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71.
Summary.
For implicit RK-methods applied to
singularly perturbed systems of ODEs it is shown
that the resulting discrete systems preserve the
geometric properties of the underlying ODE. This
invariant manifold result is used to derive sharp
bounds on the global error of RK-solutions.
Received August 26, 1993 / Revised version received May 10,
1994 相似文献
72.
It is shown that with probability 1 on , resp. ongx the irrational rotation algebra
with respect to the CAT map and the generalized Price-Powers shiftA
X
are asymptotically highly anticommutative. 相似文献
73.
X. -D. Cao 《Periodica Mathematica Hungarica》1994,28(1):43-54
Let
, wheref(n) is the characteristic function of square-full integers. A formula is proved that can be used to obtain better upper bound estimate for (x). We get (x)=O(x
5/33+), which improves the exponent 11/72 obtained by R. Blasubramania and K. Ramachandra. 相似文献
74.
75.
A. González Arias A. del Cueto J. M. Muñoz C. de Francisco L. Torres A. G. Flores M. Zazo J. Iñiguez 《Applied Physics A: Materials Science & Processing》1996,63(5):453-459
Silica may dissolve up to about 0.05 wt% in an iron excess NiZnCo spinel matrix, affecting noticeably the magnetic properties at low and high values of the applied field. The initial permeability is reduced by about 50% with the addition of only 0.1 % SiO2, while the coercivity almost triples, without noticeable changes in porosity or grain distribution. The vacancy and Fe2+ content of the sintered material also show a considerable change. The energy associated to the transformation Fe3+ Fe2+ for the samples without SiO2 was found to be 0.41–0.42 eV, while for the samples with SiO2 additions it decreased to 0.26 eV. The changes in magnetic properties are thought to be caused, more than because of the mentioned changes in ion distribution, by the stresses and defects created in the lattice due to the very small size of the Si4+ ion, which substitutes Fe3+ ions in tetrahedral sites. The transition Fe3+ Fe2+ seems to take place exclusively in the octahedral sites. 相似文献
76.
Best possibility of the Furuta inequality 总被引:5,自引:0,他引:5
Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but .
77.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
78.
Robert D. Skeel 《BIT Numerical Mathematics》1993,33(1):172-175
For fixed step-sizeh the Störmer method is stable for the standard test equationÿ=
2
y,>0, if and only ifh<2. We show that for variable step sizeh
n there does not exist a (positive) limit onh which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratioh
n/h
n–1.This work was supported in part by National Science Foundation Grant DMS 90 15533. 相似文献
79.
The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science. 相似文献
80.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain
Thomas M. Fischer 《Numerische Mathematik》1993,66(1):159-179
Summary The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parametera and the numberN of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, ifa is varied proportional to 1/N
with an exponent 0<<1, then the approximate eigenvalue converges faster than any finite power of 1/N asN. Some numerical examles are given. 相似文献