Related papers: Jet closures and the local isomorphism problem
Given two tuples of subspaces, can you tell whether the tuples are isomorphic? We develop theory and algorithms to address this fundamental question. We focus on isomorphisms in which the ambient vector space is acted on by either a unitary…
A discretisation scheme that preserves topological features of a physical problem is extended so that differential geometric structures can be approximated in a consistent way thus giving access to the study of physical systems which are…
This paper shows some criteria for a scheme of finite type over an algebraically closed field to be non-singular in terms of jet schemes. For the base field of characteristic zero, the scheme is non-singular if and only if one of the…
For a fixed ring, different classes of ring epimorphisms and localisation maps are compared. In fact, we provide sufficient conditions for a ring epimorphism to be a universal localisation. Furthermore, we consider recollements induced by…
We define an operation of jets on graphs inspired by the corresponding notion in commutative algebra and algebraic geometry. We examine a few graph theoretic properties and invariants of this construction, including chromatic numbers,…
We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of…
This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…
In a reconfiguration problem, we are given two feasible solutions of a combinatorial problem and our goal is to determine whether it is possible to reconfigure one into the other, with the steps dictated by specific reconfiguration rules.…
For a surjective self-morphism on a projective variety defined over a number field, we study the preimages question, which asks if the set of rational points on the iterated preimages of an invariant closed subscheme eventually stabilize.…
This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…
Isomorphisms p between pattern classes A and B are considered. It is shown that, if p is not a symmetry of the entire set of permutations, then, to within symmetry, A is a subset of one a small set of pattern classes whose structure,…
In an earlier article, we have "derived" space, as a part of the Random Dynamics project. In order to get locality we need to obtain reparametrization symmetry, or equivalently, diffeomorphism symmetry. There we sketched a procedure for how…
For a given singularity of a plane curve we consider the locus of nodal deformations of the singularity with the given number of nodes and describe possible components of the locus. As applications, we solve the local symplectic isotopy for…
For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated invertible R-module is free. We give many examples illustrating this property.
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Problem of global integration of geometric structures arising in the theory of dynamical systems admitting the normal shift is considered. In the case when such integration is possible the problem of globalization for shift maps is studied.
The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of…
The jet charge is an old observable that has proven uniquely useful for discrimination of jets initiated by different flavors of light quarks, for example. In this Letter, we propose an approach to understanding the jet charge by…
We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective…
We express explicitly the integral closures of some ring extensions; this is done for all Bring-Jerrard extensions of any degree as well as for all general extensions of degree < 6; so far such an explicit expression is known only for…