Đề tài " Lagrangian intersections and the Serre spectral sequence " ppt

... Mathematics Lagrangian intersections and the Serre spectral sequence By Jean-Franc¸ois Barraud and Octav Cornea* LAGRANGIAN INTERSECTIONS AND THE SERRE SPECTRAL SEQUENCE 675 generic ... given by the S ∗ (E k )’s. The spectral sequence associated to this filtration is, by definition, the Serre spectral sequence of the statement [35]....

Ngày tải lên: 22/03/2014, 20:20

... [29, §6]) together with the maximal ergodic theorem for U ab as in (9) in Section 2.1. 3. More about entropy and the high entropy case A well-known theorem by Ledrappier and Young [19] relates the entropy, the ... κ(x, x  ) −1 . The additional statement in the parenthesis follows similarly, the only difference being the use of a slightly different value for θ in both cases,...

Ngày tải lên: 15/03/2014, 09:20

... H q should then attract poles and zeros of the “nearby” meromorphic H q . The following result partly justifies the latter: Theorem 2.3. Let |q k | =1,k ≥ 1, and assume that (2.8) lim k→∞ q k = q. (a) Then ... H q (z). The crucial point in the last line is that the convergence takes place away from the zeros of both G q (z) and G q (βqz). The zeros of G q (βqz) need not b...

Ngày tải lên: 22/03/2014, 15:21

... H ⊂ H 3 , and H corresponds to D ⊂ S 2 . The hyperbolic metric on H is isometric to the Poincar´e metric on D, and the isometry induces the identity on the common boundary ∂D = ∂H. The relative ... G, on the other hand, lies entirely above the upper arc. The dotted line indicates the boundary of D. Now ∆ log ρ D = ρ D 2 and ∆ log ρ Ω = ρ Ω 2 . Here ∆ is the euclide...

Ngày tải lên: 22/03/2014, 16:20

... ε k  A∈J δ A . Therefore the result follows by induction on |J \ J 1 | and the triangle inequality (and the fact that ε k = ε). If we now consider the case when J 1 is empty, then we obtain the following corollary, ... map from the vertex set of Γ to the set X ∪ Y ∪ Z ∪ T. And the product of all the terms involving G is telling us whether a particular assignment to th...

Ngày tải lên: 22/03/2014, 20:21

... get 2mq +2p intersections of α and γ. To count self -intersections one must count the intersections of the graph of u(x) = sin(2π p q x) wrapped up on the cylinder Γ = (R/Z) × R, i.e. the intersections ... of the equator ±ζ, the great circle through (x,  ξ) intersects the equator in two points. In one of these intersections the great circle crosses the equator f...

Ngày tải lên: 29/03/2014, 07:20

... this and the endogeneity problem, Arellano and Bond propose using the lagged values of the levels of the variables as instruments. Under the assumptions that there is no serial correlation in the ... differences and levels, with the moment conditions in (11) applied to the first part of the system, the regressions in differences, and the moment conditions in (13)...

Ngày tải lên: 27/01/2014, 11:20

... Proofs of the main theorems Now we are ready to prove the main theorems. We first note that the theorems can be reduced to the ones in the real analytic category by approx- imations. The key fact ... ∆ b is the sub-Laplacian, R and A 11, 11 are respectively the scalar curva- ture and the second covariant derivative of the torsion of the Tanaka-Webster connection for θ...

Ngày tải lên: 16/02/2014, 05:20

... degree m and n, respectively. Therefore, they are smooth, irreducible and they transver- sally intersect each other in mn points. Consider the surfaces: X 1 = D 1 × P 1 and X 2 = D 2 × P 1 . The union ... and there are two irreducible components X 1 and X 2 meeting along a conic. If there are THE K 2 OF DEGENERATIONS OF SURFACES 361 other components, then there is a component...

Ngày tải lên: 16/02/2014, 06:20

... tangential vector of the curve  at ˆx. Then all ξ 1 ,ξ n ,ζ 1 , and ζ n > 0. Let θ 1 denote the 1002 NEIL S. TRUDINGER AND XU-JIA WANG angle between ξ and ζ at ˆx, and θ 2 the angle between ξ and the x 1 -axis. ... on the boundary. By the C 1,α estimate (Lemma 3.5) and the equation itself, we can then infer a continuity estimate for D 2 u on the boundary. Howev...

Ngày tải lên: 16/02/2014, 06:20