We prove that there exists a positive integer νn depending only on n such that for every smooth projective n-fold of general type X defined over C, | mKX | gives a birational rational map from X into a projective space for every m ≥ νn. This paper is a concise and refined version of [17]. MSC 32J25

The second neighborhood conjecture of Seymour asserts that for any orientation G = (V,E), there exists a vertex v ∈ V so that |N(v)| ≤ |N(v)|. The conjecture was resolved by Fisher for tournaments. In this paper we prove the second neighborhood conjecture for several additional classes of dense orientations. We also prove some approximation results, and reduce an asymptotic version of the conje...

Let (X, T) and (F, T) be transformation groups with the same phase group T. A homomorphism f: X—» F is a continuous mapping such that (xt)f=(xf)t (ïGZ, tÇUT). A transformation group (X, T) is called a minimal set if (xT)~ = cls[xt/tÇzT]=X(xÇzX). In this note it will be proved that given any abstract group T there exists a minimal set (M, T) with compact phase space M such that any minimal set (...

For any natural number n we define f(n) to be the minimum number with the following property. Given any arrangement A(L) of n blue lines in the real projective plane one can find f(n) red lines different from the blue lines such that any edge in the arrangement A(L) is crossed by a red line. We define h(n) to be the minimum number with the following property. Given any arrangement A(L) of n blu...

Let (Mt )0≤t≤1 be a continuous martingale with initial law M0 ∼ μ0, and terminal law M1 ∼ μ1, and let S = sup0≤t≤1Mt . In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. Furthermore a martingale is constructed which attains this minimum by solving a Skorokho...

Relative quantifier scope in German depends, in contrast to English, very much on word order. The scope possibilities of a quantifier are determined by its surface position, its base position and the type of the quantifier. In this paper we propose a multicomponent analysis for German quantifiers computing the scope of the quantifier, in particular its minimal nuclear scope, depending on the sy...

In this paper it has been proposed that concession should be analysed as involving scalar implicatures and that an alternative set of situations have to be assumed to account for the the relative nature of likelihood of event occurrence. This paper also claims that the notion of likelihood is the basis of the corresponding pragmatic inference and a universal quantification effect. Unexpectednes...

We show that the Schreier sets Sα (α < ω1) satisfy the following dichotomy property. For every hereditary collection F of finite subsets of N, either there exists infinite M = (mi)1 ⊆ N such that Sα(M) = {{mi : i ∈ E} : E ∈ Sα} ⊆ F , or there exist infinite M = (mi)1 , N ⊆ N such that F [N ](M) = {{mi : i ∈ F} : F ∈ F and F ⊂ N} ⊆ Sα.