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1.
Corentin Pontreau 《Monatshefte für Mathematik》2009,342(2):267-281
We prove a sharper so-called Mordell-Lang plus Bogomolov type result for curves lying in the two-dimensional linear torus.
We mainly follow the approach of Rémond in (Comp Math 134:337–366, 2002), using Vojta and Mumford type inequalities. In the
special case we consider, we improve Rémond’s main result using a better Bogomolov property and an elementary arithmetic Bézout
theorem. 相似文献
2.
Fabien Morel 《K-Theory》2005,35(1-2):1-68
3.
Thomas Schick 《Mathematische Annalen》2000,317(4):727-750
The Atiyah conjecture predicts that the -Betti numbers of a finite CW-complex with torsion-free fundamental group are integers. We establish the Atiyah conjecture, under the condition that it
holds for G and that is a normal subgroup, for amalgamated free products . Here F is a free group and is an arbitrary semi-direct product. This includes free products G*F and semi-direct products . We also show that the Atiyah conjecture holds (with an additional technical condition) for direct and inverse limits of
groups for which it is true. As a corollary it holds for positive 1-relator groups with torsion free abelianization. Putting
everything together we establish a new (bigger) class of groups for which the Atiyah conjecture holds, which contains all
free groups and in particular is closed under taking subgroups, direct sums, free products, extensions with torsion-free elementary
amenable quotient or with free quotient, and under certain direct and inverse limits.
Received: 22 August 1998/ Revised: 10 Jannary 2000 / Published online: 28 June 2000 相似文献
4.
5.
Lars Olsen 《Monatshefte für Mathematik》2011,25(2):89-117
In this paper we study the Hausdorff and packing dimensions and the Rényi dimensions of random self-affine multifractal Sierpinski
sponges in
\mathbbRd{\mathbb{R}^{d}}. 相似文献
6.
7.
Rational proper holomorphic maps from the unit ball in ℂ2 into the unit ball ℂ
N
with degree 2 are studied. Any such map must be equivalent to one of the four types of maps.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
8.
Let , n ≥ 3, be a smoothly bounded domain. Suppose that Ω admits a smooth defining function which is plurisubharmonic on the boundary
of Ω. Then a Diederich–Forn?ss exponent can be chosen arbitrarily close to 1, and the closure of Ω admits a Stein neighborhood
basis.
Research of J. E. Forn?ss was partially supported by an NSF grant. Research of A.-K. Herbig was supported by FWF grant P19147. 相似文献
9.
10.
Given a finite subset
A{\cal A}
of an additive group
\Bbb G{\Bbb G}
such as
\Bbb Zn{\Bbb Z}^n
or
\Bbb Rn{\Bbb R}^n
, we are interested in efficient covering of
\Bbb G{\Bbb G}
by translates of
A{\cal A}
, and efficient packing of translates of
A{\cal A}
in
\Bbb G{\Bbb G}
. A set
S ì \Bbb G{\cal S} \subset {\Bbb G}
provides a covering if the translates
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
cover
\Bbb G{\Bbb G}
(i.e., their union is
\Bbb G{\Bbb G}
), and the covering will be efficient if
S{\cal S}
has small density in
\Bbb G{\Bbb G}
. On the other hand, a set
S ì \Bbb G{\cal S} \subset {\Bbb G}
will provide a packing if the translated sets
A + s{\cal A} + s
with
s ? Ss \in {\cal S}
are mutually disjoint, and the packing is efficient if
S{\cal S}
has large density.
In the present part (I) we will derive some facts on these concepts when
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
A ì \Bbb Zn{\cal A} \subset {\Bbb Z}^n
. In part (II) we will again deal with
\Bbb G = \Bbb Zn{\Bbb G} = {\Bbb Z}^n
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
\Bbb G = \Bbb Rn{\Bbb G} = {\Bbb R}^n
. 相似文献
11.
Consider oriented surfaces immersed in
. Associated to them,
here are studied pairs of transversal foliations with
singularities, defined on the Elliptic region, where the
Gaussian curvature
, given
by the product of the principal curvatures
k
1,
k
2 is
positive. The leaves of the foliations are the
lines of harmonic mean
curvature, also called characteristic or
diagonal lines, along which
the normal curvature of the immersion is given by
, where
is the
arithmetic mean curvature. That is,
is the harmonic mean of the
principal curvatures k
1,
k
2 of
the immersion. The singularities of the foliations are the
umbilic points and
parabolic curves, where
k
1 =
k
2 and
, respectively.Here are determined the structurally stable patterns of
harmonic mean curvature lines
near the umbilic points, parabolic
curves and harmonic mean
curvature cycles, the periodic leaves of the
foliations. The genericity of these patterns is
established.This provides the three essential local ingredients to
establish sufficient conditions, likely to be also necessary,
for Harmonic Mean Curvature Structural
Stability of immersed surfaces. This study, outlined
towards the end of the paper, is a natural analog and complement
for that carried out previously by the authors for the
Arithmetic Mean Curvature and
the Asymptotic Structural
Stability of immersed surfaces, [13, 14, 17], and
also extended recently to the case of the
Geometric Mean Curvature
Configuration [15].The first author was partially supported by FUNAPE/UFG.
Both authors are fellows of CNPq.
This work was done under the project PRONEX/FINEP/MCT -
Conv. 76.97.1080.00 - Teoria Qualitativa das Equações Diferenciais
Ordinárias and CNPq - Grant 476886/2001-5. 相似文献
12.
In 1938 Morse and Hedlund proved that a function is periodic if the number of different n-blocks with does not exceed n for some n. In 1940 they studied such functions f with for all positive integers n. These are closely related to Sturmian sequences, which occur in many branches of mathematics, computer science and physics.
Recently the authors studied k-dimensional functions with , where is the set of different vectors with for a given configuration . In this paper, we characterize functions satisfying for all configurations . Our proof requires a separation theorem for convex sets of lattice points, which may be of independent interest.
Received July 20, 1998 相似文献
13.
In this paper, we establish several decidability results for pseudovariety joins of the form
\sf Vú\sf W{\sf V}\vee{\sf W}
, where
\sf V{\sf V}
is a subpseudovariety of
\sf J{\sf J}
or the pseudovariety
\sf R{\sf R}
. Here,
\sf J{\sf J}
(resp.
\sf R{\sf R}
) denotes the pseudovariety of all
J{\cal J}
-trivial (resp.
?{\cal R}
-trivial) semigroups. In particular, we show that the pseudovariety
\sf Vú\sf W{\sf V}\vee{\sf W}
is (completely) κ-tame when
\sf V{\sf V}
is a subpseudovariety of
\sf J{\sf J}
with decidable κ-word problem and
\sf W{\sf W}
is (completely) κ-tame. Moreover, if
\sf W{\sf W}
is a κ-tame pseudovariety which satisfies the pseudoidentity x1 ⋯ xryω+1ztω = x1 ⋯ xryztω, then we prove that
\sf Rú\sf W{\sf R}\vee{\sf W}
is also κ-tame. In particular the joins
\sf Rú\sf Ab{\sf R}\vee{\sf Ab}
,
\sf Rú\sf G{\sf R}\vee{\sf G}
,
\sf Rú\sf OCR{\sf R}\vee{\sf OCR}
, and
\sf Rú\sf CR{\sf R}\vee{\sf CR}
are decidable. 相似文献
14.
Bernhard Burgstaller 《Monatshefte für Mathematik》2009,157(1):1-11
There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x
1, x
2, ... we have . Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra such that for an independent sequence x
1, x
2, ... of μ-distributed random elements x
i
we have . We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1]
d
) is d.
B. Burgstaller was supported by the Austrian Schr?dinger stipend J2471-N12. 相似文献
15.
Richard Urzúa Luz 《Bulletin of the Brazilian Mathematical Society》2003,34(2):287-302
Let a minimal affine
-action on the torus
T
q
,
p 2 and
q 1. The cohomology of
(see definition below) depends on both the algebraic properties
of the induced action on H
1(T
q
,
) and the arithmetical
properties of the translation cocycle. We give a Diophantine
condition that characterizes those affine actions whose first
cohomology group is finite dimensional. In this case it is
necessarily isomorphic to
. Thus the
-action
F
obtained by suspension of is parameter
rigid, i.e., any other
-action with the same
orbit foliation is smoothly conjugate to a reparametrization of
F
by
an automorphism of
.*Partially supported by CNPq fellowship by Fondecyt Grant
1000047 and DGICT-UCN and fundación Andes, Chile. 相似文献
16.
Masao Yamazaki 《Mathematische Annalen》2000,317(4):635-675
Abstract. We consider the Navier-Stokes equations with time-dependent external force, either in the whole time or in positive time
with initial data, with domain either the whole space, the half space or an exterior domain of dimension . We give conditions on the external force sufficient for the unique existence of small solutions in the weak- space bounded for all time. In particular, this result gives sufficient conditions for the unique existence and the stability
of small time-periodic solutions or almost periodic solutions. This result generalizes the previous result on the unique existence
and the stability of small stationary solutions in the weak- space with time-independent external force.
Received: 30 March 1999 / Accepted: 21 September 1999 / Published online: 28 June 2000 相似文献
17.
Pierangelo Marcati Manuela Molinari 《NoDEA : Nonlinear Differential Equations and Applications》2009,6(2):119-132
In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by
Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized
motion existing for each time.
Received November 24, 1997 相似文献
18.
The notion of pseudo-randomness of subsets of
\mathbb Zn{\mathbb Z_n} is defined, and the measures of pseudo-randomness are introduced. Then a construction (based on the use of hybrid character
sums) will be presented for subsets of
\mathbb Zp{\mathbb Z_p} with strong pseudo-random properties. 相似文献
19.
Debashish Bose Shobha Madan Parasar Mohanty Saurabh Shrivastava 《Proceedings Mathematical Sciences》2009,119(4):501-512
In this paper we prove the bilinear analogue of de Leeuw’s result for periodic bilinear multipliers and some Jodeit type extension
results for bilinear multipliers. 相似文献
20.
An orthogonal complex structure on a domain in is a complex structure which is integrable and is compatible with the Euclidean metric. This gives rise to a first order
system of partial differential equations which is conformally invariant. We prove two Liouville-type uniqueness theorems for
solutions of this system, and use these to give an alternative proof of the classification of compact locally conformally
flat Hermitian surfaces first proved by Pontecorvo. We also give a classification of non-degenerate quadrics in under the action of the conformal group SO
°(1, 5). Using this classification, we show that generic quadrics give rise to orthogonal complex structures defined on the
complement of unknotted solid tori which are smoothly embedded in .
To Nigel Hitchin on the occasion of his 60th birthday.
This work was partially supported by MIUR (Metriche Riemanniane e Varietà Differenziabili, PRIN05)
and NSF Grant DMS-0503506. 相似文献