abstract   introduction: conductive hearing loss attenuates and delays sound transmission in the middle ear. it can make variety of central auditory processing disorders; that persists even after resolve of peripheral auditory system problems. one of the aspects of central auditory processing is the temporal processing, which is important for understanding speech, including temporal resolution,...

Let and be randomly chosen subsets of the first positive integers cardinalities , such that their sumset has size . We show asymptotically almost surely are fully contained in arithmetic progressions with same common difference approximately also prove a counting theorem for pairs sets arbitrary abelian groups. The results hold Our main tool is an asymmetric version method hypergraph containers...

Given integers i, j, k, L,M , we establish a new double bounded q−series identity from which the three parameter (i, j, k) key identity of Alladi-Andrews-Gordon for Göllnitz’s (big) theorem follows if L,M → ∞. When L = M , the identity yields a strong refinement of Göllnitz’s theorem with a bound on the parts given by L. This is the first time a bounded version of Göllnitz’s (big) theorem has b...

trace function 45, 46-48, 50, 51, 56, 62, 64 adapted stratification 12, 24, 26, 37, 38, 46, 48, 63, 121, 408 additive character sums 2, 7, 8, 111-158, 161-183, 270-280, 427-428 analytic rank 8, 443, 444, 445, 447, 449, 451, 453 analytic rank, geometric see "geometric analytic rank" analytic rank, quadratic see "quadratic analytic rank" Analytic Rank Theorem 445, 450-454 approximate trace fu...