共查询到20条相似文献,搜索用时 656 毫秒
1.
Jesús Gonzalo Pérez 《Geometriae Dedicata》2008,132(1):105-119
A simple dynamical condition is given for line fields within a contact structure, which is satisfied exactly by those line
fields which are common kernels of contact circles. Some convexity properties are established which are useful in the study
of contact circles up to homotopy. A necessary condition for extending a contact form to a contact circle is given. Based
on work of Lisca–Matić and Honda, concrete examples are given which show that the condition is not just homotopic but a geometric
one. The paper ends with an open question.
Dedicated to Fernando Varela, for many reasons. 相似文献
2.
LexX be a homogeneous polynomial vector field of degreen≥3 on S2 having finitely many invariant circles. Then, for such a vector fieldX we find upper bounds for the number of invariant circles, invariant great circles, invariant circles intersecting at a same
point and parallel circles with the same director vector. We give examples of homogeneous polynomial vector fields of degree
3 on S2 having finitely many invariant circles which are not great circles, which are limit cycles, but are not great circles and
invariant great circles that are limit cycles. Moreover, for the casen=3 we determine the maximum number of parallel invariant circles with the same director vector.
The authors are partially supported by a MCYT grant BFM2002-04236-C02-02 and by a CIRIT grant number 2001SGR 00173. 相似文献
3.
Gehová López-González Gerardo Altamirano-Gómez Eduardo Bayro-Corrochano 《Advances in Applied Clifford Algebras》2016,26(3):1045-1059
Traditional methods for geometric entities resort to the Hough transform and tensor voting schemes for detect lines and circles. In this work, the authors extend these approaches using representations in terms of k-vectors of the Conformal Geometric Algebra. Of interest is the detection of lines and circles in images, and planes, circles, and spheres in the 3-D visual space; for that, we use the randomized Hough transform, and by means of k-blades we code such geometric entities. Motivated by tensor voting, we have generalized this approach for any kind of geometric entities or geometric flags formulating the perceptual saliency function involving k-vectors. The experiments using real images show the performance of the algorithms. 相似文献
4.
V. A. Timorin 《Functional Analysis and Its Applications》2004,38(1):45-51
Consider a smooth map of a neighborhood of the origin in a real vector space into a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though the origin to the same circles as a Hopf map coming from a representation of a Clifford algebra. We also describe a connection between our result and the Hurwitz–Radon theorem about sums of squares. 相似文献
5.
In the paper we give the best possible estimate for the minimal number of unit circles determined by n points passing through an arbitrarily chosen point. 相似文献
6.
Consider a horizontal line in the plane and let γ(A) be a collection of n circles, possibly of different sizes all tangent to the line on the same side. We define the tangent circle graph associated to γ(A) as the intersection graph of the circles. We also define an irreflexive and asymmetric binary relation P on A; the pair (a,b) representing two circles of γ(A) is in P iff the circle associated to a lies to the right of the circle associated to b and does not intersect it. This defines a new nontransitive preference structure that generalizes the semi-order structure. We study its properties and relationships with other well-known order structures, provide a numerical representation and establish a sufficient condition implying that P is transitive. The tangent circle preference structure offers a geometric interpretation of a model of preference relations defined by means of a numerical representation with multiplicative threshold; this representation has appeared in several recently published papers. 相似文献
7.
Andreas E. Schroth 《Journal of Geometry》1994,51(1-2):138-149
The number of circles of a four-dimensional locally compact Laguerre plane touching three given circles or points depends only on the given geometric configuration but not on the Laguerre plane. 相似文献
8.
Andreas E. Schroth 《Journal of Geometry》1991,42(1-2):141-147
The number of circles of a flat Laguerre plane touching three given circles or points depends only on the given geometric configuration but not on the Laguerre plane.Dedicated to Prof. J. Joussen on his 60th birthday 相似文献
9.
The family of separating circles of two finite sets in the plane consists of all the circles that enclose the first set but exclude the second set. We prove some theoretical results on distances between families of circles, and properties about enclosure and intersection. Most of these results state that a property that involves one or more infinite families of circles can be verified by examining a finite subcollection of circles. As a result enclosure and intersection can be decided, and distances can be computed with simple geometric algorithms. Furthermore, the circles of the finite subcollections correspond to the vertices of a polytope in the parameter space of separating circles. A polytope of separating circle parameters is well-known computational geometry, but we prove some new properties and we introduce the concept of an elementary circular separation as a concise way to define such a polytope. 相似文献
10.
Ronald L. Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan 《Discrete and Computational Geometry》2006,35(1):1-36
Apollonian circle packings arise by repeatedly filling the interstices
between four mutually tangent circles with further tangent circles.
