共查询到20条相似文献,搜索用时 31 毫秒
1.
Pekka Tukia 《Journal d'Analyse Mathématique》2004,92(1):137-189
A classical Teichmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where φ is a quadratic differential and 0≤k
i<1 are numbers such thatk
i→1 asi→∞. This situation occurs in the Teichmüller theory when one moves along a Teichmüller geodesic toward the boundary. The central
result is that if τ is a vertical trajectory associated to φ, then there is often, for instance if the sequence is normalized
so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ (Theorem 4.1). If the limit is injective, it is an embedding of τ
if τ does not contain points such that τ returns infinitely often to every neighborhood of the point. The main idea is to
composef
i locally with a map ϱi so that the composed mapf
iϱi is conformal and coincides withf
i on τ. Normal family arguments are applied to the sequencef
iϱi. Various extensions are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献
2.
Jean-Philippe Furter 《manuscripta mathematica》1999,98(2):183-193
For a polynomial automorphism f of ?2
ℂ, we set τ = deg f
2)/(deg f). We prove that τ≤ 1 if and only if f is triangularizable. In this situation, we show (by using a deep result from number theory known as the theorem of Skolem–Mahler–Lech)
that the sequence (deg f
n
)
n
∈ℕ is periodic for large n. In the opposite case, we prove that τ is an integer (τ≥ 2) and that the sequence (deg f
n
)
n
∈ℕ is a geometric progression of ratio τ. In particular, if f is any automorphism, we obtain the rationality of the formal series .
Received: 1 December 1997 相似文献
3.
Pekka Tukia 《Journal d'Analyse Mathématique》2006,99(1):35-87
We extend the results of [T2] to the situation where there is a compatibility with the action of a Kleinian group. A classical
Techmüller sequence is a sequence of quasiconformal mapsf
i with complex dilatations of the form
, where ϕ is a quadratic differential and 0<-k
i<1 are numbers such thatk
i→1 asi→∞. We proved in [T2] that if τ is a vertical trajectory associated to ϕ, then there is often, for instance if the sequence
is normalized so thatf
i fix 3 points, a subsequence such thatf
i tend either toward a constant or an injective map of τ. If there is compatibility with the action of a non-elementary finitely
generated Kleinian groupG, we can given a precise characterization which of these cases occurs. Suppose thatf
i induce isomorphisms ϕi ofG onto another Kleinian group and that ϕi have algebraic limit ϕ. If the quadratic differential is defined on a component of the ordinary set ofG, if there are no parabolic elements, and if τ is extended maximally so that all branches coming together at a singular point
are included, then we can state the main result as follows. The limit is a constantc if the stabilizerG
τ of τ is elementary; and, if it is non-elementary, then the limit is injective. In the first case, ϕ(g) is parabolic with fixpointc wheneverg∈G
τ is of infinite order; and in the latter case, the limitf is an embedding of τ in a natural topology of τ, andf embeds τ into a component of the limit set of ϕG whose stabilizer is ϕG
τ. Various extensions and generalizations are presented.
The research for this paper has been supported by the project 51749 of the Academy of Finland. 相似文献
4.
M. A. Berezhnoi 《Ukrainian Mathematical Journal》2009,61(3):361-382
We study the asymptotic behavior of solutions of the problem that describes small motions of a viscous incompressible fluid
filling a domain Ω with a large number of suspended small solid interacting particles concentrated in a small neighborhood
of a certain smooth surface Γ ⊂ Ω. We prove that, under certain conditions, the limit of these solutions satisfies the original equations in the domain Ω\Γ and some averaged boundary conditions (conjugation conditions) on Γ. 相似文献
5.
Sheng You WEN 《数学学报(英文版)》2007,23(10):1769-1776
Let τ be a premeasure on a complete separable metric space and let τ* be the Method I measure constructed from τ. We give conditions on T such that τ* has a regularity as follows: Every τ*-measurable set has measure equivalent to the supremum of premeasures of its compact subsets. Then we prove that the packing measure has this regularity if and only if the corresponding packing premeasure is locally finite. 相似文献
6.
