Related papers: Pebble Minimization of Polyregular Functions
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and integer coefficients. As to their relationship with respect…
We study various boundary and inner regularity questions for $p(\cdot)$-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for $p(\cdot)$-harmonic…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We consider functionals given by the sum of the perimeter and the double integral of some kernel $g:\mathbb R^N\times\mathbb R^N\to \mathbb R^+$, multiplied by a "mass parameter" $\varepsilon$. We show that, whenever $g$ is admissible,…
In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, $\mathbb{Z}$-translates of itself. Refinable functions used in connection with wavelets are…
A design is additive under an abelian group $G$ (briefly, $G$-additive) if, up to isomorphism, its point set is contained in $G$ and the elements of each block sum up to zero. The only known Steiner 2-designs that are $G$-additive for some…
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular…
For any proper polynomial map $f:C^k\longrightarrow C^k$ define the function \alpha as $$\alpha(z):=\limsup_{n\to\infty} \frac{\log^+\log^+|f^n(z)|}{n} where \log^+:=\max(\log, 0).$$ Let f=(P_1,...,P_k) be a proper polynomial map. We define…
Several results on constrained spline smoothing are obtained. In particular, we establish a general result, showing how one can constructively smooth any monotone or convex piecewise polynomial function (ppf) (or any $q$-monotone ppf,…
In the two-parameter setting, we say a function belongs to the mean little $BMO$, if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by…
The theory of slice regular functions of a quaternionic variable extends the notion of holomorphic function to the quaternionic setting. This theory, already rich of results, is sometimes surprisingly different from the theory of…
This paper studies balance properties for billiard words. Billiard words generalize Sturmian words by coding trajectories in hypercubic billiards. In the setting of aperiodic order, they also provide the simplest examples of quasicrystals,…
A function $f:R\to R$, where $R$ is a commutative ring with unit element, is called polyfunction if it admits a polynomial representative $p\in R[x]$. Based on this notion we introduce ring invariants which associate to $R$ the numbers…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
The notion of regularity has been used by S. Kleiman in the construction of bounded families of ideals or sheaves with given Hilbert polynomial, a crucial point in the construction of Hilbert or Picard scheme. In a related direction,…
We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…
We study a new class of functions that arise naturally in quaternionic analysis, we call them "quasi regular functions". Like the well-known quaternionic regular functions, these functions provide representations of the quaternionic…
Let $x$ and $y$ be words. We consider the languages whose words $z$ are those for which the numbers of occurrences of $x$ and $y$, as subwords of $z$, are the same (resp., the number of $x$'s is less than the number of $y$'s, resp., is less…
We study the regularity properties of H\"older continuous minimizers to non-autonomous functionals satisfying $(p,q)$-growth conditions, under Besov assumptions on the coefficients. In particular, we are able to prove higher integrability…
We define a very general notion of regularity for functions taking values in an alternative real $*$-algebra. Over Clifford numbers, this notion subsumes the well-established notions of monogenic function and slice-monogenic function. Over…