Related papers: On Countable Stationary Towers

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is…

We prove exponential instability properties for the fractional Calder\'on problem and the conductivity formulation of the fractional Calder\'on problem in the regime of fractional powers $s\in (0,1)$. We particularly focus on two settings:…

We extend the definition of the Costas property to functions in the continuum, namely on intervals of the reals or the rationals, and argue that such functions can be used in the same applications as discrete Costas arrays. We construct…

We present constructions of countable two-dimensional subshifts of finite type (SFTs) with interesting properties. Our main focus is on properties of the topological derivatives and subpattern posets of these objects. We present a countable…

We show the existence of regular combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise…

The property of countable metacompactness of a topological space gets its importance from Dowker's 1951 theorem that the product of a normal space X with the unit interval is again normal iff X is countably metacompact. In a recent paper,…

Under the fundamental theorem of arithmetic, any integer $n>1$ can be uniquely written as a product of prime powers $p^a$; factoring each exponent $a$ as a product of prime powers $q^b$, and so on, one will obtain what is called the tower…

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

A simple construction is given of a class of Euclidean invariant, reflection positive measures on a compactification of the space of distributions. An unusual feature is that the regularizations used are not reflection positive.

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

We present distributions of countable models and correspondent structural characteristics of complete theories with continuum many types: for prime models over finite sets relative to Rudin-Keisler preorders, for limit models over types and…

We consider a convective bulk-surface Cahn--Hilliard system with dynamic boundary conditions and singular potentials. For this model, well-posedness results concerning weak and strong solutions have already been established in the…

This paper provides two characterizations of regularity for near-vector spaces: first, by expressing them as a direct sum of vector spaces over division rings formed by distributive elements; second, by expressing their dimension in term of…

Let $\lambda$ be a limit of Woodin cardinals. It was shown by the second author that the pointclass of ${<\lambda}$-homogeneously Suslin sets has the scale property. We give a new proof of this fact, which avoids the use of stationary tower…

The main goal of this paper is to generalize several results concerning cardinal invariants to the statements about the associated families of sets. We also discuss the relationship between the additive properties of sets and their Borel…

Fix a positive integer X. We quantify the cardinality of the set $\{\lfloor X/n \rfloor\}_{n=1}^X$. We discuss restricting the set to those elements that are prime, semiprime or similar.

An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…

The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…