Let H be a closed half-space of n-dimensional Euclidean space. Suppose S is a unit sphere in H that touches the supporting hyperplane of H . The one-sided kissing number B(n) is the maximal number of unit nonoverlapping spheres in H that can touch S. Clearly, B(2) = 4. It was proved that B(3) = 9. Recently, K. Bezdek proved that B(4) = 18 or 19, and conjectured that B(4) = 18. We present a proo...

Let S be a finite set of words such that Fact(S) 6= Σ. We deal with the problem of finding bounds on the minimal length of words in Σ \ Fact(S) in terms of the maximal length of words in S.

Let (X, d, μ) be a metric measure space. For ∅ 6= R ⊆ (0,∞) consider the Hardy-Littlewood maximal operator MRf(x) def = sup r∈R 1 μ(B(x, r)) ∫

We propose an approach via Frobenius manifolds to the study (began in [BCK2]) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding “abelianized” quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonab...

Let G be a connected complex semi-simple group, B ⊂ G a Borel subgroup, and T ⊂ B a maximal torus. We construct a class of smooth T stable subvarieties inside the flag variety G/B, each of which is an embedding of a product of projective lines.

We prove that in the presence of a maximal giant graviton state in N = 4 SYM, the states dual to open strings attached to the giant graviton give rise to an PSU(2, 2|4) open spin chain model with integrable boundary conditions in the SO(6) sector of the spin chain to one loop order.

A set S of edge-disjoint hamilton cycles in a graph G is said to be maximal if the edges in the hamilton cycles in S induce a subgraph H of G such that G EðHÞ contains no hamilton cycles. In this context, the spectrum SðGÞ of a graph G is the set of integersm such that G contains a maximal set of m edge-disjoint hamilton cycles. This spectrum has

In this note we investigate some properties of lines of maximal size in a finite linear space. Also, we give a new and unified proof of two theorems by Hanani [6], (and Varga [10]) and Melone [9].

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on R n-trees. We first prove that Sela's limit groups do have a free action on an R n-tree. We then prove that a finitely generated group having a free action on an R n-tree can be obtained from free abelian groups and surface groups by a finite sequence of free products and amalgamations over cyclic ...

In this paper we study hyperbolic sets with nonempty interior. We prove the folklore theorem that every transitive hyperbolic set with interior is Anosov. We also show that on a compact surface every locally maximal hyperbolic set with nonempty interior is Anosov. Finally, we give examples of hyperbolic sets with nonempty interior for a non-Anosov diffeomorphism.