Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... 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 asymptotic expansion of the linear independent solution y2 n to the original ... we discuss the case when k > The next paper Error bounds for asymptotic solutions of second-order linear difference equations II: the second case is dedicated to the case when k < 1.1 The Result...
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Báo cáo toán học: " New Lower Bounds for Some Multicolored Ramsey Numbers" pot
... 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 the Ramsey Numbers N(k, , k; 2) ... Kalbfleisch, Chromatic Graphs and Ramsey s Theorem, (Ph.D Thesis), University of Waterloo, January 1966 [KLR] D.L Kreher, Li Wei, and S Radziszowski, Lower Bounds for Multi-Colored Ramsey Numbers from Group...
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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 ... 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 values of I obtaining: M (I, ... Colbourn, Difference Triangle Sets”, Chapter in The CRC Handbook of Combinatorial Designs by C.J Colbourn and J Dintz (ISBN 0-8493-8948-8), 1996, p 312-317 [2] T Kløve, Bounds and Construction for Difference...
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Báo cáo toán học: " Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers" potx
... 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 that, since divides 45, multiplying by and ... [4], and the second follows from (2) and the bounds for R5 (3) given in S Radziszowski’s survey paper [6] For earlier work on lower bounds for S(k) see H Fredricksen [5] and A Beutelspacher and...
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Báo cáo toán học: "New lower bounds for Heilbronn numbers" pps
... 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 algorithm for Heilbronn s ... procedure, we present new lower bounds for the first Heilbronn numbers for which no optimal value is known, namely ≤ n ≤ 12 We have no proof for the optimality of the new bounds, but the optimization method...
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Báo cáo toán học: "A New Method to Construct Lower Bounds for Van der Waerden Numbers" pdf
... 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 well as the best known lower bounds and their ... lower bounds, but also provides certificates for all the other proved and currently known lower bounds for Van der Waerden numbers with even r The only exception is the lower bound of the Van der Waerden...
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Báo cáo toán học: "Lower bounds for the football pool problem for 7 and 8 matches" pdf
... 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 have 8k5 + 15k6 + 22k7 ≤ 29 ... + 3|L 7 | by |B ∩ L| ≤ for L ∈ L≥5 ≤ 4(k5 + 2k6 + by (2) ki ) i 7 ≤ 28 by Lemma and (13) follows by ( 18) the electronic journal of combinatorics 14 (20 07) , #R 27 Proof of Theorem Let C ⊂ F7 be...
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Báo cáo toán học: "Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates" pps
... 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 lower bound to ... σi The probability of this occurring is the product of the number of occurrences of 2413 in 35827146, the number of different orderings of four elements, and the probability of picking one point...
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Báo cáo toán học: "Lower Bounds for the Size of Random Maximal H-Free Graphs" pdf
... 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 This allows one to express the random ... This concludes the proof of (8) Next we prove (7) Let Yt denote the number of induced matchings of size t in G Since the expectation of Yt is an upper bound on the probability that there exists...
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Báo cáo toán học: "Lower Bounds for q-ary Codes with Large Covering Radius" ppsx
... 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, North Holland, Amsterdam, ... Schlage-Puchta, Lower Bounds on Covering Codes via Partition Matrices, J Combin Theory Ser A 116 (2009), 478-484 [4] W Haas, J Quistorff, J.-C Schlage-Puchta, New Lower Bounds for Covering Codes, preprint...
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Báo cáo toán học: "A generalization of generalized Paley graphs and new lower bounds for R(3, q)" pot
... 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] In 1979, Clapham generalized the Paley graphs ... results R(3, 22) 125, R(3, 23) 136, R(3, 25) 153, R(3, 28) 172, R(3, 29) 182, R(3, 30) 187, R(3, 31) 198, R(3, 32) 212 We would also like to mention that our result R(3, 22) 131 and the formula...
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Báo cáo toán học: "Upper and lower bounds for Fv (4, 4; 5)" pps
... 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 there is exactly one graph in the set of (2, 2, 4; 5; ... 2001, Nenov [13] proved that Fv (3, 4; 5) = 13 It might be not easy to determine the exact value of Fv (4, 4; 5) In 2006, Kolev and Nenov [7] proved that Fv (4, 4; 5) 26 Later in 2007, Kolev...
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Báo cáo toán học: "Lower bounds for identifying codes in some infinite grids" potx
... 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 tifying vertices in the two-dimensional ... Cranston and Gexin Yu A new lower bound on the density of vertex identifying codes for the in nite hexagonal grid Electron J Combin., 16(1):R113, 2009 [5] Iiro Honkala and Antoine Lobstein On the density...
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Báo cáo toán học: "Lower Bounds for the Average Genus of a CF-graph" doc
... 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 average genus of the graphs approach a finite ... real number, then only finitely many real numbers less than r are possible values of average genus for CF-graphs Theorem 6.2 (see [15]) The average genus of a graph is not less than the average...
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Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square
... 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 Unfortunately, Fibonacci cubature formulae ... (I2 ) with respect to the method Q The the cubature error for a non-periodic function f ∈ Bp,θ N following theorem gives an upper bound for the worst-case cubature error of the method QN with...
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