作者：TARDOS, G
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences
摘要：The Hanna Neumann Conjecture says that the intersection of subgroups of rank n + 1 and m + 1 of a free group has rank at most nm + 1. This paper proves the conjecture for the case m = 1. (See Theorem 1.) Our methods imply that the strengthened Hanna Neumann Conjecture is also true in this case (Theorem 2').
作者：WILF, HS; ZEILBERGER, D
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
摘要：It is shown that every 'proper-hypergeometric' multisum/integral identity, or q-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here. We give many examples of the method, including computer-generated proofs of identities of Mehta...
作者：RAIKOV, GD
摘要：We consider the Schrodinger operator H = - DELTA + W + V acting in L2 (R(m)), m greater-than-or-equal-to 2, with periodic potential W perturbed by a potential V which decays slowly at infinity. We study the asymptotic behaviour of the discrete spectrum of H near any given boundary point of the essential spectrum.
