相关论文: Characterization of preclones by matrix collection…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
Garret Birkhoff observed that any binary relation between two sets determines a Galois connection between the powersets, or equivalently, closure operators on the powersets, or equivalently, complete lattices of subsets that are dually…
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
The Galois group of an infinite Galois extension has a natural topology, called the Krull topology, which has the important property of being profinite. It is impossible to talk about Galois representations, and hence the Langlands Program,…
In recent work, we introduced a new semantics for conditionals, covering a large class of what we call preconditionals. In this paper, we undertake an axiomatic study of preconditionals and subclasses of preconditionals. We then prove that…
We investigate the topological structures of Galois covers of surfaces of minimal degree (i.e., degree n) in n+1 dimensional complex projective space. We prove that for n is greater than or equal to 5, the Galois covers of any surfaces of…
A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals. In this article, we explore various aspects of closed graphs, including the number of closed labelings…
Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=\pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The…
If the Continuum Hypothesis is false, it implies the existence of cardinalities between the integers and the real numbers. In studying these "cardinal characteristics of the continuum", it was discovered that many of the associated…
The difference Galois theory of Mahler equations is an active research area. The present paper aims at developing the analytic aspects of this theory. We first attach a pair of connection matrices to any regular singular Mahler equation. We…
We construct Galois theory for sublattices of certain complete modular lattices and their automorphism groups. A well-known description of the intermediate subgroups of the general linear group over a semilocal ring containing the group of…
It was recently shown that a large class of phylogenetic networks, the `labellable' networks, is in bijection with the set of `expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks…
Many Properties of a category X, as for instance the existence of an adjoint or a factorization system, are a consequence of the cowellpoweredness of X. In the absence of cowellpoweredness, for general results, fairly strong assumption on…
We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown…
Assume that $X$ and $Y$ are arithmetic schemes, i.e., integral schemes of finite types over $Spec(\mathbb{Z})$. Then $X$ is said to be quasi-galois closed over $Y$ if $X$ has a unique conjugate over $Y$ in some certain algebraically closed…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
Our aim is to describe the theory of Cartesian decompositions preserved by some member of a large family of finite transitive permutation groups called innatelytransitive groups.
This note presents Galois theory for finite fields. It was written as a handout for the MAT401 course ``Polynomial equations and fields'' taught at the University of Toronto in Spring 2026. We use without proofs some basic properties of…