We study the possibility of the existence of a Katona type proof for the Erdős-Ko-Rado theorem for 2and 3-intersecting families of sets. An Erdős-Ko-Rado type theorem for 2-intersecting integer arithmetic progressions and a model theoretic argument show that such an approach works in the 2-intersecting case.

A class of examples of Riemannian metrics with holonomy G2 on compact 7-manifolds was constructed by the author in [Ko] using a certain ‘generalized connected sum’ of two asymptotically cylindrical manifolds with holonomy SU(3). We consider, on each of the two initial SU(3)-manifolds, a fibration arising from a Lefschetz pencil of K3 surfaces. The gluing of the two K3 fibrations yields a coasso...

Research on organizational IT innovations has generated a substantial body of insights. In this paper we draw particular attention to the thesis that IT implementations build crucial capabilities which are then typically redeployed for future IT innovations. Indeed, it is commonly accepted that organizational innovations do not take place in a historical vacuum but instead, the history of prior...

A family 9 of distinct k-element subsets of the n-element set X is called intersecting if Fn F’ # @ holds for all F, F’ E 9. Erdos, Ko, and Rado proved that for n > 2k necessarily ) 9 ) < (1: :) holds, which is clearly best possible (take all k-sets through a fixed element). For a family 9, its maximum degree d(9) is the maximum number of sets in .P= containing any particular element of X. For ...

We show a stability estimate for the degenerate complex Monge-Ampère operator that generalizes a result of Ko lodziej [11]. In particular, we obtain the optimal stability exponent and also treat the case when the right hand side is a general Borel measure satisfying certain regularity conditions. Moreover our result holds for functions plurisubharmonic with respect to a big form generalizing th...

Given an r × r complex matrix T , if T = U |T | is the polar decomposition of T , then the Aluthge transform is defined by ∆ (T ) = |T |U |T |. Let ∆n(T ) denote the n-times iterated Aluthge transform of T , i.e. ∆0(T ) = T and ∆n(T ) = ∆(∆n−1(T )), n ∈ N. In this paper we make a brief survey on the known properties and applications of the Aluthge trasnsorm, particularly the recent proof of the...

Article history: Received 28 January 2013 Available online 27 September 2014

Let n i , k i be positive integers , i 5 1 , . . . , d , satisfying n i > 2 k i . Let X 1 , . . . , X d be pairwise disjoint sets with u X i u 5 n i . Let * be the family of those ( k 1 1 ? ? ? 1 k d )-element sets which have exactly k i elements in X i , i 5 1 , . . . , d . It is shown that if ̂ ’ * is an intersecting family then u ̂ u / u * u < max i k i / n i , and this is best possible . The ...