Báo cáo toán học: "Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates" pps

... Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates Cathleen Battiste Presutti Department of Mathematics Bryn Mawr College, Bryn ... bound and introduce a generalized method involving weighted templates as a way for computing lower bounds for δ(π), the packing density of a non-layered pattern π. Furthermore, we...

Ngày tải lên: 07/08/2014, 15:23

... 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 6 new lower bounds. Currently ... prime, q,forwhich3 does not divide q − 1. This can be accomplished automaticly by using the procedure pryme. By using the procedure res we produce all of the cub...

Ngày tải lên: 07/08/2014, 06:20

... Bertram-Kretzberg, T. Hofmeister, and H. Lefmann [3], which for a discretization of the problem finds a triangle with area log n/n 2 for every fixed n; lower bounds on higher dimensional versions of the problem, ... value for H 5 .Theyalso improved the lower bound for H 7 . In this note, and by using a simple implementation of simulated annealing and a further optimization...

Ngày tải lên: 07/08/2014, 06:23

... Acknowledgment The author thanks Prof. Yair Caro and Raphael Yuster for sending reference [7]. The author also thanks Prof. Cheng Zhao for his advice. References [1] J.A. Bondy and ... result. Theorem. Let t = 27720r + 169 (r ≥ 1), then f(n) ≥ n +32t −1 for n ≥ 6911 16 t 2 + 514441 8 t − 3309665 16 . 2 Proof of Theorem Proof. Let t = 27720r + 169,r ≥ 1,n t = 6911 16 t 2 + 514441 8 t ....

Ngày tải lên: 07/08/2014, 06:22

... Upper bounds for µ(n, d) obtained by µ(n, d)  nµ(n − 1, d) Proof. For each i, a i |C| counts the number of pairs of permutations (φ, ψ) with φ, ψ ∈ C and φψ −1 ∈ C i , or, equivalently, the sum for ... action of Iso(n) (see [4] for more infor matio n on invariants). Theorem 6 (LP bound for permutation codes (Tarnanen,[15])). Let D be a subset of {1, . . . , m} and E any s...

Ngày tải lên: 08/08/2014, 12:22

... approximately 3 dB gain of SNR at 10 -10 of outage probability under the symmetric channels. Figures 2 and 3 are the comparison of the ergodic capacity versus K. Due to the lower bounds of both PDF and ... mutually, and have presented the exact closed-form expression for outage probability in integral form as well as the lower bound. A more overall investigation of the TWOR-...

Ngày tải lên: 20/06/2014, 21:20

... 1994 Abstract For k ≥ 5, we establish new lower bounds on the Schur numbers S(k) and on the k-color Ramsey numbers of K 3 . For integers m and n ,let[ m, n ]denotetheset{ i | m ≤ i ≤ n }.AsetSof integers ... k-coloring of the edges of K t , there is a complete subgraph K n all of whose edges have the same color. A sum-free partition of [1 ,s ] gives rise to a K 3 -free edge...

Ngày tải lên: 07/08/2014, 06:20

... γ(n, δ) for n ≤ 16. In Table 1 we give a list of values (or bounds) for γ(n, δ) when n ≤ 16. In this section we justify the entries of this table. See Table 3 in Appendix A for a summary of how ... proof.  Proposition 3.2. (1) γ(n, n − 1) = γ r (n, n − 1)= 1for any n ≥ 1. (2) γ(n, n − 2) = γ r (n, n − 2)= 1for odd n ≥ 2. (3) γ(n, n − 2) = γ r (n, n − 2)= 2for even n ≥ 2. Proo...

Ngày tải lên: 07/08/2014, 06:20

... approximations of the roots for specific values of d are found easily, and so are the inverses of the roots of smallest modulus giving us the entries of first line of table 2. the electronic journal of combinatorics ... eight. However, the determination of the asymptotic behavior of the number of walks of finite memory is much easier. We can use the automaton directly fo...

Ngày tải lên: 07/08/2014, 06:20

... entry in the table of values of γ(n, δ)in[2] Acknowledgement We wish to thank Gordon Royle for providing Cayley tables for the 14 groups of order 16 and Cayley graphs of groups of orders up to 31. References [1] ... }. the electronic journal of combinatorics 7 (2000), #R58 17 5 Exact values of δ 3 (n) for small n. In this section we give exact values of δ 3 (n) for 6 ≤...

Ngày tải lên: 07/08/2014, 06:22