We compute the Nike Air Max 2011 Womens
number of rhombus tilings of a hexagon with side lengths N, M,N , N, M, N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N = M of one of our results solves a problem posed by Propp. In the proofs, Hankel determinants featuring Bernoulli numbers play an important role.
Several small universal register machines are constructed. The number of instructions vary from 32 to 14, depending on the chosen instruction base and the chosen notion of universality. The proof uses a special Air Yeezy
coding function for finite sequences of positive integers and some strong classical results concerning distribution of primes.
An optimization problem of minimizing a real-valued function of certain elements of a symmetric matrix subject to this matrix being nonnegative definite is considered. Optimality conditions are proposed. The duality result of Olkin and Pukelsheim (1982) is extended to a wide class of such problems. Applications are discussed.
We developed a cross-linking far-western blotting (WB) technique to detect weak protein–protein interactions. In addition, by comparison of the banding patterns resulting from the conventional and cross-linking methods, weak interactions can be identified by monitoring the enhancement of band intensities.