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Microsoft Word - Atolani_30112011_proof.doc

Kigelia pinnata root-oil composition KPRH; UV (Hexane) λmax (log ε) 426 (3.4), 419.5 (3.4), 348.5 (4.0), 305.5 (4.0), 250.5 (2.3) nm; IR υmax 3429, 3007, 2955, 2854, 1743, 1710, 1465, 1379, 1166, 1100- [...] Area Base Peak KRI 1. Undecane C11H24 11.145 0.24 422353 57 1115 2. 3,3-Dimethyl-hepta-4,5-dien-2-one C9H14O 12.772 0.49 876643 95 NA 3. Tridecane C13H28 13.647 0.25 452824 57 1313 4. (R)-(-)-14-Methyl- [...] obtained from Sigma-Aldrich (Germany), Folin- Ciocalteu, reagent, Na2CO3, aluminium chloride, potassium acetate, phosphate buf- fer, K3Fe(CN)6, trichloroacetic, acid (TCA), ferric chloride, HCl, Dragendorff's …

are given by {±ei,±2ei,±ei ± ej : 1 ≤ i, j ≤ q}. In this case we have 3 classes of roots (c.f. Example 4.3(3)) which correspond to 3 different root spaces in the root space decomposition (41). These roots [...] Propo- sition 6.3 for all p > 2q − 1, ∣∣∣E(ϕp λ/ √ n−iρ(S̃ p n))− ( 1− i〈λ,mp 1(µ)〉√ n −λm p 2(µ)λt 2n )∣∣∣ (87) ≤ ∑ l∈Nq ,|l|=3 mp l (µ) λl11 ...λ lq q l1!...lq! ≤ 1 n3/2 ∑ l∈Nq ,|l|=3 (m̃l(µ) + C/ √ p) [...] ≤ K1 ‖λ‖3 ∞ n3/2 (88) for some constant K1 > 0 which is independent of p. Analogously, for all p > 2q−1, (89) ∣∣∣∣ei〈λ,√nmp1(µ)〉 − ( 1 + i〈λ,mp 1(µ)〉√ n − 〈λ,m p 1(µ)〉2 2n )∣∣∣∣ 6 K2 ‖λ‖3 ∞ n3/2 for some …

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