, Ivan Matychyn.