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In topological dynamics, the Of course, the statement is preceded by the presentation of the concepts of an entropy structure and its superenvelopes, adapted from the case of

We introduce generalizations of o-minimality ( -o-minimality and weak -p.o.-lin-minimality) and study their properties.

We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We also provide a short proof that algebraically closed valued fields with separated analytic structure (in any rank) are C -minimal.

Let (X,T)(X,T) be a topological dynamical system, and F\\mathcal {F} be a family of subsets of Z+\\mathbb {Z}_+. (X,T)(X,T) is strongly F\\mathcal {F}-sensitive if there is δ>0\\delta >0 such that for each non-empty open subset UU there are x,y∈Ux,y\\in U with {n∈Z+:d(Tnx,Tny)>δ}∈F\\{n\\in \\mathbb {Z}_+: d(T^nx,T^ny)>\\delta \\}\\in \\mathcal {F}. Let Ft\\mathcal {F}_t (resp. Fip\\mathcal {F}_{ip}, Ffip\\mathcal {F}_{fip}) consist of thick sets (resp. IP-sets, subsets containing arbitrarily long finite IP-sets). The following Auslander-Yorke’s type dichotomy theorems are obtained: (1) a minimal system is either strongly Ffip\\mathcal {F}_{fip}-sensitive or an almost one-to-one extension of its ∞\\infty-step nilfactor; (2) a minimal system is either strongly Fip\\mathcal {F}_{ip}-sensitive or an almost one-to-one extension of its maximal distal factor; (3) a minimal system is either strongly Ft\\mathcal {F}_{t}-sensitive or a proximal extension of its maximal distal factor.

According to the Müller-Takano Generalization (Müller 1993; Takano 1994), a remnant that contains a trace resulting from a given type of movement cannot itself undergo that same type of movement. I argue that Richards’ (2004) data from Bulgarian “Russian-doll” wh-questions constitute principled exceptions to this generalization under an approach that derives it from a minimality condition on movement paths. Alternative approaches to the generalization have a harder time deriving such exceptions.

We discuss the denseness of the strong stable and unstable manifolds of partially hyperbolic diffeomorphisms. To this end, we introduce the concept of m -minimality, wich means that m -almost every point in M has its strong stable and unstable manifolds dense in M . We show that this property has both topological and ergodic consequences. Also, we prove the abundance of m -minimal partially hyperbolic diffeomorphisms in the volume preserving and symplectic scenario.

For commuting contractions$T_1,\\dots,T_n$acting on a Hilbert space$\\mathscr{H}$with$T=\\prod_{i=1}^n T_i$, we find a necessary and sufficient condition such that$(T_1,\\dots,T_n)$dilates to a commuting tuple of isometries$(V_1,\\dots,V_n)$on the minimal isometric dilation space of T with$V=\\prod_{i=1}^nV_i$being the minimal isometric dilation of T . This isometric dilation provides a commutant lifting of$(T_1, \\dots, T_n)$on the minimal isometric dilation space of T . We construct both Schäffer and Sz. Nagy–Foias-type isometric dilations for$(T_1,\\dots,T_n)$on the minimal dilation spaces of T . Also, a different dilation is constructed when the product T is a$C._0$contraction, that is,${T^*}^n \\rightarrow 0$as$n \\rightarrow \\infty$. As a consequence of these dilation theorems, we obtain different functional models for$(T_1,\\dots,T_n)$in terms of multiplication operators on vectorial Hardy spaces. One notable fact about our models is that the multipliers are all analytic functions in one variable. The dilation when T is a$C._0$contraction leads to a conditional factorization of T . Several examples have been constructed.

This article investigates the Final-over-Final Constraint (FOFC): a head-initial category cannot be the immediate structural complement of a head-final category within the same extended projection. This universal cannot be formulated without reference to the kind of hierarchical structure generated by standard models of phrase structure. First, we document the empirical evidence: logically possible but crosslinguistically unattested combinations of head-final and head-initial orders. Second, we propose a theory, based on a version of Kayne's (1994) Linear Correspondence Axiom, where FOFC is an effect of the distribution of a movement-triggering feature in extended projections, subject to Relativized Minimality.

On an abelian scheme over a smooth curve over ℚ̅ a symmetric relatively ample line bundle defines a fiberwise Néron–Tate height. If the base curve is inside a projective space, we also have a height on its ℚ̅-points that serves as a measure of each fiber, an abelian variety. Silverman proved an asymptotic equality between these two heights on a curve in the abelian scheme. In this paper we prove an inequality between these heights on a subvariety of any dimension of the abelian scheme. As an application we prove the Geometric Bogomolov Conjecture for the function field of a curve defined over ℚ̅. Using Moriwaki's height we sketch how to extend our result when the base field of the curve has characteristic 0.