共查询到20条相似文献,搜索用时 250 毫秒
1.
In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τr in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f−1(x)f−1(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ). 相似文献
2.
Let Γ be a distance-regular graph of diameter D. Let X denote the vertex set of Γ and let Y be a nonempty subset of X. We define an algebra τ = τ(Y). This algebra is finite dimensional and semisimple. If Y consists of a single vertex then τ is the corresponding subconstituent algebra defined by P. Terwilliger. We investigate the irreducible τ-modules. We define endpoints and thin condition on irreducible τ-modules as a generalization of the case when Y consists of a single vertex. We determine when an irreducible module is thin. When the module is generated by the characteristic vector of Y, it is thin if and only if Y is a completely regular code of Γ. By considering a suitable subset Y, every irreducible τ(x)-module of endpoint i can be regarded as an irreducible τ(Y)-module of endpoint 0.This research was partially supported by the Grant-in-Aid for Scientific Research (No. 12640039), Japan Society of the Promotion of Science. A part of the research was done when the author was visiting the Ohio State University. 相似文献
3.
Alfio Giarlotta 《Topology and its Applications》2005,150(1-3):157-177
For each pair of linear orderings (L,M), the representability number reprM(L) of L in M is the least ordinal α such that L can be order-embedded into the lexicographic power . The case is relevant to utility theory. The main results in this paper are as follows. (i) If κ is a regular cardinal that is not order-embeddable in M, then reprM(κ)=κ; as a consequence, for each κω1. (ii) If M is an uncountable linear ordering with the property that A×lex2 is not order-embeddable in M for each uncountable AM, then for any ordinal α; in particular, . (iii) If L is either an Aronszajn line or a Souslin line, then . 相似文献
4.
We present an algorithm for the routing problem for two-terminal nets in generalized switchboxes. A generalized switchbox is any subset R of the planar rectangular grid with no nontrivial holes, i.e., every finite face has exactly four incident vertices. A net is a pair of nodes of nonmaximal degree on the boundary of R. A solution is a set of edge-disjoint paths, one for each net. Our algorithm solves standard generalized switchbox routing problems in time O(n(log n)2) where n is the number of vertices of R, i.e., it either finds a solution or indicates that there is none. A problem is standard if deg(ν) + ter(ν) is even for all vertices ν where deg(ν) is the degree of ν and ter(ν) is the number of nets which have ν as a terminal. For nonstandard problems we can find a solution in time O(n(log n)2 + |U|2) where U is the set of vertices ν with deg(ν) + ter(ν) is odd. 相似文献
5.
Orthonormal polynomials with weight ¦τ¦ exp(−τ4) have leading coefficients with recurrence properties which motivate the more general equations ξm(ξm − 1 + ξm + ξm + 1) = γm2, M = 1, 2,…, where ξo is a fixed nonnegative value and γ1, γ2,… are positive constants. For this broader problem, the existence of a nonnegative solution is proved and criteria are found for its uniqueness. Then, for the motivating problem, an asymptotic expansion of its unique nonnegative solution is obtained and a fast computational algorithm, with error estimates, is given. 相似文献
6.
N. Mukhopadhyay 《Journal of multivariate analysis》1999,68(2):463
We consider the classical fixed-size confidence region estimation problem for the mean vectorμin theNp(μ, Σ) population where Σ is unknown but positive definite. We writeλ1for the largest characteristic root of Σ and assume thatλ1is simple. Moreover, we suppose that, in many practical applications, we will often have available a numberλ*(>0) and that we can assumeλ1>λ*. Given this addi- tional, and yet very minimal, knowledge regardingλ1, the two-stage procedure of Chatterjee (Calcutta Statist. Assoc. Bull.8(1959a), 121–148;9(1959b), 20–28;11(1962), 144–159) is revised appropriately. The highlight in this paper involves the verification ofsecond-order propertiesassociated with such revised two-stage estimation techniques, along with the maintenance of the nominal confidence coefficient. 相似文献
7.
Harry Kesten R. A. Maller 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》1999,35(6):685
We show that the passage time, T*(r), of a random walk Sn above a horizontal boundary at r (r≥0) is stable (in probability) in the sense that
as r→∞ for a deterministic function C(r)>0, if and only if the random walk is relatively stable in the sense that
as n→∞ for a deterministic sequence Bn>0. The stability of a passage time is an important ingredient in some proofs in sequential analysis, where it arises during applications of Anscombe's Theorem. We also prove a counterpart for the almost sure stability of T*(r), which we show is equivalent to E|X|<∞, EX>0. Similarly, counterparts for the exit of the random walk from the strip {|y|≤r} are proved. The conditions arefurther related to the relative stability of the maximal sum and the maximum modulus of the sums. Another result shows that the exit position of the random walk outside the boundaries at ±r drifts to ∞ as r→∞ if and only if the random walk drifts to ∞. 相似文献
8.
Edward Minieka Niranjani H. Patel 《Journal of Algorithms in Cognition, Informatics and Logic》1983,4(4):345-352
A core of a graph G is a path P in G that is central with respect to the property of minizining d(P) = ΣυεV(G)d(υ, P), where d(υ, P) is the distance from vertex υ to path P. This paper explores some properties of a core of a specified length. 相似文献
9.
