共查询到20条相似文献,搜索用时 305 毫秒
1.
Ulrich Faigle 《Discrete Applied Mathematics》1984,9(2):209-211
Generalizing the multiple basis exchange property for matroids, the following theorem is proved: If x and y are vectors of a submodular system in and such that x = x1 + x2, then there are such that y = y1 + y2 and both x1 + y1 and x2 + y2 belong to the submodular system.An integral analogue holds for the integral submodular systems and a non-negative analogue for polymatroids. 相似文献
2.
The intent of this paper is to show that the Nordsieck-Gear methods with maximum polynomial degree k+1, first described in [1], admit of matched starting methods which are exact for all polynomials of degree ?k+1. In general, it is shown that these starting methods yield starting errors of the required order, O(hk+2), for all initial-value problemswhere f is k+1 times continuously differentiable in a neighborhood of the graph of the exact solution (x,?(x)), x?[0,X]. Two theorems are proved. The first is the constructive existence of an algorithm which requires (k-p+1)(k-p+2)/2 evaluations of the function f to obtain approximations of the method's required higher-order scaled derivatives at the origin:each of which is accurate to O(hk+2). The second, less general theorem, shows that when f is a polynomial in x, y, and its higher order derivatives y(1),y(2),…,y(p?1), an algorithm can be constructed for obtaining the higher-order scaled derivatives exactly. These results lay to rest once and for all any heuristic arguments against varying corrector minus predictor coefficients for preserving maximal order (polynomial degree) because starting values are inexact. Furthermore, and perhaps most importantly, the maximum-polynomial-degree Nordsieck-Gear methods are shown to have a unique property of zero starting error for an important class of ordinary differential equations. 相似文献
3.
Let λ1 and λN be, respectively, the greatest and smallest eigenvalues of an N×N hermitian matrix H=(hij), and x=(x1,x2,…,xN) with (x,x)=1. Then, it is known that (1) λ1?(x,Hx)?λN and (2) if, in addition, H is positive definite, . Assuming that y=(y1,y2,…, yN) and |yi|?1, i=1,2,…,N, it is shown in this paper that these inequalities remain true if H and H?1 are, respectively, replaced by the Hadamard products and , where M(y) is a matrix defined by . Subsequently, these results are extended to improve the spectral bounds of . 相似文献
4.
Wolfgang Wasow 《Linear algebra and its applications》1977,18(2):163-170
Let A(x,ε) be an n×n matrix function holomorphic for |x|?x0, 0<ε?ε0, and possessing, uniformly in x, an asymptotic expansion , as ε→0+. An invertible, holomorphic matrix function P(x,ε) with an asymptotic expansion , as ε→0+, is constructed, such that the transformation y = P(x,ε)z takes the differential equation a positive integer, into , where B(x,ε) is asymptotically equal, to all orders, to a matrix in a canonical form for holomorphic matrices due to V.I. Arnold. 相似文献
5.
P.J. Cook 《Journal of Number Theory》1977,9(1):142-152
It is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio is irrational then the values taken by for integer values of x1 ,…, x6, y are everywhere dense on the real line. A similar result holds for expressions of the form . 相似文献
6.
I.M. Longman 《Journal of Computational and Applied Mathematics》1984,10(2):141-146
The approximate solution of the finite moment problem , k = 1, 2, 3, …, is considered. This problem is related to the problem of finding a best polynomial least squares approximation to a given function in [0,1]. The connection with Laplace transform inversion is emphasized, and a set of special square matrices with integral elements is introduced, which has an intimate relation to the above two problems. These matrices are the well-known inverses of finite segments of the infinite Hilbert matrix. 相似文献
7.
We consider prenormal forms associated to generic perturbations of the system . It is known that they have a formal normal form , where [Differential Equations 158 (1) (1999) 152–173]. We show that the series A0 and the normalizing transformations are divergent, but 1-summable. To cite this article: M. Canalis-Durand, R. Schäfke, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
8.
Milton Rosenberg 《Journal of multivariate analysis》1978,8(2):295-316
Let p, q be arbitrary parameter sets, and let be a Hilbert space. We say that x = (xi)i?q, xi ? , is a bounded operator-forming vector (?Fq) if the Gram matrix 〈x, x〉 = [(xi, xj)]i?q,j?q is the matrix of a bounded (necessarily ≥ 0) operator on , the Hilbert space of square-summable complex-valued functions on q. Let A be p × q, i.e., let A be a linear operator from to . Then exists a linear operator ǎ from (the Banach space) Fq to Fp on (A) = {x:x ? Fq, is p × q bounded on } such that y = ǎx satisfies yj?σ(x) = {space spanned by the xi}, 〈y, x〉 = A〈x, x〉 and . This is a generalization of our earlier [J. Multivariate Anal.4 (1974), 166–209; 6 (1976), 538–571] results for the case of a spectral measure concentrated on one point. We apply these tools to investigate q-variate wide-sense Markov processes. 相似文献
9.
