Related papers: On tolerances representable as $R \circ R^-$

A 4-regular planar graph $G$ is said to be circle representable if there exists a collection of circles drawn on the plane such that the touching and crossing points correspond to the vertices of $G$, and the circular arcs between those…

Let $\{U_n\}_{n \geqslant 0}$ and $\{G_m\}_{m \geqslant 0}$ be two linear recurrence sequences defined over the integers. We establish an asymptotic formula for the number of integers $c$ in the range $[-x, x]$ which can be represented as…

Using the algebraic approach Lie symmetries of time dependent Schroedinger equations for charged particles interacting with superpositions of scalar and vector potentials are classified. Namely, all the inequivalent equations admitting…

We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…

We provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers. We exhibit a non-trivial real linear system which is not controllable by real static…

We study the interplay between different models of the same irreducible representation of the $F$-points of a reductive group over a local field.

Positivity constrains the allowed domain for sets of spin observables in exclusive or inclusive reactions. Examples are given for strangeness-echange reactions and photoproduction.

Let $\psi$ and $F$ be positive definite forms with integral coefficients of equal degree. Using the circle method, we establish an asymptotic formula for the number of identical representations of $\psi$ by $F$, provided $\psi$ is…

We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.

Commensurable groups are bi-interpretable, under suitable definability conditions.

We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.

The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…

We present an elementary proof concerning reciprocal transmittances and reflectances. The proof is direct, simple, and valid for the diverse objects that can be absorptive and induce diffraction and scattering, as long as the objects…

Let X be a locally compact space, and let A and B be Co(X)-algebras. We define the notion of an asymptotic Co(X)-morphism from A to B and construct representable E-theory groups RE(X;A,B). These are the universal groups on the category of…

A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calder\'{o}n's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory's…

Let $G$ be a group and let $\rho\colon G\to\operatorname{Sym}(V)$ be a permutation representation of $G$ on a set $V$. We prove that there is a faithful $G$-coalgebra $C$ such that $G$ arises as the image of the restriction of…

Given a subshift over an arbitrary alphabet, we construct a representation of the associated unital algebra. We describe a criteria for the faithfulness of this representation in terms of the existence of cycles with no exits. Subsequently,…

We explicitly construct and list all unitary superconformal multiplets, along with their index contributions, in five and six dimensions. From this data, we uncover various unifying themes in the representation theory of five- and…