Related papers: Finite Localities II
We discuss an extension of classical combinatorics theory to the case of spatially distributed objects.
The species of finite topological spaces admits two graded bimonoid structures, recently defined by F. Fauvet, L. Foissy, and the second author. In this article, we define a doubling of this species in two different ways. We build a…
We derive a fluid theory for spin-1/2 particles starting from an extended kinetic model based on a spin-projected density matrix formalism. The evolution equation for the spin density is found to contain a pressure-like term. We give an…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.
The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.
This note informally describes a way to build certain cubical n-categories by iterating a process of taking models of certain finite limits theories. We base this discussion on a construction of "double bicategories" as bicategories…
Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field $\mathbb F_2$ (with respect to all $\mathbb F_2$-algebra automorphisms) are fully described.
In this two-part essay, we distinguish several senses in which general relativity has been regarded as "locally special relativistic". Here, in Part 1, we focus on senses in which a relativistic spacetime has been said to be "locally…
We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to…
The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.
In this paper we introduce a link between geometry of ordinary continued fractions and trajectories of points that moves according to the second Kepler law. We expand geometric interpretation of ordinary continued fractions to the case of…
A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…
In this paper we first survey some basic results in the cohomology of finite groups, and then discuss recent work on constructing free actions of finite groups on products of spheres.
This is an introduction to the theory of normal bases of finite fields. The first few chapters cover a wide range of topics on the theory of normal bases of finite fields. Most standard definitions and results, including proofs are given.…
This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics
We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…
The notion of finitary spacetime sheaves is introduced based on locally finite approximations of the continuous topology of a bounded region of a spacetime manifold. Finitary spacetime sheaves are seen to be sound mathematical models of…
We survey new results on finite groups of birational transformations of algebraic varieties.
This is a review of Parshin's higher local class field theory in characteristic p.