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and (7.17) follows withµ = 0, b = Γ(1 α) cos(πα/2) > 0, β = 1.2) Let now1 < α < 2. ... 2+. 1 β. 2exp(b ex. ), (10.9). where, according to (2.9),β 1 andb = Γ(1 α) cos(πα/2) 1.

Second, if cos(ωa) = 0,then ω is one of the numbers (8) and. ... Bj=1. r=1. 1. r2. (2. B 1. )r cos(rθj)aj. , (24).

m. T. With. T. B. T. T. m. =. -. =. -. cos. sin. sin. cos. sin. sin. éq. 2.1-10. Displacements in physical space are obtained by the formula of Ritz:. ... cos. cos. cos. cos. &. cos. cos. cos. cos. X T.

cos. sin. =. éq 2.3.3.2-3. where. N. Yk. and. N. ... RN. m. One a:. (). (). N. K. K. K. =. 0. cos. sin. and. N. m. defined in a similar way.

A B min(λ1(A),λ1(B)) (1cos(θ)).with cos(θ) = maxψBker(B),ψAker(A) |〈ψA|ψB〉|. Thus if we can bound the gap of A (see Lemma 2.6 ... F(ρ0A,ρB(k)). 2(n 2)4(n 1). n(1 cos(2πk/D)). 4(n 1). This fidelity is clearly maximized for the lowest

0. 0. cos has. cos has. Z. 0. 0. 0. 0. ... 08/01/98. Author (S):. B. QUINNEZ. Key:. V2.03.002-C. Page:. 4/6. Manual of Validation.

2. cos. ,. ,. where. S. is the surface of the section. (). ... 2. 1. 1. 1. 1. 2. 2. exp. sin. cos. ,. µ. damping coefficient proportional. C. M. K. =. µ. (. ). µ. µ. 1. 0. 2. 2. 2. 0. 4. 4. 2.

Consider a, b Rn, and for all θ R let cθ = a sin θ b cos θ anddθ = a cos θ b sin θ. ... Ifeither n 3 or p 2 (or both) then B is nearly positive.

This reference covers the case where, in (1.4),σ = (σi,j)1i,jd is an invertible matrix with constant entries, b = (b. ... Applying twice the inequality (a b)2 12a2 b2 yields. dj=1. di=1.

O. O. O. O. O. O. (. cos (. ). sin (. )) /. cos. /. cos. /. sin. /. sin. /. 2. ... Fvent =. L Sin qo Q. Vvy Cos qo Q. Vvx Sin qo Q.