Tài liệu Đề tài " The topological classification of minimal surfaces in R3 " pptx

... lie in the same pair of pants or in the punctured copy of ∂ − H. If the two endpoints of the bad arc coincide with the two endpoints of another bad arc, then let d(k) = 0. If both arcs lie in the ... cycle of Γ disjoint from HP i in the desired region. There are two cases. 1. The two endpoints of k lie in the same boundary component of the same pair...

Ngày tải lên: 16/02/2014, 06:20

... 76 80 81 82 CONTENTS 14 15 Water is crucial for all aspects of life, the defining feature of our planet. Ninety seven and a half per cent of all water is found in the oceans, of the remaining freshwater only one per cent ... dazzling array of services – food, medicines, recreational amenity, shoreline protection, processing our waste, and sequestering carbon. At the be...

Ngày tải lên: 17/02/2014, 10:20

... obtained by reflecting Q λ in a line of slope −1.) Theorem 2. Let K(λ) be the set of nonergodic directions that can be obtain using Lemma 1.1. If λ is Diophantine, then H.dim K(λ)=1/2. Proof of Theorem ... attached to the lower edge of the slit in the other, and similarly for the remaining edges. The induced map π : X λ → T is the branched double cover obtained by mak...

Ngày tải lên: 14/02/2014, 17:20

... and generalization of the proof of Proposition 3 in [3]. We outline the main steps, while skipping the details. Step 1. One of the basic ingredients in the proof in [3] is to approximate the volume of the Wiener ... second term on the right-hand side of the analogue of (2.93). 4. Proof of Theorem 3 In Sections 4–6 we prove Theorems 3–5. The proof foll...

Ngày tải lên: 14/02/2014, 17:20

... by the removal of D from Z d . 5. Proofs of main results Proof of Theorem 1.1. Denote m =  d−1 4 . By applying Corollary 3.4 to m + 1 independent copies of the USF relation, and invoking Theorems 4.2 ... U(W; x, y) the intersection of U(W) with the event that the path connecting x, y in the USF is edge-disjoint from the oriented USF paths connecting the vertices...

Ngày tải lên: 14/02/2014, 17:20

... proof of uniquenss of the Q-system using an intermediate extension. We later obtained another proof based on 2-cohomology vanishing for the tensor category SU(2) k in [39]. An outline of the ... entries in the commutant of the unitary representations of SL(2, Z) arising from the Vi- rasoro net Vir c with c<1. Such modular invariants of the minimal models are...

Ngày tải lên: 14/02/2014, 17:20

... 8: The separation w for a multi-valued graph in (II.1.1). PLANAR DOMAINS 535 The main result of the next two sections is the following theorem (Γ 1 (∂) is the component of B 1 ∩ Γ containing ... boundary of an intrinsic ball is strictly convex. In this section we give similar estimates for half of normal tubular neighborhoods of curves lying in the intersection of...

Ngày tải lên: 14/02/2014, 17:20

... describe the general strategy behind the proofs of Theorems A and B. (1) We consider a certain set of nonregular parameters of full measure and describe (in a probabilistic way) the dynamics of the ... continuous way. Thus, loosely speaking, the domain of L i induces a persistent partition of the interval I i . STATISTICAL PROPERTIES IN THE QUADRATIC FAMILY 841 Al...

Ngày tải lên: 16/02/2014, 05:20

... is the diameter of ϕ(V )inM; on contracted components one may take the smallest ε with V contained in the ε-thin part. The latter consists of endpoints of loops around the singular points of ... It is instructive to compare the linearizations of the equa- tions characterizing J-holomorphic cycles of the coordinate dependent descrip- tion in this proposition and...

Ngày tải lên: 16/02/2014, 05:20

... desired in the proof of (93). The remaining term on the left-hand side of (93) is easier to treat. 7. Proof of the L 2 − L ∞ decay estimate; Theorem 2.1 In this section we rely on the Boundedness Theorem ... equal to 1 in the wave zone region u ≤ t 2 . 17 The level hypersurfaces of u are outgoing null cones C u with vertices on the time axis Γ t . NONLINEAR WAVE...

Ngày tải lên: 16/02/2014, 05:20