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991.
Let a set of points in the Euclidean plane be given. We are going to investigate the levels of the function measuring the sum of distances from the elements of the pointset which are called foci. Levels with only one focus are circles. In case of two different points as foci they are ellipses in the usual sense. If the set of the foci consists of more than two points then we have the so-called polyellipses. In this paper we investigate them from the viewpoint of differential geometry. We give a lower and upper bound for the curvature involving explicit constants. They depend on the number of the foci, the rate of the level and the global minimum of the function measuring the sum of the distances. The minimizer will be characterized by a theorem due to E. Weiszfeld together with a new proof. Explicit examples will also be given. As an application we present a new proof for a theorem due to P. Erd?s and I. Vincze. The result states that the approximation of a regular triangle by circumscribed polyellipses has an absolute error in the sense that there is no way to exceed it even if the number of the foci are arbitrary large. 相似文献
992.
We consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. From [P. Daniels, K. Kunen, H. Zhou, On the open-open game, Fund. Math. 145 (3) (1994) 205-220] and [D. Fremlin, T. Natkaniec, I. Rec?aw, Universally Kuratowski-Ulam spaces, Fund. Math. 165 (3) (2000) 239-247] topological arguments are extracted to show that: Every I-favorable space is universally Kuratowski-Ulam, Theorem 8; If a compact space Y is I-favorable, then the hyperspaceexp(Y)with the Vietoris topology is I-favorable, and hence universally Kuratowski-Ulam, Theorems 6 and 9. Notions of uK-U and uK-U∗ spaces are compared. 相似文献
993.
O. Uteza P. Delaporte B. Fontaine B. Forestier M. Sentis I. Tassy J.P. Truong 《Applied physics. B, Lasers and optics》1997,64(5):531-537
Received: 2 May 1996/Revised version: 9 October 1996 相似文献
994.
Summary Quasiperiodic tilings of kite-and-dart type, widely used as models for quasicrystals with decagonal symmetry, are constructed by means of somewhat artificial matching rules for the tiles. The proof of aperiodicity uses a self-similarity property, or inflation procedure, which requires drawing auxiliary lines. We introduce a modification of the kite-and-dart tilings which comes very naturally with both properties: the tiles are strictly self-similar, and their fractal boundaries provide perfect matching rules. 相似文献
995.
Andreas Knauf 《manuscripta mathematica》1998,95(4):519-527
Among all embedded closed manifolds with positive exterior curvature ≤k the ratio between the (d-1)-Hausdorff measure of the shadow boundary projection and the volume of M
d
is maximized by the sphere of radius 1/k.
Received: 22 August 1997 / Revised version: 2 December 1997 相似文献
996.
997.
Guillaume Aubrun 《Positivity》2006,10(4):755-759
We show that two limit results from random matrix theory, due to Marčenko–Pastur and Bai–Yin, are also valid for matrices
with independent rows (as opposed to independent entries in the classical theory), when rows are uniformly distributed on
the unit ball of ℓnp, under proper normalization.
Research was supported in part by the European Network PHD, FP6 Marie Curie Actions, MCRN-511953 and was done in part while
the author was visiting the University of Athens. 相似文献
998.
Michael Reid 《Journal of Combinatorial Theory, Series A》2005,111(1):89-105
Let T be a protoset of d-dimensional polyominoes. Which boxes (rectangular parallelepipeds) can be tiled by T? A nice result of Klarner and Göbel asserts that the answer to this question can always be given in a particularly simple form, namely, by giving a finite list of “prime” boxes. All other boxes that can be tiled can be deduced from these prime boxes. We give a new, simpler proof of this fundamental result. We also show that there is no upper bound to the number of prime boxes, even when restricting attention to singleton protosets. In the last section, we determine the set of prime rectangles for several small polyominoes. 相似文献
999.
On Hyers-Ulam stability for a class of functional equations 总被引:1,自引:0,他引:1
Costanza Borelli 《Aequationes Mathematicae》1997,54(1-2):74-86
Summary In this paper we prove some stability theorems for functional equations of the formg[F(x, y)]=H[g(x), g(y), x, y]. As special cases we obtain well known results for Cauchy and Jensen equations and for functional equations in a single variable.
Work supported by M.U.R.S.T. Research funds (60%). 相似文献
1000.
We study farthest points and cut loci on doubly covered convex polygons, and determine them explicitly on doubly covered n-dimensional simplices. 相似文献