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1.
An affine pseudo-plane X is a smooth affine surface defined over
which is endowed with an
-fibration such that every fiber is irreducible and only one fiber is a multiple fiber. If there is a hyperbolic
-action on X and X is an
-surface, we shall show that the universal covering
is isomorphic to an affine hypersurface
in the affine 3-space
and X is the quotient of
by the cyclic group
via the action
where
and
It is also shown that a
-homology plane X with
and a nontrivial
-action is an affine pseudo-plane. The automorphism group
is determined in the last section. 相似文献
2.
Lisa Jeffrey Young-Hoon Kiem Frances C. Kirwan Jonathan Woolf 《Transformation Groups》2006,11(3):439-494
This paper studies intersection theory on the compactified moduli space
of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface
of genus
where n and d may have common factors. Because of the presence of singularities we work with the intersection cohomology
groups
defined by Goresky and MacPherson and the ordinary cohomology groups of a certain partial resolution of singularities
of
Based on our earlier work [25], we give a precise formula for the intersection cohomology pairings and provide a method to
calculate pairings on
The case when n = 2 is discussed in detail. Finally Witten's integral is considered for this singular case. 相似文献
3.
Jan Draisma 《Transformation Groups》2006,11(4):609-624
For a finite-dimensional representation
of a group G, the diagonal action of G on
p-tuples of elements of M, is usually poorly understood. The algorithm presented here computes a geometric characteristic
of this action in the case where G is connected and reductive, and
is a morphism of algebraic groups: The algorithm takes as input the
weight system of M, and it returns the number of irreducible components
of the null-cone of G on
for large p. The paper concludes with a theorem that if the characteristic is zero and G is semisimple, then only few M have
the property that
is small for all p. 相似文献
4.
Kernel and Trace Operators for Extensions of Brandt Semigroups 总被引:1,自引:0,他引:1
Mario Petrich 《Semigroup Forum》2007,75(1):18-44
Let S be an (ideal) extension of a Brandt semigroup S0 by a Brandt semigroup S1 and let
denote the congruence lattice of S. For
denote by
and
the least and the greatest congruences on S with the same kernel as
respectively, and let
and
have the analogous meaning relative to trace. We establish necessary and sufficient conditions on S in order that one or
more of the operators
be
- or
-homomorphisms on
The conditions are expressed directly in terms of a construction of an extension of S0 and S1 and the proofs make use of a construction of congruences on S expressed by means of congruences on S0 and S1. 相似文献
5.
We continue the investigation of some problems in learning theory in the setting formulated by F. Cucker and S. Smale. The
goal is to find an estimator
on the base of given data
that approximates well the regression function
of an unknown Borel probability measure
defined on
We assume that
belongs to a function class
It is known from previous works that the behavior of the entropy numbers
of
in the uniform norm
plays an important role in the above problem. The standard way of measuring the error between a target function
and an estimator
is to use the
norm (
is the marginal probability measure on X generated by
). This method has been used in previous papers. We continue to use this method in this paper. The use of the
norm in measuring the error has motivated us to study the case when we make an assumption on the entropy numbers
of
in the
norm. This is the main new ingredient of thispaper. We construct good estimators in different settings: (1) we know both
and
; (2) we know
but we do not know
and (3) we only know that
is from a known collection of classes but we do not know
An estimator from the third setting is called a universal estimator. 相似文献
6.
In this paper we study the worst-case error (of numerical integration) on the unit sphere
for all functions in the unit ball of the Sobolev space
where
More precisely, we consider infinite sequences
of m(n)-point numerical integration rules
where: (i)
is exact for all spherical polynomials of degree
and (ii)
has positive weights or, alternatively to (ii), the sequence
satisfies a certain local regularity property. Then we show that the worst-case error (of numerical integration)
in
has the upper bound
where the constant c depends on s and d (and possibly the sequence
This extends the recent results for the sphere
by K. Hesse and I.H. Sloan to spheres
of arbitrary dimension
by using an alternative representation of the worst-case error. If the sequence
of numerical integration rules satisfies
an order-optimal rate of convergence is achieved. 相似文献
7.
