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An n x m sonar sequence is a subset of the n x m grid with exactly one point in each column, such that the (r~) vectors determined by them are all distinct. We show that for fixed n the maximal m for which a sonar sequence exists satisfies n-Cn 11/20 < m < n + 4n 2/3 for all n and m > n + c log n log log n for infinitely many n. Another problem concerns the(More)
Here we show that Ramsey numbers M(k 1 , • • • , k..) give sharp upper bounds for the independence numbers of product graphs, in terms of the independence numbers of the factors. The Ramsey number M(k 1f • • • , kn) is the smallest integer m with the property that no matter how the (2) edges of the complete graph on m nodes are partitioned into n colors,(More)
1. The fall in chlorine concentration of Dakin's hypochlorite solution is more rapid in contact with necrotic than in contact with normal tissue. 2. The fall in chlorine concentration of chloramine-T solution is very slight when applied to necrotic tissue and is negligible when applied to normal tissue. 3. The action of the hypochlorite solution on tissue(More)