Related papers: Semifields, relative difference sets, and bent fun…
In this article we completely characterise constant length substitution shifts which have an almost automorphic factor, or which have a bijective substitution factor. Our approach is algebraic: we study these dynamical properties in terms…
Let $e^{2\pi i\Q}$ denote the set of roots of unity. We consider subsets $E\subset e^{2\pi i\Q}$ that are quasi-independent or algebraically independent (as subsets of the discrete plane). A bijective map on $e^{2\pi i\Q}$ preserves the…
The aim of this note is to show the existence of a correspondance between certain algebraic continued fractions in fields of power series over a finite field and automatic sequences in the same finite field. this connection is illustrated…
A finite semifield is a finite nonassociative ring with identity such that the set of its nonzero elements is closed under the product. From any finite semifield a projective plane can be constructed. In this paper we obtain new semifield…
A partial field is an algebraic object that allows one to simultaneously abstract several different representability properties of matroids. In this paper we study partial fields as algebraic objects in their own right. We characterize the…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the…
The aim of this article is to give an expository account of the equivalence between modest sets and partial equivalence relations. Our proof is entirely self-contained in that we do not assume any knowledge of categorical realizability. At…
I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an…
We revisit Sz.-Nagy's criteria for similarity of Hilbert space bounded linear operators to isometries or unitaries and present new ones. We also discuss counterparts of the Dixmier-Day theorem concerning bounded representations of amenable…
Negabent functions as a class of generalized bent functions have attracted a lot of attention recently due to their applications in cryptography and coding theory. In this paper, we consider the constructions of negabent functions over…
In this paper we collect and improve the techniques for calculating the nuclei of a semifield and we use these tools to determine the order of the nuclei and of the center of some commutative presemifields of odd characteristic recently…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
This paper is devoted to the study of semigroups of composition operators and semigroups of holomorphic mappings. We establish conditions under which these semigroups can be extended in their parameter to sector given a priori. We show that…
As one of the fundamental tasks in computer vision, semantic segmentation plays an important role in real world applications. Although numerous deep learning models have made notable progress on several mainstream datasets with the rapid…
We generalize the concept of a field by allowing addition to be a partial operation. We show that elements of such a "partially additive field" share many similarities with physical quantities. In particular, they form subsets of mutually…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to behave well in standard ring extensions, with the notable…
We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by…
It is well-known that degree two finite field extensions can be equipped with a Hermitian-like structure similar to the extension of the complex field over the reals. In this contribution, using this structure, we develop a modular…
The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…