共查询到20条相似文献,搜索用时 31 毫秒
1.
Aviva Szpirglas 《manuscripta mathematica》2001,104(1):71-95
We describe the general homological framework (the variation arrays and variation homological diagrams) in which can be studied hypersurface isolated singularities as well as boundary singularities and corner singularities from
the point of view of duality. We then show that any corner singularity is extension, in a sense which is defined, of the corner
singularities of less dimension on which it is built. This framework is also used to rewrite Thom–Sebastiani type properties
for isolated singularities and to establish them for boundary singularities.
Received: 27 June 2000 / Revised version: 18 October 2000 相似文献
2.
Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when .
Received: 28 May 2001 / Published online: 26 April 2002 相似文献
3.
Variant fountain theorems and their applications 总被引:5,自引:0,他引:5
Wenming Zou 《manuscripta mathematica》2001,104(3):343-358
In this paper we establish some variant fountain theorems without (P.S.)-type assumption. The abstract results will be used to study the symmetric nonlinear Schr?dinger equations and Dirichlet boundary value problems. Under no Ambrosetti–Rabinowitz's superquadraticity condition, we obtain infinitely many large energy and small negative energy solutions respectively. Received: 12 September 2000 相似文献
4.
Summary. For analytic functions the remainder term of quadrature rules can be represented as a contour integral with a complex kernel function. From this representation different remainder term estimates involving the kernel are obtained. It is studied in detail how polynomial biorthogonal systems can be applied to derive sharp bounds for the kernel function. It is shown that these bounds are practical to use and can easily be computed. Finally, various numerical examples are presented. Received March 11, 1998 / Revised version January 22, 1999/ Published online November 17, 1999 相似文献
5.
Rémi Léandre 《Probability Theory and Related Fields》2001,120(2):168-182
We define a stochastic cohomology theory related to a stochastic diffeology for the Hoelder loop space. We show that the stochastic de Rham cohomology groups are equal to the deterministic de Rham cohomology groups of the Hoelder loop space. As an application, we show that a stochastic line bundle over the Brownian bridge (with fiber almost surely defined) is isomorphic to a true line bundle over the Hoelder loop space. Received: 9 November 1998 / Revised version: 14 July 2000 / Published online: 26 April 2001 相似文献
6.
Multiderivations of Coxeter arrangements 总被引:3,自引:0,他引:3
Hiroaki Terao 《Inventiones Mathematicae》2002,148(3):659-674
Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α
H
∈V
* such that H=ker(α
H
). For each nonnegative integer m, define the derivation module D
(m)
(?)={θ∈Der
S
|θ(α
H
)∈Sα
m
H
}. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D
(m)
(?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m
i
(1≤i≤ℓ) (when m is odd). Here m
1≤···≤m
ℓ are the exponents of G and h=m
ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure
for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result.
Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002 相似文献
7.
Pascal Lambrechts 《manuscripta mathematica》2000,103(2):143-160
A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X. We give a model for the cochain complex of the boundary of that manifold, C
*(δM), as a module over the cochain algebra C
*(X). We also show how to construct an algebraic model of the rational homotopy type of δC
*(M) from a model of X. Using this rational model, we prove a new formula for the rational Lusternik–Schnirelmann category of X.
Received: 24 September 1999 相似文献
8.
Summary.
In an abstract framework we present a formalism which
specifies the notions of consistency and stability of
Petrov-Galerkin
methods used to approximate nonlinear problems which are, in many
practical situations, strongly nonlinear elliptic problems. This
formalism gives rise to a priori and a posteriori error estimates which
can be used for the refinement of the mesh in adaptive finite element
methods applied to elliptic nonlinear problems. This theory is
illustrated with the example: in a two
dimensional domain with Dirichlet boundary conditions.
Received June 10, 1992 / Revised version received February
28, 1994 相似文献
9.
10.
