Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square

... problem of obtaining error bounds for these asymptotic solutions to 1.2 is still open The purpose of this and the next paper Error bounds for asymptotic solutions of second-order linear difference equations ... Difference Equations 3.2 The Error Bound for the Asymptotic Expansion of y2 (n) Now we estimate the error bound of the asymptot...

Ngày tải lên: 21/06/2014, 11:20

... Harvesting Some Lower Bounds for Ramsey Numbers It is amazing that the result of this section has not been observed for the 25 years since [C] was published Using this observation we will give new lower ... 87-95 [R] S Radziszowski, Small Ramsey Numbers, Electronic Journal of Combinatorics, Dynamic Survey DS1, 1994, 28pp [S] Song En Min, New Lower Bound Formulas for th...

Ngày tải lên: 07/08/2014, 06:20

... 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 ... incorrect) The Lorentzen and Nilsen [3] lower bound for this case is 75, the lower bound in this paper is 77 Remark 2: For small values of J we can solve the LP for all v...

Ngày tải lên: 07/08/2014, 06:20

... same), and of the 24 have depth 13 For sum-free partitions of 13 into sets all three partitions are symmetric and equivalent Another interesting aside, for depth 44 symmetric sum-free partitions ... maximal for set partitions For partitions of 44 into sets all 24 = φ(45) symmetric sum-free partitions of the 273 sum-free partitions are equivalent (note t...

Ngày tải lên: 07/08/2014, 06:20

... the determination of optimal values and lower bounds for every Hn Besides the trivial cases H3 and H4 , Golberg showed constructions providing lower bounds for n ≤ 15 A.W.M Dress, Yang Lu, Zhang ... Barequet, A lower bound for for Heilbronn s triangle problem in d dimensions SIAM J Discrete Math 14 (2001), no 2, 230–236 [3] C Bertram–Kretzberg, T Hofmeister, and H Lefmann, An...

Ngày tải lên: 07/08/2014, 06:23

... we presented a method to construct lower bounds for Van der Waerden numbers The final results are shown in table Table 4: Known Van der Waerden numbers and known and improved lower bounds r\k 27 ... #R6 2.2 Current bounds of Van der Waerden numbers Only five smaller Van der Waerden numbers are known at present The known Van der Waerden numbers, as...

Ngày tải lên: 07/08/2014, 15:22

... Lemma with n = and s = 27 and get ki ≤ 58 8k5 + 15k6 + 22k7 + 29 (8) i 8 Multiplication with 3/22 and rounding off yields Lemma the electronic journal of combinatorics 14 (20 07) , #R 27 Some preliminaries ... that i 8 ki > holds From F) follows i 8 ki ≤ If equality holds, then by (8) k5 = k6 = k7 = and thus k5 +2k6 +3 i 7 ki = contradicting F) If i 8 ki = 1, then by (8) we h...

Ngày tải lên: 07/08/2014, 15:22

... therefore approaches a limit (Varying forms of the proof appear in a variety of published works, e.g.[1, 4].) Thus we define the packing density of π as δ(π) = lim δn (π) n→∞ In [1], the lower ... that the choice of template has a large impact on how good the lower bound is when using the uniformly weighted method 15 When we let T8 = 13862745, we found the uniformly weighted...

Ngày tải lên: 07/08/2014, 15:23

... key ingredient of our proof Given the informal discussion above, the proof of Theorem 1.1 looks very roughly as follows At the first part of the proof we consider the graph G(n, ρ) for a relatively ... to the evolving graph), Bohman expresses the expected change in the values of the random variables in the collection, using the same set of random variables...

Ngày tải lên: 07/08/2014, 21:21

... k = For k > the computational effort became too large for a systematical treatment Here we got only a few sporadic new bounds: six bounds for k = 6, two bounds for k = and still a new bound for ... [1] W Chen, I S Honkala, Lower bounds for q-ary covering codes, IEEE Trans Inform Theory 36 (1990), 664-671 [2] G Cohen, I Honkala, S Litsyn, A Lobstein, Covering Codes,...

Ngày tải lên: 08/08/2014, 01:20

... isomorphism properties of generalized Paley graphs In this paper we use this tool to study cyclic graphs of non-prime order and give a new generalization of generalized Paley graphs, which we will ... lower bounds R(3, 3) and R(4, 4) 18 These graphs were Paley graphs, and the same method produced results such like R(6, 6) 102 [6] and R(8, 8) 282 [2] I...

Ngày tải lên: 08/08/2014, 11:20

... prove that Fv (4, 4; 5) Fv (2, 3, 4; 5) Fv (2, 2, 2, 4; 5) 17 In addition, we find a (4, 4; 5; 23)v graph to show that F (4, 4; 5) 23 The lower bound For a graph G, a complete graph K and vertex ... that Fv (4, 4; 5) 16 In this note, we will improve the upper and lower bounds for Fv (4, 4; 5) With the help of computer, we obtain that th...

Ngày tải lên: 08/08/2014, 11:20

... Antoine Lobstein General bounds e for identifying codes in some in nite regular graphs Electron J Combin., 8(1):R39, 2001 [2] Ir`ne Charon, Olivier Hudry, and Antoine Lobstein Identifying codes with ... small e radius in some in nite regular graphs Electron J Combin., 9(1):R11, 2002 [3] G´rard D Cohen, Iiro Honkala, Antoine Lobstein, and Gilles Z´mor On codes idene e t...

Ngày tải lên: 08/08/2014, 12:22

... subgraph of Gi+1 for all i In [4] it was proved that the values of the average genus for 2-connected graphs have limit points Note that the average genus for bar-amalgamation of a cactus and the ... number of graphs in the sequence can be obtained by attaching ears serially or by bar-amalgamation of a cactus to GN Proof Suppose the values of the av...

Ngày tải lên: 08/08/2014, 12:23

... in this case The proof is complete 3.3 Integration of non-periodic functions The problem of the optimal numerical integration of non-periodic functions is more involved The cubature formula below ... Thus, the optimal integration error decays as quickly as in the univariate case In fact, this represents one of the motivations to consider the third index θ Unf...

Ngày tải lên: 14/10/2015, 15:32