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Since order intervals are convex, we have (x_{1} preceq x_{2} preceq T(x_{1})).
(1) Since order intervals are convex, we have (x_{1} leq x_{2} leq T(x_{1})).
The few algorithms that handle colored sources require exact knowledge of the channel order, a drawback since order determination is a difficult issue.
Since order intervals are closed and convex, we conclude that (x_{n} leqomega), for any (n geq1), since ({x_{n}}) is a monotone increasing sequence.
This is reasonable since order one mass loss or heat source terms are supposed to induce significant order one changes in the density (and therefore in temperature).
First note that if (f leq g) holds, then we have (f leq lambda f + 1-lambda gg leq g) since order intervals are convex.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com