Đề tài " Uniform expansion bounds for Cayley graphs of SL2(Fp) " pptx

... of Mathematics Uniform expansion bounds for Cayley graphs of SL2(Fp) By Jean Bourgain and Alex Gamburd* Annals of Mathematics, 167 (2008), 625–642 Uniform expansion bounds for Cayley ... [1]. UNIFORM EXPANSION BOUNDS FOR CAYLEY GRAPHS OF SL 2 (F p ) 627 Our second result shows that random Cayley graphs of SL 2 (F p ) are ex- pander...

Ngày tải lên: 29/03/2014, 07:20

... simplify the statement of our main result. It is simpler to speak of the shape of the set (1/t)B(t) as a subset of R d , than of the discrete set (1/t)  B(t). The aim of this paper is to describe ... the proof of Proposition 5 of [KSb]. The right-hand inclusion in (1.3) then says that for all ε>0 (3.11) P {there exist genealogical paths from z 0 to some point outside (1...

Ngày tải lên: 16/02/2014, 06:20

... entire side of at least one of these triangles but not necessarily of both of them. In Section 3, we give a more general definition of admissibility for a sys- tem of triangles suitable for nonconvex ... admissible for D if T ∩ D = ∅, the base of T lies on ∂D (the base of T need not consist of an entire side of D), S ∩ D = ∅, and if each (closed) side (not base!) of...

Ngày tải lên: 14/03/2014, 22:20

... y)dy, Annals of Mathematics Uniform bounds for the bilinear Hilbert transforms, I By Loukas Grafakos and Xiaochun Li UNIFORM BOUNDS FOR THE BILINEAR HILBERT TRANSFORMS, I 907 and    Φ 1,k,l (·)e −2πic(ω 1,k,l )(·)   (x)   ≤ ... of m. The core of the proof consists of the proofs of these lemmata. These will be given in the next section. We now state...

Ngày tải lên: 14/02/2014, 17:20

... ∈ [u, u +2]. 4. Proof of Theorems 2.4 and 2.5 We shall only provide the proof of Theorem 2.4, the proof of Theorem 2.5 being entirely similar. We take q to be the product of all the primes in 618 ... of providing a better localization of the sign changes of E for small values of u. Our main result of this section is the following: AN UNCERTAINTY PRINCIPLE FOR ARITHMETIC...

Ngày tải lên: 16/02/2014, 06:20

... proof of the “geometric rank conjecture” for mapping class groups, formulated by Brock and Farb [BF], which states: Rank Theorem. The geometric rank of the mapping class group of a surface of ... obtained, for S 2,0 , by Brock- Masur [BM], as a consequence of an analysis of the special properties of quasi- geodesics in the pants graph for the genus 2 case. Recall that the...

Ngày tải lên: 16/02/2014, 06:20

... technology. In every branch, include type of faculty: -Faculty of information technology. -Faculty of economy. -Faculty of build. -Faculty of foreign language. -Faculty of electron. In addition, every ... tools. We have one way for control information overflow, the way is use algorithm queue for arrange traffic and determine some methods for decentralization priority of tr...

Ngày tải lên: 17/02/2014, 19:46

... After a change of the w-coordinate of the form w := ϕ(w), we may assume that restriction of f(z,w) to the vertical line {z =0} takes the form f (0,w)=w. Similarly, to the proof of Theorem 1 in ... Transformation of an analytic function of several variables to a canonical form, Duke Math. J . 288 (1961), 345–353. [9] F. Loray, Analytic normal forms for nondegenerate singularities...

Ngày tải lên: 06/03/2014, 08:21

... smallest n for which a sums -of- squares formula of type [r, s, n] exists. Many papers have studied lower bounds on r ∗ F s, but for a long time such results were known only for fields of characteristic ... Yuzvinsky [Y] for special values of r, s, and n. In [SS] a weaker version of the condition was proved for arbitrary fields and arbitrary values of r, s, and n. Stiefel’...

Ngày tải lên: 06/03/2014, 08:21

... affine actions of G, and then apply fixed point theorems. The proof of weak relative compactness of the range of Φ uses estimates with similar decomposition methods, as in the proof of Lemma 5.5. THE ... immediate analogue of the proof of [J1, Th. 2.5] for amenable groups; see also [GRW, L. 2.1]). It follows easily from the invariance of the mean that for any μ  in the close...

Ngày tải lên: 06/03/2014, 08:21