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41.
This paper presents a new composition law for Runge-Kutta methods when applied to index-2 differential-algebraic systems. Applications of this result to the study of the order of composite methods and of symmetric methods are given. 相似文献
42.
For any graph G, let ni be the number of vertices of degree i, and . This is a general lower bound on the irregularity strength of graph G. All known facts suggest that for connected graphs, this is the actual irregularity strength up to an additive constant. In fact, this was conjectured to be the truth for regular graphs and for trees. Here we find an infinite sequence of trees with λ(T) = n1 but strength converging to . © 2004 Wiley Periodicals, Inc. J Graph Theory 45: 241–254, 2004 相似文献
43.
Minimal Length Elements of Thompson's Group F 总被引:1,自引:1,他引:0
S. Blake Fordham 《Geometriae Dedicata》2003,99(1):179-220
Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this representation and reviews the known relationship between elements of F and binary trees. In the main section we give a method of determining the minimal lengths of elements of Thompson's group F in the two generator presentation
This method is an effective algorithm in that its order is linear in the size of the trees representing an element of F. We also give a method for constructing all minimal length representatives of an element in F. 相似文献
44.
In this note, we consider a finite set X and maps
W from the set $ \mathcal{S}_{2|2} (X) $ of all 2, 2-
splits of X into $ \mathbb{R}_{\geq 0} $. We show that such a map
W is induced, in a canonical way, by a binary
X-tree for which a positive length $ \mathcal{l} (e) $ is
associated to every inner edge e if and only if (i) exactly
two of the three numbers W(ab|cd),W(ac|bd), and
W(ad|cb) vanish, for any four distinct elements
a, b, c, d in X,
(ii) $ a \neq d \quad\mathrm{and}\quad W (ab|xc) + W(ax|cd) = W(ab|cd) $ holds for all
a, b, c, d, x
in X with
#{a, b, c, x} = #{b, c, d, x} = 4
and $ W(ab|cx),W(ax|cd) $ > 0, and (iii) $ W (ab|uv) \geq \quad \mathrm{min} (W(ab|uw), W(ab|vw)) $
holds for any five distinct elements a, b, u, v, w in
X. Possible generalizations
regarding arbitrary $ \mathbb{R} $-trees and applications regarding tree-reconstruction algorithms
are indicated.AMS Subject Classification: 05C05, 92D15, 92B05. 相似文献
45.
Yun S. Song 《Annals of Combinatorics》2003,7(3):365-379
We study subtree-prune-and-regraft (SPR) operations on
leaf-labelled rooted binary trees, also known as rooted binary phylogenetic trees.
This study is motivated by the problem of
graphically representing evolutionary histories of biological sequences subject to recombination.
We investigate some basic properties of the induced SPR-metric on the space
of leaf-labelled
rooted binary trees with n leaves. In contrast to the case of
unrooted trees, the number |U(T)| of trees in
which are one SPR operation away from a given tree
depends on the
topology of T. In this paper, we construct recursion relations which allow one to determine the
unit-neighbourhood size |U(T)| efficiently for any tree topology. In fact, using the recursion
relations we are able to derive a simple closed-form formula for the unit-neighbourhood size.
As a corollary, we construct sharp upper and lower bounds on the size of unit-neighbourhoods
and investigate the diameter of
.
Lastly, we consider an enumeration problem relevant to population genetics.AMS Subject Classification: 05C05, 92D15. 相似文献
46.
The Hardy operator Ta on a tree is defined by Properties of Ta as a map from Lp() into itselfare established for 1 p . The main result is that, with appropriateassumptions on u and v, the approximation numbers an(Ta) ofTa satisfy for a specified constant p and 1 p < . This extends results of Naimark, Newmanand Solomyak for p = 2. Hitherto, for p 2, (*) was unknowneven when is an interval. Also, upper and lower estimates forthe lq and weak-lq norms of an(Ta) are determined. 2000 MathematicalSubject Classification: 47G10, 47B10. 相似文献
47.
Spiros A. Argyros 《Proceedings of the American Mathematical Society》2001,129(11):3231-3239
It is shown that every separable Banach space universal for the class of reflexive Hereditarily Indecomposable space contains isomorphically and hence it is universal for all separable spaces. This result shows the large variety of reflexive H.I. spaces.
48.
Hans H. Brungs Joachim Grä ter 《Transactions of the American Mathematical Society》2000,352(7):3357-3379
A subring of a division algebra is called a valuation ring of if or holds for all nonzero in . The set of all valuation rings of is a partially ordered set with respect to inclusion, having as its maximal element. As a graph is a rooted tree (called the valuation tree of ), and in contrast to the commutative case, may have finitely many but more than one vertices. This paper is mainly concerned with the question of whether each finite, rooted tree can be realized as a valuation tree of a division algebra , and one main result here is a positive answer to this question where can be chosen as a quaternion division algebra over a commutative field.
49.
T. S. Evans 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):65-69
Evolving networks with a constant number of edges may be
modelled using a rewiring process. These models are used to
describe many real-world processes including the evolution of
cultural artifacts such as family names, the evolution of gene
variations, and the popularity of strategies in simple
econophysics models such as the minority game. The model is
closely related to Urn models used for glasses, quantum gravity
and wealth distributions. The full mean field equation for the
degree distribution is found and its exact solution and generating
solution are given. 相似文献
50.
Zhongzhi Zhang Shuigeng Zhou Lichao Chen Jihong Guan Lujun Fang Yichao Zhang 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(1):99-107
We propose a geometric growth model for weighted
scale-free networks, which is controlled by two tunable parameters.
We derive exactly the main characteristics of the networks, which
are partially determined by the parameters. Analytical results
indicate that the resulting networks have power-law distributions of
degree, strength, weight and betweenness, a scale-free behavior for
degree correlations, logarithmic small average path length and
diameter with network size. The obtained properties are in agreement
with empirical data observed in many real-life networks, which shows
that the presented model may provide valuable insight into the real
systems. 相似文献