It has been proved by J . Cousty et al . that when the markers of the IFT corresponds to extrema of the weight function, the cut induced by the forest is a watershed cut.
22.
The infinities are not well-defined; but the finite values can be associated with the functions used as the weight functions to get the finite values, and that can be well-defined.
23.
However, it is well known that, in specific parameter ranges of the model under consideration, the oscillatory nature of the weight function can lead to a bad statistical convergence of the numerical integration procedure.
24.
For \ alpha = \ beta = 0, these are called the Legendre polynomials ( for which the interval of orthogonality is [ & minus; 1, 1 ] and the weight function is simply 1 ):
25.
The GJMS operator also represents the obstruction term to a formal asymptotic solution of the Cauchy problem for extending a weight function off the null cone in the ambient space to a harmonic function in the full ambient space.
26.
Many authors, particularly probabilists, use an alternate definition of the Hermite polynomials, with a weight function of e ^ {-x ^ 2 / 2 } instead of e ^ {-x ^ 2 }.
27.
Baxter's theorem states that the Verblunsky coefficients form an absolutely convergent series if and only if the moments of ? form an absolutely convergent series and the weight function " w " is strictly positive everywhere.
28.
If \ scriptstyle b ( k ) : \ mathbb { N } \ rightarrow \ mathbb { R } is a weight function that depends only on the size " k " of the cycle and for brevity we write
29.
The pole in the ( \ phi, V \ psi ^ { \ pm } ) from the Lippmann Schwinger equation reflects the time-uncertainty of the interaction, while that in the wavepackets weight function reflects the duration of the interaction.
30.
Another case where weight functions are especially useful is if the integrand is unknown but has a known singularity of some form, e . g . a known discontinuity or integrable divergence ( such as 1 / " " x " ) at some point.
