Related papers: Circle immersions that can be divided into two arc…

A criterion for the existence of a birational embedding of an algebraic curve into a projective plane with two Galois points is presented. Several novel examples of plane curves with two inner Galois points as an application are described.

General criteria are given for when an embedding of a Mori dream space into another satisfies certain nice combinatorial conditions on some of their associated cones. An explicit example of such an embedding is studied.

Associating to each pre-order on the indices 1,...,n the corresponding structural matrix ring, or incidence algebra, embeds the lattice of n-element pre-orders into the lattice of n x n matrix rings. Rings within the order-convex hull of…

We present a slight generalization of the notion of completely integrable systems to get them being integrable by quadratures. We use this generalization to integrate dynamical systems on double Lie groups.

A circle pattern is a configuration of circles in the plane whose combinatorics is given by a planar graph G such that to each vertex of G corresponds a circle. If two vertices are connected by an edge in G, the corresponding circles…

The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants…

We introduce and study a new integral ray transform called the head wave transform. The head wave transform integrates a function along a piecewise linear (in general geodesic) path consisting of three parts. The geometry of such paths…

In a linear chord diagram a short chord is one which joins adjacent vertices. We define a bubble to be a region in a linear chord diagram devoid of short chords. We derive a formal generating function counting bubbles by their size and find…

In this paper we introduce an algorithm of construction of cyclic space-filling curves. One particular construction provides a family of space-filling curves in all dimensions (H-curves). They are compared here with the Hilbert curve in the…

We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…

We prove that a sequence of possibly branched, weak immersions of the two-sphere $S^2$ into an arbitrary compact riemannian manifold $(M^m,h)$ with uniformly bounded area and uniformly bounded $L^2-$norm of the second fundamental form…

In a linear chord diagram a short chord joins adjacent vertices while a bubble is a region devoid of short chords. We define a bridge to be a chord joining a vertex interior to a bubble to one exterior to it. Building on earlier work, we…

A regular cover of a connected graph is called {\em cyclic} or {\em dihedral} if its transformation group is cyclic or dihedral respectively, and {\em arc-transitive} (or {\em symmetric}) if the fibre-preserving automorphism subgroup acts…

A digraph is $3$-dicritical if it cannot be vertex-partitioned into two sets inducing acyclic digraphs, but each of its proper subdigraphs can. We give a human-readable proof that the number of 3-dicritical semi-complete digraphs is finite.…

We prove that every polynomially convex arc is contained in a polynomially convex simple closed curve. We also establish results about polynomial hulls of arcs and curves that are locally rectifiable outside a polynomially convex subset.

In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…

We prove that a surface in real 3-space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point.

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form…

The analogue of Hadwiger's conjecture for the immersion relation states that every graph $G$ contains an immersion of $K_{\chi(G)}$. For graphs with independence number 2, this is equivalent to stating that every such $n$-vertex graph…

Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…