Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a one-factor added. It is proved in this paper that there exists an m-cycle system of Kn,n + I if and only if n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n, and n(n + 1) ≡ 0 (mod m).

Under suitable assumptions, we extend the inclusion of an additive subcategory X ⊂ A ( = stable category of an exact category with enough injectives) to an S-functor [15] H0]X → A , where H0]X is the homotopy category of chain complexes concentrated in positive degrees. We thereby obtain a new proof for the key result of J. Rickard’s ’Morita theory for Derived categories‘ [17] and a sharpening ...

Using a reconstituted skin culture model we have analysed the effects of oncogenic human papillomavirus (HPV) and mutant TP53 genes on the proliferation and differentiation of human keratinocytes. Immortal cell lines generated by transfection of early passage normal human keratinocytes with HPV16 E7 plus mutant human TP53 (KN #1), HPV16 E7/E6 (KN #2), or HPV16 E7 plus murine p53 (KN #3) were ex...

Suppose Π is an exchangeable random partition of the positive integers and Πn is its restriction to {1, . . . , n}. Let Kn denote the number of blocks of Πn, and let Kn,r denote the number of blocks of Πn containing r integers. We show that if 0 < α < 1 and Kn/(n l(n)) converges in probability to Γ(1 − α), where l is a slowly varying function, then Kn,r/(n l(n)) converges in probability to αΓ(r...

We prove that every real number ξ > 1 is the Diophantine exponent of some binary word ω. More precisely, we show that Dio(ω) = ξ for ω = 101102103 · · · , where kn = [ξ] for ξ > 2, kn = [ν] with ν = (−ξ + 1 + √ 6ξ − 3ξ2 + 1)/(4− 2ξ) for 1 < ξ < 2, and kn = n for ξ = 1.

LetK be a nonempty closed convex subset of a real Banach space E, T : K → K a uniformly L-Lipschitzian asymptotically pseudocontractive mapping with sequence {kn}n≥0 ⊂ [1,∞), lim n→∞ kn = 1 such that p ∈ F (T ) = {x ∈ K : Tx = x}. Let {an}n≥0, {bn}n≥0 , {cn}n≥0 be real sequences in [0, 1] satisfying the following conditions: (i) an + bn + cn = 1; (ii) ∑ n≥0 bn =∞; (iii) cn = o(bn); (iv) lim n→∞...