infinity]](p')) as a function of water content, with a nonvanishing
The null hypersurface of such space-time admits a nonvanishing
Killing vector field, say l, which may or may not be the Killing vector field of the landing space-time.
However, it is well known that GCV and AIC-based methods are not consistent for model selection in the sense that as n [right arrow] [infinity], they may select irrelevant predictors with nonvanishing
probability [22, 36].
n] [right arrow] C is a complex valued Lebesgue integrable mapping, which is summable and nonvanishing
on each measurable subset of [R.
Indeed, the SM model predicts a nonvanishing
eddy viscosity when the flow is laminar and this results in more stable shear layers when the incoming flow is smooth.
both of which destroy the electron and proton Compton radii because the equations are nonvanishing
i+2,i+1] has at most three nonvanishing
entries, and the submatrix [K.
For a given system, in order to determine the stability of a solution, the only significant term in the return map is the first nonvanishing
term that makes it differ from the identity map.
There are two distinct cases with and without nonvanishing
modulo l of Fourier coefficients of half-integral weight modular forms, Duke Math.
On deciding nonvanishing
of a Littlewood-Richardson
Unfortunately, to ignore the nonvanishing
value of [C.