共查询到20条相似文献,搜索用时 15 毫秒
1.
We propose an approach via Frobenius manifolds to the study (began in [BCK2] of the relation between rational Gromov–Witten
invariants of nonabelian quotients X//G and those of the corresponding “abelianized” quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov–Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonabelian quotients are partial flag manifolds. 相似文献
2.
3.
Danny Fundinger 《Journal of Nonlinear Science》2008,18(4):391-413
This paper presents a new numerical method for computing global stable manifolds and global stable sets of nonlinear discrete
dynamical systems. For a given map f:ℝ
d
→ℝ
d
, the proposed method is capable of yielding large parts of stable manifolds and sets within a certain compact region M⊂ℝ
d
. The algorithm divides the region M in sets and uses an adaptive subdivision technique to approximate an outer covering of the manifolds. In contrast to similar
approaches, the method requires neither the system’s inverse nor its Jacobian. Hence, it can also be applied to noninvertible
and piecewise-smooth maps. The successful application of the method is illustrated by computation of one- and two-dimensional
stable manifolds and global stable sets. 相似文献
4.
Nader Yeganefar 《Arkiv f?r Matematik》2005,43(2):427-434
We compute theL
p
-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently
pinched negative curvature, and conformally compact manifolds.
This paper has been (partially) supported by the European Commission through the Research Training Network HPRN-CT-1999-00118
“Geometric Analysis”. 相似文献
5.
Maciej Paluszyński Hrvoje Šikić Guido Weiss Shaoliang Xiao 《Journal of Geometric Analysis》2001,11(2):311-342
A tight frame wavelet ψ is an L
2(ℝ) function such that {ψ jk(x)} = {2j/2
ψ(2
j
x −k), j, k ∈ ℤ},is a tight frame for L
2 (ℝ).We introduce a class of “generalized low pass filters” that allows us to define (and construct) the subclass of MRA tight
frame wavelets. This leads us to an associated class of “generalized scaling functions” that are not necessarily obtained
from a multiresolution analysis. We study several properties of these classes of “generalized” wavelets, scaling functions
and filters (such as their multipliers and their connectivity). We also compare our approach with those recently obtained
by other authors. 相似文献
6.
V. E. Nazaikinskii A. Yu. Savin B. Yu. Sternin 《Journal of Mathematical Sciences》2010,164(4):603-636
The computation of a stable homotopic classification of elliptic operators is an important problem of elliptic theory. The
classical solution of this problem is given by Atiyah and Singer for the case of smooth compact manifolds. It is formulated
in terms of K-theory for a cotangent fibering of the given manifold. It cannot be extended for the case of nonsmooth manifolds because
their cotangent fiberings do not contain all necessary information. Another Atiyah definition might fit in such a case: it
is based on the concept of abstract elliptic operators and is given in term of K-homologies of the manifold itself (instead of its fiberings). Indeed, this theorem is recently extended for manifolds with
conic singularities, ribs, and general so-called stratified manifolds: it suffices just to replace the phrase “smooth manifold”
by the phrase “stratified manifold” (of the corresponding class). Thus, stratified manifolds is a strange phenomenon in a
way: the algebra of symbols of differential (pseudodifferential) operators is quite noncommutative on such manifolds (the
symbol components corresponding to strata of positive codimensions are operator-valued functions), but the solution of the
classification problem can be found in purely geometric terms. In general, it is impossible for other classes of nonsmooth
manifolds. In particular, the authors recently found that, for manifolds with angles, the classification is given by a K-group of a noncommutative C* -algebra and it cannot be reduced to a commutative algebra if normal fiberings of faces of the considered manifold are nontrivial.
Note that the proofs are based on noncommutative geometry (more exactly, the K-theory of C* -algebras) even in the case of stratified manifolds though the results are “classical.” In this paper, we provide a review
of the abovementioned classification results for elliptic operators on manifolds with singularities and corresponding methods
of noncommutative geometry (in particular, the localization principle in C* -algebras). 相似文献
7.
Jean Bourgain 《Israel Journal of Mathematics》1992,79(2-3):193-206
In this paper, new results are obtained concerning the uniform approximation property (UAP) inL
p-spaces (p≠2,1,∞). First, it is shown that the “uniform approximation function” does not allow a polynomial estimate. This fact is rather
surprising since it disproves the analogy between UAP-features and the presence of “large” euclidian subspaces in the space
and its dual. The examples are translation invariant spaces on the Cantor group and this extra structure permits one to replace
the problem with statements about the nonexistence of certain multipliers in harmonic analysis. Secondly, it is proved that
the UAP-function has an exponential upper estimate (this was known forp=1, ∞). The argument uses Schauder’s fix point theorem. Its precise behaviour is left unclarified here. It appears as a difficult
question, even in the translation invariant context. 相似文献
8.