Thek-plane Radon transform assigns to a functionsf(x) on ℝ
n
the collection of integralsf(τ)=∫
τ
f over allk-dimensional planesτ. We give a systematic treatment of two inversion methods for this transform, namely, the method of Riesz potentials, and
the method of spherical means. We develop new analytic tools which allow to invertf(τ) under minimal assumptions forf. It is assumed thatfεL
p
, 1≤p<n/k, orf is a continuous function with minimal rate of decay at infinity. In the framework of the first method, our approach employs
intertwining fractional integrals associated to thek-plane transform. Following the second method, we extend the original formula of Radon for continuous functions on ℝ2 tofεL
p
(ℝ
n
) and all 1≤k<n. New integral formulae and estimates, generalizing those of Fuglede and Solmon, are obtained.
The work was supported in part by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored
by the Minerva Foundation (Germany). 相似文献
7.
Gábor Tardos 《Combinatorica》1995,15(1):123-134
Fix two distinct parallel linese andf. A 2-interval is the union of an interval one and an interval onf. We study thetransversal number τ (ℋ) of families of 2-intervals ℋ. This is the cardinality of the smallest set which intersects every 2-interval in ℋ. A
Gyárfás and J. Lehel [6] proved that τ(ℋ)=O(υ(ℋ)2) where ν(ℋ) is the maximum number of disjoint 2-intervals in ℋ. In the present paper we prove the tight bond τ(ℋ)≤2v(ℋ).
Our result has applications in the estimation of the transversal number of other types of set systems.
The method we use is topological. We associate a simplicial complexK with our system of 2-intervals and prove that a given subcomplex is contractible inK unless the required transversal exists. Then we construct a cocycle of (another subcomplex of)K to prove that the subcomplex is not contractible inK. We hope that this approach will be applicable to a wider variety of combinatorial optimization problems.
Supported by the NSF grant No. CCR-92-00788 and the (Hungarian) National Scientific Research Fund (OTKA) grant No. T4271.
The author was visiting the Computation and Automation Institute of the Hungarian Academy of Sciences while part of this research
was done. 相似文献
8.
Dirk Schütz 《Mathematische Zeitschrift》2006,252(3):623-654
Let X be a finite connected CW-complex and ρ: a regular covering space with free abelian covering transformation group. For ξ ∈ H1 (Xℝ) we define the notion of ξ-contractibility of X. This notion is closely related to the vanishing of the Novikov homology of the pair (X,ξ). We show that finite domination of is equivalent to X being ξ-contractible for every nonzero ξ with ρ*ξ =0 ∈ H1(; ℝ). If M is a closed connected smooth manifold the condition that M is ξ-contractible is necessary for the existence of a nonsingular closed 1-form representing ξ. Also ξ-contractibility guarantees the definition of the Latour obstruction τL(M,ξ) whose vanishing is then sufficient for the existence of a nonsingular closed 1-form provided dim M≥6. Now if ρ: is a finitely dominated regular ℤk-covering space we get that τL(M,ξ) is defined for every nonzero ξ with ρ*ξ=0 and the vanishing of one such obstruction implies the vanishing of all such τL(M,ξ). 相似文献
9.
We prove that for cardinalsτ satisfying τω=τ and forτ=ω
1, there do not exist universal Eberlein Compacts of weightτ, or universal WCG spaces of density characterτ. Ifτ is a strong limit cardinal of countable cofinality such universal spaces do exist. Thus under GCH universal spaces exist
forτ iff cof(τ)=ω.
The research of the second author was supported by a grant from the United States-Israel Binational Science Foundation and
the Fund for the Promotion of Research at the Technion. 相似文献
10.
Frank Jonas 《manuscripta mathematica》1990,67(1):35-39
Zusammenfassung LetD:G→GL(n,C) be an irreducible linear representation of a finite groupG with the characterX. IfD is realizible in Q(ξ
m
) and Q(ξ
m′
) we give a condition for then realizability ofD in Q(ξ(m′)). If the degreen is a prime ≠ 2, we show thatD realizible in Q(ξ
f
), wheref is the conductor of the abelian extensionQ(X)/Q. 相似文献
11.
Let T denote a binding component of an open book (S, f){(\Sigma, \phi)} compatible with a closed contact 3-manifold (M, ξ). We describe an explicit open book (S¢, f¢){(\Sigma', \phi')} compatible with (M, ζ), where ζ is the contact structure obtained from ξ by performing a full Lutz twist along T. Here, (S¢, f¢){(\Sigma', \phi')} is obtained from (S, f){(\Sigma, \phi)} by a local modification near the binding. 相似文献
12.
Age-dependent branching processes in random environments 总被引:4,自引:0,他引:4
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R , and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments. 相似文献
13.
