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141.
Jenó Szigeti 《Order》1990,7(1):77-81
Given a linearly ordered set (A,
R
) and an R-monotone function f: AA, we give a necessary and sufficient condition on A, f,
R
, involving generating sets and forbidden subalgebras, for
R
to be a well-ordering.Partially supported by Hungarian National Foundation for Scientific Research Grant nr. 1813. 相似文献
142.
Summary Utilizing kernel structure properties a unified construction of Hankel matrix inversion algorithms is presented. Three types of algorithms are obtained: 1)O(n
2) complexity Levinson type, 2)O (n) parallel complexity Schur-type, and 3)O(n log2
n) complexity asymptotically fast ones. All algorithms work without additional assumption (like strong nonsingularity). 相似文献
143.
Equilibria of Runge-Kutta methods 总被引:2,自引:0,他引:2
Summary It is known that certain Runge-Kutta methods share the property that, in a constant-step implementation, if a solution trajectory converges to a bounded limit then it must be a fixed point of the underlying differential system. Such methods are calledregular. In the present paper we provide a recursive test to check whether given method is regular. Moreover, by examining solution trajectories of linear equations, we prove that the order of ans-stage regular method may not exceed 2[(s+2)/2] and that the maximal order of regular Runge-Kutta method with an irreducible stability function is 4. 相似文献
144.
Robert Hermann 《Acta Appl Math》1990,18(1):17-57
This paper aims to develop the differential-geometric and Lie-theoretic foundations of perturbation theory for control systems, extending the classical methods of Poincaré from the differential equation-dynamical system level where they are traditionally considered, to the situation where the element of control is added. It will be guided by general geometric principles of the theory of differential systems, seeking approximate solutions of the feedback linearization equations for nonlinear affine control systems. In this study, certain algebraic problems of compatibility of prolonged differential systems are encountered. The methods developed by D. C. Spencer and H. Goldschmidt for studying over-determined systems of partial differential equations are needed. Work in the direction of applying theio theory is presented.Supported by grants from the Ames Research Center of NASA and the Applied Mathematics and Systems Research Programs of the National Science Foundation 相似文献
145.
In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented. 相似文献
146.
Lothar Berg 《Aequationes Mathematicae》1990,40(1):44-53
Summary A certain class of entire functionsF(s) of order zero which are asymptotically equal to the sum of just two neighbouring terms of their power series when |s| with |args| < – for any fixed > 0, is investigated. Which two terms one has to take, depends upons. It is shown that these functions have infinitely many negative zeros, and the asymptotic behaviour of the zeros is also determined. 相似文献
147.
IfK is a field of characteristic 0 then the following is shown. Iff, g, h: M
n
(K) K are non-constant solutions of the Binet—Pexider functional equation
相似文献
148.
H. Haruki 《Aequationes Mathematicae》1990,40(1):271-280
The purpose of this paper is to solve the following Pythagorean functional equation:(e
p(x,y)
)
2
) = q(x,y)
2
+ r(x, y)
2, where each ofp(x,y), q(x, y) andr(x, y) is a real-valued unknown harmonic function of the real variablesx, y on the wholexy-planeR
2.The result is as follows. 相似文献
149.
E. Mieloszyk 《Periodica Mathematica Hungarica》1990,21(1):43-53
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