Related papers: Quotients by finite equivalence relations
We classify integer abc-equations c = a + b (to be defined), according to their radical R(abc) and prove that the resulting equivalence classes contain only a finite number of such equations. The proof depends on a 1933 theorem of Kurt…
Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive…
This paper concerns partial groups, objective partial groups, and (finite) localities, with special attention given to the quotient of a locality by a partial normal subgroup.
We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also…
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two…
We present an elementary description of sofic equivalence relations, as well as some permanence properties for soficity. We answer a question by Conley, Kechris and Tucker-Drob of determining soficity in terms of the full group for…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
These notes are devoted to lattices in products of trees and related topics. They provide an introduction to the construction, by M. Burger and S. Mozes, of examples of such lattices that are simple as abstract groups. Two features of that…
This paper is an appendix to the paper "Reasoning with Justifiable Exceptions in Contextual Hierarchies" by Bozzato, Serafini and Eiter, 2018. It provides further details on the language, the complexity results and the datalog translation…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. We provide three new transendence criteria, that apply to a broad class of…
This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We investigate computability in the lattice of equivalence relations on the natural numbers. We mostly investigate whether the subsets of appropriately defined subrecursive equivalence relations -for example the set of all polynomial-time…
We consider d-minimal expansions of ordered fields. We demonstrate the existence of definable quotients of definable sets by definable equivalence relations when several technical conditions are satisfied. These conditions are satisfied…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
It is shown that Feynman's formulation of quantum mechanics can be reproduced as a description of the set of intermediate cardinality. Properties of the set follow directly from the independence of the continuum hypothesis. Six referee…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…