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Maximal buttonings of trees

100%

Short I.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 2

415-420

A buttoning of a tree that has vertices v1, v2, . . . , vn is a closed walk that starts at v1 and travels along the shortest path in the tree to v2, and then along the shortest path to v3, and so forth, finishing with the shortest path from vn to v1. Inspired by a problem about buttoning a shirt inefficiently, we determine the maximum length of buttonings of trees

Estimates of the Transition Densities for the Reflected Brownian Motion on Simple Nested Fractals

86%

Olszewski M.

Probability and Mathematical Statistics

2019

tom Vol. 39, Fasc. 2

423--440

We give sharp two-sided estimates for the functions gM (t, x, y) and gM (t, x, y) − g(t, x, y), where gM (t, x, y) are the transition probability densities of the reflected Brownian motion on an M-complex of order M ∈ Z of an unbounded planar simple nested fractal and g(t, x, y) are the transition probability densities of the “free” Brownian motion on this fractal. This is done for a large class of planar simple nested fractals with the good labeling property.