共查询到20条相似文献,搜索用时 31 毫秒
1.
We study two questions posed by Johnson, Lindenstrauss, Preiss, and
Schechtman, concerning the structure of level sets of uniform and Lipschitz
quotient mappings from
. We show that if
, is a uniform quotient mapping then for every
has
a bounded number of components, each component of
separates
and the upper bound of the number of components depends
only on
and the moduli of co-uniform and uniform continuity of
.Next we prove that all level sets of any co-Lipschitz uniformly
continuous mapping from
to
are locally connected, and we show
that for every pair of a constant
and a function
with
, there exists a natural number
, so that
for every co-Lipschitz uniformly continuous map
with a
co-Lipschitz constant
and a modulus of uniform continuity
, there
exists a natural number
and a finite set
with
card
so that for all
has exactly
components,
has exactly
components and
each component of
is homeomorphic with the real line and
separates the plane into exactly 2 components. The number and form
of components of
for
are also described - they have a
finite tree structure. 相似文献
2.
In this note we prove that the Laplacian with generalized Wentzell boundary
conditions on an open bounded regular domain in
defined by
generates an analytic semigroup of angle
on
for every > 0 and
(for the definition of
cf. (1.3)).Received: 13 July 2002 相似文献
3.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
4.
We prove that a finite group G is
-constrained if and only if it contains a nilpotent subgroup
I satisfying
for all
.Received: 22 July 2002 相似文献
5.
6.
7.
To every egglike inversive plane
there is associated a family
of involutions of the point set of
such that
circles of
are the fixed point sets of the involutions in
. Korchmaros and Olanda characterized a family
of involutions on a set of size n2 + 1to be
for
an egglike inversive plane of order n by four conditions. In this
paper, we give an alternative proof where the Galois space PG(3,n) in
which
is embedded is built up directly by using concepts and
results on finite linear spaces. 相似文献
8.
Summary.
Let
We say that
preserves the distance d 0 if
for each
implies
Let A
n
denote the set of all positive numbers
d such that any map
that preserves unit distance preserves also distance
d.
Let D
n
denote the set of all positive numbers
d with the property: if
and
then there exists a finite set
S
xy
with
such that any map
that preserves unit distance preserves also the distance between
x and y.
Obviously,
We prove:
(1)
(2)
for n 2
D
n
is a
dense subset of
(2) implies that each mapping
f
from
to
(n 2)
preserving unit distance preserves all distances,
if f is continuous with respect to the product topologies
on
and
相似文献
9.
Cancellative residuated lattices are natural generalizations of lattice-ordered
groups (
-groups).
Although cancellative monoids are defined by quasi-equations, the class
of cancellative residuated lattices is a variety.
We prove that there are only two
commutative subvarieties of
that cover the trivial variety, namely the varieties
generated by the integers and the negative integers (with zero). We also construct examples
showing that in contrast to
-groups, the lattice reducts of cancellative residuated lattices
need not be distributive. In fact we prove that every lattice can be embedded in the
lattice reduct of a cancellative residuated lattice. Moreover, we show that there exists an
order-preserving injection of the lattice of all lattice varieties into the subvariety lattice of
.We define generalized MV-algebras and generalized BL-algebras and prove that the
cancellative integral members of these varieties are precisely the negative cones of
-groups, hence the latter form a variety, denoted by
. Furthermore we prove that the map that sends a subvariety of
-groups to the corresponding class of negative cones is a lattice
isomorphism from the lattice of subvarieties of
to the lattice of subvarieties of
.
Finally, we show how to translate equational bases between corresponding subvarieties, and
briefly discuss these results in the context of R. McKenzies characterization of categorically
equivalent varieties. 相似文献
10.
Let p be a prime,
a finite p-group,
any finite group with order divisible by p,
and
any action of
on
. We show that the cardinality of the set of all derivations
with respect to this action is a multiple of
p. This
generalises theorems of Frobenius and Hall.
Received: 16 June 2003 相似文献
11.
It is well known that (i) for every irrational number the Kronecker
sequence m (m = 1,...,M) is equidistributed modulo one in the
limit
, and (ii) closed horocycles of length
become equidistributed
in the unit tangent bundle
of a hyperbolic surface
of finite area, as
. In the present paper both equidistribution
problems are studied simultaneously: we prove that for any constant
the Kronecker sequence embedded in
along a long closed
horocycle becomes equidistributed in
for almost all , provided
that
. This equidistribution result holds in fact under
explicit diophantine conditions on (e.g. for = 2) provided that
,
with additional assumptions on the Fourier coefficients
of certain automorphic forms. Finally, we show that for
, our
equidistribution theorem implies a recent result of Rudnick and Sarnak
on the uniformity of the pair correlation density of the sequence
n2 modulo one. 相似文献
12.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
13.
Mark Pankov 《Journal of Geometry》2004,79(1-2):169-176
Let
be a finite-dimensional projective space
and
be the Grassmannian consisting of
all k-dimensional subspaces of
. In the paper we show that
transformations of
sending base subsets
to base subsets are induced by collineations of
to itself or to the dual projective space
.
This statement generalizes the main result of the authors paper [19]. 相似文献
16.
Marilyn Breen 《Aequationes Mathematicae》2004,67(3):263-275
Summary.
We establish the following Helly-type result for infinite families
of starshaped sets in
Define the function f on
{1, 2} by
f(1) = 4,
f(2) = 3.
Let
be a fixed positive number, and let
be a uniformly bounded family of compact sets
in the plane. For k = 1, 2, if every
f(k)
(not necessarily distinct) members of
intersect in a starshaped set whose
kernel contains a k-dimensional
neighborhood of radius
, then
is a starshaped set whose kernel is at least
k-dimensional.
The number f(k) is best in each case.
In addition, we present a few results concerning the dimension of
the kernel in an intersection of starshaped sets in
Some of these involve finite families of sets, while others
involve infinite families and make use of the Hausdorff metric. 相似文献
17.
In this work we determine the group of modular automorphisms of the
Drinfeld modular curve
for any nonconstant polynomial
.Received: 19 September 2002 相似文献
18.
Consider the Schrödinger operator
with a complex-valued
potential v of period
Let
and
be the eigenvalues of L that are close to
respectively, with periodic (for n even),
antiperiodic (for n odd), and Dirichelet
boundary conditions on [0,1], and let
be the diameter of the spectral
triangle with vertices
We prove the following statement: If
then v(x) is a Gevrey function, and moreover
相似文献
19.
A class of bounded operators on Sobolev spaces 总被引:2,自引:0,他引:2
We describe a class of nonlinear operators which are bounded on the
Sobolev spaces
, for
and 1 < p <
. As a corollary, we prove that the Hardy-Littlewood maximal operator is bounded on
, for
and 1 < p <
; this extends the result of J. Kinnunen [7], valid for s = 1.
Received: 5 December 2000 相似文献
20.
In this paper we study the concept of
-isologisms among the
-marginal extensions of groups, with respect to a given variety of groups
. We also give some equivalent conditions under which two extensions
are
-isologic.
Received: 9 January 2002 相似文献