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61.
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
62.
Olaf Steinbach 《Numerische Mathematik》2002,90(4):775-786
Summary. In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid
coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability
of a generalized projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces,
the stability of the generalized projection is proved assuming some mesh conditions locally.
Received April 11, 2000 / Revised version received February 15, 2001 / Published online July 25, 2001 相似文献
63.
Non-local approximation of the Mumford-Shah functional 总被引:3,自引:0,他引:3
The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of -convergence by a sequence of non-local integral functionals.
Received June 6, 1996 / Accepted July 11, 1996 相似文献
64.
65.
We answer some questions posed in [L. Grunenfelder, M. Mastnak, On bimeasurings, J. Pure Appl. Algebra 204 (2006) 258-269] concerning the universal bimeasuring bialgebra via a construction of suitable subcoalgebras of the universal measuring coalgebra. 相似文献
66.
In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on
an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness
with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended
Mbekhta decomposition gives a characterization of circularly isolated spectral sets. 相似文献
67.
The present paper deals with the study of a Durrmeyer-type integral modification of certain modified Baskakov operators. Here
we study simultaneous approximation properties for these operators by using the iterative combinations. We obtain an asymptotic
formula and an error estimation in terms of higher order modulus of continuity for these operators.
相似文献
68.
Shuguang Wang 《Geometriae Dedicata》1995,57(2):207-215
We classify, in terms of simple algebraic equations, the fixed point sets of the moduli space of stable bundles over genus 2 curves with anti-holomorphic involutions.Research supported by SRF of University of Missouri. 相似文献
69.
Loïc Foissy 《Journal of Pure and Applied Algebra》2007,209(2):439-459
We introduce bidendriform bialgebras, which are bialgebras such that both product and coproduct can be split into two parts satisfying good compatibilities. For example, the Malvenuto-Reutenauer Hopf algebra and the non-commutative Connes-Kreimer Hopf algebras of planar decorated rooted trees are bidendriform bialgebras. We prove that all connected bidendriform bialgebras are generated by their primitive elements as a dendriform algebra (bidendriform Milnor-Moore theorem) and then is isomorphic to a Connes-Kreimer Hopf algebra. As a corollary, the Hopf algebra of Malvenuto-Reutenauer is isomorphic to the Connes-Kreimer Hopf algebra of planar rooted trees decorated by a certain set. We deduce that the Lie algebra of its primitive elements is free in characteristic zero (G. Duchamp, F. Hivert and J.-Y. Thibon conjecture). 相似文献
70.
Katharina Habermann Lutz Habermann Paul Rosenthal 《Calculus of Variations and Partial Differential Equations》2007,30(2):137-152
A Yang–Mills theory in a purely symplectic framework is developed. The corresponding Euler–Lagrange equations are derived
and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic connections. 相似文献