Hence, the projection is continuous and compact.
It follows from (14) that R=L −T L −1 and hence, the projection is determined by the Cholesky factor of the covariance matrix R. Squaring (13), we have l^{2} = mathbf{u}^{T} mathbf{Ru}, (15).
Then, by Lemma 3.1, the folding point is actually inside V, hence its projection on the first coordinate (z/a) belongs to (U') so it is bounded away from the critical points of p (and the bound is independent of a).
Nick Kounis, economist at ABN Amro, said: "The IMF's report on Greek debt makes grim reading but its growth assumptions are too optimistic, hence debt projections are too low".
However, the projected increase in winter precipitation across the mid- and high-latitude regions [2] makes the timing of modeled snowmelt, and hence future projections of phenological shifts, uncertain [76].
Hence, some projections of the future cancer burden assume that the global cancer incidence rates will remain constant over time and that the number of cancer cases and deaths will be affected only by growth and aging of the population.
Hence, (generalized) gradient projection method (GGPM) based on the Rosen gradient projection method [23] has been developed for solving inequality constrained optimization problems.
If E = H, a Hilbert space, J is the identity mapping, and hence the Bregman projection P C f ( x ) reduces to the metric projection of H on to C, P C ( x ).
Hence, noting the projection inequality (2.3), we obtain (3.9).
Hence, from the projection theorem of the Hilbert spaces ξ ^ WL ( t ) = η ( t ) a.s.s