Provability interpretations of modal logic 总被引:5,自引:0,他引:5
Robert M. Solovay 《Israel Journal of Mathematics》1976,25(3-4):287-304
We consider interpretations of modal logic in Peano arithmetic (P) determined by an assignment of a sentencev
* ofP to each propositional variablev. We put (⊥)*=“0 = 1”, (χ → ψ)* = “χ* → ψ*” and let (□ψ)* be a formalization of “ψ)* is a theorem ofP”. We say that a modal formula, χ, isvalid if ψ* is a theorem ofP in each such interpretation. We provide an axiomitization of the class of valid formulae and prove that this class is recursive. 相似文献
9.
This paper deals with sparse approximations by means of convex combinations of elements from a predetermined “basis” subsetS of a function space. Specifically, the focus is on therate at which the lowest achievable error can be reduced as larger subsets ofS are allowed when constructing an approximant. The new results extend those given for Hilbert spaces by Jones and Barron,
including, in particular, a computationally attractive incremental approximation scheme. Bounds are derived for broad classes
of Banach spaces; in particular, forL
p spaces with 1<p<∞, theO (n
−1/2) bounds of Barron and Jones are recovered whenp=2.
One motivation for the questions studied here arises from the area of “artificial neural networks,” where the problem can
be stated in terms of the growth in the number of “neurons” (the elements ofS) needed in order to achieve a desired error rate. The focus on non-Hilbert spaces is due to the desire to understand approximation
in the more “robust” (resistant to exemplar noise)L
p, 1 ≤p<2, norms.
The techniques used borrow from results regarding moduli of smoothness in functional analysis as well as from the theory of
stochastic processes on function spaces. 相似文献
10.
Miloslav Feistauer Václav Kučera Karel Najzar Jaroslava Prokopová 《Numerische Mathematik》2011,117(2):251-288
The paper presents the theory of the discontinuous Galerkin finite element method for the space–time discretization of a nonstationary
convection–diffusion initial-boundary value problem with nonlinear convection and linear diffusion. The problem is not singularly
perturbed with dominating convection. The discontinuous Galerkin method is applied separately in space and time using, in
general, different space grids on different time levels and different polynomial degrees p and q in space and time dicretization. In the space discretization the nonsymmetric, symmetric and incomplete interior and boundary
penalty (NIPG, SIPG, IIPG) approximation of diffusion terms is used. The paper is concerned with the proof of error estimates
in “L
2(L
2)”- and “DG”-norm formed by the “L
2(H
1)”-seminorm and penalty terms. A special technique based on the use of the Gauss–Radau interpolation and numerical integration
has been used for the derivation of an abstract error estimate. In the “DG”-norm the error estimates are optimal with respect
to the size of the space grid. They are optimal with respect to the time step, if the Dirichlet boundary condition has behaviour
in time as a polynomial of degree ≤ q. 相似文献
11.
Jacob Feldman 《Israel Journal of Mathematics》1980,36(3-4):321-345
A new approach is given to the entropy of a probability-preserving group action (in the context ofZ and ofR
n
), by defining an approximate “r-entropy”, 0<r<1, and lettingr → 0. If the usual entropy may be described as the growth rate of the number of essential names, then ther-entropy is the growth rate of the number of essential “groups of names” of width≦r, in an appropriate sense. The approach is especially useful for actions of continuous groups. We apply these techniques to
state and prove a “second order” equipartition theorem forZ
m
×R
n
and to give a “natural” proof of Ornstein’s isomorphism theorem for Bernoulli actions ofZ
m
×R
n
, as well as a characterization of such actions which seems to be the appropriate generalization of “finitely determined”. 相似文献
12.
Kwan Hui Nam 《Geometriae Dedicata》2012,157(1):205-216
As first defined by Smillie, an affine manifold with diagonal holonomy is a manifold equipped with an atlas such that the
changes of charts are restrictions of elements of the subgroup of Aff (
\mathbbRn{\mathbb{R}^n}) formed by diagonal matrices. Refining Smillie’s theorem, Benoist proved that if a compact manifold M is split into manifolds with corners corresponding to complete simplicial fans of a fixed frame by its hypersurfaces with
normal crossing, then the product of M and a torus of suitable dimension is a finite cover of an affine manifold with diagonal holonomy, and conversely. Motivated
by the result of Benoist, we introduce a “Benoist manifold” and a natural definition of complexity for them. In particular,
we study some properties of “Benoist manifolds”. 相似文献
13.