I Herbst 《Journal of Functional Analysis》1982,48(2):224-251
Let , with ? a normalized Gaussian. Suppose ≠ 0 and that has no eigenfunctions in L2(3N. If H1ψ = μψ with μ < infσess(H1), then (ψ, e?itHψ) decays exponentially at a rate governed by the positions of the resonances of H. 相似文献
10.
Sums of Dedekind type are defined by the formula , where each of A(x) and B(x) satisfies a multiplication formula of the form . Properties of these sums are obtained, including an extension of M. I. Knopp's identity for the classical Dedekind sums s(h, k). 相似文献
11.
The system is investigated, where x and y are scalar functions of time (t ? 0), and n space variables , and F and G are nonlinear functions. Under certain hypotheses on F and G it is proved that there exists a unique spherically symmetric solution , which is bounded for r ? 0 and satisfies x(0) >x0, y(0) > y0, x′(0) = 0, y′(0) = 0, and x′ < 0, y′ > 0, ?r > 0. Thus, (x(r), y(r)) represents a time independent equilibrium solution of the system. Further, the linearization of the system restricted to spherically symmetric solutions, around (x(r), y(r)), has a unique positive eigenvalue. This is in contrast to the case n = 1 (i.e., one space dimension) in which zero is an eigenvalue. The uniqueness of the positive eigenvalue is used in the proof that the spherically symmetric solution described is unique. 相似文献
12.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
13.
R.J Cook 《Journal of Number Theory》1983,17(1):80-92
Let k be an odd positive integer. Davenport and Lewis have shown that the equations with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that Here it is shown that for any ? > 0 and k > k0(?) the equations have a nontrivial solution provided that 相似文献
14.
Philip W. Smith 《Journal of Approximation Theory》1974,10(4):337-357
In [3] Golomb describes, for 1 < p < ∞, the Hr,p(R)-extremal extension of a function (i.e., the Hr,p-spline with knots in E) and studies the cone of all such splines. We study the problem of determining when is in Wr,p ≡ Hr,p ∩ Lp. If , then is called a Wr,p-spline, and we denote by the cone of all such splines. If E is quasiuniform, then if and only if . The cone with E quasiuniform is shown to be homeomorphic to lp. Similarly, is homeomorphic to hr,p. Approximation properties of the Wr,p-splines are studied and error bounds in terms of the mesh size are calculated. Restricting ourselves to the case p = 2 and to quasiuniform partitions E, the second integral relation is proved and better error bounds in terms of are derived. 相似文献
15.
Miklós Ajtai János Komlós Endre Szemerédi 《Journal of Combinatorial Theory, Series A》1980,29(3):354-360
Upper bounds are found for the Ramsey function. We prove and, for each k ? 3, asymptotically in x. 相似文献
16.
R.N. Buttsworth 《Journal of Number Theory》1980,12(4):487-498
The polynomial functions f1, f2,…, fm are found to have highest common factor h for a set of values of the variables x1, x2,…,xm whose asymptotic density is For the special case f1(x) = f2(x) = … = fm(x) = x and h = 1 the above formula reduces to , the density if m-tuples with highest common factor 1. Necessary and sufficient conditions on the polynomials f1, f2,…, fm for the asymptotic density to be zero are found. In particular it is shown that either the polynomials may never have highest common factor h or else h is the highest common factor infinitely often and in fact with positive density. 相似文献
17.
We prove global well-posedness results for small initial data in , and in , sk=1/2?1/k, for the generalized Benjamin–Ono equation . We also consider the cases k=2,3. To cite this article: L. Molinet, F. Ribaud, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
18.
Consider the matrix problem in the case where A is known precisely, the problem is ill conditioned, and ε is a random noise vector. Compute regularized “ridge” estimates,,where 1 denotes matrix transpose. Of great concern is the determination of the value of λ for which x?λ “best” approximates . Let ,and define λ0 to be the value of λ for which Q is a minimum. We look for λ0 among solutions of dQ/dλ = 0. Though Q is not computable (since ε is unknown), we can use this approach to study the behavior of λ0 as a function of y and ε. Theorems involving “noise to signal ratios” determine when λ0 exists and define the cases λ0 > 0 and λ0 = ∞. Estimates for λ0 and the minimum square error Q0 = Q(λ0) are derived. 相似文献
19.
Structure is developed on the set of real-valued stochastic processes in terms of the authors recently defined statistical measures making explicit an -calculus over the structure. This proves that the stochastic-differential equation y=x, where x is a stochastic process and is an nth order linear-stochastic differential operator with up to n ? 1 stochastic-process coefficients, is solved by Adomian's series, and finally, establishes the existence and uniqueness of the statistical measures of the solution process. 相似文献
20.
The matrices of order n defined, in terms of the n arbitrary numbers xj, by the formulae , are representations of the multiplicative operator ξ and of the differential operator d/dξ in a space spanned by the polynomials in ξ of degree less than n. This elementary fact implies a number of remarkable formulae involving these matrices, including novel representations of the classical polynomials. 相似文献