We construct a new family {Kn} of simply connected symplectic 4-manifolds with the property c1(Kn)/χh(KN ) → 9 (as n → ∞).

Among bovine rotavirus strains, there are three G serotypes (G6, G8, and G10) and three P (VP4) serotypes (PB1, PB2, and PB3, which are defined on the basis of strains NCDV, UK, and B223, respectively). Plaque reduction neutralization assays with hyperimmune antisera disclosed two-way antigenic relationships of strain KN-4 with strain KK-3 (G10, PB3) as well as with strains NCDV (G6, PB1) and 0...

Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n ...

The altitude of a graphG, denoted f(G), is the largest integer k such that under each ordering of E(G), there exists a path of length k which traverses edges in increasing order. In 1971, Chvátal and Komlós asked for f(Kn), where Kn is the complete graph on n vertices. In 1973, Graham and Kleitman proved that f(Kn) ≥ √ n− 3/4− 1/2 and in 1984, Calderbank, Chung, and Sturtevant proved that f(Kn)...

A decomposition of Kn \L, the complete graph of order n with a subgraph L (called the leave) removed, into edge disjoint copies of a graph G is called a maximum packing of Kn with G if L contains as few edges as possible. A decomposition of Kn U P, the complete graph union a graph P (called the padding), into edge disjoint copies of a graph G is called a minimum covering of Kn with G if P conta...

Let G be a graph and H a subgraph of G. A D(G,H, λ) design is a collection D of subgraphs of G each isomorphic to H so that every 2-path (path of length 2) in G lies in exactly λ subgraphs in D. The problem of constructing D(Kn, Cn, 1) designs is the so-called Dudeney’s round table problem. We denote by Ck a cycle on k vertices and by Pk a path on k vertices. In this paper, we construct D(Kn,n,...

Kinetin (Kn) is a cytokinin growth factor that exerts several anti-aging and antioxidant effects on cells and organs. To investigate the mechanism underlying apoptotic events in aging cells induced by D-galactose (D-gal), we examined the effect of Kn delivered via nuchal subcutaneous injection on D-gal-induced aging and apoptosis in rats. Our results showed that interleukin (IL)-2 levels and mi...

In an earlier paper the authors showed that with one exception the nonorientable genus of the graph Km +Kn with m ≥ n−1, the join of a complete graph with a large edgeless graph, is the same as the nonorientable genus of the spanning subgraph Km+Kn = Km,n. The orientable genus problem for Km +Kn with m ≥ n−1 seems to be more difficult, but in this paper we find the orientable genus of some of t...

r∈Z f̂(r)e In the last lecture, we proved Fejér’s theorem f ∗ kn → f where the ∗ denotes convolution and kn (Fejér kernels) are trignometric polynomials that satisfy 1. kn ≥ 0 2. ∫ T kn = 1 3. kn(s) → 0 uniformly as n→∞ outside [−δ, δ] for any δ > 0. If X is a finite abelian group, then the space of all functions f : X → C forms an algebra with the operations (+, ∗) where + is the usual pointwis...