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We give upper and lower bounds for the largest integer not representable as a posi- tive linear combination of three given integers, disproving an upper bound conjectured by
However, our congruence is more versatile, and we exploit it in the final section together with The- orem 1.1 to prove the congruences involving Bernoulli numbers stated in
Next, we prove bounds for the dimensions of p-adic MLV-spaces in Section 3, assuming results in Section 4, and make a conjecture about a special element in the motivic Galois group
In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE
Reently, the authors established a number of inequalities involving integer powers of the Hadamard produt of two positive denite Hermitian matries.. Here these results are extended
In earlier work (Wilson, 2001) we derived upper and lower bounds on the mixing time of a variety of Markov chains, including Markov chains on lozenge tilings, card shuffling,
We prove that the tilted tree corresponding to a connected component of C with a fixed number of surplus edges can be built in a similar way: the difference consists in a bias in
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined