共查询到20条相似文献,搜索用时 15 毫秒
1.
We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus,
the Lq-spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.
Received: 4 August 2008, Revised: 19 January 2009 相似文献
2.
Scaling properties of Hausdorff and packing measures 总被引:1,自引:0,他引:1
Let . Let be a continuous increasing function defined on , for which and is a decreasing function of t. Let be a norm on , and let , , denote the corresponding metric, and Hausdorff and packing measures, respectively. We characterize those functions such that the corresponding Hausdorff or packing measure scales with exponent by showing it must be of the form , where L is slowly varying. We also show that for continuous increasing functions and defined on , for which , is either trivially true or false: we show that if , then for a constant c, where is the Lebesgue measure on . Received June 17, 2000 / Accepted September 6, 2000 / Published online March 12, 2001 相似文献
3.
Marisa Zymonopoulou 《Archiv der Mathematik》2008,91(5):436-449
The complex Busemann-Petty problem asks whether origin symmetric convex bodies in with smaller central hyperplane sections necessarily have smaller volume. The answer is affirmative if and negative if . In this article we show that the answer remains the same if the volume is replaced by an “almost” arbitrary measure. This
result is the complex analogue of Zvavitch’s generalization to arbitrary measures of the original real Busemann-Petty problem.
Received: 6 May 2008 相似文献
4.
We extend two theorems due to P. Flavell [6] to arbitrary fusion systems.
Received: 18 June 2008 相似文献
5.
Jae-Young Chung 《Aequationes Mathematicae》2008,75(3):271-275
6.
Let X and Y be Banach spaces. A set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (x
n) in X, there exists a subsequence (x
k(n)) so that (Txk(n)) is uniformly weakly convergent for T ∈ M. In this paper, the notion of weakly equicompact set is used to obtain characterizations of spaces X such that
X ↩̸ ℓ1, of spaces X such that B
X*
is weak* sequentially compact and also to obtain several results concerning to the weak operator and the strong operator
topologies. As another application of weak equicompactness, we conclude a characterization of relatively compact sets in
when this space is endowed with the topology of uniform convergence on the class of all weakly null sequences. Finally, we
show that similar arguments can be applied to the study of uniformly completely continuous sets.
Received: 5 July 2006 相似文献
7.
We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed
by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave
equations
, u(0) = u0, ut (0) = v0, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear
stochastic heat equation
, u(0) = u0, endowed with Dirichlet boundary conditions.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
8.
Outer Minkowski content for some classes of closed sets 总被引:1,自引:0,他引:1
We find conditions ensuring the existence of the outer Minkowski content for d-dimensional closed sets in , in connection with regularity properties of their boundaries. Moreover, we provide a class of sets (including all sufficiently
regular sets) stable under finite unions for which the outer Minkowski content exists. It follows, in particular, that finite
unions of sets with Lipschitz boundary and a type of sets with positive reach belong to this class. 相似文献
9.
Karen Yagdjian 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(4):612-645
This paper analyses the properties of the family of self-similar solutions of the generalized Tricomi equation
in the domain
by considering initial conditions on the functions and their derivatives, posed as the Cauchy problem with homogeneous initial
data. For specific values of the power k ( = 1/2 or = 3/2) and n = 1 this problem has applications in the aerodynamics of airfoils operating in transonic flows of perfect or dense gases,
respectively. An integral transformation is suggested and used to represent the solutions of the Cauchy problem with homogeneous
initial functions in terms of fundamental solutions of the classical wave equation (the case k = 0). Then the Cauchy problem with homogeneous initial functions for the wave equation in
is solved. These results are used to derive estimates of the upper bound for solutions’ size and to obtain the asymptotics
for self-similar solutions of the wave equation and of the Tricomi-type equation in the neighbourhood of their light cones. 相似文献
10.
Linsen Xie 《Archiv der Mathematik》2008,91(1):86-96
In this paper we study the saturation class for the linear combinations of Bernstein operators. The characterization of the
saturation class involving the modulus of smoothness is proved under certain assumption.
Received: 1 September 2007 相似文献
11.
We introduce and study a multi-valued integral of Aumann-type where the selectors are Gould integrals of real functions with
respect to finitely additive vector-valued measures. We also discuss the relationship between this kind of integral and the
M-Gould set-valued integral with respect to a finitely additive multimeasure M.
Received: November 17, 2006, Revised: September 17, 2007 and January, 8, 2008, Accepted: March 13, 2008. 相似文献
12.
Hell and Kirkpatrick proved that in an undirected graph, a maximum size packing by a set of non-singleton stars can be found
in polynomial time if this star-set is of the form {S
1, S
2, ..., S
k
} for some k∈ℤ+ (S
i
is the star with i leaves), and it is NP-hard otherwise. This may raise the question whether it is possible to enlarge a set of stars not of
the form {S
1, S
2, ..., S
k
} by other non-star graphs to get a polynomially solvable graph packing problem. This paper shows such families of depth 2
trees. We show two approaches to this problem, a polynomial alternating forest algorithm, which implies a Berge-Tutte type
min-max theorem, and a reduction to the degree constrained subgraph problem of Lovász.
Research is supported by OTKA grants K60802, TS049788 and by European MCRTN Adonet, Contract Grant No. 504438. 相似文献
13.
We find all finite unavoidable ordered sets, finite unavoidable semilattices and finite unavoidable lattices.
While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was
also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839
financed by MSMT. 相似文献
14.
Takashi Noiri 《Rendiconti del Circolo Matematico di Palermo》2007,56(2):171-184
We introduce a new set calledmg-closed which is defined on a family of sets satisfying some minimal conditions. This set enables us to unify certain kind
of modifications of generalized closed sets due to Levine [17]. 相似文献
15.
A colorful theorem on transversal lines to plane convex sets 总被引:1,自引:0,他引:1
We prove a colorful version of Hadwiger’s transversal line theorem: if a family of colored and numbered convex sets in the
plane has the property that any three differently colored members have a transversal line that meet the sets consistently
with the numbering, then there exists a color such that all the convex sets of that color have a transversal line.
All authors are partially supported by CONACYT research grant 5040017. 相似文献
16.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献
17.
We characterize families of vector measures of uniformly bounded variation and semivariation in terms of additivity properties.
A classical theorem of Rickart and a simplified proof of Nikodym’s boundedness theorem follow.
Received: 3 January 2006; Revised: 31 March 2006
The second named author was supported by Estonian Science Foundation Grant 5704. 相似文献
18.
We characterize convergence in measure of a sequence (fn)n of measurable functions to a measurable function f by elements of c0, which express the quality of convergence of (fn)n to f. This characterization motivates the introduction of a new notion of convergence, called “p-convergence in measure” (p > 0), which is stronger than convergence in measure. We prove the existence of “minimal” elements in c0 which characterize the convergence in measure of (fn)n to f.
相似文献
19.
Teresa Bermúdez Isabel Marrero Antonio Martinón 《Integral Equations and Operator Theory》2009,64(4):487-494
A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if . We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace EN such that the orbit of T at EN is dense in H.
To Professor José Rodríguez Expósito on his 60th birthday 相似文献