Summary. In this paper the balancing domain decomposition method is extended to nonconforming plate elements. The condition number
of the preconditioned system is shown to be bounded by , where H measures the diameters of the subdomains, h is the mesh size of the triangulation, and the constant C is independent of H, h and the number of subdomains.
Received August 14, 1997 相似文献
11.
Summary. This paper generalizes the idea of approximation on sparse grids to discrete differential forms that include )- and -conforming mixed finite element spaces as special cases. We elaborate on the construction of the spaces, introduce suitable
nodal interpolation operators on sparse grids and establish their approximation properties. We discuss how nodal interpolation
operators can be approximated. The stability of -conforming finite elements on sparse grids, when used to approximate second order elliptic problems in mixed formulation,
is investigated both theoretically and in numerical experiments.
Received November 2, 2000 / Revised version received October 23, 2001 / Published online January 30, 2002
This work was supported by DFG.
This paper is dedicated to Ch. Zenger on the occasion of his 60th birthday. 相似文献
12.
Sven Winklmann 《Calculus of Variations and Partial Differential Equations》2003,16(4):439-447
We define a generalized notion of mean curvature for regular hypersurfaces in . This enables us to introduce a new class of geometric curvature flows for which we prove enclosure theorems, using methods
of Dierkes [D] and Hildebrandt [H]. In particular, we obtain “neck-pinching” results that generalize previous observations
by Ecker [E] concerning the classical mean curvature flow.
Received: 8 October 2001 / Accepted: 1 March 2002 / Published online: 23 May 2002 相似文献
13.
14.
Summary. We prove the existence of a Gaussian quadrature formula for Tchebycheff systems, based on integrals over non-overlapping
subintervals of arbitrary fixed lengths and the uniqueness of this formula in the case the subintervals have equal lengths.
Received July 6, 1999 / Published online August 24, 2000 相似文献
15.
Summary. We construct a quadrature formula for integration on the unit disc which is based on line integrals over distinct chords in the disc and integrates exactly all polynomials in two variables of total degree .
Received August 8, 1996 / Revised version received July 2, 1997 相似文献
16.
Summary. We consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational
problems posed in the Hilbert spaces and in three dimensions. We show that if appropriate finite element spaces and appropriate additive or multiplicative Schwarz
smoothers are used, then the multigrid V-cycle is an efficient solver and preconditioner for the discrete operator. All results
are uniform with respect to the mesh size, the number of mesh levels, and weights on the two terms in the inner products.
Received June 12, 1998 / Revised version received March 12, 1999 / Published online January 27, 2000 相似文献
17.
Summary.
We give a relatively complete analysis for the
regularization method, which is usually used in solving
non-differentiable minimization problems. The model problem
considered in the paper is an obstacle
problem. In addition to the usual convergence result and a-priori
error estimates, we provide a-posteriori error estimates which are
highly desired
for practical implementation of the regularization method.
Received March 22, 1993 / Revised version received October
11, 1993 相似文献
18.
Zhiping Li 《Numerische Mathematik》1995,71(3):317-330
Summary.
A numerical
method, with truncation methods as a special case, for computing
singular minimizers in variational problems is described. It is
proved that the method can avoid Lavrentiev phenomenon and detect
singular minimizers. The
convergence of the method is also established. Numerical results
on a 2-D problem are given.
Received September 21, 1994 相似文献
19.
We improve a recent result of Mauduit and Sárk?zy (2000) on the well-distribution measure of pseudorandom sequences and complement
another of their results on the correlation measure.
Received 12 September 2000; in revised form 1 March 2001 相似文献
20.
Summary. We analyze a fully discrete numerical scheme approximating the evolution of n–dimensional graphs under anisotropic mean curvature. The highly nonlinear problem is discretized by piecewise linear finite
elements in space and semi–implicitly in time. The scheme is unconditionally stable und we obtain optimal error estimates
in natural norms. We also present numerical examples which confirm our theoretical results.
Received October 2, 2000 / Published online July 25, 2001 相似文献