共查询到20条相似文献,搜索用时 531 毫秒
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
This research was accomplished with the financial support of the Russian Foundation for Fundamental Research, grant No. 93-011-154. 相似文献
13.
14.
15.
16.
17.
Yves Nievergelt 《Numerische Mathematik》2010,114(4):573-606
A generalized hypersphere is either a hyperplane or a hypersphere, which consists of all points equidistant from a center. Geometrically, a weighted median hypersphere minimizes a weighted average of the distances from it to finitely many data points. As proved here, for each finite data
set there exists at least one weighted median generalized hypersphere. Moreover, denote the sums of the weights of the data
points inside by W
−, outside by W
+, and on the hypersphere by W
0. The present results show that each weighted median hypersphere is a weighted pseudo-halving hypersphere, in the sense that |W
− − W
+| < W
0, and passes through at least two distinct data points. Combinatorically, a hypersphere is blocked if and only if it passes through data points in general position, in the sense that no other hypersphere passes through the
same data points. A hypersphere is a halving hypersphere if and only if it is blocked, contains exactly k data points inside, confines exactly ℓ data points outside, and |k − ℓ| ≤ 1. In the plane, the present results also show that if a median circle is not a halving circle, then moving its center
along a median between two data points on it until it passes through the next data point yields a halving circle. Relative
to the center, if the direction cosines of the external and internal data points have the same mean and variance, then the
median circle must be blocked, and stays so under sufficiently small perturbations of the data. Moreover, for every set of four points, at least one unweighted median circle is blocked. These results lend credence to a variant of a method
used by archaeologists, and explain some findings from operations research. 相似文献
18.
This is a survey on polling systems, focussing on the basic single-server multi-queue polling system in which the server visits the queues in cyclic order. The main goals of the paper are: (i) to discuss a number of the key methodologies in analyzing polling models; (ii) to give an overview of recent polling developments; and (iii) to present a number of challenging open problems. 相似文献
19.
20.
Journal of Mathematical Sciences - 相似文献