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1.
Let
be a group of affine transformations of the plane that contains a strict contraction and all translations. It is shown that
any two topological discs
are congruent dissection with respect to
such that only three topological discs are used as pieces of dissection. Two pieces of dissection do not suffice in general
even if
consists of all affine transformations.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
Ferenc Weisz 《Acta Mathematica Hungarica》2002,96(1-2):149-160
A general summability method of two-dimensional Fourier transforms is given with the help of an integrable function
. Under some conditions on
we show that the maximal operator of the Marcinkiewicz-
-means of a tempered distribution is bounded from
to
for all
and, consequently, is of weak type
, where
depends only on
. As a consequence we obtain a generalization for Fourier transforms of a summability result due to Marcinkievicz and Zhizhiashvili,
more exactly, the Marcinkiewicz-
-means of a function
converge a.e. to the function in question. Moreover, we prove that the Marcinkiewicz-
-means are uniformly bounded on the spaces
and so they converge in norm
. Some special cases of the Marcinkievicz-
-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de la Vallée-Poussin, Rogosinski and Riesz summations.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H
1, which may be considered over
and
. We also draw corollaries for the corresponding Hardy spaces over
2 and
2.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
The best m-term approximation and greedy algorithms 总被引:5,自引:0,他引:5
Two theorems on nonlinear
‐term approximation in
, are proved in this paper. The first one (theorem 2.1) says that if a basis
is
‐equivalent to the Haar basis then a near best
>‐term approximation to any
can be realized by the following simple greedy type algorithm. Take the expansion
and form a sum of
terms with the largest
out of this expansion.
The second one (theorem 3.3) states that nonlinear
‐term approximations with regard to two dictionaries: the Haar basis and the set of all characteristic functions of intervals
are equivalent in a very strong sense.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
6.
In this paper, we give a direct proof that every strongly
inverse semigroup can be embedded into a 0-semidirect product of a semilattice with zero by a group. As a corollary, we obtain a new proof of the structure theory of strongly
inverse semigroups described in [1]. We also prove that the strongly
inverse semigroups are precisely
inverse semigroups equipped with a
, idempotent pure prehomomorphism to a primitive inverse semigroup. 相似文献
7.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
8.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献
9.
For a given homogeneous elliptic partial differential operator
with constant complex coefficients, two Banach spaces
and
of distributions in
, and compact sets
and
in
, we study joint approximations in the norms of the spaces
and
(the spaces of Whitney jet-distributions) by the solutions of the equation
in neighborhoods of the set
. We obtain a localization theorem, which, under certain conditions, allows one to reduce the above-cited approximation problem to the corresponding separate problems in each of the spaces. 相似文献
10.
Let
denote the unit sphere in
and
the geodesic distance in
. A spherical‐basis function approximant is a function of the form
, where
are real constants,
is a fixed function, and
is a set of distinct points in
. It is known that if
is a strictly positive definite function in
, then the interpolation matrix
is positive definite, hence invertible, for every choice of distinct points
and every positive integer M. The paper studies a salient subclass of such functions
, and provides stability estimates for the associated interpolation matrices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
A subsemigroup S of a semigroup Q is a straight left order in Q and Q is a semigroup of straight left quotients of S if every q ∈ Q can be written as
for some
with a
b in Q and if, in addition, every element of S that is square cancellable lies in a subgroup of Q. Here a
♯ denotes the group inverse of a in some (hence any) subgroup of Q. If S is a straight left order in Q, then Q is necessarily regular; the idea is that Q has a better understood structure than that of S. Necessary and sufficient conditions exist on a semigroup S for S to be a straight left order. The technique is to consider a pair
of preorders on S. If such a pair satisfies conditions mimicking those satisfied by
on a regular semigroup, and if certain subsemigroups of S are right reversible, then S is a straight left order. The conditions required for
to satisfy are somewhat lengthy. In this paper we aim to circumvent some of these by specialising in two ways. First we consider
only fully stratified left orders, that is, the case where
(certainly the most natural choice for
) and the other is to insist that S be abundant, that is, every
-class and every
-class of S contains an idempotent.
