Through their employment in combinatorics on one hand and connection to the Yang-Baxter equation on the other, Rota-Baxter algebras found their way into mathematical physics, in particular the renormalisation
of quantum field theories  and, most recently, integrable systems .
This proposal formulates several advancements and developments for the theoretical and computational study of continuous quantum systems, gauge theories and exotic quantum phases, but also for establishing the intricate relation between entanglement, renormalisation
and geometry in the context of the holographic principle.
We are asking whether allowing e-cigarettes to be used in enclosed public spaces contributes to the renormalisation
of smoking and whether e-cigarettes act as a gateway product introducing a new generation to an addictive and harmful habit.
k] [not equal to] 0 are small radii of circles centered at [rho] = 0 when G is divergent at [rho] = 0 and a special renormalisation
procedure has to be applied.
Transport equations for variables k and [epsilon] in the RNG k-[epsilon] model, which is derived from Navier-Stokes equations using the renormalisation
group theory (Yakhot, Orszag 1986) can be written as:
The constants in the obtained asymptotics involve some rationnal-valued intersection numbers whose generating function, up to some renormalisation
, satisfy Painleve's equation I([d.
Therefore, the renormalisation
group (RNG) k-[epsilon] model was used in the CFD simulation.
There was significant renormalisation
of the biochemical parameters of liver functions after 30 days of treatment with the herbal formulation.
Schindler  describes a further method that allows byte-by-byte output from the renormalisation
loop, based upon the loop guard R [is less than] [2.
This is to the extent that they defeat not only ""standard"" stochastic PDE techniques (as developed by Da Prato / Zabczyk / RE[micro]ckner / Walsh / Krylov / etc), but also more recent approaches based on Wick renormalisation
of nonlinearities (Da Prato / Debussche / etc).
Thereby a revised renormalisation
procedure is applied to make this divergence result in a finite net integrated charge.