Proof Let Y be the respective one of the spaces c 0 or ℓ ∞, and take any a = ( a k ) ∈ X β.
Now, for every given x ∈ X, let y ∈ Y be an associated sequence space defined by (2.2), where Y is the respective one of the spaces c 0 or ℓ ∞.
Lemma 3.7 Let X be any of the spaces c 0 ( B ) or ℓ ∞ ( B ), let Y be the respective one of the spaces c 0 or ℓ ∞, Z be a sequence space and A = ( a n k ) be an infinite matrix.
Comparing each of these values with the respective ones of the BPT model, the estimates of the Poisson models are about two times larger than those of the BPT model.
The obtained acoustic insulation gain was then compared with the respective ones of traditional sound insulation products (e.g. glass wool and expanded polystyrene) and also with different alternative natural sound insulation products (e.g. kenaf, coco fibre, sheep wool, cork and cellulose).
With the great growth of interest in the field of nanochemistry, the study of nanocrystalline semiconductors has become increasingly important over a few decades due to their unique optical and electrical properties compared with the respective ones of bulk semiconductors [1, 2].
Compared with the respective ones of CdS QDs, whereas the λ 1 peak of d-Cu CdS (e-Cu:Cd-Cu CdSis some-Cu CdSd-shifte-Cu CdS (41) nm, the λ 2 and λ 3 peaks of d-Cu:CdS (e-Cu:CdS) QDs are hishly red-somewhatby 127 (130) and 180 (171) nm, respectively.
Applying an optimality criteria method to the relaxed problem, simulations give us numerical evidence that the original design problem admits classical solutions (i.e. there is no microstructure) and those are the same as the respective ones for the case of small deflections.
One- and two-year probabilities of death with mention of HCC subsequent to first-time hospitalisation for HCC were 53 and 58%, respectively; the respective one- and two-year probabilities of death from any cause were 62 and 70%.
If one replaces the respective one parameter semigroups of generalized Lipschitzian mappings in Theorems 3.1 and 3.2 with respective semigroups of iterates of generalized Lipschitzian mappings, then one can immediately derive the following two corollaries.
I actually cried and cheered when Idol almni Fantasia Barrino, Ruben Studdard, and inaugural winner, Kelly Clarkson, snagged their respective crowns on one of television's longest-running and most successful talent competitions.
