Integer partitions which are simultaneously t–cores for distinct values of t have attracted significant interest in recent years. When s and t are relatively prime, Olsson and Stanton have determined the size of the maximal (s, t)-core κs,t. When k > 2, a conjecture of Amdeberhan on the maximal (2k − 1, 2k, 2k + 1)-core κ2k−1,2k,2k+1 has also recently been verified by numerous authors. In this ...

the aim of this paper is a) if σak2 < ∞ then σak rk(x) is in bmo that{rk(x)} is rademacher system. b) p1k=1 ak!nk (x) 2 bmo; 2k  nk < 2k+1that f!n(x)g is walsh system. c) if jakj < 1k then p1k=1 ak!k(x) 2 bmo.

The aim of this paper is a) if Σak2 < ∞ then Σak rk(x) is in BMO that{rk(x)} is Rademacher system. b) P1k=1 ak!nk (x) 2 BMO; 2k nk < 2k+1that f!n(x)g is Walsh system. c) If jakj < 1k then P1k=1 ak!k(x) 2 BMO.

A P ℓ -decomposition of a graph G is set paths with edges in that cover the edge . Favaron, Genest, and Kouider (2010) conjectured every ( 2 k + 1 ) -regular contains perfect matching admits -decomposition. They also verified this conjecture for 5-regular graphs without cycles length 4. In 2015, Botler, Mota, Wakabayashi triangles. paper, we verify it contain th power spanning cycle; special 4-...

I. PROOF OF PROPOSITION 1 Proof: Consider a simple example of n = 2 servers in a super time slot. At t = 2k, assume without loss of generality that X 1 (2k) > X 2 (2k). At the exploration slot t = 2k+1 with exploration probability γ 2k , the expected number of users is thus E [X 1 (2k + 1)] = X 1 (2k)(1 − γ 2k) + X 2 (2k)γ 2k E [X 2 (2k + 1)] = X 2 (2k)(1 − γ 2k) + X 1 (2k)γ 2k. On one hand, ea...