共查询到20条相似文献,搜索用时 640 毫秒
1.
Meike Tewes 《Discrete Applied Mathematics》2002,120(1-3):239-249
An in-tournament is an oriented graph such that the negative neighborhood of every vertex induces a tournament. In this paper, pancyclic orderings of a strong in-tournament D are investigated. This is a labeling, say x1,x2,…,xn, of the vertex set of D such that D[{x1,x2,…,xt}] is Hamiltonian for t=3,4,…,n. Moreover, we consider the related problem on weak pancyclic orderings, where the same holds for t4 and x1 belongs to an arbitrary oriented 3-cycle. We present sharp lower bounds for the minimum indegree ensuring the existence of a pancyclic or a weak pancyclic ordering in strong in-tournaments. 相似文献
2.
The 2-color Rado number for the equation x1+x2−2x3=c, which for each constant
we denote by S1(c), is the least integer, if it exists, such that every 2-coloring, Δ : [1,S1(c)]→{0,1}, of the natural numbers admits a monochromatic solution to x1+x2−2x3=c, and otherwise S1(c)=∞. We determine the 2-color Rado number for the equation x1+x2−2x3=c, when additional inequality restraints on the variables are added. In particular, the case where we require x2<x3<x1, is a generalization of the 3-term arithmetic progression; and the work done here improves previously established upper bounds to an exact value. 相似文献
3.
Avram Sidi 《Linear algebra and its applications》1998,280(2-3):129-162
In this paper we propose a general approach by which eigenvalues with a special property of a given matrix A can be obtained. In this approach we first determine a scalar function ψ: C → C whose modulus is maximized by the eigenvalues that have the special property. Next, we compute the generalized power iterations uinj + 1 = ψ(A)uj, j = 0, 1,…, where u0 is an arbitrary initial vector. Finally, we apply known Krylov subspace methods, such as the Arnoldi and Lanczos methods, to the vector un for some sufficiently large n. We can also apply the simultaneous iteration method to the subspace span{x(n)1,…,x(n)k} with some sufficiently large n, where x(j+1)m = ψ(A)x(j)m, j = 0, 1,…, m = 1,…, k. In all cases the resulting Ritz pairs are approximations to the eigenpairs of A with the special property. We provide a rather thorough convergence analysis of the approach involving all three methods as n → ∞ for the case in which A is a normal matrix. We also discuss the connections and similarities of our approach with the existing methods and approaches in the literature. 相似文献
4.
Ludwin A.BASILIO-HERNáNDEZ Walter CARBALLOSA Jesús LEA?OS José M.SIGARRETA 《数学学报(英文版)》2019,35(3):338-354
We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G. 相似文献
5.
《Stochastic Processes and their Applications》1995,60(2):247-260
In this paper we consider continuity properties of a stochastic heat equation of the form ∂u(t,x)/∂t = ∂2u(t,x)/∂x2 + f(u(t,x))Wx,t. We prove that the solutions of this equation depend continuously on the function f and give some new estimates for this connection. 相似文献
6.
In this paper we investigate the behaviour of the solutions of equations ΣI=1n aixi = b, where Σi=1n, ai = 0 and b ≠ 0, with respect to colorings of the set N of positive integers. It turns out that for any b ≠ 0 there exists an 8-coloring of N, admitting no monochromatic solution of x3 − x2 = x2 − x1 + b. For this equation, for b odd and 2-colorings, only an odd-even coloring prevents a monochromatic solution. For b even and 2-colorings, always monochromatic solutions can be found, and bounds for the corresponding Rado numbers are given. If one imposes the ordering x1 < x2 < x3, then there exists already a 4-coloring of N, which prevents a monochromatic solution of x3 − x2 = x2 − x1 + b, where b ε N. 相似文献
7.
