Consider a soccer competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The complexity of this question depends on the way scores are allocated according to the outcome of a match. For example, the ...

A set T ⊂ GF(q), q = ph is a super-Vandermonde set if ∑y∈T yk = 0 for 0 < k < |T |. We determine the structure of super-Vandermonde sets of size p + 1 (almost small) and size q/p − 1 (almost large).

Ganea conjectured that for any finite CW complex and any k > 0, cat(X×Sk) = cat(X) + 1. In this paper we prove two special cases of this conjecture. The main result is the following. Let X be a (p − 1) connected n dimensional CW complex (not necessarily finite). We show that if cat(X) = ⌊ n p ⌋ + 1 and n 6≡ −1 mod p (which implies p > 1), then cat(X×Sk) = cat(X) + 1. This is proved by showing t...

Let B denote the Beurling-Ahlfors transform defined on L(C), 1 < p < ∞. The celebrated conjecture of T. Iwaniec states that its L norm ‖B‖p = p∗ − 1 where p∗ = max{p, p p−1}. In this paper the new upper estimate ‖B‖p ≤ 1.575 (p − 1), 1 < p < ∞ is found.

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano t...

In 2000, L. Héthelyi and B. Külshammer proved that if p is a prime number dividing the order of a finite solvable group G, then G has at least 2 √ p − 1 conjugacy classes. In this paper we show that if p is large, the result remains true for arbitrary finite groups.