An acyclic graphoidal cover of a graph G is a collection ψ of paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ and every edge of G is in exactly one path in ψ. The minimum cardinality of an acyclic graphoidal cover of G is called the acyclic graphoidal covering number of G and is denoted by ηa. A path partition of a graph G is a collection P of paths in G such that every edge of G is in exactly one path in P. The minimum cardinality of a path partition of G is called thepath partition number of G and is denoted by π. In this paper we determine ηa and π for several classes of graphs and obtain a characterization of all graphs with Δ 4 and ηa = Δ − 1. We also obtain a characterization of all graphs for which ηa = π. 相似文献
10.
Perron F. 《Journal of multivariate analysis》1993,46(2)
We consider the problem of estimating a p-dimensional vector μ1 based on independent variables X1, X2, and U, where X1 is Np(μ1, σ2Σ1), X2 is Np(μ2, σ2Σ2), and U is σ2χ2n (Σ1 and Σ2 are known). A family of minimax estimators is proposed. Some of these estimators can be obtained via Bayesian arguments as well. Comparisons between our results and the one of Ghosh and Sinha (1988, J. Multivariate Anal.27 206-207) are presented. 相似文献
11.
Rasul A. Khan 《Journal of multivariate analysis》1978,8(4):550-558
Let X1, X2,… be idd random vectors with a multivariate normal distribution N(μ, Σ). A sequence of subsets {Rn(a1, a2,…, an), n ≥ m} of the space of μ is said to be a (1 − α)-level sequence of confidence sets for μ if P(μ Rn(X1, X2,…, Xn) for every n ≥ m) ≥ 1 − α. In this note we use the ideas of Robbins Ann. Math. Statist. 41 (1970) to construct confidence sequences for the mean vector μ when Σ is either known or unknown. The constructed sequence Rn(X1, X2, …, Xn) depends on Mahalanobis'
or Hotelling's
according as Σ is known or unknown. Confidence sequences for the vector-valued parameter in the general linear model are also given. 相似文献
12.
Peter Bella Daniel Krl Bojan Mohar Katarína Quittnerov 《European Journal of Combinatorics》2007,28(8):2201
An L(2,1)-labeling of a graph is a mapping c:V(G)→{0,…,K} such that the labels assigned to neighboring vertices differ by at least 2 and the labels of vertices at distance two are different. The smallest K for which an L(2,1)-labeling of a graph G exists is denoted by λ2,1(G). Griggs and Yeh [J.R. Griggs, R.K. Yeh, Labeling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586–595] conjectured that λ2,1(G)≤Δ2 for every graph G with maximum degree Δ≥2. We prove the conjecture for planar graphs with maximum degree Δ≠3. All our results also generalize to the list-coloring setting. 相似文献
13.
For the GMANOVA–MANOVA model with normal error: , , we study in this paper the sphericity hypothesis test problem with respect to covariance matrix: Σ=λIq (λ is unknown). It is shown that, as a function of the likelihood ratio statistic Λ, the null distribution of Λ2/n can be expressed by Meijer’s function, and the asymptotic null distribution of −2logΛ is (as n→∞). In addition, the Bartlett type correction −2ρlogΛ for logΛ is indicated to be asymptotically distributed as with order n−2 for an appropriate Bartlett adjustment factor −2ρ under null hypothesis. 相似文献
14.
Let
be the space of self-adjoint Segal measurable operators affiliated to a W*-algebra
(for x=∫λex(dλ), x
ex((−∞, −n)(n, ∞)) is a finite projection in
for n large enough). The limit in probability is unique in
. xn → x in probability enProj
;en→1 strongly and (xn − x) en → 0. The following proposition proves to be important in the investigation of
. If 1 − ƒ is a finite projection in
and 1 − en → 0 strongly, enProj
, then
strongly. 相似文献
15.
M. Nussbaum 《Journal of multivariate analysis》1984,14(3):300-314
We consider estimation of the parameter B in a multivariate linear functional relationship Xi=ξi+ξ1i, Yi=Bξi+ξ2i, i=1,…,n, where the errors (ζ1i′, ζ2i′) are independent standard normal and (ξi, i
) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n−1/2 is also established. 相似文献
16.
Let T = {T(t)}t ≥ 0 be a C0-semigroup on a Banach space X. In this paper, we study the relations between the abscissa ωLp(T) of weak p-integrability of T (1 ≤ p < ∞), the abscissa ωpR(A) of p-boundedness of the resolvent of the generator A of T (1 ≤ p ≤ ∞), and the growth bounds ωβ(T), β ≥ 0, of T. Our main results are as follows.
- 1. (i) Let T be a C0-semigroup on a B-convex Banach space such that the resolvent of its generator is uniformly bounded in the right half plane. Then ω1 − ε(T) < 0 for some ε > 0.
- 2. (ii) Let T be a C0-semigroup on Lp such that the resolvent of the generator is uniformly bounded in the right half plane. Then ωβ(T) < 0 for all β>¦1/p − 1/p′¦, 1/p + 1/p′ = 1.
- 3. (iii) Let 1 ≤ p ≤ 2 and let T be a weakly Lp-stable C0-semigroup on a Banach space X. Then for all β>1/p we have ωβ(T) ≤ 0.
17.
In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).