相关论文: The Largest Respectful Function

A rational function is the ratio of two complex polynomials in one variable without common roots. Its degree is the maximum of the degrees of the numerator and the denominator. Rational functions belong to the same class if one turns into…

We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…

The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of…

In decision-making, maxitive functions are used for worst-case and best-case evaluations. Maxitivity gives rise to a rich structure that is well-studied in the context of the pointwise order. In this article, we investigate maxitivity with…

Building on the concept of pretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

This paper introduces a robust class of functions from finite words to integers that we call Z-polyregular functions. We show that it admits natural characterizations in terms of logics, Z-rational expressions, Z-rational series and…

We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and…

In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in…

Fixpoints are ubiquitous in computer science as they play a central role in providing a meaning to recursive and cyclic definitions. Bisimilarity, behavioural metrics, termination probabilities for Markov chains and stochastic games are…

A new continuity for set-valued functions is introduced, and an existence theorem is proved for such continuous set-valued functions.

The aim of this paper is to show that every representative function of a maximal monotone operator is the Fitzpatrick transform of a bifunction corresponding to the operator. In this way we exhibit the relation between the recent theory of…

The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given…

Admissible orders play a key role in ranking subintervals of the unit interval. In 2013, Bustince et al. proposed constructing such relations by means of admissible pairs of aggregation functions. The only significant example in the…

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Machine learning systems are increasingly used to make decisions about people's lives, such as whether to give someone a loan or whether to interview someone for a job. This has led to considerable interest in making such machine learning…

This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…

Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls…

The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two…

We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…