Our results may be used to show that the monoid of endomorphisms of a hereditary basis algebra of finite rank is a fully stratified
straight left order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
12.
We consider a Skorohod map
which takes paths in
to paths which stay in the positive orthant
. We let
be the domain of definition of
. A convex and lower semi-continuous function
and a set
are given. We are concerned with the calculation of the infimum of the value
for t ⩾ 0 and absolutely continuous
subject to the conditions
and
. We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state
distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems.
This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for
its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations
of heavily loaded queueing networks.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
We consider the series
and
whose coefficients satisfy the condition
for
, where the sequence
can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If
as
, then the series
is uniformly convergent. If
for all
, then the sequence of partial sums of this series is uniformly bounded. If the series
is convergent for
and
as
, then this series is uniformly convergent. If the sequence of partial sums of the series
for
is bounded and
for all
, then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence
is lacunary. In the general case, they are not necessary. 相似文献
14.
A. M. Protopopov 《Algebra and Logic》2003,42(4):279-286
We study into the question of whether a partial order can be induced from a partially right-ordered group
onto a space
of right cosets of
w.r.t. some subgroup
of
. Examples are constructed showing that the condition of being convex for
in
is insufficient for this. A necessary and sufficient condition (in terms of a subgroup
and a positive cone
of
) is specified under which an order of
can be induced onto
. Sufficient conditions are also given. We establish properties of the class of partially right-ordered groups
for which
is partially ordered for every convex subgroup
, and properties of the class of groups such that
is partially ordered for every partial right order
on
and every subgroup
that is convex under
. 相似文献
15.
An urn contains colored balls,
~balls of each of
different colors. The balls are drawn sequentially and equiprobably, one ball at a time, and then each drawn ball drawn is either returned to the urn (sampling with replacement) or left outside the urn (sampling without replacement). The drawing continues until some
colors are drawn at least
~times each. Observable statistics are the numbers
,
, of colors that have appeared precisely
~times each by the stopping time. The asymptotic behavior as
of these values for each of the two sampling models is studied; the possibility of their use for identifying the model is discussed. 相似文献
16.
Izu Vaisman 《Annals of Global Analysis and Geometry》2001,19(3):209-234
The transversal twistor space of a foliation
of an even codimension is the bundle
of the complex structures of the fibers of the transversalbundle of
. On
there exists a foliation
by covering spaces of the leaves of
, and any Bottconnection of
produces an ordered pair
of transversal almost complex structures of
. The existence of a Bott connection which yields a structure
1 that is projectable to the space of leaves isequivalent to the fact that
is a transversallyprojective foliation. A Bott connection which yields a projectablestructure
2 exists iff
isa transversally projective foliation which satisfies a supplementarycohomological condition, and, in this case,
1is projectable as well.
2 is never integrable.The essential integrability condition of
1 isthe flatness of the transversal projective structure of
. 相似文献
17.
Qi S. Zhang 《Journal of Computational Analysis and Applications》2000,2(4):277-292
We study the inhomogeneous semilinear wave equations
on
with initial values
and
,where
is a noncompact, complete manifold. We founda new critical behavior in the following sense. There exists ap* > 0. When 1 < p p*, the above problem hasno global solution for any nonnegative
not identicallyzero and for any
and
; when
the problem has a global solution for some
and some
and
. If
, which is equipped with the Euclideanmetric, then
. If
we show that
belongs to the blow upcase. Although homogeneous semilinear wave equations are known to exhibit acritical behavior for a long time, this seems to be the first result oninhomogeneous ones. 相似文献
18.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
19.
Solutions
of a semilinear elliptic boundary value problem,
(with
bounded below) can be put into a one-to-one correspondence with zeros
of a function
. Often d is small. The function
is called the bifurcation function. It can also be shown that the eigenvalues of the matrix
characterize the stability properties of the solutions of the elliptic problem as rest points of
. A finite element method that can be used for computing B and B
c has recently been proposed. An overview of these results and the finite element method is given.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
20.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献