Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx
Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx
... which is the composition of blow-ups at points of the central fibre, such that Xis smooth.Annals of Mathematics On the K2 of degenerations of surfaces and the multiple point formula ... component of type (i), then the intersection in codimensionone of any two distinct components can only be a line.If there is no component of type (i), then the intersection in codimensionone of ... components X1 and X2meeting along a conic. If there are THE K2 OF DEGENERATIONS OF SURFACES 361other components, then there is a component Xmeeting all the rest along aline. Thus, the hyperplane...
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Tài liệu Đề tài " On the volume of the intersection of two Wiener sausages " ppt
... secondterm on the right-hand side of the analogue of (2.93).4. Proof of Theorem 3In Sections 4–6 we prove Theorems 3–5. The proof follows the same line of reasoning as in [3, §5], but there ... N-boxes), and therefore the estimate in (2.63) implies that most of the intersection volume is unaffectedby the reflections.8. Before giving the proof of Propositions 5 and 6, we complete the proof of ... 1.(2.93)Substitution into (2.82) yields the claim in (2.80). This completes the proof of Lemma 6.This completes the proof of Proposition 4 and hence of Theorem 1.3. Proof of Theorem 2In this section we...
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Tài liệu Đề tài " On the holomorphicity of genus two Lefschetz fibrations " pptx
... for the size of the neighbourhood V of the singular set on noncontracted components is the diameter of ϕ(V )inM; on contracted components one may take the smallestε with V contained in the ε-thin ... if and only if |C| is smooth and m(C) = 0 if and only if C has no multiple components. The definition of the C0-topology on the space of pseudo-holomorphiccycles implies semi-continuity of the ... pull-back of the relative tangent bundle. The ¯∂J-equation givingJ-holomorphic deformations of σ acts on the latter bundle. On the other hand, the middle term exhibits variations of the coefficients...
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Tài liệu Đề tài " On the complexity of algebraic numbers I. Expansions in integer bases " ppt
... to the proof of Theorem 5. Keep the notation and the assumptions of this theorem. Assume that the parameter w>1 is fixed,as well as the sequences (Un)n≥1 and (Vn)n≥1occurring in the ... get, on the one hand, that|Un||Vn|≤|W1|1+|W2|≤ r − 1 and, on the other hand, that σn(u) is a prefix of Vn of length at least 1/rtimes the length of Vn. It follows that Condition ... [17], concerning the values of thetaseries at algebraic points. The proofs of Theorems 1 to 4 are given in Section 5. The key point for them is a new transcendence criterion, derived from the Schmidt...
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Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt
... Diophantine. The construction of this Cantor set is based on Lemma 1.1 and is presented inSection 2. The proof of Theorem 2 is completed in Section 3 if we assume the statement of Theorem 3, whose proof ... integer satisfies the hypothesis of Theorem 1.Some generalizations of Theorem 1 are mentioned in Section 2. For the class of Veech billiards (see [V2]) the set of nonergodic directions is countable.It ... q)=1}area(Σ).R2R2/QαFigure 2. The parallelogram Σ(α, R, Q). The proof of Theorem 2 relies on the following fact:Theorem 3. Let Spec(α) be the sequence of heights formed by the convergents of α. There exist constants...
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Tài liệu Đề tài " Higher composition laws II: On cubic analogues of Gauss composition " ppt
... HIGHER COMPOSITION LAWS II873 The proof of Theorem 2 not only gives a complete description of the nondegenerate orbits of the representation of Γ on Z2⊗ Z3⊗ Z3in terms of cubic rings, ... of Sections 2.3 and 3.1.As shown in Section 2.3, the GL2factor of L acts on the basis of a cubicring R, while the two SL3factors act on the bases of two ideals I and I of R(where I and ... where in the projective case the condition“(I,I) balanced” turns into the condition “I2∼ 1 in the class group of R” after the symmetrization. Thus the composition law on pairs of ternary...
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Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx
... further condition on the occurrence of S, then we should also contract the edges in K1 and delete the edges in K2.Therefore, conditionally on ΥR and the occurrence of S, the path γRhas the distribution ... be the USF on Zd, and denote by ΓD the event that there are no orientededges in F from Dcto D. Then the distribution of F ∩Dcconditioned on ΓD,is the same as the distribution of the ... that the free and the wired USF on G are the same, by Theorem 7.3 of BLPS [2] (so it is clear what we meanby the USF on G). By Theorem 10.1 of BLPS [2] a.s. each component of the USF on G has one...
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Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc
... ˜σ1|[a,b]is noncontractible, then we are done. Otherwise, if˜σ1|[a,b]bounds a disk, then we apply the Gauss-Bonnet theorem to see that˜σ1|(a,b)contains a break and proceed as in the proof of ... .(II.1.14)Proof. Following the first two steps of the proof of Lemma II.1.11 (with the obvious modifications), we get a simple closed broken geodesic ˜σ1which isnoncontractible with length and the number ... DOMAINS535 The main result of the next two sections is the following theorem (Γ1(∂)is the component of B1∩ Γ containing B1∩ ∂Γ):Theorem II.1.2 (see Figure 9). Given N, τ > 0, there exist...
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Tài liệu Đề tài " Statistical properties of unimodal maps: the quadratic family " pptx
... ∈Ξi(Cdi) ∩Fκthen Ξi(Cdi)=Ji+1[g].We will concentrate on the analysis of the regularity of Ξifor the spe-cial class of simple maps f: one of the good properties of the class of simplemaps ... describe the generalstrategy 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 ... belong to T(k)ithen |Dfn(x)| >Cλn.This lemma is a simple consequence of a general theorem of Guckenheimer on hyperbolicity of maps of the interval without critical points and nonhyper-bolic...
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