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51.
We generalize several results on bounded analytic interpolation of Fitzgerald and Horn, which work by majorization by positive
definite kernels, to the cases of several complex variables and operator-valued interpolation. Using a lemma of Kolmogorov,
we complement a simplification due to Szafraniec in the proofs of the theorems.
Received: November 21, 2006. Accepted: August 03, 2007. 相似文献
52.
Sans résumé
相似文献
相似文献
53.
For a conformal manifold we introduce the notion of an ambient connection, an affine connection on an ambient manifold of
the conformal manifold, possibly with torsion, and with conditions relating it to the conformal structure. The purpose of
this construction is to realise the normal conformal Tractor holonomy as affine holonomy of such a connection. We give an
example of an ambient connection for which this is the case, and which is torsion free if we start the construction with a
C-space, and in addition Ricci-flat if we start with an Einstein manifold. Thus, for a C-space this example leads to an ambient metric in the weaker sense of Čap and Gover, and for an Einstein space to a Ricci-flat
ambient metric in the sense of Fefferman and Graham.
Current address for first author: Erwin Schr?dinger International Institute for Mathematical Physics (ESI), Boltzmanngasse
9, 1090 Vienna, Austria
Current address for second author: Department of Mathematics, University of Hamburg, Bundesstra?e 55, 20146 Hamburg, Germany 相似文献
54.
Takashi Kishimoto 《Journal of Pure and Applied Algebra》2007,208(1):189-204
Let X?(T,D) be a compactification of an affine 3-fold X into a smooth projective 3-fold T such that the (reduced) boundary divisor D is SNC. In this paper, as an affine counterpart to the work due to S. Mori (cf. [S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982) 133-176]), we shall classify (K+D)-negative extremal rays on T. In particular, if such an extremal ray R=R+[C] intersects K non-negatively, we shall describe the log flips and divisorial contractions appearing explicitly. 相似文献
55.
A fictitious domain approach to the numerical solution of PDEs in stochastic domains 总被引:1,自引:0,他引:1
We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains
are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial
chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition
enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is
invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic
variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection
method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and
convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial
chaos order, in any subdomain which does not contain the random boundaries. 相似文献
56.
For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.
The first author is partially supported by grant MI1503/2005 of the Bulgarian Foundation for Scientific Research. 相似文献
57.
In this paper we investigate the electrostatic problem of determining conductivity profiles from the knowledge of boundary
currents and voltages. We obtain an improved estimate for the voltage potential of a two-dimensional conductor having finitely
many circular inclusions and piecewise constant conductivity profile. We derive an asymptotic expansion for the voltage potential
in terms of the reference voltage potential and the location, size, and conductivity of the inhomogeneities. This representation
is used to formulate the nonlinear least squares problem for estimating the location and size of the inhomogeneities. Required
boundary data for the voltage potential are generated numerically by solving a system of integral equations. Computational
experiments are presented to demonstrate the effectiveness of our identification procedure. 相似文献
58.
C. Foias A. E. Frazho I. Gohberg M. A. Kaashoek 《Integral Equations and Operator Theory》1997,29(4):455-490
The family of all solutions of the three chains completion problem with a prescribed tolerance is described explicitly. It is shown that this family can be parameterized by a natural set of contractive upper triangular operators. As an application all solutions to a suboptimal nonstationary Nehari problem are described. 相似文献
59.
Reinhard Farwig 《Acta Appl Math》1994,37(1-2):41-51
In this note, we discuss the reflection principle of the Stokes system in a half space for the threedimensional case, and of the biharmonic equation. Admitting different boundary conditions, we use the reflection principle to prove uniqueness of solutions of the Stokes system or the biharmonic equation in weightedLq-spaces 相似文献
60.
Let E\subset \Bbb R
s
be compact and let d
n
E
denote the dimension of the space of polynomials of degree at most n in s variables restricted to E . We introduce the notion of an asymptotic interpolation measure (AIM). Such a measure, if it exists , describes the asymptotic behavior of any scheme τ
n
={ \bf x
k,n
}
k=1
dnE
, n=1,2,\ldots , of nodes for multivariate polynomial interpolation for which the norms of the corresponding interpolation operators do
not grow geometrically large with n . We demonstrate the existence of AIMs for the finite union of compact subsets of certain algebraic curves in R
2
. It turns out that the theory of logarithmic potentials with external fields plays a useful role in the investigation. Furthermore,
for the sets mentioned above, we give a computationally simple construction for ``good' interpolation schemes.
November 9, 2000. Date revised: August 4, 2001. Date accepted: September 14, 2001. 相似文献