Note that for the cases M = 2 and M = 3, both changes of variables and transformed PDEs
are obtained from (2.3) and (2.4) by considering only variables [y.sub.1] and [y.sub.2] or [y.sub.1], [y.sub.2] and [y.sub.3], respectively.
Similar to ODEs, any first-order PDE
with one dependent and two independent variables, in the form
From the PDEs
(2)-(6), if the volatility falls into the exercise region V [member of] [0, [V.sub.f]([tau])] for [tau] [member of] [0, [infinity]), then the value of American volatility put is given by P(V, [tau]) = K - V, and we can verify that it is equivalent to the following PDE
The Boundary Value Methods have been used to approximate second-order PDEs
. This has been achieved by using the Lanczos-Chebyshev reduction technique to transform the PDEs
into an equivalent second-order system.
Both the inducible nitric oxide synthase (iNOS) and the PDEs
enzymes are expressed in numerous cell types including macrophages, dendritic cells, T cells, and neutrophils [15, 16].
Future work could also include adding physiological or biological complexity to the coupled PDEs
. For example, instead of choosing the proliferation rate as a constant, it could depend on the size of the tumor [4, 26, 27]; thus the growth term can be represented by the logistic or Gompertz growth.
The EDP1-001(1) extract was further investigated for acute oral toxicity in male mice because it gave the highest activity of PDEs
inhibition and high NO release stimulation activity with no cytotoxicity in the EA.hy926 cells (Table 4).
Among a wide variety of image noise removal methods two important classes of techniques are variational regularization and partial differential equation (PDE
) based filters .
These results indicate that BFBO significantly potentiates relaxations induced by cyclic nucleotide-elevating agents, suggesting that BFBO might stimulate the formation of cyclic GMP and/or cyclic AMP, and/or possibly also, decrease their degradation by inhibiting PDEs
The mathematical analysis of these PDEs
remains to be done.
These guidances, in turn, expand on earlier methodologies for setting OELs or PDEs
, first-in-human doses for pharmaceuticals, acceptable or tolerable daily intakes (ADIs or TDIs) for additives and/or contaminants in food and/or drinking water, and reference doses and concentrations (RfDs, RfCs) for chemicals of environmental concern (Table 1).