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991.
T. N. Venkataramana 《Monatshefte für Mathematik》2002,135(3):221-244
We give a criterion to determine when the cycle class of a locally symmetric subvariety of a compact locally symmetric variety generates a non-trivial module under the action of Hecke operators, and give several examples where this criterion is satisfied.
We also exhibit examples of subvarieties which do generate the trivial module under the action of Hecke operators. We show that all Hodge classes (in degree ) on the locally symmetric variety associated to certain arithmetric subgroups Γ of are algebraic (provided that ).
Received 16 January 2001; in revised form 18 October 2001 相似文献
992.
Ole Christensen 《Journal of Fourier Analysis and Applications》2000,6(1):79-91
A frame in a Hilbert space
allows every element in
to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of
those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually
it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce
a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate
the frame coefficients (even inl
2) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg
frames and wavelet frames. 相似文献
993.
Gerald Beer 《Monatshefte für Mathematik》2000,129(4):267-280
By a metric mode of convergence to infinity in a regular Hausdorff space X, we mean a sequence of closed subsets of X with and , and a sequence (or net) in X is convergent to infinity with respect to provided for each contains eventually. Modulo a natural equivalence relation, these correspond to one-point extensions of the space with a countable
base at the ideal point, and in the metrizable setting, they correspond to metric boundedness structures for the space. In
this article, we study the interplay between these objects and certain continuous functions that may determine the metric
mode of convergence to infinity, called forcing functions. Falling out of our results is a simple proof that each noncompact
metrizable space admits uncountably many distinct metric uniformities.
(Received 2 March 1999) 相似文献
994.
Haruhisa Nakajima 《manuscripta mathematica》2000,102(2):139-158
In order to inquire into invariants of non-semisimple groups, we introduce and study relative versions of equidimensionality
and stabilty, which are called relative quasi-equidimensionality and relative stability, of actions of affine algebraic groups,
especially of reductive groups, on affine varieties. As an application of our results, for complex reductive groups of semisimple
rank one, we characterize, respectively, relatively stable representations and relatively equidimensional representations
and, consequently, show that every equidimensional representation is cofree.
Received: 23 October 1998 相似文献
995.
Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval 总被引:12,自引:0,他引:12
Summary. A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a
semi-infinite interval. By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin
approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based
on the Laguerre-Galerkin approximations to the transformed equations is developed and implemented. Numerical results indicating
the high accuracy and effectiveness of this algorithm are presented.
Received October 6, 1997 / Revised version received July 22, 1999 / Published online June 21, 2000 相似文献
996.
Arthur W. Apter 《Archive for Mathematical Logic》2000,39(3):209-211
We give a new proof using iterated Prikry forcing of Magidor's theorem that it is consistent to assume that the least strongly
compact cardinal is the least supercompact cardinal.
Received: 8 December 1997 / Revised version: 12 November 1998 相似文献
997.
Lutz Angermann 《Numerische Mathematik》2000,85(2):175-195
Summary. The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained. Received August 7, 1997 / Revised version received July 15, 1998 / Published online December 6, 1999 相似文献
998.
Frank Stephan 《Archive for Mathematical Logic》2001,40(7):489-513
One-sided classifiers are computable devices which read the characteristic function of a set and output a sequence of guesses
which converges to 1 iff the set on the input belongs to the gven class. Such a classifier istwo-sided if the sequence of
its output in addition converges to 0 on setsnot belonging to the class. The present work obtains the below mentionedresults
for one-sided classes (= Σ0
2 classes) with respect to four areas: Turing complexity, 1-reductions, index sets and measure.
There are one-sided classes which are not two-sided. This can have two reasons: (1) the class has only high Turing complexity.
Then there are some oracles which allow to construct noncomputale two-sided classifiers. (2) The class is difficult because
of some topological constraints and then there are also no nonrecursive two-sided classifiers. For case (1), several results
are obtainedto localize the Turing complexity of certain types of one-sided classes.
The concepts of 1-reduction, 1-completeness and simple sets is transferred to one-sided classes: There are 1-complete classes
and simple classes, but no class is at the same time 1-complete nd simple.
The one-sided classes have a natural numbering. Most of the common index sets relative to this numbering have the high complexity
Π1
1: the index set of the class {0,1}∞, the index set of the equality problem and the index set of all two-sided classes. On the other side the index set of the
empty class has complexity Π0
2; Π0
2 and Σ0
2 are the least complexities any nontrivial index set can have.
Lusin showed that any one-sided class is measurable. Concerning the effectiveness of this measure, it is shown that a one-sided
class has recursive measure 0 if it has measure 0, but that thre are one-sided classes having measure 1 without having measure
1 effectively. The measure of a two-sided class can be computed in the limit.
Received: 2 December 1999 / Revised version: 28 February 2000 / Published online: 15 June 2001 相似文献
999.
The iterates of expanding maps of the unit interval into itself have many of the properties of a more conventional stochastic
process, when the expanding map satisfies some regularity conditions and when the starting point is suitably chosen at random.
In this paper, we show that the sequence of iterates can be closely tied to an m-dependent process. This enables us to prove good bounds on the accuracy of Gaussian approximations. Our main tools are coupling
and Stein's method.
Received: 27 June 1997 / Revised version: 21 September 1998 相似文献
1000.
This paper deals with the iterative solution of stage equations which arise when some fully implicit Runge-Kutta methods,
in particular those based on Gauss, Radau and Lobatto points, are applied to stiff ordinary differential equations. The error
behaviour in the iterates generated by Newton-type and, particularly, by single-Newton schemes which are proposed for the
solution of stage equations is studied. We consider stiff systems y'(t) = f(t,y(t)) which are dissipative with respect to
a scalar product and satisfy a condition on the relative variation of the Jacobian of f(t,y) with respect to y, similar to
the condition considered by van Dorsselaer and Spijker in [7] and [17]. We prove new convergence results for the single-Newton
iteration and derive estimates of the iteration error that are independent of the stiffness. Finally, some numerical experiments
which confirm the theoretical results are presented.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献