Feng Rong 《Arkiv f?r Matematik》2010,48(2):361-370
In [Rong, F., Quasi-parabolic analytic transformations of C
n
, J. Math. Anal. Appl.
343 (2008), 99–109], we showed the existence of “parabolic curves” for certain quasi-parabolic analytic transformations of C
n
. Under some extra assumptions, we show the existence of “parabolic manifolds” for such transformations. 相似文献
14.
Edoardo Ballico 《Rendiconti del Circolo Matematico di Palermo》1993,42(3):404-416
Here we construct many possible free resolutions fors points inP
n
. In suitable ranges we construct configurations of points with “good” minimal free resolution and other configurations for
which the difference with respect to a “good” resolution is prescribed in advance. 相似文献
15.
Myriam Ounaies 《Arkiv f?r Matematik》2001,39(2):375-381
It is known that, unlike the one dimensional case it is not possible to find an upper bound for the zeros of an entire map
fromC
n
toC
n
,n≥2, in terms of the growth of the map. However, if we only consider the “non-degenerate” zeros, that is, the zeros where the
jacobian is not “too small”, it becomes possible. We give a new proof of this fact.
相似文献
16.
A new relation between morphisms in a category is introduced—roughly speaking (accurately in the categories Set and Top), f ∥ g iff morphisms w:dom(f)→dom(g) never map subobjects of fibres of f non-constantly to fibres of g. (In the algebraic setting replace fibre with kernel.) This relation and a slight weakening of it are used to define “connectedness”
versus “disconnectedness” for morphisms. This parallels and generalises the classical treatment of connectedness versus disconnectedness
for objects in a category (in terms of constant morphisms). The central items of study are pairs (F,G)({\mathcal F},{\mathcal G}) of classes of morphisms which are corresponding fixed points of the polarity induced by the ∥-relation. Properties of such
pairs are examined and in particular their relation to (pre)factorisation systems is analysed. The main theorems characterise:
(a) |
factorisation systems which factor morphisms through a regular epimorphic “connected” morphism followed by a “disconnected”
morphism, and 相似文献
17.
In this paper we study the asymptotics of the discrete spectrum in the gap (−1, 1) of the perturbed Dirac operatorD(α)=D
0−αV1 acting inL
2(R
3;C
4) with large coupling constant α. In particular some “non-standard” asymptotic formulae are obtained. 相似文献
18.
In this paper, we prove that any weak solution to the non-stationary Stokes system in 3D with right hand side -div f satisfying (1.4) below, belongs to C( ]0, T[; C
α (Ω)). The proof is based on Campanato-type inequalities and the existence of a local pressure introduced in Wolf [13].
Proc. Conference “Variational analysis and PDE’s”. Intern. Centre “E. Majorana”, Erice, July 5–14, 2006. 相似文献
19.
Baouendi M. S. Mir Nordine Rothschild Linda Preiss 《Journal of Geometric Analysis》2002,12(4):543-580
Results on finite determination and convergence of formal mappings between smooth generic submanifolds in ℂ
N
are established in this article. The finite determination result gibes sufficient conditions to guarantee that a formal map
is uniquely determined by its jet, of a preassigned order, at a point. Convergence of formal mappings for real-analytic generic
submanifolds under appropriate assumptions is proved, and natural geometric conditions are given to assure that if two germs
of such submanifolds are formally equivalent, then, they are necessarily biholomorphically equivalent. It is also shown that
if two real-algebraic hypersurfaces in ℂ
N
are biholomorphically equivalent, then, they are algebraically equivalent. All the results are first proved in the more general
context of “reflection ideals” associated to formal mappings between formal as well as real-analytic and real-algebraic manifolds. 相似文献
20.
Laurent Stolovitch 《Publications Mathématiques de L'IHéS》2005,102(1):99-165
Let X be a germ of holomorphic vector field at the origin of Cn and vanishing there. We assume that X is a good perturbation of a “nondegenerate” singular completely integrable system.
The latter is associated to a family of linear diagonal vector fields which is assumed to have nontrivial polynomial first
integrals (they are generated by the so called “resonant monomials”). We show that X admits many invariant analytic subsets
in a neighborhood of the origin. These are biholomorphic to the intersection of a polydisc with an analytic set of the form
“resonant monomials = constants”. Such a biholomorphism conjugates the restriction of X to one of its invariant varieties
to the restriction of a linear diagonal vector field to a toric variety. Moreover, we show that the set of “frequencies” defining
the invariant sets is of positive measure. 相似文献
|