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71.
In this paper, problems related to the approximation of a holomorphic function f on a compact subset E of the complex plane C by rational functions from the class of all rational functions of order (n,m) are considered. Let ρ
n,m
= ρ
n,m
(f;E) be the distance of f in the uniform metric on E from the class . We obtain results characterizing the rate of convergence to zero of the sequence of the best rational approximation { ρ
n,m(n)
}
n=0
∞
, m(n)/n
→
θ
∈ (0,1] as n
→
∞ . In particular, we give an upper estimate for the liminf
n →∞
ρ
n,m(n)
1/(n+m(n))
in terms of the solution to a certain minimum energy problem with respect to the logarithmic potential. The proofs of the
results obtained are based on the methods of the theory of Hankel operators.
June 16, 1997. Date revised: December 1, 1997. Date accepted: December 1, 1997. Communicated by Ronald A. DeVore. 相似文献
72.
73.
74.
本文提出一种能同时考虑地基的瞬时变形,团结变形和流变的地基基础与上部结构共同作用的一种新的计算方法,在这种方法中,土的计算考虑了Biot固结理论和流变,上部结构利用子结构法进行凝聚可得边界刚度矩阵和边界力,利用位移协讯条件则可以得到共同作用的控制方程,对上述方程进行Laplace变换,可以得到Laplace变换域内的控制方程,在Laplace变换域内对上述方程进行数值求解并进行相应的Laplace逆变换则可以得到时间境内任意时刻的解。 相似文献
75.
A. Berlinet 《Applied Numerical Mathematics》1985,1(6):531-544
A number of sequence transformations are actually used in statistics to solve different kinds of problems. In the two first parts of this paper we set the statistical problem of estimating the unknown orders of an ARMA process and we give its equivalent formulation in terms of invariance properties of sequence transformations: the most used among them are reviewed in the third part. The study of this estimation problem occuring in the Box-Jenkins method has led to new properties of Hankel determinants which are given in the part four. 相似文献
76.
Roger A. Roybal 《Proceedings of the American Mathematical Society》2007,135(12):3967-3975
Using the smallest eigenvalues of Hankel forms associated with a multidimensional moment problem, we establish a condition equivalent to the existence of a reproducing kernel. This result is a multivariate analogue of Berg, Chen, and Ismail's 2002 result. We also present a class of measures for which the existence of a reproducing kernel implies indeterminacy.
77.
As an example of a problem involving two finite contiguous domains, the boundary element method is used to compute the eddy current density in a conductor subjected to a transverse magnetic field. 相似文献
78.
S. Bermudo S. A. M. Marcantognini M. D. Morán 《Czechoslovak Mathematical Journal》2006,56(4):1147-1163
Hankel operators and their symbols, as generalized by V. Pták and P. Vrbová, are considered. The present note provides a parametric
labeling of all the Hankel symbols of a given Hankel operator X by means of Schur class functions. The result includes uniqueness criteria and a Schur like formula. As a by-product, a new
proof of the existence of Hankel symbols is obtained. The proof is established by associating to the data of the problem a
suitable isometry V so that there is a bijective correspondence between the symbols of X and the minimal unitary extensions of V. 相似文献
79.
Thermoelasticity problem in a thick-walled cylinder is solved analytically using the finite Hankel transform. Time-dependent thermal boundary conditions are assumed to act on the inner surface of the cylinder. For the mechanical boundary conditions two different cases are assumed: Traction–displacement problem (traction is prescribed on the inner surface and the fixed displacement boundary condition on the outer one) and Traction–Traction problem (tractions are prescribed on both the inner and outer surfaces of the hollow cylinder). The quasi-static solution of the thermoelasticity problem is derived analytically, i.e., the transient thermal response of the cylinder is derived and then, quasi-static structural problem is solved and closed form relations are extracted for the thermal stresses in the two problems. The results show to be in accordance with that cited in the literature in the special cases. 相似文献
80.
Manuel Aguirre Téllez Rubén Alejandro Cerutti Susana Elena Trione 《Acta Appl Math》1997,48(3):235-284
The present note contains the Tables of Fourier, Laplace and Hankel transforms of several dimensional generalized functions. They are, mainly, based on the Laplace transform of retarded, Lorentz-invariant functions and the Fourier transforms of causal distributions. 相似文献