共查询到20条相似文献,搜索用时 31 毫秒
1.
Richard N. Draper 《Mathematische Annalen》1969,180(3):175-204
2.
H.J Ryser 《Journal of Combinatorial Theory, Series A》1973,14(1):79-92
Let X1, X2, …, Xm be finite sets. The present paper is concerned with the m2 ? m intersection numbers |Xi ∩ Xj| (i ≠ j). We prove several theorems on families of sets with the same prescribed intersection numbers. We state here one of our conclusions that requires no further terminology. Let T1, T2, …, Tm be finite sets and let m ? 3. We assume that each of the elements in the set union T1 ∪ T2 ∪ … ∪ Tm occurs in at least two of the subsets T1, T2, …, Tm. We further assume that every pair of sets Ti and Tj (i ≠ j) intersect in at most one element and that for every such pair of sets there exists exactly one set Tk (k ≠ i, k ≠ j) such that Tk intersects both Ti and Tj. Then it follows that the integer m = 2m′ + 1 is odd and apart from the labeling of sets and elements there exist exactly m′ + 1 such families of sets. The unique family with the minimal number of elements is {1}, {2}, …, {m′}, {1}, {2}, …, {m′}, {1, 2, …, m′}. 相似文献
3.
A family of sets is calledn-pierceable if there exists a set ofn points such that each member of the family contains at least one of the points. Helly’s theorem on intersections of convex sets concerns 1-pierceable families. Here the following Helly-type problem is investigated: Ifd andn are positive integers, what is the leasth =h(d, n) such that a family of boxes (with parallel edges) ind-space isn-pierceable if each of itsh-membered subfamilies isn-pierceable? The somewhat unexpected solution is: (i)h(d, 2) equals3d for oddd and 3d?1 for evend; (ii)h(2, 3)=16; and (iii)h(d, n) is infinite for all (d, n) withd≧2 andn≧3 except for (d, n)=(2, 3). 相似文献
4.
If is a finite digraph, a directed cut is a subset of arcs in having tail in some subset and head in . In this paper we prove two general results concerning intersections between maximal paths, cycles and maximal directed cuts in . As a direct consequence of these results, we deduce that there is a path, or a cycle, in that crosses each maximal directed cut. 相似文献
5.
Jürgen Eckhoff 《Israel Journal of Mathematics》1991,73(2):129-149
In a previous paper (this Journal, Vol. 62, pp. 283–301) we proved an Upper-Bound Theorem for finite families of boxes inR
d
with edges parallel to the coordinate axes. This theorem concerns the maximum possible numbers of intersecting subfamilies
of a family having a given number of members and a given clique number. Here we give an intrinsic characterization ofextremal families of boxes, i.e., families for which all the respective maximum numbers are achieved. We also deal with the problem
of enumerating the possible intersection types of extremal families. 相似文献
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The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand. 相似文献
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10.
Jürgen Eckhoff 《Israel Journal of Mathematics》1988,62(3):283-301
LetP be a family ofn boxes inR
d
(with edges parallel to the coordinate axes). Fork=0, 1, 2, …, denote byf
k
(P) the number of subfamilies ofP of sizek+1 with non-empty intersection. We show that iff
r
(P)=0 for somer≦n, then
where thef
k
(n, d, r) are ceg196rtain definite numbers defined by (3.4) below. The result is best possible for eachk. Fork=1 it was conjectured by G. Kalai (Israel J. Math.48 (1984), 161–174). As an application, we prove a ‘fractional’ Helly theorem for families of boxes inR
d
. 相似文献
11.
GONGCHU HUANGQIDE DUJIANGCHUAN LIUHONGJIAN 《高校应用数学学报(英文版)》1995,10(1):89-102
How to increase the speed in drawing and recognizing curves has always been a major concern. From the Breshenham Algorithm and DDA Algorithm in the sixties to the double-step and quadruple-step line generation iu the eighties, curves were all dragon point by point. The algorithm in this paper fully utilizes machine commands to accelerate the generation of lines and curves. We introduce and prove for the first time characterization theorems of the segment code order of digital lines and curyes. These theorems give new methods in the recognition and the measure of smoothness of lines and curves. 相似文献
12.
