We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on l(Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently...

In the present study we propose a context wherein the endorsement rate of the scalar inference from ‘some’ to ‘not all’ either increases or decreases. It is known that people tend to interpret the quantifier ‘some’ as ‘not all’, though logically some means ‘some and possibly all’. However, we argue that this tendency to derive the scalar inference is variable and depends on the attitude of the ...

Given a mapping f : A → B from a (pre-)ordered set A into an unstructured set B, we study the problem of defining a suitable (pre-)ordering relation on B such that there exists a mapping g : B → A such that the pair of mappings (f, g) forms an adjunction between (pre-)ordered sets. The necessary and sufficient conditions obtained are then expressed in terms of closure operators and closure syst...

Chvfital stated in 1972 the following conjecture: If Y~ is a hereditary hypergraph on S and .gCcy~ is a family of maximum cardinality of pairwise intersecting members of ~, then there exists an xeS such that d~(x)=l{HeYe:xeH}l=l.al. Berge and Schrnheim proved that 1~1~½ I~el for every ~ and ~. Now we prove that if there exists an .~, I~1 = [½ I~el] then Chvfital's conjecture is true for this ~.

A well-known challenge for accounts of exhaustivity implications is the granularity problem: that adding a non-weakest disjunct to an utterance (e.g., “or both”) may prevent exhaustivity implications. Recent approaches to this problem apply exhaustivity operators either globally, i.e., to the disjunction as a whole, or locally, i.e., to each disjunct separately. This paper seeks to contribute t...

A theorem of Dekking in the combinatorics of words implies that there exists an injective order-preserving transformation f : {0, 1, . . . , n} → {0, 1, . . . , 2n} with the restriction f(i + 1) ≤ f(i) + 2 such that for every 5-term arithmetic progression P its image f(P ) is not an arithmetic progression. In this paper we consider symmetric sets in place of arithmetic progressions and prove lo...

and Applied Analysis 3 Proposition 1.2. Function σ t is μ-measurable. Proof. Pick a dense set {ri}i 1 in 0,∞ and set Bk { t ∈ T : M ( t, 1 2 rk ) 1 2 M t, rk } , qk t rkχBk t k ∈ N . 1.7 It is easy to see that for all k ∈ N, σ t ≥ qk t μ-a.e on T . Hence, supk≥1qk t ≤ σ t . For μ-a.e t ∈ T , arbitrarily choose ε ∈ 0, σ t . Then, there exists rk ∈ σ t − ε, σ t such that M t, 1/2 rk 1/2 M t, rk ,...

We prove that given any smooth metric γ and smooth positive function H on S, there is a constant λ > 0, depending on (γ,H), and an asymptotically flat solution (M, g, u) of the static vacuum Einstein equations on M = R \ B, such that the induced metric and mean curvature of (M, g, u) at ∂M are given by (γ, λH). This gives a partial resolution of a conjecture of Bartnik.

defining a function f(x, y) of the two independent complex variables x, y within the regions | x | < i?,, | y \ < R2 ( Rx > 0, R2 > 0 ), to determine the value of this function at any point in its domain of existence, f It is our special purpose to demonstrate the following theorem : Theorem. If in the series (1) the function a(u, v) considered as a function of the two independent, complex vari...