We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it characterizes disjoint frequent hypercyclicity for family of unilateral pseudo-shifts on c0(N) ?p(N), 1?p<?. As an application, we characterize frequently hypercyclic weighted shifts. give analogous results the weaker notions upper reiterative hypercyclicity. Finally, provide counterexamples showing that, although hypercycl...

We study “disjoint” versions of the notions trivial, locally strictly singular and super-strictly quasi-linear maps in context Köthe function spaces. Among other results, we show: (i) (locally) trivial disjointly coincide on reflexive spaces; (ii) non-atomic superreflexive spaces, no centralizer is singular, although most are singular. (iii) supersingular exist between spaces Kalton—Peck centra...

In this paper we consider graphs which have no k vertex-disjoint cycles. For given integers k, let f (k, ) be the maximum order of a graph G with independence number (G) , which has no k vertex-disjoint cycles. We prove that f (k, ) = 3k + 2 − 3 if 1 5 or 1 k 2, and f (k, ) 3k + 2 − 3 in general. We also prove the following results: (1) there exists a constant c (depending only on ) such that f...

In the paper a short proof is given for Kneser's conjecture. The proof is based on Borsuk's theorem and on a theorem of Gale. Recently, LOV~SZ has given a proof for Kneser's conjecture [4]. He used Borsuk's theorem. This fact gave the author the idea of the proof we present here. THEOREM (Kneser's conjecture [3]). If the n-tuples of a set of 2n + k elements are partitioned into k + 1 classes, t...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

The combination of intersection types, a merge operator and parametric polymorphism enables important applications for programming. However, such combination makes it hard to achieve the desirable property of a coherent semantics: all valid reductions for the same expression should have the same value. Recent work proposed disjoint intersections types as a means to ensure coherence in a simply ...