共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
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
3.
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
4.
Proof of the Ergodic Hypothesis
for Typical Hard Ball Systems 总被引:3,自引:0,他引:3
We consider the system of
hard balls with masses
and radius r in the flat torus
of size
. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost
every selection
of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the
case
. The method of that proof was primarily dynamical-geometric, whereas
the present approach is inherently algebraic.
Communicated by Eduard ZehnderSubmitted 17/10/02, accepted 01/12/03 相似文献
5.
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
6.
In this paper, the Quaternion-valued Hardy spaces and conjugate Hardyspaces on
are characterized. In analogy with the decomposition of square-integrable function space on the real line
into the direct sum of Hardy space and conjugate Hardy space, the square-integrable Quaternion -valued function space on
is decomposed into the orthogonal sum of the Quaternion Hardy and conjugate Hardy spaces. 相似文献
7.
In this paper, using the generalized Wronskian, we obtain a new sharp
bound for the generalized Masons theorem [1] for functions of several variables.
We also show that the Diophantine equation (The generalized Fermat-Catalan equation)
where
, such that k out of the
n-polynomials
are constant, and
under certain conditions for
has no non-constant solution.
Received: 20 March 2003 相似文献
8.
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
9.
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
10.
Let
be a family of holomorphic functions in the unit disk
,
which are also holomorphic in a parameter
. We express
cyclicity (=generalized multiplicity) of a zero of
at
via
some algebraic characteristics of the ideal generated by the Taylor
coefficients of
. As an example we estimate the cyclicity of the
family of generalized exponential polynomials. 相似文献
13.
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
14.
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
15.
We establish a new 3G-Theorem for the Green’s function for the half space
We exploit this result to introduce a new class of potentials
that we characterize by means of the Gauss semigroup on
. Next, we define a subclass
of
and we study it. In particular, we prove that
properly contains the classical Kato class
. Finally, we study the existence of positive continuous solutions in
of the following nonlinear elliptic problem
where h is a Borel measurable function in
satisfying some appropriate conditions related to the class
.
Mathematics Subject Classification (1991): Primary: 34B27, 34B16, 34J65; Secondary: 35B50, 31B05 相似文献
16.
17.
Let
be the set of all coloured permutations on the symbols 1, 2, . . . , n
with colours 1, 2, . . . , r, which is the analogous of the
symmetric group when r = 1, and the hyperoctahedral
group when r = 2. Let
be a subset of d colours; we define
to be the set of all coloured permutations
.
We prove that the number of
-avoiding coloured permutations in
.
We then prove that for any
,
the number of coloured permutations in
which avoid all patterns in
except for and contain exactly once equals
.
Finally, for any
,
this number equals
.
These results generalize recent results due to Mansour, Mansour and West, and Simion.AMS Subject Classification: 05A05, 05A15. 相似文献
18.
In the 3-dimensional de Sitter Space
, a surface is said to be a
spherical (resp. hyperbolic or parabolic) rotation surface, if it is a orbit of a
regular curve under the action of the orthogonal transformations of the 4-dimensional
Minkowski space
which leave a timelike (resp. spacelike or degenerate) plane
pointwise fixed. In this paper, we give all spacelike and timelike Weingarten rotation
surfaces in
. 相似文献
19.
There are exactlytwo non-equivalent [32,11,12]-codes in the binaryReed-Muller code
which contain
and have the weight set {0,12,16,20,32}. Alternatively,the 4-spaces in the projective space
over the vector space
for which all points have rank 4 fall into exactlytwo orbits under the natural action of PGL(5) on
. 相似文献
20.
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