We discuss the defective intertwining property of generators of semigroups.
We give a plane graph to characterize the intertwining property of basins of attraction of the dynamical systems.
In fact, if system (2.1) has the intertwining property at the point p, which is a regular point since there exist no equilibria in X ∖ A 1 ∪ A 2 ∪ { O }, then the orbit pR is contained in α ( q ).
Then system (2.1) has the intertwining property if the α-limit set α ( q ) of q ∈ ∂ W 1 s ( O ) ∖ { O } (or ∂ W 2 s ( O ) ∖ { O } ) is at least two common points.
There exist no equilibria in X ∖ A 1 ∪ A 2 ∪ { O } if system (2.1) has the intertwining property if and only if the α-limit set α ( q ) of q ∈ ∂ W 1 s ( O ) ∖ { O } (or ∂ W 2 s ( O ) ∖ { O } ) is at least two common points.
We say that { B i } i = 1 n has an intertwining property at a point p ∈ ⋂ i = 1 n ∂ B i, provided: (1) p is inaccessible from { B i } i = 1 n ; (2) for each arc ς in { B i } i = 1 n from p to a point x ∈ B i for some i ∈ { 1, 2, …, n }, then ς ∩ B j = ∅ holds for every j ∈ { 1, 2, …, n }. .
Because species locations are so intertwined with geophysical properties, many current conservation areas chosen for a single population of a rare species, an unusual community type, or a taxonomic hotspot, already represent unique combinations of geophysical factors (e.g. serpentine barren or limestone fen) that benefit many species.
Although these properties are likely intertwined with transformation at some level, their individual contributions remain largely unknown.
The mechanical properties of arrays of curved, intertwined, but nominally vertical carbon nanotubes (CNTs), referred to as turfs, have been measured using nanoindentation.
This property, which easily follows from the intertwining relation (21) for Heisenberg Weyl operators, is essential in our context, since our aim is precisely to show how symplectic covariance properties provide a powerful tool for the study of transformations of Gabor frames.
