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1.
A minimum Steiner tree for a given setX of points is a network interconnecting the points ofX having minimum possible total length. In this note we investigate various properties of minimum Steiner trees in normed planes, i.e., where the unit disk is an arbitrary compact convex centrally symmetric domainD having nonempty interior. We show that if the boundary ofD is strictly convex and differentiable, then each edge of a full minimum Steiner tree is in one of three fixed directions. We also investigate the Steiner ratio(D) forD, and show that, for anyD, 0.623<(D)<0.8686.Part of this work was done while Ding-Zhu Du was at the Computer Science Department, Princeton University and the Center for Discrete Mathematics and Theoretical Computer Science at Rutgers. Supported by NSF under Grant STC88-09648.  相似文献   

2.
The article is devoted to the problem of finding an optimal schedule for a class of functionals ƒ which allows for the existence of a structural set of activities. The functionalƒ(R), where, is defined in the following way: where {i(t)} is a structural set of functions, and the function F is defined on any finite set of arguments and satisfies the following conditions: 1)F(x)=(x); 2) F(x1,x2)=(x1,x2), F(x1,x2,...x3)= (x1, F(x2,...,xs)), S2; 3) and do not decrease in each of their arguments, and moreover, 3a) strictly increases with the increase of both arguments, 3b) if (x1,x2)>(x1, x2 (x2, x3)> (x2,x3), then F(x1,x2,x3)>F(x1,x2,x3).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 5–20, 1983.  相似文献   

3.
It is consistent that there exists a set mappingF with <F(, )< for + 2 >w 2 with no uncountable free sets.Research supported by Hungarian National Research Fund No. 1805 and 1908.  相似文献   

4.
Summary We consider the d-dimensional basic contact process obtaining the limit value of the probability of survival when d+, and showing that the finite dimensional distributions of the upper invariant measure become of the product form as d+.  相似文献   

5.
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if · E(M,) is not proportional to · L 2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council  相似文献   

6.
Necessary and sufficient conditions for the functional central limit theorem for a double array of random variables are sought. It is argued that this is a martingale problem only if the variables truncated at some fixed point c are asymptotically a martingale difference array. Under this hypothesis, necessary and sufficient conditions for convergence in distribution to a Brownian motion are obtained when the normalization is given (i) by the sums of squares of the variables, (ii) by the conditional variances and (iii) by the variances. The results are proved by comparing the various normalizations with a natural normalization.Research sponsored in part by the Office of Naval Research, Contract N00014-75-C-0809  相似文献   

7.
Consider a triangular array of standard Gaussian random variables {n,i, i 0, n 1} such that {n,i, i 0} is a stationary normal sequence for each n 1. Let n,k = corr(n,i,n,i+k). If (1-n,k)log n k (0,) as n for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still the Gumbel distribution as in the stationary or i.i.d. case, but shifted by a parameter measuring the clustering. Triangular arrays of Gaussian sequences are used to approximate a continuous Gaussian process X(t), t 0. The cluster behavior of the random sequence refers to the behavior of the extremes values of the continuous process. The relation is analyzed. It reveals a new definition of the constants H used for the limiting distribution of maxima of continuous Gaussian processes and provides further understanding of the limit result for these extremes.  相似文献   

8.
Let (E, ) be a barrelled locally convex space. The aim of this paper is to describe the barrelled topologies on E weaker than . When the completion Ê of (E, ) is B-complete, various properties of the barrelled topologies weaker than are proved. Some examples are given to illustrate the possible situations.  相似文献   

9.
For a fixed positive integer k, consider the collection of all affine hyperplanes in n-space given by xi – xj = m, where i, j [n], i j, and m {0, 1,..., k}. Let Ln,k be the set of all nonempty affine subspaces (including the empty space) which can be obtained by intersecting some subset of these affine hyperplanes. Now give Ln,k a lattice structure by ordering its elements by reverse inclusion. The symmetric group Gn acts naturally on Ln,k by permuting the coordinates of the space, and this action extends to an action on the top homology of Ln,k. It is easy to show by computing the character of this action that the top homology is isomorphic as an Gn-module to a direct sum of copies of the regular representation, CGn. In this paper, we construct an explicit basis for the top homology of Ln,k, where the basis elements are indexed by all labelled, rooted, (k + 1)-ary trees on n-vertices in which the root has no 0-child. This construction gives an explicit Gn-equivariant isomorphism between the top homology of Ln,k and a direct sum of copies of CGn.  相似文献   

10.
The fundamental result: if and v are two finite Borel measures, defined in the spaceL p[0, 1] (1p<) or in C(K) (K is a metric compactum without isolated points), then from the equalities (B)=v(B) for all balls B of radius 1 there follows that =v. In addition, in the spaces C(K) and p (1p<) from the inequalities (B) v(B) there follows that v.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 122–128, 1989.  相似文献   

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