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Consider a Markov chain with n states and a symmetric tridiagonal transition probability matrix P. Let C be a class of vectors I p(O) I such that half the elements of p(O) are zero and another half are 1. The problem is to find the vector p(O) in C such that the value IIp(Or - p(oo)11 is the minimum for any large nonnegative integer N, where p(oo) = (1/2,1/2, ... , 1/2) and p(oo) is Galled a stationary concentration vector. The solution is stated as follows. The optimal vectors in a sense defined in this paper are of the form (PO,Pl'··· ,P n -l) which satisfy the following conditions: Pk = P3-k' Pk = P4gtk for 0:'£ k :'£ 3 and 0:'£ g:'£ 1 m - 2 _1, where n = 2 m

AN OPTIMIZATION PROBLEM IN A FINITE MARKOV CHAIN APPLIED TO SOLID PARTICLE MIXING