In this paper, we introduce a weight function
[w.sub.L](k; x) in (8) whose values cluster to 0 for x < L/2 and to 1 for x > L/2 when k is large enough.
We shall call the generalised halfspace depth with the band weight function
the band depth.
Let m* be any weight function
satisfying m*(N, M) [less than or equal to] [C.sub.N] re(M) for all M, N [member of] [Z.sup.2d].
Here the two step iterative method (7) is considered with new weight function
given by (6).The order of convergence is analyzed in the following Theorem.
Proposition 3 If for a given graph G and a weight function
w there exists a compact circular r-coloring, where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], then there exists a compact r-coloring of (G, w).
The weight functions
vary with one or more factors and may be more robust than the drilling factors employed in the MRI, but the weights are not calibrated with drilling data.
The above described weight function
method has been adopted for a total 13 number of large scale landslides (volume more than 10million cubic meters).
[f.sub.is]--spatial irregularity weight function
of ith form.
In particular, the differentiation matrices should at least differentiate the weight function
[Alpha](x) perfectly (in exact arithmetic, that is).
When it used to deal with discontinuous interface problems such as crack, its base function, weight function
argument and approximate function etc.
(1.2) [w.sub.1](x; [alpha]) = - log(1 - [alpha][e.sup.|x|]) on [-[infinity],[infinity]], 0 < [alpha] < 1, is what may be called the generalized Binet weight function
. We are interested in the poly-nomials orthogonal with respect to the weight functions
(1.1) and (1.2), in particular, in the recurrence formulas