the loop invariant for lower bounds

... (with k = resp k = 5) In the case n = the best previously known lower bound k3 (7) ≥ 153 is due to Habsieger [5] We show Theorem k3 (7) ≥ 156 For the case of matches the best lower bound k3 (8) ≥ ... lower bounds, Discr Mathematics 256 (2002), 161-178 [4] L Habsieger, Lower bounds for q-ary coverings by spheres of radius one, J Comb Theory Ser A 67 (1994), 199-222 [5] L Habsieger, A new lower ... new lower bound for the football pool problem for matches, J de Th des Nombres de Bordeaux (1996), 481-484 [6] L Habsieger, A Plagne, New lower bounds for covering codes, Discr Mathematics 222...

Ngày tải lên: 07/08/2014, 15:22

... −2)/(eH −1) ) Note that the above lower bounds trivially imply similar lower bounds on the expectation of e(Mn (H)) It is worth mentioning that all of the above lower bounds on the expectation of ... 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 large ρ, and show that for ... given at Section 3.1, we lower bound the probability of the event E1 In the second part we lower bound the probability of the event E2 (f ) Since these two lower bounds would be shown to be − o(1),...

Ngày tải lên: 07/08/2014, 21:21

... obtained the following result for the maximum genus of a CF-graph Theorem 1.3 (See [9]) Let G be a CF-graph with minimum degree at least Then lower bounds on the maximum genus are given in Table The ... show a lower bound for the average genus of a CF-graph which is a linear function of its Betti Number Theorem 1.4 Let G be a CF-graph with minimum degree at least Then lower bounds on the average ... empty, the theorem is true Otherwise B1 is nonempty, for any x2 ∈ B1 , on the basis of orientability and x2 and x1 parallel, the only possibility is x− ∈ B1 From the known condition, there is...

Ngày tải lên: 08/08/2014, 12:23

... estimate the remaining terms in (3.31) in a similar fashion Altogether we end up with (3.19) which concludes the proof Lower bounds for optimal cubature This section is devoted to lower bounds for the ... proves the theorem for the case θ ≥ To prove the theorem for the case θ < 1, we take k ∈ Zd+ with |k|1 = m + 1, and consider the function on Td gk := C 2−αm g˜k,s s∈S∗ (k) Similarly to the argument ... play the central role in the definition of the associated integration lattice In the sequel, the symbol bn is always reserved for (3.1) For n ∈ N we are going to study the Fibonacci cubature formula...

Ngày tải lên: 14/10/2015, 15:32

... on the other side), then we added links from each of these words to NULL Second, if n words on one side of the bitext aligned to m words on the other side with m > n then we added NULL links for ... Table gives descriptive statistics for the remaining data The table also shows the upper bound of the 95% confidence intervals for the coverage rates reported later The results of experiments on different ... linked to one word, it ignored one of the two links Our lower bounds would be higher if they accounted for this kind of discontinuity ITG For the rest of the paper, we restrict our attention to...

Ngày tải lên: 17/03/2014, 04:20

... Lower Bounds 5.1 Lower Bounds W e could be in a better position to address the question o f the relative difficulty of interest if we could establish a rough estimate of the upper and lower bounds ... "cheat" and let the baseline system peek at the test set and "estimate" the most likely sense for each word as the more frequent sense in the test set Consequently, the performance of the baseline ... of the prior probabilities of the senses, so they would be at a disadvantage relative to the baseline if one of the senses had a very high prior, as is the case for the test word issue 10 The...

Ngày tải lên: 17/03/2014, 08:20

... 4(6.48)r−1 + r times holds for all r For R(6, 6, 6) there was no established nontrivial lower bound Consider the number R(5, 5, 5) To find a lower bound, L, we are searching for a three coloring of ... Color the edges of KL as follows: If j − i is a cubic residue color the edge connecting i and j red, if it is in the second coset, color the edge blue, and if it is the third coset, color the edge ... of Z∗ , for a p given prime, p We then use the procedure siv to discard any residue, R, for which R − is not a residue We now have a much more manageable list to search We then call the procedure...

Ngày tải lên: 07/08/2014, 06:20

... there is still a considerable gap between these 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 ... procedure for ≤ I ≤ 15, ≤ J ≤ 20 (for J ≤ the solution gives the trivial bound M (I, J) ≥ IJ(J + 1)/2 mentioned in Remark above) The resulting lower bounds on M (I, J) are listed in Table These bounds ... 962 and the lower bound in this paper is 974 This remains far from the best upper bound known for M (15, 10), 1415 (from [1]) The fault may be more with the upper bound than with the lower bound...

Ngày tải lên: 07/08/2014, 06:20

... obtain the following lower bounds for the Ramsey numbers R6 (3) and R7 (3): R6 (3) ≥ 538 R7 (3) ≥1682 This improves the bounds given in Radziszowski’s survey paper Note that the bound for R7 ... [6] For earlier work on lower bounds for S(k) see H Fredricksen [5] and A Beutelspacher and W Brestovansky [2] The best previously known lower bound S(6) ≥ 481 for S(6) follows from (1) At the ... computer that S(4) = 44 The best known bounds for S(5) are 160 ≤ S(5) ≤ 315 (3) The first inequality in (3) is due to G Exoo [4], and the second follows from (2) and the bounds for R5 (3) given in...

