Let Q : [C.sub.R](K) [right arrow] [C.sub.R](L) denote the restriction map
and [??] : X [right arrow] [C.sub.R](L) be defined by [??](a) = Q [omicron] T(a + [parallel]a[parallel][e.sub.0]) - Q [omicron] T([parallel]a[parallel][e.sub.0]), a [member of] X.
Soykan, "Restriction maps," International Journal of Mathematical Analysis, vol.
Soykan, "Restriction maps on the Hardy spaces of the unit disc," International Journal of Mathematical Analysis, vol.
Figure 1 represents the construction of a comprehensive restriction map
of this clone.
induced by the restriction map
, where [T.sub.F] is a maximal torus of [G.sub.F] and W is the Weyl group [N.sub.[G.sub.F]]([T.sub.F])/[T.sub.F].
Then there is a unique section [??] to the restriction map
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that the mod 2 reduction of the section is [sigma].
Using the above notation, the restriction map
from [H.sup.0] (X,M(D)) to [H.sub.0] (D, M(D) [|.sub.D]) is an isomorphism, for all D and M(D) in the following table:
We say that Y is linearly defined in X with respect to [L.sub.1],..., [L.sub.r] if the restriction map
[Mathematical Expression Omitted] is surjective and its kernel is generated as an ideal by elements of total degree 1.
The Red polygon in figure (3.B) indicated the restriction for the existing dumping site at Mehmood Booti Lahore whereas figure 3 (C, D and E) depicted the restriction maps
for the roads, water bodies and tube wells, respectively.
of the ITS1 sequences were done using the software Primer-Premier.
These mutations were mapped to specific regions on either of the two restriction maps
. Using these data, gene trees depicting the most parsimonious phylogeny of the mtDNA haplotypes were empirically derived (Avise 1989).
Evolutionary inferences from restriction maps
of nine taxa of Xenopus frogs.