David Walnut 《Journal of Fourier Analysis and Applications》1995,2(5):435-452
It is shown that a function
is completely determined by the samples of
on sets
where
and
is irrational if
and of
If
then the samples of
on
and only the first k derivatives of
at 0 are required to determine f completely. Higher dimensional analogues of these results, which apply to functions
and
are proven. The sampling results are sharp in the sense that if any condition is omitted, there exist nonzero
and
satisfying the rest. It is shown that the one-dimensional sampling sets correspond to Bessel sequences of complex exponentials
that are not Riesz bases for
A signal processing application in which such sampling sets arise naturally is described in detail. 相似文献
8.
9.
We show that every function in the Hardy space can be approximated by linear combinations of translates and dilates of a synthesizer
, provided only that
and
satisfies a mild regularity condition. Explicitly, we prove scale averaged approximation for each
,
where
is an arbitrary lacunary sequence (such as
) and the coefficients
are local averages of f. This formula holds in particular if the synthesizer
is in the Schwartz class, or if it has compact support and belongs to
for some
in terms of differences of
. 相似文献
10.
Mohan S. Putcha 《Semigroup Forum》2007,75(3):543-553
Let M be a finite monoid with unit group G. By the work of Munn and Ponizovski, the irreducible complex representations of
M are classified according to which J-class (apex) they come from. Consider the irreducible representations of M with apex
. These representations restrict to representations of G, whose components we view as coming from J-classes below G. The remaining
irreducible representations (and their characters) of G are called cuspidal. We show that an irreducible character
of G is cuspidal if and only if
for all idempotents
, where
. 相似文献
11.
A.J.E.M. Janssen 《Journal of Fourier Analysis and Applications》1994,1(4):403-436
Let
and let
In this paper we investigate the relation between the frame operator
and the matrix
whose entries
are given by
for
Here
, for any
We show that
is bounded as a mapping of
into
if and only if
is bounded as a mapping of
into
Also we show that
if and
only if
where
denotes the identity operator of
and
respectively, and
Next, when
generates a frame, we have that
has an upper frame bound, and the minimal dual function
can be computed as
The results of this paper extend, generalize, and rigourize results of Wexler and Raz and of Qian, D. Chen, K. Chen, and
Li on the computation of dual functions for finite, discrete-time Gabor expansions to the infinite, continuous-time case.
Furthermore, we present a framework in which one can show that certain smoothness and decay properties of a
generating a frame are inherited by
In particular, we show that
when
generates a frame
Schwartz space). The proofs of the main results of this paper rely heavily on a technique introduced by Tolimieri and Orr
for relating frame bound questions on complementary lattices by means of the Poisson summation formula. 相似文献
12.
In this paper, we deal with the dual of the semigroup algebras
for an extensive class of locally compact semigroups S under certain locally convex topologies. We first introduce and study
a locally convex topology on
under which the Banach space
can be identified with its strong dual. We then show that, except for the case where S is finite, there are infinitely many
such locally convex topologies
on
. Finally, we characterize the spectrum of
in terms of semicharacters on S. 相似文献
13.
Consider the diagonal action of
on the affine space
where
an algebraically closed field of characteristic
We construct a "standard monomial" basis for the ring of invariants
As a consequence, we deduce that
is Cohen-Macaulay. As the first application, we present the first and second fundamental theorems for
-actions. As the second application, assuming that the characteristic of K is
we give a characteristic-free proof of the Cohen-Macaulayness of the moduli space
of equivalence classes of semi-stable, rank 2, degree 0 vector bundles on a smooth projective curve of genus > 2. As the
third application, we describe a K-basis for the ring of invariants for the adjoint action of
on m copies of
in terms of traces. 相似文献
14.
