Báo cáo toán học: "Sets of integers that do not contain long arithmetic progression" pot

... journal of combinatorics 18 (2011), #P59 5 Sets of integers that do not contain long arithmetic progressions Kevin O’Bryant ∗ Department of Mathematics The City University of New York College of Staten ... for all k = 4. We denote by r k (N) the maximum possible size of a subset of {1, 2, . . . , N} that does not contain k numbers in arithmetic progression...

Ngày tải lên: 08/08/2014, 14:22

... integer in that equivalence class. Given an interval I, we will denote by S I the set of equivalence classes of products of integers in I. Note that S I is closed under multiplication, a fact that ... +1, so that all of the prime factors of m are certainly ≤ m ≤ √ 2z + √ z +1. But then, all of the prime factors of m belong to S J (as we saw in the first paragraph of t...

Ngày tải lên: 07/08/2014, 06:22

... non-negative over the domains of integration).  We are now in a position to prove the theorem. Proof of theorem 3.1 Let m =  1 3  2 √ 3  d+1  , and randomly pick a set S of 3m point vectors, ... bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers. 1 Introduction Let us say that a set...

Ngày tải lên: 07/08/2014, 13:21

... C(||f || H 1 /λ) n/(n−δ) . This completes the proof of Theorem 3.  Proof of Theorem 4 (i). It suffices to show that there exists a constant C>0 such that for every H 1 (w)-atom a with suppa ⊂ Q ... by the vanishing moment of a and for u ∈ 3Q \ 2Q, 130 Liu Lanzhe Proof of Theorem 2. It suffices to show that there exists a constant C>0such that for every H 1 -atom a (that is...

Ngày tải lên: 06/08/2014, 05:20

... E 0 ∩E 1 = ∅. Let r denote the minimum degree in G 0 . The edges of the second graph are labelled by positive integers. The label of e ∈ E 1 is denoted by l(e). Denote the number of edges of label i starting ... that 2 r − 4 t − s − 1 >N=  n q  = 1 q! n q + O(n q−1 ), provided n>n 0 (q). According to Theorem 1.3, there is a Hamiltonian cycle H in G 0 that does not cont...

Ngày tải lên: 07/08/2014, 06:23

... results clearly demonstrate that moderate doses of dolomite lime (5 T·ha -1 ) can modify potential net N transformations in the forest soil of the Belgian Ardenne. Responses ... respectively. Twelve square plots of 225 m2 were established in each forest type around a central dominant or co-dominant tree, selected randomly. A minimum of 5 m...

Ngày tải lên: 08/08/2014, 14:21

... peptide of dominant-negative TORC1. They found that acute delivery of TORC1 dominant-negat- ive peptide into rat hippocampal slices blocked the maintenance of L-LTP induced by three trains of high frequency ... we found that the induction of L-LTP, but not E-LTP, triggers robust nuclear and perinuclear accumulation of TORC1 in the CA1 neurons of hippocampal slices (Fig. 1A...

Ngày tải lên: 30/03/2014, 08:20

Ngày tải lên: 05/08/2014, 10:20

... factor of v.ThenX −{v} is also an unavoidable set, which contradicts the minimality of X. Thus (i) must hold. (ii) Now assume that the condition (ii) does not hold, i.e. there exists u in X such that ... quotient of X by Y , denoted by XY −1 ,isthesetofallxy −1 with x ∈ X and y ∈ Y . The left quotient of X by Y , denoted by Y −1 X, is defined similarly. Given X ⊆ A ∗ and u, w ∈ A...

Ngày tải lên: 06/08/2014, 05:20