共查询到20条相似文献,搜索用时 93 毫秒
1.
Nathanaël Enriquez Jacques Franchi Yves Le Jan 《Probability Theory and Related Fields》2001,119(2):213-255
Let ℳ be a geometrically finite hyperbolic surface with infinite volume, having at least one cusp. We obtain the limit law
under the Patterson-Sullivan measure on T
1ℳ of the windings of the geodesics of ℳ around the cusps. This limit law is stable with parameter 2δ− 1, where δ is the Hausdorff
dimension of the limit set of the subgroup Γ of M?bius isometries associated with ℳ. The normalization is t
−1/(2δ−1), for geodesics of length t. Our method relies on a precise comparison between geodesics and diffusion paths, for which we need to approach the Patterson-Sullivan
measure mentioned above by measures that are regular along the stable leaves.
Received: 8 October 1999 / Revised version: 2 June 2000 / Published online: 21 December 2000 相似文献
2.
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov
type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes
over . We also study the asymptotic of linear error-block codes. We define the real valued function α
q,m,a
(δ), which is an analog of the important real valued function α
q
(δ) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert–Varshamov and algebraic geometry
type lower bounds on α
q,m,a
(δ). We compare these lower bounds in graphs.
相似文献
3.
4.
Let (B
δ (t))
t ≥ 0 be a Brownian motion starting at 0 with drift δ > 0. Define by induction S
1=− inf
t ≥ 0
B
δ (t), ρ1 the last time such that B
δ (ρ1)=−S
1, S
2=sup0≤ t ≤ρ 1
B
δ (t), ρ2 the last time such that B
δ (ρ2)=S
2 and so on. Setting A
k
=S
k
+S
k+1; k ≥ 1, we compute the law of (A
1,...,A
k
) and the distribution of (B
δ (t+ρ l) − B
δ (ρ
l
); 0 ≤ t ≤ ρ
l-1 − ρ
l
)2 ≤ l ≤ k
for any k ≥ 2, conditionally on (A
1,...,A
k
). We determine the law of the range R
δ (t) of (B
δ (s))
s≥ 0 at time t, and the first range time θδ (a) (i.e. θδ (a)=inf{t > 0; R
δ (t) > a}). We also investigate the asymptotic behaviour of θ δ (a) (resp. R
δ (t)) as a → ∞ (resp. t → ∞). 相似文献
5.
Q. X. Yang 《Proceedings Mathematical Sciences》2005,115(3):347-368
In this paper, we characterize the symbol in Hormander symbol classS
ρ
m
,δ (m ∈ R, ρ, δ ≥ 0) by its wavelet coefficients. Consequently, we analyse the kerneldistribution property for the symbol in the symbol classS
ρ
m
,δ (m ∈R, ρ > 0, δ≥ 0) which is more general than known results ; for non-regular symbol operators, we establish sharp L2-continuity which is better than Calderón and Vaillancourt’s result, and establishL
p
(1 ≤p ≤∞) continuity which is new and sharp. Our new idea is to analyse the symbol operators in phase space with relative wavelets,
and to establish the kernel distribution property and the operator’s continuity on the basis of the wavelets coefficients
in phase space. 相似文献
6.
New concepts of fuzzy semi δ-V and fuzzy semi δ-Λ sets were introduced in our work “On fuzzy semi δ-Λ sets and fuzzy semi δ-V sets V-6,” J. Trip. Math. Soc., 6, 81–88 (2004). It was shown that the family of all fuzzy semi δ-V sets forms a fuzzy supra topological space on X denoted by (X, FS
δV
). The aim of this paper is to introduce the concept of fuzzy semi δ-V continuity in a fuzzy δ-V topological space. Finally, some properties, preservation theorems, etc., are studied.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 712–717, May, 2008. 相似文献
7.
P. B. Zatitskiy 《Journal of Mathematical Sciences》2009,158(6):853-857
Recall the two classical canonical isometric embeddings of a finite metric space X into a Banach space. That is, the Hausdorff–Kuratowsky embedding x → ρ(x, ⋅) into the space of continuous functions on X with the max-norm, and the Kantorovich–Rubinshtein embedding x → δ
x
(where δ
x
, is the δ-measure concentrated at x) with the transportation norm. We prove that these embeddings are not equivalent if |X| > 4. Bibliography: 2 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 360, 2008, pp. 153–161. 相似文献
8.
Sebastian W. Hensel 《Geometriae Dedicata》2011,155(1):31-67
Let X be a closed hyperbolic surface and λ, η be weighted geodesic multicurves which are short on X. We show that the iterated grafting along λ and η is close in the Teichmüller metric to grafting along a single multicurve which can be given explicitly in terms of λ and
η. Using this result, we study the holonomy lifts gr
λ
ρ
X,λ of Teichmüller geodesics ρ
X,λ for integral laminations λ and show that all of them have bounded Teichmüller distance to the geodesic ρ
X,λ. We obtain analogous results for grafting rays. Finally we consider the asymptotic behaviour of iterated grafting sequences
gr
nλ
X and show that they converge geometrically to a punctured surface. 相似文献
9.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献
10.
Ricardo Bianconi Nikolay Gusevskii Helen Klimenko 《Bulletin of the Brazilian Mathematical Society》1995,26(1):1-45
We construct geometrically finite free Kleinian groups acting onS
3 whose limit sets are wild Cantor sets.Partially supported by CNPqSupported by CNPq 相似文献
11.
