Related papers: Rigged configurations and the $*$-involution
In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.
Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and…
B-fields over a groupoid with involution are defined as Real graded Dixmier-Douady bundles. We use these to introduce the Real graded Brauer group which constitutes the set of twistings for Atiyah's KR-functor in the category of locally…
We will introduce the notion of a near-isometric covariant representation of a $C^*$-correspondence and prove its Wold-type decomposition. Wold-type decomposition for doubly twisted left-invertible covariant representations of a product…
We construct a theory of motivic integration for smooth rigid varieties. As an application new invariants of degenerations are obtained.
Composite rigging systems, involving membranes that meet on strings that meet on monopoles, arise naturally by the Kibble mechanism as topological defects in field theories involving spontaneous symmetry breaking. Such systems will tend to…
In this article, we first briefly review the solution of Z(2) kink solitons. Then we construct some multi-kink soliton configurations which are static and show their few features which are actually important to characterize their stability…
We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…
Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…
We study the b-functions of relative invariants of the prehomogeneous vector spaces associated with quivers of type A. By applying the decomposition formula for b-functions, we determine explicitly the b-functions of one variable for each…
We investigate a rotated, orthogonal gravitational wedge billiard - a special case of the asymmetric wedge billiard - in which the dynamics are integrable. We derive equations and conditions under which periodic orbits may be constructed…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
We investigate the representation of the symmetric group afforded by the action on its conjugacy class of fixed point free involutions, over an algebraically closed field of finite characteristic p. We discuss the general form of the set of…
Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control…
In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…
Most systems exhibit significant variability in their dynamics, including variations in system parameters and large high-frequency dynamic uncertainties. Traditional uncertainty modelling techniques consolidate all such variations into a…
In this paper, which is a complement of \cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known…
An involution over finite fields is a permutation polynomial whose inverse is itself. Owing to this property, involutions over finite fields have been widely used in applications such as cryptography and coding theory. As far as we know,…
In this introductory chapter of the Special Issue entitled `The Structure and Evolution of Stars', we highlight the recent major progress made in our understanding in the physics that governs stellar interiors. In so doing, we combine…
We provide a relation which describes how the entanglement of two d-level systems evolves as either system undergoes an arbitrary physical process. The dynamics of the entanglement turns out to be of a simple form, and is fully captured by…