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These are then shown to be equal to 1 which is a well known result [23]. In fact, it is shown in [16] that the calculations in [51] are justified for the 1-point Green’s function. Remark 18. Formula (55) also holds for the case where vr ’s are all equal to 0. Then R1 (z) = 0. Therefore a contour integration leads to da Sm (a + ı , a − ı ) e = R 1 2πı B dd q 1 |∇q E0 (q)|2 d (2π) 2ı ∼ ↓0 −1 . Comparison with Theorem 10 shows that σdiff (R) = 1 as expected for free particles. Remark 19. The two other integrable models considered by Khorunzhy and Pastur [47] have a conductivity measure which is absolutely continuous with respect to the Lebesgue measure on R2 [47, Eq.

X. Zhong, J. Bellissard and R. Mosseri, “Green function analysis of energy spectra scaling properties”, J. Phys: Condens. Matter 7 (1995) 3507–3514. THEORY OF CONNECTIONS ON GRADED PRINCIPAL BUNDLES T. fr Received 26 December 1996 Revised 12 May 1997 1991 Mathematical Subject Classification: 58A50, 53C15 The geometry of graded principal bundles is discussed in the framework of graded manifold theory of Kostant–Berezin–Leites. We first review the basic elements of this theory establishing at the same time supplementary properties of graded Lie groups and their actions.

As this holds for any neighborhood of ω, ω ∈ Ωnw ˆ . H w nw Now either ω0 ∈ ΩHˆ or ω0 ∈ ΩHˆ . In the first case, Orb(ω0 ) ⊂ Ωw ˆ . According H nw ∞ and Ω = Ω . To deal with the second case, let to the above, Orb(ω0 ) = Ωw ˆ ˆ ˆ H H H us choose a metric on Ω compatible with the topology of Ω. Open balls of radius r around ω ∈ Ω are denoted by B(ω, r). Because ω0 ∈ Ωnw ˆ , there exists for any H 1 1 d ak k ∈ N an ak ∈ Z∗ such that B(ω0 , k ) ∩ T B(ω0 , k ) = ∅. Therefore the sequence ∞ T ak ω0 converges to ω0 .

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Physics Letters B vol 57 by Elsevier

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