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981.
982.
When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution
is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical
systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite.
So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are
used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed
in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates.
Received March 15, 1996 / Revised version received January 3, 1997 相似文献
983.
R. Pendavingh 《Combinatorica》1998,18(2):281-292
, where μ and λ are minor-monotone graph invariants introduced by Colin de Verdière [3] and van der Holst, Laurent, and Schrijver
[5]. It is also shown that a graph G exists with . The graphs G with maximal planar complement and , characterised by Kotlov, Lovász, and Vempala, are shown to be forbidden minors for .
Received: June 13, 1997 相似文献
984.
985.
986.
Wolfgang M. Ruppert 《manuscripta mathematica》1998,96(1):17-22
If K is a number field of degree n over Q with discriminant D
K
and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are
infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d
2 such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real
number field of prime degree n then one can find an integral generator α with .
Received: 10 January 1997 / Revised version: 13 January 1998 相似文献
987.
A q × n array with entries from 0, 1,…,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,… q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C1, C2,…, Ct of t columns and for each choice = (1,…,t) Δ of signs, the linear combination ∑j=1t jCj contains (mod q) each entry of [0, 1,…, q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (1, …, t) of signs in δ, the linear combination ∑j=1t jCj contains each entry of [0, 1,…, q t- 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described. 相似文献
988.
Mohamed Krir 《manuscripta mathematica》1998,96(1):9-16
Let R be a complete discrete valuation ring with mixed characteristic. Denote by K its field of fractions and by k its residue field. Let 0 →A
K
→B
K
→C
K
→ 0 be an exact sequence of abelian varieties over K and consider the corresponding complex of Nérons models 0 →A→B→C→ 0, over R. We assume that the identity component B
k
0 of the special fibre B
k
of B is a torus and we study the defect of exactmess at B in this last sequence.
Re?u: 4 décembre 1997/ Version revisée: 15 décembre 1997 相似文献
989.
灰色模型的最优化及其参数的直接求法 总被引:2,自引:0,他引:2
基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好. 相似文献
990.
We investigate certain classes of normal completely positive (CP) maps on the hyperfinite II1 factorA. Using the representation theory of a suitable irrational rotation algebra, we propose some computable invariants for such
CP maps.
Dedicated to Professor K B Sinha 相似文献