Related papers: Associative idempotent nondecreasing functions are…

In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…

(1) We prove that, provided n>=4, a permutably reducible n-ary quasigroup is uniquely specified by its values on the n-ples containing zero. (2) We observe that for each n,k>=2 and r<=[k/2] there exists a reducible n-ary quasigroup of order…

For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…

We prove a analogous of Stein theorem for rational functions in several variables: we bound the number of reducible fibers by a formula depending on the degree of the fraction.

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We…

In this paper, we define and study the concept of traceable regressions. These are sequences of regressions in joint or single responses for which a corresponding regression graph captures not only an independence structure but represents,…

We characterize commutative idempotent involutive residuated lattices as disjoint unions of Boolean algebras arranged over a distributive lattice. We use this description to introduce a new construction, called gluing, that allows us to…

Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…

We prove that two fixed univariate functions, namely, an arbitrary continuous non-affine function and a concrete affine function, are sufficient to approximate continuous functions of one variable under the operations of addition and…

A word-to-word function is rational if it can be realized by a non-deterministic one-way transducer. Over finite words, it is a classical result that any rational function is regular, i.e. it can be computed by a deterministic two-way…

We consider $d$-dimensional configurations, that is, colorings of the $d$-dimensional integer grid $\mathbb{Z}^d$ with finitely many colors. Moreover, we interpret the colors as integers so that configurations are functions $\mathbb{Z}^d…

We study the interplay between additivity (as in the Cauchy functional equation), subadditivity and linearity. We obtain automatic continuity results in which additive or subadditive functions, under minimal regularity conditions, are…

We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a…

We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if $x$ is a self-adjoint noncommutative martingale and $y$ is weakly differentially subordinate to $x$ then $y$ admits a…

Error: Peer-review process exposed an error in Theorem 1 that, unfourtunately, is not repairable. Idempotent semigroups are always finite. See Green and Rees [1952], Siekmann and Szab\'o [1981] for details Anti-unification is a fundamental…

We discuss some surprising phenomena from basic calculus related to oscillating functions and to the theorem on the differentiability of inverse functions. Among other things, we see that a continuously differentiable function with a strict…

Let $F$ be a field, char$(F)\neq 2$. Then every finite-dimensional $F$-algebra has either an idempotent or an absolute nilpotent if and only if over $F$ every polynomial of odd degree has a root in $F$. This is also necessary and sufficient…

Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function…

The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…