In this paper, we provide a solution of the quadrature sum problem of R. Askey for a class of Freud weights. Let r> 0, b (− ∞, 2]. We establish a full quadrature sum estimate 1 p < ∞, for every polynomial P of degree at most n + rn1/3, where W2 is a Freud weight such as exp(−¦x¦), > 1, λjn are the Christoffel numbers, xjn are the zeros of the orthonormal polynomials for the weight W2, and C is independent of n and P. We also prove a generalisation, and that such an estimate is not possible for polynomials P of degree M = m(n) if m(n) = n + ξnn1/3, where ξn → ∞ as n → ∞. Previous estimates could sum only over those xjn with ¦xjn¦ σx1n, some fixed 0 < σ < 1. 相似文献
8.
A. G. RammD. N. Ghosh Roy 《Applied Mathematics Letters》1993,6(6):15-17
Let[2+k2n(x1,x3)]u(x1,x2,x3)=−δ(x1,y1δ(x2,y2)δ(x3,y3) in R3+. Assume that u(x1,x2,x3=0,y1,y2=0,y3=0,k) is measured at the plane P {x:x3=0} for all positions of the source on the line y = (y1,y2 = 0,y3 = 0), -∞ < y1 < ∞, and receiver on the plane(x1,x2,x3 − <x1,x2 < ∞, and for low-frequencies 0 < k <k0, k0 > 0 is an arbitrary small wave number. Assume thatn(x1,x3) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determinen(x1,x3)uniquely. 相似文献
9.
In this paper, we establish three iteration methods to compute solutions for a class of (weakly) singular two-point boundary value problems (xy′)′=f(x,y), where x(0,1) and <2. We obtain the sufficient conditions for existence of a unique solution on
. Finally, we given some numerical examples. 相似文献
10.
Neighborhood unions and cyclability of graphs 总被引:1,自引:0,他引:1
A graph G is said to be cyclable if for each orientation
of G, there exists a set S of vertices such that reversing all the arcs of
with one end in S results in a hamiltonian digraph. Let G be a 3-connected graph of order n36. In this paper, we show that if for any three independent vertices x1, x2 and x3, |N(x1)N(x2)|+|N(x2)N(x3)|+|N(x3)N(x1)|2n+1, then G is cyclable. 相似文献
11.
The bandwidth B(G) of a graph G is the minimum of the quantity max{|f(x)−f(y)| : xyE(G)} taken over all proper numberings f of G. The composition of two graphs G and H, written as G[H], is the graph with vertex set V(G)×V(H) and with (u1,v1) is adjacent to (u2,v2) if either u1 is adjacent to u2 in G or u1=u2 and v1 is adjacent to v2 in H. In this paper, we investigate the bandwidth of the composition of two graphs. Let G be a connected graph. We denote the diameter of G by D(G). For two distinct vertices x,yV(G), we define wG(x,y) as the maximum number of internally vertex-disjoint (x,y)-paths whose lengths are the distance between x and y. We define w(G) as the minimum of wG(x,y) over all pairs of vertices x,y of G with the distance between x and y is equal to D(G). Let G be a non-complete connected graph and let H be any graph. Among other results, we prove that if |V(G)|=B(G)D(G)−w(G)+2, then B(G[H])=(B(G)+1)|V(H)|−1. Moreover, we show that this result determines the bandwidth of the composition of some classes of graphs composed with any graph. 相似文献
12.
13.
J. Arvesú R. Álvarez-Nodarse F. Marcellán K. Pan 《Journal of Computational and Applied Mathematics》1998,90(2):263-156
We obtain an explicit expression for the Sobolev-type orthogonal polynomials {Qn} associated with the inner product , where p(x) = (1 − x)(1 + x)β is the Jacobi weight function, ,β> − 1, A1,B1,A2,B20 and p, q P, the linear space of polynomials with real coefficients. The hypergeometric representation (6F5) and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in [−1, 1] is studied. Furthermore, we obtain some estimates for the largest zero of Qn(x). Such a zero is located outside the interval [−1, 1]. We deduce his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented. 相似文献
14.
Let G be a graph of order n, and let a and b be integers such that 1a<b. Let δ(G) be the minimum degree of G. Then we prove that if δ(G)(k−1)a, n(a+b)(k(a+b)−2)/b, and |NG(x1)NG(x2)NG(xk)|an/(a+b) for any independent subset {x1,x2,…,xk} of V(G), where k2, then G has an [a,b]-factor. This result is best possible in some sense. 相似文献
15.
