Related papers: Two $\mathfrak{b}$ or not two $\mathfrak{b}$?

We show explicitly that Boolean inverse semigroups are in duality with what we term Boolean groupoids. This generalizes the classical Stone duality, which we refer to as commutative Stone duality, between generalized Boolean algebras and…

We analyze the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such…

We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…

We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…

This paper presents duality between probability distributions and utility functions.

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

In this paper we study the genralized q-Euler numbers and polynomials. From our results, we derive some interesting congruences related tothe generalized q-Euler numbers.

Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…

There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier foundational work of such authors as Nachbin,…

We build type IIB backgrounds that can be interpreted as the dual description of field theories in which the dynamics shows many non-trivial phenomena, generalizing the baryonic branch of the Klebanov-Strassler system. We illustrate the…

The Jacobi polynomial has been advocated by many authors as a useful tool to evolve non-singlet structure functions to higher $Q^2$. In this work, it is found that the convergence of the polynomial sum is not absolute, as there is always a…

We introduce two new classes of integers. The first class consists of numbers $N$ for which there exists at least one nonnegative integer $A$, such that the sum of $A$ and the sum of digits of $N$, added to the reversal of the sum, gives…

The classification, up to isomorphism, of two-dimensional (not necessarily commutative) Jordan algebras over algebraically closed fields and $\mathbb{R}$ is presented in terms of their matrices of structure constants.

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

In this paper we investigate the distribution of zeros of Boubaker polynomials.

We continue the work of [1, 2, 3] by analyzing the equivalence relation of bi-embeddability on various classes of countable planes, most notably the class of countable non-Desarguesian projective planes. We use constructions of the second…

We give, using higher Bernstein polynomials defined in our paper [2], a stronger version of our previous result in [1] whose converse is proved in [2] and we give some complements to the results in [2] which help to compute these higher…

Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…

We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties