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161.
Roland Huber 《Geometriae Dedicata》1995,58(3):291-311
We show some topological properties of semianalytic subsets of rigid analytic varieties: curve selection lemma, the closure
of a semianalytic subsetS is semianalytic,
for every quasi-compact morphismf. As an application we show that a morphismf: X Y of rigid analytic varieties is open at a pointx X if and only if SpecO
X,x SpecO
Y,f(x) is surjective. 相似文献
162.
Harald Löwe 《Geometriae Dedicata》1995,58(1):45-51
We construct symmetric planes associated with an arbitrary locally compact connected nearfield
. If
is a proper nearfield, i.e.
{;;}, then the tangent translation plane of this symmetric plane is not classical. All previously known examples of symmetric planes have classical tangent translation planes.Herrn Professor Dr. H. Salzmann zum 65. Geburtstag gewidmet 相似文献
163.
We prove that the constant maps are the onlyp-harmonic maps for anyp 2 from an arbitrary compact Riemannian manifold into a complete Riemannian manifold which admits a strictly convex function. 相似文献
164.
Summary.
In recent years, it has been shown that many modern iterative algorithms
(multigrid schemes, multilevel preconditioners, domain decomposition
methods etc.)
for solving problems resulting from the discretization
of PDEs can be
interpreted as additive (Jacobi-like) or multiplicative
(Gauss-Seidel-like) subspace correction methods. The key to their
analysis is the study of certain metric properties of the underlying
splitting of the discretization space into a sum of subspaces
and the splitting of the variational problem on into auxiliary problems on
these subspaces.
In this paper, we propose a modification of the abstract convergence
theory of the additive and multiplicative Schwarz methods, that
makes the relation to traditional iteration methods more explicit.
The analysis of the additive and multiplicative Schwarz iterations
can be carried out in almost the same spirit as in the
traditional block-matrix
situation, making convergence proofs of multilevel and domain decomposition
methods clearer, or, at least, more classical.
In addition, we present a
new bound for the convergence rate of the appropriately scaled
multiplicative Schwarz method directly in terms
of the condition number of the corresponding additive
Schwarz operator.
These results may be viewed as an appendix to the
recent surveys [X], [Ys].
Received February 1, 1994 / Revised version received August
1, 1994 相似文献
165.
P. D. Seymour 《Combinatorica》1995,15(2):281-288
LetG be a digraph, and letk1, such that no fractional packing of directed circuits ofG has value >k, when every vertex is given capacity 1. We prove there is a set ofO (k logk logk) vertices meeting all directed circuits ofG. 相似文献
166.
M. Radavicius 《Acta Appl Math》1995,38(1):13-35
A nonparametric estimatef
* of an unknown distribution densityf W is called locally minimax iff it is minimax for all not too small neighborhoodsW
g
,g W, simultaneously, whereW is some dense subset ofW. Radaviius and Rudzkis proved the existence of such an estimate under some general conditions. However, the construction of the estimate is rather complicated. In this paper, a new estimate is proposed. This estimate is locally minimax under some additional assumptions which usually hold for orthobases of algebraic polynomial and is almost as simple as the linear projective estimate. Thus, it takes a form convenient for the construction of an adaptive estimator, which does not usea-priori information about the smoothness of the density. The adaptive estimation problem is briefly discussed and an unknown density fitting by Jacobi polynomials is investigated more explicitly. 相似文献
167.
Chuu-Lian Terng 《Journal of Geometric Analysis》1995,5(1):129-150
An isometricH-action on a Riemannian manifoldX is calledpolar if there exists a closed submanifoldS ofX that meets everyH-orbit and always meets orbits orthogonally (S is called a section). LetG be a compact Lie group equipped with a biinvariant metric,H a closed subgroup ofG ×G, and letH act onG isometrically by (h
1,h
2) ·x = h
1
xh
2
−1
· LetP(G, H) denote the group ofH
1-pathsg: [0, 1] →G such that (g(0),g (1)) ∈H, and letP(G, H) act on the Hilbert spaceV = H
0([0, 1], g) isometrically byg * u = gug
−1 −g′g
−1. We prove that if the action ofH onG is polar with a flat section then the action ofP(G, H) onV is polar. Principal orbits of polar actions onV are isoparametric submanifolds ofV and are infinite-dimensional generalized real or complex flag manifolds. We also note that the adjoint actions of affine
Kac-Moody groups and the isotropy action corresponding to an involution of an affine Kac-Moody group are special examples
ofP(G, H)-actions for suitable choice ofH andG.
Work supported partially by NSF Grant DMS 8903237 and by The Max-Planck-Institut für Mathematik in Bonn. 相似文献
168.
Ulrich Kohlenbach 《Archive for Mathematical Logic》1995,34(4):279-283
It is well-known (due to C. Parsons) that the extension of primitive recursive arithmeticPRA by first-order predicate logic and the rule of
2
0
-induction
2
0
-IR is
2
0
-conservative overPRA. We show that this is no longer true in the presence of function quantifiers and quantifier-free choice for numbersAC
0,0-qf. More precisely we show that :=PRA
2 +
2
0
-IR+AC
0,0-qf proves the totality of the Ackermann function, wherePRA
2 is the extension ofPRA by number and function quantifiers and
2
0
-IR may contain function parameters.This is true even forPRA
2 +
1
0
-IR+
2
0
-IR
–+AC
0,0-qf, where
2
0
-IR
– is the restriction of
2
0
-IR without function parameters.I am grateful to an anonymous referee whose suggestions led to an improved discussion of our results 相似文献
169.
J. F. Brasche 《Potential Analysis》1995,4(3):297-307
We present the first steps towards a general extension theory inL
2-spaces. By this theory it is possible to construct all perturbations of the Laplacian supported by a closed setN even if the classical capacity ofN equals zero. 相似文献
170.
M. Sorg 《Letters in Mathematical Physics》1995,33(2):113-125
An exact solution of Dirac's equation in an open Robertson-Walker universe is constructed such that the corresponding energy-momentum densityT
µv
obeys the cosmological principle. However, in anopen universe, this principlemust always be violated by the other physical densities of the cosmological solution (e.g. pseudoscalar, (axial-) current and polarization). If the current densityj
µ
=
isrequired to obey the cosmological principle, then the universe must beflat. 相似文献