Such packings can be described in terms of the Descartes configurations
they contain, where a Descartes configuration is a set of four mutually tangent
circles in the Riemann sphere, having disjoint interiors.
Part I showed there exists a discrete group, the Apollonian group,
acting on a parameter space of (ordered, oriented) Descartes configurations,
such that the Descartes configurations in a packing formed an
orbit under the action of this group. It is observed there
exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral
structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group,
the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric
object we call a super-packing. The circles in a super-packing never cross each other but are nested to an arbitrary depth.
Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral
and the curvature x centers of all circles are integral. We show that (up to scale) there are exactly eight different (geometric)
strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale).
We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes
configurations, which is isomorphic
to the Lorentz group O(3, 1). 相似文献
11.
《Discrete Mathematics》2019,342(12):111597
We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory. 相似文献
12.
Eberhard M. Schröder 《Journal of Geometry》2001,71(1-2):182-191
A new proof of Clifford's circle theorem is given, which is based upon simple properties of angles between Clifford circles.
Necessarily, the cases are included, where some Clifford circles degenerate to points.?The proof is valid for all miquelian
Benz-planes.
Received 8 November 1999. 相似文献
13.
软弹簧型Duffing方程在摄动下分支出的极限环 总被引:5,自引:0,他引:5
在这篇文章中,作者用Melnikov函数方法分析了软弹簧型Duffing方程[1]在摄动下异宿轨道破裂后稳定流形与不稳定流形的相对位置,给出了方程在不同摄动下分支出极限环的条件与极限环的位置. 相似文献
14.
We show that every oriented link diagram with a closed braid diagram as a sublink diagram can be deformed into a closed braid diagram by a deformation keeping the sublink diagram and, under a mild condition, the number of Seifert circles fixed. As an application, we give an upper bound for the braid index of the link obtained by reversing the orientation of its sublink by using only the information of an original link. 相似文献
15.
V. A. Timorin 《Functional Analysis and Its Applications》2006,40(2):108-116
We list all diffeomorphisms between an open subset of the four-dimensional projective space and an open subset of the four-dimensional sphere that take all line segments to arcs of round circles. These diffeomorphisms are restrictions of quaternionic Hopf fibrations and radial projections from hyperplanes to spheres. 相似文献
16.
Serge Tabachnikov 《Geometriae Dedicata》2000,80(1-3):201-209
Given a polygon A
1,...,A
n, consider the chain of circles: S
1 inscribed in the angle A
1, S
2 inscribed in the angle A
2 and tangent to S
1, S
3 inscribed in the angle A
3 and tangent to S
2, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem. 相似文献
17.
Ferenc Fodor 《Geometriae Dedicata》1999,74(2):139-145
Dense packings of n congruent circles in a circle were given by Kravitz in 1967 for n = 2,..., 16. In 1969 Pirl found the optimal packings for n 10, he also conjectured the dense configurations for 11 n 19. In 1994, Melissen provided a proof for n = 11. In this paper we exhibit the densest packing of 19 congruent circles in a circle with the help of a technique developed by Bateman and Erdös. 相似文献
18.
V.K. Srinivasan 《International Journal of Mathematical Education in Science & Technology》2013,44(5):732-739
This article deals with the construction of an equilateral triangle that must satisfy the following special constraint conditions. If the equilateral triangle is denoted by ΔABC, then the radii of the inscribed circle, the three escribed circles of ΔABC, and the circumcircle of ΔABC all must have positive integral radii. The inscribed circle radius is required to be 1 unit. The three escribed circles that have equal radii must have 3 units each, and the circumcircle of the triangle must have 2 units. All these requirements may seem outlandish. The aim is to teach crucial Geometric principles that Geometric designs must take into account before the constructions are implemented. This article hopefully may be useful to students of College Geometry as well as teachers. 相似文献
19.
In this paper, we consider a special class of the surfaces in the 3-sphere defined by one-parameter families of great circles. We give a generic classification of singularities of such surfaces and investigate the geometric meanings from the view point of spherical geometry. 相似文献
20.
The paper is dealing with the problem of finding the densest packings of equal circles in the unit square. Recently, a global optimization method based exclusively on interval arithmetic calculations has been designed for this problem. With this method it became possible to solve the previously open problems of packing 28, 29, and 30 circles in the numerical sense: tight guaranteed enclosures were given for all the optimal solutions and for the optimum value. The present paper completes the optimality proofs for these cases by determining all the optimal solutions in the geometric sense. Namely, it is proved that the currently best-known packing structures result in optimal packings, and moreover, apart from symmetric configurations and the movement of well-identified free circles, these are the only optimal packings. The required statements are verified with mathematical rigor using interval arithmetic tools. 相似文献