Ngày tải lên: 07/08/2014, 06:20

... further optimization 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, ... [7] started in 1972 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 ... papers [20, 21, 22, 6] proved that the value of H6 given by Goldberg was optimal and provided also the optimal value for H5 They also improved the lower bound for H7 In this note, and by using...

Ngày tải lên: 07/08/2014, 06:23

... presented The last column shows the lower bound obtained by the Cyclic Zipper method The lower bounds in bold are improvements over the existing lower bounds Notice that new lower bounds were ... improved 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 ... obtained, except for W (2, 3) Our website6 contains the raw certificates proving the improved lower bounds Visualizations of the certificates that represent improved lower bounds for W (4, k) and...

Ngày tải lên: 07/08/2014, 15:22

... picked from the same σi The probability of this occurring is the product of the number of σi ’s, the probability of picking all four points in the same σi , and the probability pn/8 that the four ... to determine a lower bound for δ(π), we find that we can achieve better lower bounds by allowing the lengths of the σi ’s to vary In doing so, we permit the probabilities that the σi ’s contain ... α n 1− i=1 Now we focus on the numerator Recall that the probability for the j th π-occurrence is the product of the weights of the m distinct σti ’s that make up the j th π-occurrence, m Wj...

Ngày tải lên: 07/08/2014, 15:23

... winning strategy, we are done Otherwise, check whether there exists a winning tuple of the form (a1 , 0, , 0; 1) If not, give up If yes, then repeat the procedure for the game G(n, M, q, k; a1 ... in the case k = and to q in the case 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 ... further improve Theorem to K4 (6, 3) 11 and settle K4 (5, 2) = 16 In the next section we develop a mechanical approach for the use of Theorem which is well suitable for computer calculations The...

Ngày tải lên: 08/08/2014, 01:20

... n) = Then the transform f : x → kx of Zn gives rise to isomorphisms of the graphs Gn (Ai ) for i = 1, In general, the transform f changes the parameter set Si into Si∗ and Gn (Ai ) into another ... 21) 122 These four examples give the best know lower bounds for their corresponding Ramsey numbers (compare [10]), in which R(3, 9) = 36 is even the exact value The computation of all these examples ... some new lower bounds such like R(4, 4, 4) 128 [12] and R(6, 6, 6) 1070 [11] were obtained In the past few years we have used the cyclic graphs of prime order to study the lower bounds for classical...

Ngày tải lên: 08/08/2014, 11:20

... 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; 13)v graphs Then we prove that Fv ... without common vertex in the neighborhood of v in G Therefore the degree of v in G is at least 5, so δ(G) Therefore δ(H) Now, let us give δ(H) a lower bound If δ(H) 3, and the degree of u in H is ... suppose to the contrary that H (2, 4)v , then there exists a 2-coloring, say color and color 3, of the vertices of H such that H neither contain K2 with color nor K4 with color We color the independent...

Ngày tải lên: 08/08/2014, 11:20

... for the degree of the graph Γ formed by an r-identifying code in the square grid, which allows us to prove Theorem Then we prove Lemma 9, which bounds the average degree of Γ by 7, allowing for ... lim sup Lower Bound for the Hexagonal Grid Lemma establishes an upper bound of for the degree of the graph Γ formed by an r-identifying code in the hex grid, which allows us to prove Theorem ... 1), (−1, 0) and (0, −1) witness pairs Then, for the other pairs, there are exactly choices for codewords which are not in the ball of radius for any of our other pairs See Figure Vertex (1, 1)...

Ngày tải lên: 08/08/2014, 12:22

... derived the failure envelope for the thermoplastic polymer, and their result was similar to Asp et al [1996] result Therefore, they proposed the use of a volumetric strain invariant (first invariant ... Factors in the Strain Invariant Failure Theory for Composites abbreviated as SIFT Failure of composite constituent is associated with one invariant of the fiber, and two invariants for the matrix ... 2005] Therefore, the first strain invariant J1 (Eq 3-2) is calculated with strains amplified only at the IF1, IF2 and IS positions within the matrix phase in the micromechanical block On the other...

Ngày tải lên: 05/10/2015, 13:53

... Lemma for a domain of finite type Proof of Theorem 1.4 Using Theorem 1.2 for Ω , the Schwarz-Pick lemma for the Kobayashi metric, and the upper bound of the Kobayashi metric, we obtain the following ... obtain the following Theorem 3.1 Assume that there exists a family of bumping functions on a local path V of the boundary as in the conclusion of Theorem 2.1 Fix < η < 1; then for any w ∈ V ∩ bΩ there ... which has a lower bound f (r−1 (z)) for the Levi form In step 3, we estimate the function G The properties of bumping function is checked on step Proof of Theorem 2.1 Step Since the hypersurface...

Ngày tải lên: 26/10/2015, 14:04

... components or traces are in the middle of the loop or very close to the loop Using the ground plane as one side of the loop makes the loop effectively larger while lowering resistive losses On ... parameter is the transmitter output impedance For the rfPIC12F675K/675F transmitters use 300 Ω and for the rfPIC12F675H transmitter use 250 Ω The loop size and trace width will be determined as the circuit ... connecting to the node between the L and C, we can tap into the inductor, or in this case, the capacitor This reduces the impedance by the ratio of the tap point to make a better match with the transmitter...

Ngày tải lên: 11/01/2016, 14:30

Ngày tải lên: 03/10/2012, 15:21