Đề tài " On the hardness of approximating minimum vertex cover " pot

... ∩F  );(2) Annals of Mathematics On the hardness of approximating minimum vertex cover By Irit Dinur and Samuel Safra ON THE HARDNESS OF APPROXIMATING MINIMUM VERTEX COVER 457 thus µ(F ... encapsulates all one needs to know – for the purpose of our proof – of the PCP theorem. Section 2.2 describes the reduction from an instance of hIS...

Ngày tải lên: 15/03/2014, 09:20

... 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 follows the same line of reasoning as in [3, §5], but there ... 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....

Ngày tải lên: 14/02/2014, 17:20

... 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 smallest ε with V contained in the ε-thin ... pull-back of the relative tangent bundle. The ¯ ∂ J -equation giving J-holomorphic deformations of σ acts on the latter bundle. On the other hand, the mid...

Ngày tải lên: 16/02/2014, 05:20

... component of type (i), then the intersection in codimension one of any two distinct components can only be a line. If there is no component of type (i), then the intersection in codimension one of ... X 2 meeting along a conic. If there are THE K 2 OF DEGENERATIONS OF SURFACES 361 other components, then there is a component X  meeting all the rest along a line. Thus, the...

Ngày tải lên: 16/02/2014, 06:20

... version is established (in the sense that one bounds explicitly the number of exceptional subspaces). We now turn to the proof of Theorem 5. Keep the notation and the assumptions of this theorem. ... decide whether every element of Q(β) ∩(0, 1) has an eventually periodic β-expansion. 5. Proofs of Theorems 1 to 4 We begin by a short proof of Theorem 2. Proof of Theorem...

Ngày tải lên: 16/02/2014, 06:20

... character. Another way to prove this equality is to apply (9) to the definition of the function η. 3.2. The proofs. The notations of Sections 1 and 2, and the conventions of subsection 2.4 are still ... values of the Γ-function. This leads to the conjecture of Gross-Deligne, which is described precisely in the last section of this paper. The main contribution of...

Ngày tải lên: 14/03/2014, 22:20

... Thus the sequence of maximal dilations is almost surely sub- exponential (Condition (T5) of Assumption 3.4). Condition (T4) of that as- sumption is a.s. verified by the hypotheses stated in our Theorem. ... a Perron-Frobenius theorem through the contraction of cones of ‘real-analytic’ functions. The pressure function may then be calculated as the averaged action of the...

Ngày tải lên: 15/03/2014, 09:20

... 10 to conclude the second statement of the lemma. 3.7. The tempered Case.Wecontinue the proof of Lemma 3. By virtue of the last section, we may assume that π is tempered. In this case, the repre- sentations ... is of SO(2n)type then n is even. The crucial property of representations of G-type is the following. Lemma 6. If π ∈ Π s.d. is of G-type then (0) is a non...

Ngày tải lên: 22/03/2014, 15:21

... localization techniques established in Section 2 to the computation of the Hochschild homology of the algebra E ∞ (X) of Whitney functions on X. Note that this algebra is the space of global sections of ... be the so- called t-neighborhood of the diagonal Δ k (X). In the following we want to show how the computation of the Hochschild homology of A can be es...

Ngày tải lên: 22/03/2014, 20:21

... because of the essentially different proofs for these two cases. Whereas the proof in the first case is based on results of [8], the proof in the second case involves, in addition, representation theory ... are not of Clifford type. Hence the inequality m 2 ≥ 2m 1 − 1 is also a necessary condition for this stronger version of Theorem 1.1. Our proof of Theorem 1.1 makes us...

Ngày tải lên: 22/03/2014, 20:21