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951.
952.
953.
Let G be a connected graph and S a set of vertices of G. The Steiner distance of S is the smallest number of edges in a connected subgraph of G that contains S and is denoted by dG(S) or d(S). The Steiner n-eccentricity en(v) and Steiner n-distance dn(v) of a vertex v in G are defined as en(v)=max{d(S)| SV(G), |S|=n and vS} and dn(v)=∑{d(S)| SV(G), |S|=n and vS}, respectively. The Steiner n-center Cn(G) of G is the subgraph induced by the vertices of minimum n-eccentricity. The Steiner n-median Mn(G) of G is the subgraph induced by those vertices with minimum Steiner n-distance. Let T be a tree. Oellermann and Tian [O.R. Oellermann, S. Tian, Steiner centers in graphs, J. Graph Theory 14 (1990) 585–597] showed that Cn(T) is contained in Cn+1(T) for all n2. Beineke et al. [L.W. Beineke, O.R. Oellermann, R.E. Pippert, On the Steiner median of a tree, Discrete Appl. Math. 68 (1996) 249–258] showed that Mn(T) is contained in Mn+1(T) for all n2. Then, Oellermann [O.R. Oellermann, On Steiner centers and Steiner medians of graphs, Networks 34 (1999) 258–263] asked whether these containment relationships hold for general graphs. In this note we show that for every n2 there is an infinite family of block graphs G for which Cn(G)Cn+1(G). We also show that for each n2 there is a distance–hereditary graph G such that Mn(G)Mn+1(G). Despite these negative examples, we prove that if G is a block graph then Mn(G) is contained in Mn+1(G) for all n2. Further, a linear time algorithm for finding the Steiner n-median of a block graph is presented and an efficient algorithm for finding the Steiner n-distances of all vertices in a block graph is described. 相似文献
954.
Rolando Cavazos-Cadena Daniel Hernández-Hernández 《Periodica Mathematica Hungarica》2008,56(2):183-211
This note concerns the asymptotic behavior of a Markov process obtained from normalized products of independent and identically
distributed random matrices. The weak convergence of this process is proved, as well as the law of large numbers and the central
limit theorem.
This work was supported by the PSF Organization under Grant No. 2005-7-02, and by the Consejo Nacional de Ciencia y Tecnología
under Grants 25357 and 61423. 相似文献
955.
We study the limit behavior of the χ2-distance between the distributions of the nth partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem. 相似文献
956.
In the paper we obtain an explicit formula for the intrinsic diameter of the surface of a rectangular parallelepiped in 3-dimensional
Euclidean space. As a consequence, we prove that an parallelepiped with relation
for its edge lengths has maximal surface area among all rectangular parallelepipeds with given intrinsic diameter. 相似文献
957.
Colloidal crystals formed by two types of polystyrene particles of different sizes (94 and 141 nm) at various number ratios (94:141 nm) are studied. Experiments showed that the formation time of crystals lengthens as the number ratio of the two components approaches 1:1. The dependence of the mean interparticle distance (D0), crystal structure and alloy structure on the number ratio of the two types of particles was studied by means of Kossel diffraction technique and reflection spectra. The results showed that as the number ratio decreased, the mean interparticle distance (D0) became larger. And the colloidal crystal in binary mixtures is more preferably to form the bcc structure. This study found that binary systems form the substitutional solid solution (sss)-type alloy structure in all cases except when the number ratio of two types of particles is 5:1, which results instead in the superlattice structure. 相似文献
958.
This paper considers one facility planar location problems using block distance and assuming barriers to travel. Barriers
are defined as generalized convex sets relative to the block distance. The objective function is any convex, nondecreasing
function of distance. Such problems have a non-convex feasible region and a non-convex objective function. The problem is
solved by modifying the barriers to obtain an equivalent problem and by decomposing the feasible region into a polynomial
number of convex subsets on which the objective function is convex. It is shown that solving a planar location problem with
block distance and barriers requires at most a polynomial amount of additional time over solving the same problem without
barriers. 相似文献
959.
G.?Hooghiemstra P.?Van?MieghemEmail author 《Methodology and Computing in Applied Probability》2005,7(3):285-306
We consider a graph, where the nodes have a pre-described degree distribution F, and where nodes are randomly connected in accordance to their degree. Based on a recent result (R. van der Hofstad, G. Hooghiemstra
and P. Van Mieghem, “Random graphs with finite variance degrees,” Random Structures and Algorithms, vol. 17(5) pp. 76–105, 2005), we improve the approximation of the mean distance between two randomly chosen nodes given
by M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Random graphs with arbitrary degree distribution and their application,”
Physical Review. E vol. 64, 026118, pp. 1–17, 2001. Our new expression for the mean distance involves the expectation of the logarithm of the
limit of a super-critical branching process. We compare simulations of the mean distance with the results of Newman et al.
and with our new approach.
AMS 2000 Subject Classification: 05C80, 60F05 相似文献
960.
Markku Kaikkonen 《Designs, Codes and Cryptography》1998,15(2):183-186
It is shown that A(22,10) 50, A(23,10) 76, A(25,10) 166, A(26,10) 270, A(29,10) 1460, and A(28,12) 178, where A(n,d) denotes the maximum cardinality of a binary code of length n and minimum Hamming distance d. The constructed codes are invariant under permutations of some affine (or closely related) permutation group and have been found using computer search. 相似文献