Audun Holme 《manuscripta mathematica》1988,61(2):145-162
In this paper we investigate some fundamental geometric and numerical properties ofduality for projective varieties inP
k
N
=P
N
. We take a point of view which in our opinion is somewhat moregeometric and lessalgebraic andnumerical than what has been customary in the literature, and find that this can some times yield simpler and more natural proofs, as well as yield additional insight into the situation. We first recall the standard definitions of thedual variety and theconormal scheme, introducing classical numerical invariants associated with duality. In section 2 we recall the well known duality properties these invariants have, and which was noted first byT. Urabe. In section 3 we investigate the connection between these invariants andChern classes in the singular case. In section 4 we give a treatment of the dual variety of a hyperplane section of X, and the dual procedure of taking the dual of a projection of X. This simplifies the proofs of some very interesting theorems due toR. Piene. Section 5 contains a new and simpler proof of a theorem ofA. Hefez and S. L. Kleiman. Section 6 contains some further results, geometric in nature. 相似文献
13.
Herings P. J. J. Talman A. J. J. 《Journal of Optimization Theory and Applications》1998,96(2):311-335
In all existing intersection theorems, conditions are given under which a certain subset of a collection of sets has a nonempty intersection. In this paper, conditions are formulated under which the intersection is a continuum of points satisfying some interesting topological properties. In this sense, the intersection theorems considered in this paper belong to a new class. The intersection theorems are formulated on the unit cube and it is shown that both the vector of zeroes and the vector of ones lie in the same component of the intersection. An interesting application concerns the model of an economy with price rigidities. Using the intersection theorems of this paper, it is easily shown that there exists a continuum of zero points in such a model. The intersection theorems treated give a generalization of the well-known lemmas of Knaster, Kuratowski, and Mazurkiewicz (Ref. 1), Scarf (Ref. 2), Shapley (Ref. 3), and Ichiishi (Ref. 4). Moreover, the results can be used to sharpen the usual formulation of the Scarf lemma on the cube. 相似文献
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15.
A. I. Barvinok 《Discrete and Computational Geometry》1995,13(1):189-202
A weighted graph is calledd-realizable if its vertices can be chosen ind-dimensional Euclidean space so that the Euclidean distance between every pair of adjacent vertices is equal to the prescribed
weight. We prove that if a weighted graph withk edges isd-realizable for somed, then it isd-realizable for
(this bound is sharp in the worst case). We prove that for a graphG withn vertices andk edges and for a dimensiond the image of the so-called rigidity map ℝ
dn
→ℝ
k
is a convex set in ℝ
k
provided
. These results are obtained as corollaries of a general convexity theorem for quadratic maps which also extends the Toeplitz-Hausdorff
theorem. The main ingredients of the proof are the duality for linear programming in the space of quadratic forms and the
“corank formula” for the strata of singular quadratic forms.
This research was supported by the United States Army Research Office through the Army Center of Excellence for Symbolic Methods
in Algorithmic Mathematics (ACSyAM), Mathematical Sciences Institute of Cornell University, Contract DAAL03-91-C0027. 相似文献
16.
Juan R. Romero Simon K. Alexander Shikha Baid Saurabh Jain Manos Papadakis 《Advances in Computational Mathematics》2009,31(1-3):283-328
In this paper we investigate Isotropic Multiresolution Analysis (IMRA), isotropic refinable functions, and wavelets. The main results are the characterization of IMRAs in terms of the Lax–Wiener Theorem, and the characterization of isotropic refinable functions in terms of the support of their Fourier transform. As an immediate consequence of these results, there are no compactly supported (in the space domain) isotropic refinable functions in many dimensions. Next we study the approximation properties of IMRAs. Finally, we discuss the application of IMRA wavelets to 2D and 3D-texture segmentation in natural and biomedical images. 相似文献
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本文给出了剩余交和一般剩余交的几个性质,主要讨论了剩余交的GCM性和在形变下的变化情况,并讨论了一般剩余交的GCM性,CM性和可光滑性等. 相似文献
19.
Samuel A. Ilori 《Annali di Matematica Pura ed Applicata》1981,127(1):307-319
Summary
Two sets of generators of the cohomology ring of a complex (incomplete) flag manifold are obtained in terms of Ehresmann classes. Intersection formulae of the bases elements with any Ehresmann class are then given, thus determining the ring structure of the cohomology ring. 相似文献
20.
Barbara Opozda 《Geometriae Dedicata》1995,55(2):141-163
We present a new approach — which is more general than the previous ones — to the affine differential geometry of complex hypersurfaces inC
n+1. Using this general approach we study some curvature conditions for induced connections.The research supported by Alexander von Humboldt Stiftung and KBN grant no. 2 P30103004. 相似文献