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On stability and robust stability of positive linear Volterra equations in Banach lattices

Satoru MurakamiPham Ngoc — 2010

Open Mathematics

We study positive linear Volterra integro-differential equations in Banach lattices. A characterization of positive equations is given. Furthermore, an explicit spectral criterion for uniformly asymptotic stability of positive equations is presented. Finally, we deal with problems of robust stability of positive systems under structured perturbations. Some explicit stability bounds with respect to these perturbations are given.

Spanning trees whose reducible stems have a few branch vertices

Pham Hoang HaDang Dinh HanhNguyen Thanh LoanNgoc Diep Pham — 2021

Czechoslovak Mathematical Journal

Let T be a tree. Then a vertex of T with degree one is a leaf of T and a vertex of degree at least three is a branch vertex of T . The set of leaves of T is denoted by L ( T ) and the set of branch vertices of T is denoted by B ( T ) . For two distinct vertices u , v of T , let P T [ u , v ] denote the unique path in T connecting u and v . Let T be a tree with B ( T ) . For each leaf x of T , let y x denote the nearest branch vertex to x . We delete V ( P T [ x , y x ] ) { y x } from T for all x L ( T ) . The resulting subtree of T is called the reducible stem of T and denoted...

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