Related papers: Finite Localities II
In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…
We prove several extensions of the Erdos-Fuchs theorem.
Particular solutions of the Benney equations are constructed. Their properties are discussed.
The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship…
In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space, which completes earlier approaches. Part II and III will…
The aim of this paper is to extend our old results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.
The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively…
Among other results, the paper gives new mapping theorems and new fixed point property theorems for inverse limits of inverse sequences of compact metric spaces with upper semicontinuous set-valued bonding functions. We also revisit the…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…
We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.
The first aim of this paper is to examine some important properties of soft metric spaces. Second is to introduce soft continuous mappings and investigate properties of soft continuous mappings. Third is to prove some fixed point theorems…
We describe a theory of finite sets, and investigate the analogue of Dedekind's theory of natural number systems (simply infinite systems) in this theory. Unlike the infinitary case, in our theory, natural number systems come in differing…
This paper presents a classification of locally $2$-homogeneous designs, extending Kantor's classification of 2-transitive symmetric designs (1985).
We introduce the notion of soficity for locally compact groups and list a number of open problems.
In this paper, we discuss the generalization of finitary $2$-representation theory of finitary $2$-categories to finitary birepresentation theory of finitary bicategories. In previous papers on the subject, the classification of simple…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…