Matthews and Sumner have proved in [10] that if G is a 2-connected claw-free graph of order n such that δ(G) ≥ (n − 2)/3, then G is Hamiltonian. We say that a graph is almost claw-free if for every vertex v of G, 〈N(v)〉 is 2-dominated and the set A of centers of claws of G is an independent set. Broersma et al. [5] have proved that if G is a 2-connected almost claw-free graph of order n such th...

Let ǫ > 0 be a positive number. Is there a number δ > 0 satisfying the following? Given any pair of unitaries u and v in a unital simple C∗-algebra A with [v] = 0 in K1(A) for which ‖uv − vu‖ < δ, there is a continuous path of unitaries {v(t) : t ∈ [0, 1]} ⊂ A such that v(0) = v, v(1) = 1 and ‖uv(t)− v(t)u‖ < ǫ for all t ∈ [0, 1]. An answer is given to this question when A is assumed to be a un...

for some n , acting primitively on the set of vertices. This forms a part of the programme for the classification of all finite primitive distance transitive graphs begun in [76]; for in [76] this classification is reduced to the determination of all such graphs whose automorphism group G is either almost simple (that is, T o f f S Aut T for some nonabelian simple group T ) or affine (that is, ...

The second Veronese ideal In contains a natural complete intersection Jn generated by the principal 2-minors of a symmetric (n× n)-matrix. We determine subintersections of the primary decomposition of Jn where one intersectand is omitted. If In is omitted, the result is the other end of a complete intersection link as in liaison theory. These subintersections also yield interesting insights int...

We show that as soon h ? ? $h\rightarrow \infty$ with X $X \rightarrow , almost all intervals ( x ? log ] $(x-h\log X, x]$ ? / 2 $x \in (X/2, X]$ contain a product of at most two primes. In the proof we use Richert's weighted sieve, arithmetic information eventually coming from results Deshouillers and Iwaniec on averages Kloosterman sums.

The almost Mathieu operator is the discrete Schrodinger Hα,β,θ on \(\ell ^2(\mathbb {Z})\) defined via \((H_{\alpha ,\beta ,\theta }f)(k) = f(k + 1) - \beta \cos {}(2\pi \alpha k \theta ) f(k)\). We derive explicit estimates for eigenvalues at edge of spectrum finite-dimensional \({H^{(n)}_{\alpha }}\). furthermore show that (properly rescaled) m-th Hermite function ϕm an approximate eigenvecto...