Artūras Dubickas 《Israel Journal of Mathematics》2009,170(1):95-111
Let f
1 and f
2 be two positive numbers of the field , and let f
n+2 = f
n+1 + f
n
for each n ≥ 1. Let us denote by {x} the fractional part of a real number x. We prove that, for each ξ ∉ K, the inequality {ξf
n
} > 2/3 holds for infinitely many positive integers n. On the other hand, we prove a result which implies that there is a transcendental number ξ such that {ξf
n
} < 39/40 for each n ≥ 1. Moreover, it is shown that, for every a > 1, there is an interval of positive numbers that contains uncountably many numbers ξ such that {a
n
} 6 min 2/(a − 1), (34a
2 − 32a + 7)/(9(2a − 1)2) for each n > 1. Here, the minimum is strictly smaller than 1 for each a > 1. In contrast, by an old result of Weyl, for any a > 1, the sequence {ξa
n
}, n = 1, 2, ..., is uniformly distributed in [0, 1] (and so everywhere dense in [0, 1]) for almost all real numbers ξ. 相似文献
14.
陈晋南 《中国科学A辑(英文版)》2002,45(10):1335-1350
The boundary integral technique is used to study the effect of deformation on the steady, creeping, thermocapillary migration
of a fluid particle under conditions of axisymmetry, negligible thermal convection and an insulated tube wall. The spherical
radius of the fluid particle (i.e. the radius as if the particle were a sphere, a ′= (3V
p
′
/4π)1/3, V
p
′
is the particle volume) and that of the tube are denoted, respectively, by a′and b′. For small capillary numberCa = 0.05, only for a large fluid particle (a′/b′ = 0.8) is deformation significant. Fora′/b′= 0.8, hydrodynamic stresses squeeze the particle, reduce the interaction of the particle with the wall and thereby increase
the terminal velocity. For small particles a′/b′< 0.8 and Ca = 0.05 the fluid particles translate as spheres, due to the fact
that the fluid particle is too far away from the wall to be subject to distending hydrodynamic stresses. The deformable particle
moves faster than a spherical one in the thermocapillary migration. The increase in velocity with capillary number is larger
for thermocapillary motion than for buoyancy. 相似文献
15.
The transversal number, packing number, covering number and strong stability number of hypergraphs are denoted by τ, ν, ϱ
and α, respectively. A hypergraph family t is called τ-bound (ϱ-bound) if there exists a “binding function”f(x) such that τ(H)≦f(v(H)) (ϱ(H)≦f(α(H))) for allH ∈ t. Methods are presented to show that various hypergraph families are τ-bound and/or ϱ-bound. The results can be applied
to families of geometrical nature like subforests of trees, boxes, boxes of polyominoes or to families defined by hypergraph
theoretic terms like the family where every subhypergraph has the Helly-property. 相似文献
16.
Yaochen Zhu 《数学学报(英文版)》2000,16(3):395-398
Let f (x) be a continued fraction with elements a
n
x, where coefficients a
n
are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with a
n
. For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.
Received March 27, 1998, Accepted September 28, 1998 相似文献
17.
We have random number of independent diffusion processes with absorption on boundaries in some region at initial time t = 0. The initial numbers and positions of processes in region is defined by the Poisson random measure. It is required to
estimate the number of the unabsorbed processes for the fixed time τ > 0. The Poisson random measure depends on τ and τ → ∞.
This research was partially supported by the Ministry of Education and Science of Ukraine, project 01.07/103 and University
of Salerno, Italy. 相似文献
18.
Olav Kallenberg 《Probability Theory and Related Fields》2007,139(1-2):311-310
Consider a locally compact group G acting measurably on some spaces S and T. We prove a general representation of G-invariant measures on S and the existence of invariant disintegrations of jointly invariant measures on S × T. The results are applied to Palm and related kernels associated with a stationary random pair (ξ,η), where ξ is a random
measure on S and η is a random element in T.
An erratum to this article can be found at 相似文献
19.
本文研究单位圆盘上Bergman型空间到Zygmund型空间上的一类推广的Volterra复合算子.利用符号函数ϕ和g刻画这类算子的有界性、紧性,并计算其本性范数. 相似文献
20.
Charge density fluctuation of low frequency in a dusty plasma 总被引:2,自引:0,他引:2
The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity
of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle
Ω
c
, which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation
of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω
c
, is much smaller than the dusty plasma frequency ωd, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω
c
, is much larger than ω
d
there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius
and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist. 相似文献