Related papers: Finitely Additive, Modular and Probability Functio…
Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively…
The Minkowski question mark function is a rich object which can be explored from the perspective of dynamical systems, complex dynamics, metric number theory, multifractal analysis, transfer operators, integral transforms, and as a function…
We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…
We will introduce a cyclic derivative for fully (stably) matricial functions and study its basic properties. In particular, we will show the Poincar\'{e} lemma for stably matricial functions of certain classes. We will also position…
The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert--Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients are constant. As an application, we give a…
We introduce a natural class of functions, the {\em pseudomultipliers}, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the…
This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.
We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called \textit{involutive semirings}. The semiring perspective helps us find a necessary and sufficient…
We develop a novel formal theory of finite structures, based on a view of finite structures as a fundamental artifact of computing and programming, forming a common platform for computing both within particular finite structures, and in the…
An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the class of semisimple MV-modules over a semisimple and totally…
We provide a complete classification of all tilting modules and tilting classes over almost perfect domains, which generalizes the classifications of tilting modules and tilting classes over Dedekind and 1-Gorenstein domains. Assuming the…
It is often stated that the Carlitz module is to the ring of univariate polynomials over a finite field what the multiplicative group is to the ring of integers. This analogy extends to the "rank 2" case, where Drinfeld modules play a role…
Let $\cal R$ be either the Grothendieck semiring (semiring with multiplication) of complex algebraic varieties, or the Grothendieck ring of these varieties, or the Grothendieck ring localized by the class of the complex affine line. We…
A fundamental construction in formal language theory is the Myhill-Nerode congruence on words, whose finitedness characterizes regular language. This construction was generalized to functions from $\Sigma^*$ to $\mathbb{Z}$ by Colcombet,…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
We study the probability that the product of two randomly chosen elements in a finite ring $R$ is equal to some fixed element $x \in R$. We calculate this probability for semisimple rings and some special classes of local rings, and find…
Let $ P \colon \mathbb{C} \to \mathbb{C} $ be an entire function. A Poincar\'e function $ L \colon \mathbb{C} \to \mathbb{C} $ of $ P $ is the entire extension of a linearising coordinate near a repelling fixed point of $ P $. We propose…
In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov-Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we…