Báo cáo toán học: "Improved LP Lower Bounds for Difference Triangle Sets" potx

... bounds and the best upper bounds known. For example the lower bound for M(15, 10) in [1] is 958, the lower bound using Lorentzen and Nilsen’s formulation is 962 and the lower bound in this paper is ... programming to prove lower bounds on the size of difference triangle sets. In this note we show how to improve these bounds by including additional valid linear inequalit...

Ngày tải lên: 07/08/2014, 06:20

... proved that F v (4, 4; 5)  16. In this note, we will improve the upper and lower bounds for F v (4, 4; 5). With the help of computer, we obtain that there is exactly one graph in the set of (2, ... S i for 1  i  m, if F → (2, 2, 4; 5) v , add H to the set D. Step 5. Initial a new set E = ∅. Then for every graph H ∈ D, find the family M = {S ⊆ V (H) : S is (H, +v, K 4 ) maximal },...

Ngày tải lên: 08/08/2014, 11:20

... example. O(m 2/3 n 2/3 + m + n), and asked whether a superlinear lower bound exists for M(n, n). The quantity M(n, n) gives an upper bound for the largest convexly independent subset of P ⊕ P, and it ... “Computationism as a Foundation for the Sciences” and Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promoti...

Ngày tải lên: 08/08/2014, 11:20

... Walter Williams Craigie grant from Randolph-Macon College for providing partial support. The authors also wish to thank an anonymous referee for many helpful suggestions improving the exposition ... translation equivalent to T 1 T 2 . Therefore we have not listed them above. The strategy for finding difference sets in groups of order 16 will be as follows. 1. For each group G we ident...

Ngày tải lên: 07/08/2014, 21:20

... 2.6939 18 2.6880 20 2.6832 22 2.6792 Table 2: Upper bounds for the connective constants µ (d,k) for walks with finite memory. The values shown are true upper bounds. 4 Acknowledgements We thank Tony Guttmann ... length 2 or 4 for any continuation of our walk, so it is not really neccessary to preserve the information that the previous step was taken at all – except for its contribu...

Ngày tải lên: 07/08/2014, 06:20

... before, the evaluation of the Tutte polynomial at these points is #P-hard for planar bipartite graphs [11] and even for grid graphs of maximum degree 3 [12]. The approach for obtaining the bounds ... the last decimal. 6 Lower bounds In the previous section we used the transfer-matrix method to improve the upper bounds given in [7]. In this section we improve the lower bounds...

Ngày tải lên: 07/08/2014, 07:21

... This will give the lower bound 6k − 29 stated in Theorem 3.1 for k ≥ 7, and for k<7, this bound follows immediately from the proof of the lower bound (k) ≥ 4k − 7 in [7]. For k ≥ 7, Lemma 3.2 ... order. Furthermore |w i | = 2for all 1 ≤ i ≤ k −1 except for i = m and possibly for one other value of i where w i contains an additional pair of m − 1’s. Proof. Assume m ≥ 4. For...

Ngày tải lên: 07/08/2014, 08:20

... upper bounds for G 2 , and bound (18) is the best in all known upper bounds for G 3 . Finally, bound (22) is the best upper bound for G 1 and bound (1 8) is the second-best except bound (22) for ... new and sharp upper bounds for λ(G), which are better than all of the above mentioned upper bounds in some sense, and determine the extremal g r aphs which achieve these upper b...

Ngày tải lên: 08/08/2014, 12:23

... adjusted for the amount of CdCl 2 in 0.02 M HCl added (final pH 5.5). The experiment was performed in triplicate for all CdCl 2 concentrations and all buffers. Quality control was performed ... formation prevents the formation of insoluble 111 In hydroxide. This study suggests that coordination complex formation of the buffer with 111 In is less important for efficient labelling...

Ngày tải lên: 20/06/2014, 20:20

... des for H with density 3/7 and proved that any identifying code for H must have density at least 16/39 ≈ 0.410256. Both their upper an d lower bounds were best known until now. Here we prove a lower ... authors also proved a lower bound o f 16/39. In this paper, we improve the lower bound to 12/2 9. Before we prove our main result, which is Theorem 1, we first prove a weaker low...

Ngày tải lên: 08/08/2014, 01:20