A connected graph is doubly connected if its complement is also connected. The following Ramsey-type theorem is proved in this paper. There exists a function h(n), defined on the set of integers exceeding three, such that every doubly connected graph on at least h(n) vertices must contain, as an induced subgraph, a doubly connected graph, which is either one of the following graphs or the complement of one of the following graphs:
- (1) Pn, a path on n vertices;
- (2) K1,ns, the graph obtained from K1,n by subdividing an edge once;
- (3) K2,ne, the graph obtained from K2,n by deleting an edge;
- (4) K2,n+, the graph obtained from K2,n by adding an edge between the two degree-n vertices x1 and x2, and a pendent edge at each xi.
Two applications of this result are also discussed in the paper. 相似文献
16.
The parametric resource allocation problem asks to minimize the sum of separable single-variable convex functions containing a parameter λ, Σi = 1n (ƒi(xi + λgi(xi)), under simple constraints Σi = 1n xi = M, li≤xi≤ui and xi: nonnegative integers for i = 1, 2, …, n, where M is a given positive integer, and li and ui are given lower and upper bounds on xi. This paper presents an efficient algorithm for computing the sequence of all optimal solutions when λ is continuously changed from 0 to ∞. The required time is O(G√Mlog2 n + n log n + n log(M/n)), where G = Σi = 1n ui − Σi = 1n li and an evaluation of ƒi(·) or gi(·) is assumed to be done in constant time. 相似文献
17.
E. R. LamkenS. A. Vanstone 《Discrete Mathematics》1993,120(1-3):135-148
Let V be a set of υ elements. A (1, 2; 3, υ, 1)-frame F is a square array of side v which satisfies the following properties. We index the rows and columns of F with the elements of V, V={x1,x2,…,xυ}. (1) Each cell is either empty or contains a 3-subset of V. (2) Cell (xi, xi) is empty for i=1, 2,…, υ. (3) Row xi of F contains each element of V−{xi} once and column xi of F contains each element of V−{xi} once. (4) The collection of blocks obtained from the nonempty cells of F is a (υ, 3, 2)-BIBD. A (1, 2; 3, υ, 1)-frame is a doubly near resolvable (υ, 3, 2)-BIBD. In this paper, we first present a survey of existence results on doubly near resolvable (υ, 3, 2)-BIBDs and (1, 2; 3, υ, 1)-frames. We then use frame constructions to provide a new infinite class of doubly near resolvable (υ, 3, 2)-BIBDs by constructing (1, 2; 3, υ, 1)-frames. 相似文献
18.
Renpu Ge 《Applied mathematics and computation》1989,30(3):261-288
This paper gives a parallel computing scheme for minimizing a twice continuously differentiable function with the form where x = (xT1,…,xTm)T and xi Rni, ∑mi = 1ni = n, and n a very big number. It is proved that we may use m parallel processors and an iterative procedure to find a minimizer of ƒ(x). The convergence and convergence rate are given under some conditions. The conditions for finding a global minimizer of ƒ(x by using this scheme are given, too. A similar scheme can also be used parallelly to solve a large scale system of nonlinear equations in the similar way. A more general case is also investigated. 相似文献
19.
For an integer n3, the crown Sn0 is defined to be the graph with vertex set {x0,x1,…,xn−1,y0,y1,…,yn−1} and edge set {xiyj: 0i,jn−1, i≠j}. In this paper we give some sufficient conditions for the edge decomposition of the crown into isomorphic cycles. 相似文献
20.
Shooting methods are used to obtain solutions of the three-point boundary value problem for the second-order dynamic equation, yΔΔ = f (x, y, yΔ), y(x1) = y1, y(x3) − y(x2) = y2, where f : (a, b)T × 2 → is continuous, x1 < x2 < x3 in (a, b)T, y1, y2 ε , and T is a time scale. It is assumed such solutions are unique when they exist. 相似文献