Báo cáo toán học: "A Pairing Strategy for Tic-Tac-Toe on the Integer Lattice with Numerous Directions" pot

... pairing- strategy for MB d S (m). Our conjecture is based on a pairing- strategy given by Hales and Jewett [1], [2] for the tic-tac-toe game played on Z × Z with the four standard directions. They ... 87(7):575–576, 1980. the electronic journal of combinatorics 15 (2008), #N42 6 A Pairing Strategy for Tic-Tac-Toe on the Integer Lattice with Numerous...

Ngày tải lên: 07/08/2014, 15:22

... all except for at most ℓ(ℓ + 3) points of B and therefore won the BigGame, which is a contradiction to the fact that Breaker wins the BigGame. Therefore by contradiction, it must be the case that ... sub-board to the next is due to a progression in at least one of the dimensions. There are only d dimensions, so there can be at most d switches. If there were d+1 switches, then t...

Ngày tải lên: 08/08/2014, 11:20

... case of the lightly doped silicon (N D < 17 cm −3 ), the current flow at the interface is mostly decided by thermion emission, while field emission is the main mechanism in the case of the ... calculate the contact resistance, Mg was evaporated on the n-Si wafer, and the Ag paste was printed on the Si wafer for reference. The contact resistances of Mg/Si an...

Ngày tải lên: 20/06/2014, 21:20

... metal ions and CNMs without phenylphosphonic acid. The TGA residue (mainly i ron oxide) of the products, made from SWNTs sonicated with only Fe 3+ , was nearly zero. The results proved that without ... phenylp hosphonic acid, the interaction between Fe 3+ and SWNTs was so weak that the meal ions were easily washed away. On the con- trary, the resulting residue from SWNTs son...

Ngày tải lên: 21/06/2014, 06:20

... ions (i.e., alkaline earth metals) crosslink long-chain polymers to form vesicle-like geometry, similar to DNA toroid under the mediation of multivalent cation. The synthesis conditions for the ... gelatin) provide the framework for silica precursor deposition by simply controlling chain conformation with divalent metal ions (i.e., Ca 2? ,Sr 2? ), without the intervention of a...

Ngày tải lên: 22/06/2014, 00:20

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:20

... that the more obvious objective function, the number of “monochromatic” sums in a partition, seems to be far less effective. At one point we modified the objective function so as to prefer partitions having ... 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 ]denotethese...

Ngày tải lên: 07/08/2014, 06:20

... than (1) for m ≥ 8. So the Bollobas conjecture fails for k ≥ 10. The idea of the above construction which improves on products of H 3 can be applied to products of other families as well. For example, ... starting with products of H k for any k>3 as well. Or we can start with the families F constructed above. This will allow a very slight improvement in the lower bo...

Ngày tải lên: 07/08/2014, 06:20

... that these are the smallest such graphs with the stated girth values. In addition, other similar families were considered. We relaxed the requirement that T be a tree, and also considered cubic forests. ... status of the problem can be obtained from Gordon Royle [2]. The General Construction We describe a family of cubic graphs with girths in the stated range. We begin with...

Ngày tải lên: 07/08/2014, 06:20