Related papers: Uniform bounds on growth in o-minimal structures

Let R be a sufficiently saturated o-minimal expansion of a real closed field, let O be the convex hull of the rationals in R, and let st: O^n \to \mathbb{R}^n be the standard part map. For X \subseteq R^n define st(X):=st(X \cap O^n). We…

We propose new structures called almost o-minimal structures and $\mathfrak X$-structures. The former is a first-order expansion of a dense linear order without endpoints such that the intersection of a definable set with a bounded open…

We study functional limit theorems for linear type processes with short memory under the assumption that the innovations are dependent identically distributed random variables with infinite variance and in the domain of attraction of stable…

For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with…

In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…

We compare possibilities of extension of bounded and unbounded Baire-one functions from subspaces of topological spaces.

In functional analysis, there are different notions of limit for a bounded sequence of $L^1$ functions. Besides the pointwise limit, that does not always exist, the behaviour of a bounded sequence of $L^1$ functions can be described in…

Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:\mathbb{R}\to M_{n\times n}$ and lower $\ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for…

We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \cite{BPP10} for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \cite{jM83}. We prove that every abstract…

We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…

We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…

For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…

Limit can be defined by two axioms: 1. Strict inequality between limits implies, ultimately, strict inequality between functions. 2. For constant functions limit is trivial. How can basic results on convergence be derived from these axioms?…

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…

In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from $1$ to $k$ as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in…

Let Y be an infinite covering space of a projective manifold M in P^N of dimension n geq 2. Let C be the intersection with M of at most n-1 generic hypersurfaces of degree d in P^N. The preimage X of C in Y is a connected submanifold. Let…

In this paper, we prove functional limit theorems for P\'olya urn processes whose number of draws and initial number of balls tend to infinity together. This is motivated by recent work of Borovkov [5], where they prove a functional limit…

We give examples of $L^{1}$-functions that are essentially unbounded on every nonempty open subset of their domains of definition. We obtain such functions as limits of weighted sums of functions with the unboundedly increasing number of…

This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.

A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…