Báo cáo toán học: "Discrepancy of Cartesian Products of Arithmetic Progressions" potx

... behavior of the coefficients of large powers of multivariate generating functions and their application to mul- tivariate Lagrange inversion. In Theorem 2 of [5] we studied coefficients of large powers of ... our theorem for products of powers. In Section 3 we explain how the theorem applies to Lagrange inversion of a single function and discuss the problem of conditioning on...

Ngày tải lên: 07/08/2014, 06:20

... arbitrary discrete sets of points in n .LetP be a discrete set of points and let L be a fixed set of lines in n .AcoloringofP is nonrepetitive (with respect to L) if no sequence of consecutive points ... and look for rainbow copies of subsets of Euclidean spaces. We show that there are k-colorings of n such that every set of k points has a rainbow translated copy of itself ly...

Ngày tải lên: 07/08/2014, 07:21

... combinatorial discrepancy of the hypergraph H of cartesian products of d arithmetic progressions in the [N] d –lattice ([N ]={0, 1, ,N − 1}). The study of such higher dimensional arithmetic progressions ... introduced in the beginning of this article: We have disc(G, 2) = 2 disc(G). the electronic journal of combinat orics 11 (2004), #R5 8 Discrepancy of Cartesian Pro...

Ngày tải lên: 07/08/2014, 08:20

... c-color discrepancy of such products. In particular, we show that the bound disc(∆ d H, 2) ≤ disc(H , 2) proven for all d in [B. Doerr, A. Srivastav, and P. Wehr, Discrepancy of Cartesian products of arithmetic ... respect to χ. Proof of Lemma 7. The proof is based on an argument from Ramsey theory. First we verify the statement of Lemma 7 for a fixed simplex. Then, by inducti...

Ngày tải lên: 07/08/2014, 13:21

... journal of combinatorics 6 (1999), #R15 9 the column sum vector of C 1 .ThusC = C 2 ∈J. This contradicts the choice of C. ✷ Theorem 2 |U| = |V |. Proof. Let D =(d ij ). By the choice of D,wehave|U|≤|V ... completes the proof of the lemma. ✷ Suppose S is monotone. For each A ∈A(R, S), we can partition A into two regions according to the shape of ¯ A; that is, region 1 consists of...

Ngày tải lên: 07/08/2014, 06:20

... [MS96]. Discrepancies of related set systems were also studied. One possible extension of the original problem is to consider set systems formed by sums of arithmetic progressions, where a sum of k arithmetic ... set system of all arithmetic progressions on [n] is known to have a discrep- ancy of order n 1/4 . We investigate the discrepancy for the set system S 3 n formed by...

Ngày tải lên: 07/08/2014, 13:21

... symmetric group of permutations of [n]. For any finite set I, let Π(I) denote the poset of partitions of the set I, where a partition π of I is a set of nonempty disjoint subsets of I whose union ... d [1]). (4.17) the electronic journal of combinatorics 13 (2006), #R87 19 of (conjugate) parabolic subsystems of a root system of type B n all of whose components are of...

Ngày tải lên: 07/08/2014, 13:21

... average number of reached nodes— it is a sort of approximated indicator of the “depth” of the propagation process. Since the RE can be interpreted as the ratio between the average number of reached ... conditions— this is the very idea of IF. The shape of p, as a function of d, is shown in Figure 5, for different values of c and ρ s . It can be observed that the PAF of SIF...

Ngày tải lên: 20/06/2014, 20:20

... the large amount of cadmium-containing waste during the deposi- tion process. Therefore, the development of a Cd-free buffer layer is one of the major objectives in the field of CIGS solar cells. Today, ... 7:26 http://www.nanoscalereslett.com/content/7/1/26 Page 7 of 7 The influence of the substrate temperatures on the sur- face morphology of the films was investigated using th...

Ngày tải lên: 20/06/2014, 21:20

... force microscopy [AFM] images of the TiO 2 /ZrO 2 thin films. One can clearly seethatthesurfacemorphologyofthefilmsdepends on the annealing temperature. The RMS roughness of the as-deposited film ... 7:31 http://www.nanoscalereslett.com/content/7/1/31 Page 3 of 5 Acknowledgements This work is supported in part by the National Nature Science Foundation of China (No. 51072049), STD and...

Ngày tải lên: 20/06/2014, 21:20