The mul function in operator (and the * operator) can take an integer k and a tuple and return a new tuple that consists of k copies of the tuple argument.
The main difficulty is that, for (pneq2), it is impossible for us to find a Green's function in the equivalent integral operator since the differential operator (D_{q,0^^{beta}varphi_{p} ( D_{q,0^^{alpha} ) ) is nonlinear.
However, for p ≠ 2, it is impossible for us to find a Green's function in the equivalent integral operator since the differential operator (ϕ p (u'))' is nonlinear.
We decompose the equilibrium distribution function in the BGK collision operator into ideal and non-ideal parts and employ second-order Chapman Enskog expansion for treatment of both parts.
Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values.
This relation is due to the existence of ∂2/∂V2 (the curvature of a function) in the Fokker-Planck operator, LFP, which makes higher eigenfunctions more oscillatory functions of V.
We take into account the gravitational effects, both variable permeability and porosity of porous medium, and explicit spatially varying capillary pressure, in the diffusive fluxes, and explicit spatially varying flux functions, in the hyperbolic operator.
If the car of that compound form is a symbol, that symbol is the name of an operator, and the form is either a special form, a macro form, or a function form, depending on the function binding of the operator in the current lexical environment.
Hμ denoting the regular part of the Green's function
