Let p(n) denote the ordinary partition function. Subbarao conjectured that in every arithmetic progression r (mod t) there are infinitely many integers N ≡ r (mod t) for which p(N) is even, and infinitely many integers M ≡ r (mod t) for which p(M) is odd. In the even case the conjecture was settled by Ken Ono. In this paper we prove the odd part of the conjecture which together with Ono’s resul...

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In a recent paper Folsom and Ono constructed a grid of Poincaré series of weights 3/2 and 1/2. They conjectured that the coefficients of the holomorphic parts of these series are rational integers. We prove that these coefficients are indeed rational numbers with bounded denominators.

this study concerns about quantum chemical modeling behavior of 02 on cr (100)surface by using density functional theory (dft) by lanl2dz and 6 — 31g* basissets, we presented the results of our first principles electronic structure calculationson the 02 molecules and their interface with cr (100) surface. the chromium metalhas the body-centered cubic structure, and chromium cluster has five cr ...