Đề tài " The Parisi formula " pdf

... write µ  (f)=E  V 1 ···V −1 γ ⊗2  (f)  . As in the case of Theorem 2.1, we obtain η  (v)=I+  0≤p≤κ II(p),(3.27) Annals of Mathematics The Parisi formula By Michel Talagrand THE PARISI FORMULA 239 where I= √ t 2N √ v E  T  R 1,2 =u (H(σ 1 )+H(σ 2 )) ... relies on the same principles as the proof of Theorem 2.1. The main new feature is that new terms ar...

Ngày tải lên: 29/03/2014, 07:20

... p k (a), the sphere ˜ S(y k ,θ ∗ k ) touches the sphere ˜ S σ(a) at p k (a). If some sphere touches the intersections of spheres, then the touching point belongs to the great sphere passing through the ... Γ ψ (Y ) are of degree 3, then the sum of the degrees equals 15, i.e. is not an even number. There exists only one type of Γ ψ (Y ) with these conditions (Fig. 6). The len...

Ngày tải lên: 06/03/2014, 08:21

... ty Rượu Bia Miền Nam Nhà máy Bia Chợ Lớn Nhà máy Bia Sài Gòn

Ngày tải lên: 15/03/2014, 01:20

... (a r ) t∈T α ,   n i=1 a γ i y α γ i ≤  t∈T α a t y α t . Furthermore, each Y α will K-embed into Y . Just as in the proof of Theorem 7, it then follows from index theory that the Banach space spanned by (x i ) ∞ i=1 embeds ... , the Lipschitz distance d L (X, Y ) between them is defined to be the infimum of Lip (f) · Lip (f −1 ), where the infimum is taken over all biLipschitz m...

Ngày tải lên: 15/03/2014, 09:20

... just the limiting direction of the geodesic, while w and − ˆ Ξ, which are constant under the flow, give the initial conditions of the geodesic. 3.5. Fibred scattering structure. There is yet another ... within the pencil and then Λ indicates how far along the geodesic one must travel to get to the initial point w. The direction Ξatw is the direction of that geodesic at w. H...

Ngày tải lên: 15/03/2014, 09:20

... Skeleton of the proof of the main Theorems 1.1 and 1.4 The purpose of this section is to give the skeleton of the proof of the main Theorems 1.1 and 1.4, but in the proofs referring forward to the remaining sections ... by Theorem 8.2(3), so the assumption of Theorem 2.2(1) is vac- uously satisfied. The assumption of Theorem 2.2(2) holds by the Obstruction Vanishing Theor...

Ngày tải lên: 22/03/2014, 20:21

... be the map corresponding to f ± under (9), then µ ± satisfies the conclusions of the theorem. Let L ± E ∈ Λ denote the p-adic L-functions defined by the first author in Section 6.2.2 of [Po]. These ... 461 Using the formulas of Theorems 3.2(iv) and 5.1 to compute the left-hand side, and Theorem 7.1 for the right-hand side, we deduce that if the order of χ is p n > 1 and ε =(...

Ngày tải lên: 28/03/2014, 22:20

... use the linear forms condition to control the left-hand side of (3.6) because the linear components of the forms x + h j are all the same. The correlation condition has been designed with the ... this generalization.) The following result is one of the main theorems of the paper. It asserts that for the purposes of Szemer´edi’s theorem (and ignoring o(1) errors), there i...

Ngày tải lên: 29/03/2014, 07:20