In the present paper, we study a topologically contractible irreducible algebraic curve C on a ℚ-homology plane S with
We determine such a pair (S,C) when
and C is smooth. Moreover, we prove that if C is not smooth, then C has exactly one singular point and theMakar-Limanov invariant
of S is trivial.
An erratum to this article is available at . 相似文献
15.
Wolter Groenevelt 《Transformation Groups》2007,12(1):77-116
We introduce an algebra
consisting of difference-reflection operators and multiplication operators that can be considered as a q = 1 analogue of
Sahi's double affine Hecke algebra related to the affine root system of type
. We study eigenfunctions of a Dunkl-Cherednik-type operator in the algebra
, and the corresponding Fourier transforms. These eigenfunctions are nonsymmetric versions of the Wilson polynomials and the
Wilson functions. 相似文献
16.
Given a collection S of subsets of some set
and
the set cover problem is to find the smallest subcollection
that covers
that is,
where
denotes
We assume of course that S covers
While the general problem is NP-hard to solve, even approximately, here we consider some geometric special cases, where usually
Combining previously known techniques [4], [5], we show that polynomial-time approximation algorithms with provable performance
exist, under a certain general condition: that for a random subset
and nondecreasing function f(·), there is a decomposition of the complement
into an expected at most f(|R|) regions, each region of a particular simple form. Under this condition, a cover of size O(f(|C|))
can be found in polynomial time. Using this result, and combinatorial geometry results implying bounding functions f(c) that
are nearly linear, we obtain o(log c) approximation algorithms for covering by fat triangles, by pseudo-disks, by a family
of fat objects, and others. Similarly, constant-factor approximations follow for similar-sized fat triangles and fat objects,
and for fat wedges. With more work, we obtain constant-factor approximation algorithms for covering by unit cubes in
and for guarding an x-monotone polygonal chain. 相似文献
17.
The digitisation
of a real disc
having radius
and centre
consists of all integer points inside
, i.e.,
In this paper we show that there are
different (up to translations) digitisations of discs having radius
. More formally,
The result is of interest in the area of digital image processing because it describes how large the impact of the object
position can be on its digitisation. 相似文献
18.
Mario Petrich 《Semigroup Forum》2007,75(1):45-69
A normal cryptogroup S is a completely regular semigroup in which
is a congruence and
is a normal band. We represent S as a strong semilattice of completely simple semigroups, and may set
For each
we set
and represent
by means of an h-quintuple
These parameters are used to characterize certain quasivarieties of normal cryptogroups. Specifically, we construct the lattice
of quasivarieties generated by the (quasi)varieties
and
This is the lattice generated by the lattice of quasivarieties of normal bands, groups and completely simple semigroups.
We also determine the B-relation on the lattice of all quasivarieties of normal cryptogroups. Each quasivariety studied is
characterized in several ways. 相似文献
19.
A compact set
is staircase connected if every two points
can be connected by a polygonal path with sides parallel to the coordinate axes, which is both x-monotone and y-monotone.
denotes the smallest number of edges of such a path.
is an integer-valued metric on S. We investigate this metric and introduce stars and kernels. Our main result is that the
r-th kernel is nonempty, compact and staircase connected provided
. 相似文献
20.
Zachary Mesyan 《Semigroup Forum》2007,75(3):648-675
Let
be a countably infinite set,
the group of permutations of
, and
the monoid of self-maps of
. Given two subgroups
, let us write
if there exists a finite subset
such that the groups generated by
and
are equal. Bergman and Shelah showed that the subgroups which are closed in the function topology on S fall into exactly
four equivalence classes with respect to
. Letting
denote the obvious analog of
for submonoids of E, we prove an analogous result for a certain class of submonoids of E, from which the theorem for groups
can be recovered. Along the way, we show that given two subgroups
which are closed in the function topology on S, we have
if and only if
(as submonoids of E), and that
for every subgroup
(where
denotes the closure of G in the function topology in S and
its closure in the function topology in E). 相似文献