共查询到20条相似文献,搜索用时 0 毫秒
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For every $k>3$ k > 3 , we give a construction of planar point sets with many collinear $k$ k -tuples and no collinear $(k+1)$ ( k + 1 ) -tuples. We show that there are $n_0=n_0(k)$ n 0 = n 0 ( k ) and $c=c(k)$ c = c ( k ) such that if $n\ge n_0$ n ≥ n 0 , then there exists a set of $n$ n points in the plane that does not contain $k+1$ k + 1 points on a line, but it contains at least $n^{2-({c}/{\sqrt{\log n}})}$ n 2 - ( c / log n ) collinear $k$ k -tuples of points. Thus, we significantly improve the previously best known lower bound for the largest number of collinear $k$ k -tuples in such a set, and get reasonably close to the trivial upper bound $O(n^2)$ O ( n 2 ) . 相似文献
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Consider the following problem: how many collinear triples of points must a transversal of
have? This question is connected with venerable issues in discrete geometry. We show that the answer, for n prime, is between (n − 1)/4 and (n − 1)/2, and consider an analogous question for collinear quadruples. We conjecture that the upper bound is the truth and suggest several other interesting problems in this area.Received August 29, 2004 相似文献
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Enumerating Constrained Non-crossing Minimally Rigid Frameworks 总被引:2,自引:1,他引:1
David Avis Naoki Katoh Makoto Ohsaki Ileana Streinu Shin-ichi Tanigawa 《Discrete and Computational Geometry》2008,40(1):31-46
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid
bar-and-joint frameworks under edge constraints, which we call constrained non-crossing Laman frameworks, on a given set of
n points in the plane. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph
in O(n
4) time and O(n) space, or, with a slightly different implementation, in O(n
3) time and O(n
2) space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is
connected by flips which preserve the Laman property.
D. Avis’s research was supported by NSERC and FQRNT grants.
N. Katoh’s, M. Ohsaki’s and S.-i. Tanigawa’s research was supported by NEXT Grant-in-Aid for Scientific Research on priority
areas of New Horizons in Computing.
I. Streinu’s research was supported by NSF grant CCF-0430990 and NSF-DARPA CARGO CCR-0310661. 相似文献
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各向异性材料中共线刚性线夹杂的纵向剪切问题 总被引:6,自引:2,他引:6
本文研究各向异性材料中共线刚性线夹杂,(有时称作“硬裂纹”或“反裂纹”问题)的纵向剪切问题。利用复变函数方法,提出了一般问题的公式和某些实际重要问题的封闭形式解,考察了刚性线端点附近的应力分布.从本文解答的特殊情形,可以直接导出各向同性材料相应问题的公式和结果,包括某些已有的结果 ̄[7]. 相似文献
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Zachary Abel Brad Ballinger Prosenjit Bose S��bastien Collette Vida Dujmovi? Ferran Hurtado Scott Duke Kominers Stefan Langerman Attila P��r David R. Wood 《Graphs and Combinatorics》2011,27(1):47-60
We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture
of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005]. 相似文献
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《Journal of Complexity》2002,18(2):641-659
In this paper we present a new algorithm for the two-dimensional fixed point problem f(x)=x on the domain [0, 1]×[0, 1], where f is a Lipschitz continuous function with respect to the infinity norm, with constant 1. The computed approximation x satisfies 6f(x)−x6∞⩽ε for a specified tolerance ε<0.5. The upper bound on the number of required function evaluations is given by 2⌈log2(1/ε)⌉+1. Similar bounds were derived for the case of the 2-norm by Z. Huang et al. (1999, J. Complexity15, 200–213), our bound is the first for the infinity norm case. 相似文献
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We exhibit 3-generator Artin groups which have finite two-dimensional Eilenberg-Mac Lane spaces, but which do not act properly discontinuously by semi-simple isometries on a two-dimensional CAT(0) complex. We prove that infinitely many of these groups are the fundamental groups of compact, non-positively curved 3-complexes. These examples show that the geometric dimension of a CAT(0) group may be strictly less than its CAT(0) dimension. 相似文献
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In this paper, we study the bifurcation problems of rough heteroclinic loops connecting three saddle points for a higher-dimensional
system. Under some transversal conditions and the nontwisted condition, the existence, uniqueness, and incoexistence of the
1-heteroclinic loop with three or two saddle points, 1-homoclinic orbit and 1-periodic orbit near Γ are obtained. Meanwhile,
the bifurcation surfaces and existence regions are also given. Moreover, the above bifurcation results are extended to the
case for heteroclinic loop with l saddle points.
Received January 4, 2001, Accepted July 3, 2001. 相似文献
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We study the semilocal dynamics of two-dimensional symplectic diffeomorphisms with homoclinic tangencies. Conditions for the existence of infinitely many generic elliptic periodic orbits of successive periods starting with some integer are found. Bibliography: 14 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 155–166. 相似文献
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Kushnir R. M. Tokovyi Yu. V. Yuzvyak M. Y. Yasinskyi A.V. 《Ukrainian Mathematical Journal》2022,73(10):1566-1579
Ukrainian Mathematical Journal - We propose a generalization of the method of direct integration of the original equations of two-dimensional problems of thermoelasticity for solids with corner... 相似文献
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文中研究了一类具有三个转向点的大参数奇摄动方程的渐近解.首先利用Liouville-Green变换构造方程在不同区域的外部解.然后利用1/3阶和-1/3阶Bessel函数,分别构造出方程在三个转向点附近的内层解.最后利用匹配原理得到外部解和内层解中任意常数满足的匹配条件. 相似文献
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K. V. Chesnokova 《Moscow University Mathematics Bulletin》2018,73(1):17-23
For the Euclidean plane ? the Steiner mapping associating any three points a, b, c with their median s, and the corresponding operator P D of metric projection of the space l 1 3 (?) onto its diagonal subspace D = {(x,x,x): x ∈ ?}, P D (a,b,c) = (s,s,s): s are considered. The exact value of the linearity coefficient of P D is calculated. 相似文献
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Nyurgun Lazarev Galina Semenova 《Journal of Optimization Theory and Applications》2018,178(2):614-626
The equilibrium problem for a two-dimensional body with a crack is studied. We suppose that the body consists of two parts: an elastic part and a rigid thin stiffener on the outer edge of the body. Inequality-type boundary conditions are prescribed at the crack faces providing a non-penetration between the crack faces. For a family of variational problems, dependence of their solutions on the length of the thin rigid stiffener is investigated. It is shown that there exists a solution of an optimal control problem. For this problem, the cost functional is defined by a continuous functional on a solution space, while the length parameter serves as a control parameter. 相似文献
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Ismailescu 《Discrete and Computational Geometry》2002,28(4):571-575
Abstract. Given k≥ 3 , denote by t'
k
(N) the largest integer for which there is a set of N points in the plane, no k+1 of them on a line such that there are t'
k
(N) lines, each containing exactly k of the points. Erdos (1962) raised the problem of estimating the order of magnitude of t'
k
(N) . We prove that
improving a previous bound of Grunbaum for all k≥ 5 . The proof for k≥ 18 uses an argument of Brass with his permission. 相似文献