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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...

A novel approach to the evaluation of interface roughness scattering form factor in intersubband transitions

Nguyen Thanh TienPham Thi Bich ThaoLe Tuan — 2014

Nanoscale Systems: Mathematical Modeling, Theory and Applications

We propose a modification of the interface roughness (IFR) scattering form factor in intersubband transitions.We properly derived a formula for the form factor for IFR scattering in terms of the integrals of the envelope wave functions. This novel form factor is more global nature than the old one (proposed by Ando) and may be suitable for a wide range of applications. In this paper, we calculate and compare the absorption linewidth with the application of the old form factor and novel one. In different...

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