相关论文: Self-Similar Jordan Arcs Which Do Not Satisfy OSC

We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set $\Omega$. We prove existence, regularity and some structural properties of minimizers. In particular, when $\Omega$ is…

Singleton arc consistency is an important type of local consistency which has been recently shown to solve all constraint satisfaction problems (CSPs) over constraint languages of bounded width. We aim to characterise all classes of CSPs…

A closed convex conic subset $\mathcal{S}$ of the positive semidefinite (PSD) cone is rank-one generated (ROG) if all of its extreme rays are generated by rank-one matrices. The ROG property of $\mathcal{S}$ is closely related to the…

For any locally analytic curve we show that arc length can be complexified and seen as a conformal parameter. As an application, we show that any such curve defines a unique maximal one and that the notions of analytic Jordan curve…

We determine three-dimensional algebraic varieties whose groups of birational selfmaps do not satisfy the Jordan property.

We show that the Jordan-H\"older property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived…

We study intersecting extremal black attractors in non chiral 8D N=1 supergravity with moduli space ((SO(2,N))/(SO(2)\times SO(N)))\times SO(1,1) and work out explicitly the attractor mechanism for various black p-brane configurations with…

The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic…

We show that a set of $n$ algebraic plane curves of constant maximum degree can be cut into $O(n^{3/2}\operatorname{polylog} n)$ Jordan arcs, so that each pair of arcs intersect at most once, i.e., they form a collection of pseudo-segments.…

A new equivalence relation, named relation of 'similarity' is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named 'similar' trajectories) are obtained; they have the theoretical…

In this paper we show that any linear vector field $\mathcal{X}$ on a connected Lie group $G$ admits a Jordan decomposition and the recurrent set of the associated ow of automorphisms is given as the intersection of the fixed points of the…

We define a Jordan homomorphism $\varphi$ from a ring $R$ to a ring $R'$ to be splittable if the ideal (of the subring generated by the image of $\varphi$) generated by all $\varphi(xy)-\varphi(x)\varphi(y)$, $x,y\in R$, has trivial…

Given a hyperbolic surface $\S$, a classic result of Birman and Series states that for each $K$, all complete geodesics with at most $K$ self-intersections can only pass through a certain nowhere dense, Hausdorff dimension 1 subset of $\S$.…

For two disjoint rectifiable star-shaped Jordan curves (including round circles) in the asymptotic boundary of hyperbolic 3-space, if the distance (see Definition 1.8) between these two Jordan curves are bounded from above by some constant,…

We study the {\it arc and curve} complex $AC(S)$ of an oriented connected surface $S$ of finite type with punctures. We show that if the surface is not a sphere with one, two or three punctures nor a torus with one puncture, then the…

The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-repeller pair, which are attractor-repellent sets for all other…

We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of such intersection as the attractor of a graph-directed…

Parallel to the main results of [13] and [14], which explore the equivalence between prox-regularity, the exterior sphere condition, and $S$-convexity, we present novel characterizations of the $r$-strong convexity property, namely, of the…

We extend the classical Carath\'eodory extension theorem to quasiconformal Jordan domains $( Y, d_{Y} )$. We say that a metric space $( Y, d_{Y} )$ is a quasiconformal Jordan domain if the completion $\overline{Y}$ of $( Y, d_{Y} )$ has…

In this note we consider asymptotics of the multipoint Pad\'e approximants to Cauchy integrals of analytic non-vanishing densities defined on a Jordan arc connecting $ -1 $ and $ 1 $. We allow for the situation where the (symmetric) contour…