Đề tài "The Erd˝os-Szemer´edi problem on sum set and product set" ppt

... Erd˝os-Szemer´edi problem on sum set and product set By Mei-Chu Chang* Summary The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both ... (2002), 399–419. [C2] ,Factorization in generalized arithmetic progressions and applications to the Erd¨os-Szemer´edi sum- product problems, GAFA,toappear. [El]...

Ngày tải lên: 22/03/2014, 15:21

... (y, z]. By a theorem of Filaseta and Trifonov [13], this last condition holds unconditionally with g = 1 2 provided z ≥ y + Ky 1/5 log y 394 KEVIN FORD for a large constant K. We obtain H ∗ (x, ... a 1960 con- jecture of Erd˝os and some conjectures of Tenenbaum. One key element of the proofs is a new result on the distribution of uniform order statistics. Contents 1. Introduction 2. Pre...

Ngày tải lên: 06/03/2014, 08:21

... functions on  Sp 2n (k) spanned by the integrals (2.43). Then t ψ (σ) consists of ψ  U,1 -Whittaker functions and affords a smooth representation, by right translations of  Sp 2n (k). By construction, ... k ∗ (this is clear from the action by conjugation of the diagonal subgroup on  U). Thus, we may replace ψ by ψ α 2 , and hence we may just assume that α =1,sothat there is a nontr...

Ngày tải lên: 22/03/2014, 15:21

... voltage and cur- rent measurements at the boundary of the body. Substantial progress has been made on this problem since Calder on s pioneer contribution [3], and is also known as Calder on s problem, ... cone of supp (q)atz 0 and we get a contradiction between (6.24) and the fact that all such exterior conormal directions have to belong to WF a (q). (This is the wavefront versio...

Ngày tải lên: 16/02/2014, 06:20

... harmonic forms and proof of Theorem B We now use Theorem 3.11 to identify the harmonic forms in C • ; version (B) of the strong Macdonald conjecture follows by assembling Propositions 4.5, 4.8 and ... translation action of the loop group, and a grading from the C × -action scaling z (the loop rotation). 5.2 Proposition. H • (X;Ω • ) is the direct product of its z-weight spaces, and...

Ngày tải lên: 06/03/2014, 08:21

... h ≤ 1 and by elementary measure theory, the set of these products hf generates a norm dense subspace of L 1 (Ω,λ) ). We take the constant function f = 1. We argue by contradiction and assume that ... ∞, the space W contains all continuous functions h on Ω with h  ±1 0  = 0 (but no other continuous functions). Here one can take for K the compact subsets of Ω that do not contain  ±1...

Ngày tải lên: 06/03/2014, 08:21

... - diagonal term; but as this term is independent of χ f the resulting contribution is small as long as χ f is nontrivial (otherwise one expects some matching with the contribution from the continuous ... together with (4.5) concludes the proof of Theorem 5. 5. A shifted convolution problem In this section, which is the bulk of this paper, we consider the follow- ing shifted convolution pro...

Ngày tải lên: 22/03/2014, 16:20

... enough to the one of the soliton. Here, we derive from variational estimates and conservation laws a sharp decomposition of such solutions and its basic properties. From now on, we consider u 0 ∈ ... MERLE AND PIERRE RAPHAEL This paper is organized as follows. In Section 2, we build the regular ε de- composition adapted to dispersion with the suitable orthogonality conditions on ε. I...

Ngày tải lên: 29/03/2014, 07:20

... vÏ, mµu s¾c cña nh÷ng bµi vÏ trªn. Hướng dẫn về nhà 2. Chuẩn bị bài học sau 3. Thể hiện đề tài thể thao, văn nghệ qua các chất liệu khác 1. Hoàn thiện bài trên lớp h 4 2 3 1 Hoạt

Ngày tải lên: 03/08/2013, 01:25

... em www.mamnon.com Trẻ em hôm nay – Thế giới ngày mai ĐỀ TÀI: THẾ GIỚI CÔN TRÙNG BÀI DẠY: CON KIẾN LỚP DẠY: lỚP 4-5 TUỔI Website hỗ trợ giảng dạy và chăm sóc trẻ em www.mamnon.com Trẻ ... Cho trẻ quan sát những con Kiến đang bò trong hộp và yêu cầu trẻ đưa ra nhận xét về chúng! Một số câu hỏi gợi mở: + Con thấy con Kiến có những bộ phận nào? + Các con biết gì về đời sống của ....

Ngày tải lên: 13/12/2013, 23:15