Related papers: Connection points on double regular polygons

Given a set of points in the plane, a \emph{crossing family} is a collection of segments, each joining two of the points, such that every two segments intersect internally. Aronov et al. [Combinatorica,~14(2):127-134,~1994] proved that any…

Conjugation, or Legendre transformation, is a basic tool in convex analysis, rational mechanics, economics and optimization. It maps a function on a linear topological space into another one, defined in the dual of the linear space by…

We study complex analytic (possibly singular) projective connections on the plane. We characterize some of them in terms of their families of integral curves. We also give a beginning of classification of second order odes polynomial in the…

Let $S$ be a set of $n\geq 7$ points in the plane, no three of which are collinear. Suppose that $S$ determines $n+1$ directions. That is to say, the segments whose endpoints are in $S$ form $n+1$ distinct slopes. We prove that $S$ is, up…

Let X be a smooth projective curve of genus g \geq 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend's…

We investigated singular points of translation surfaces under the linearly independent condition. In this paper, as completion, we investigate singular points of translation surfaces under the linearly dependent condition, using the…

Let f: C --> P^3 be a general curve of genus g, mapped to P^3 via a general linear series of degree d; and let Q be a general (and thus smooth) quadric. In this paper, we show that the points of intersection f(C) \cap Q give a general…

Over the projective plane and at most two-step blowups of Hirzebruch surfaces, where there are strong full exceptional sequences of line bundles, we obtain foundational results about Gaeta resolutions of coherent sheaves by these line…

We denote a polygon as a connected component in Cayley tree of order 2 containing certain number of fix vertices. We found an exact formula for a polygon counting problem for two cases, in which, for the first case the polygon contain a…

In this series, we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects such as undirected graphs, directed graphs, bidirected graphs, hypergraphs and finitary matroids.…

We introduce and study a new type of mappings in metric spaces termed $n$-point Kannan-type mappings. A fixed-point theorem is proved for these mappings. In general case such mappings are discontinuous in the domain but necessarily…

In this paper, we establish the following two results: (1) a skew translation generalized quadrangle of even order is a translation generalized quadrangle, (2) a generalized quadrangle of even order does not admit a point regular…

Here is a square problem: in a unit square, is there a point with four rational distances to the vertices? A probability argument suggests a negative answer. This paper proves several special cases of the square problem: if the point sits…

Let two distinct $N$-simplexes be given in an Euclidean or pseudo-Euclidean $N+1$ dimensional space as each is defined by the coordinates of its $N+1$ vertexes. We consider the two families of $N$-spheres passing through the vertexes of the…

Cais, Ellenberg and Zureick-Brown recently observed that over finite fields of characteristic two, all sufficiently general smooth plane projective curves of a given odd degree admit a non-trivial rational 2-torsion point on their Jacobian.…

With the intent of laying the groundwork for a program that aims at explicitly describing the space of Cartan (i.e. multiplicative) connections on a general proper Lie groupoid, we begin to investigate the space of such connections in the…

We show that on any translation surface, if a regular point is contained in a simple closed geodesic, then it is contained in infinitely many simple closed geodesics, whose directions are dense in the unit circle. Moreover, the set of…

We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to…

Two lattice points are visible to one another if there exist no other lattice points on the line segment connecting them. In this paper we study convex lattice polygons that contain a lattice point such that all other lattice points in the…