High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension 总被引:1,自引:0,他引:1
David L. Donoho 《Discrete and Computational Geometry》2006,35(4):617-652
Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in Rn. It has recently been shown
that properties of the centrosymmetric polytope P = AC are of interest for finding
sparse solutions to the underdetermined system of equations y = Ax [9]. In particular, it is valuable to know that P is
centrally k-neighborly. We study the face numbers of randomly projected cross polytopes in the proportional-dimensional case
where d ∼ δn, where the projector A is chosen uniformly at random from the Grassmann manifold of d-dimensional orthoprojectors
of Rn. We derive ρN(δ) > 0 with the property that, for any ρ < ρN(δ), with overwhelming probability for large d, the number of k-dimensional faces of P = AC is the same as for C, for 0 ≤
k ≤ ρd. This implies that P is centrally ⌊ ρ d ⌋-neighborly, and its skeleton Skel⌊ ρ d ⌋(P) is combinatorially equivalent to Skel⌊ ρ d⌋(C). We display graphs of ρN. Two weaker notions of neighborliness are also important for understanding sparse solutions of linear equations: weak neighborliness
and sectional neighborliness [9]; we study both. Weak (k,ε)-neighborliness asks if the k-faces are all simplicial and if
the number of k-dimensional faces fk(P) ≥ fk(C)(1 – ε). We characterize and compute the critical proportion ρW(δ) > 0 such that weak (k,ε) neighborliness holds at k significantly smaller than ρW · d and fails for k significantly larger than ρW · d. Sectional (k,ε)-neighborliness asks whether all, except for a small fraction ε, of the k-dimensional intrinsic sections
of P are k-dimensional cross polytopes. (Intrinsic sections intersect P with k-dimensional subspaces spanned by vertices of
P.) We characterize and compute a proportion ρS(δ) > 0 guaranteeing this property for k/d ∼ ρ < ρS(δ). We display graphs of ρS and ρW. 相似文献
12.
Let P\mathcal{P} be a locally finite circle packing in the plane ℂ invariant under a non-elementary Kleinian group Γ and with finitely many
Γ-orbits. When Γ is geometrically finite, we construct an explicit Borel measure on ℂ which describes the asymptotic distribution
of small circles in P\mathcal{P}, assuming that either the critical exponent of Γ is strictly bigger than 1 or P\mathcal{P} does not contain an infinite bouquet of tangent circles glued at a parabolic fixed point of Γ. Our construction also works
for P\mathcal{P} invariant under a geometrically infinite group Γ, provided Γ admits a finite Bowen-Margulis-Sullivan measure and the Γ-skinning size of P\mathcal{P} is finite. Some concrete circle packings to which our result applies include Apollonian circle packings, Sierpinski curves,
Schottky dances, etc. 相似文献
13.
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
15.
Christian GroßRID=""ID=""Supported by a DFG grant. 《manuscripta mathematica》2000,103(3):339-350
Let denote the eigenspace decomposition of a twisted affine Kac–Moody algebra with respect to an involution , where is a twisted loop algebra, is the center and d is the scaling element of . We endow with the standard bilinear symmetrical form.Then with and carries a Lorentzian signature. Let denote the group that corresponds to , then the adjoint representation of on can be restricted to and this submanifold is isometrical to the Hilbert space E
ε, where is the decomposition of the twisted loop algebra with respect to the induced involutionρ0.We thus obtain an affine representation on E
ε and we show that this representation is polar, i. e., there exists a submanifold that intersects all orbits, and intersects
them orthogonally.
Received: 16 February 2000
RID="
ID="Supported by a DFG grant. 相似文献
16.
We show that a compact, connected set which has uniform oscillations at all points and at all scales has dimension strictly
larger than 1. We also show that limit sets of certain Kleinian groups have this property. More generally, we show that ifG is a non-elementary, analytically finite Kleinian group, and its limit set Λ(G) is connected, then Λ(G) is either a circle or has dimension strictly bigger than 1.
The first author is partially supported by NSF Grant DMS 95-00577 and an Alfred P. Sloan research fellowship. The second author
is partially supported by NSF grant DMS-94-23746. 相似文献
17.
Jun Ling ZHOU Yan Xun CHANG 《数学学报(英文版)》2006,22(1):311-318
In this paper, we first define a doubly transitive resolvable idempotent quasigroup (DTRIQ), and show that aDTRIQ of order v exists if and only ifv ≡0(mod3) and v ≠ 2(mod4). Then we use DTRIQ to present a tripling construction for large sets of resolvable directed triple systems, which improves an earlier version of tripling construction by Kang (J. Combin. Designs, 4 (1996), 301-321). As an application, we obtain an LRDTS(4·3^n) for any integer n ≥ 1, which provides an infinite family of even orders. 相似文献
18.
We consider the set ℝω(Γ, D) of infinite real traces, over a dependence alphabet (Γ,D) with no isolated letter, equipped with the topology induced by
the prefix metric. We prove that all rational languages of infinite real traces are analytic sets. We also reprove that there
exist some rational languages of infinite real traces that are analytic but non-Borel sets; in fact, these sets are even Σ
1
1
-complete, hence have maximum possible topological complexity. For this purpose, we give an example of a Σ
1
1
-complete language that is fundamentally different from the known example of a Σ
1
1
-complete infinitary rational relation given by Finkel (2003). Bibliography: 35 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 316, 2004, pp. 205–223. 相似文献
19.
We consider a group Γ of isometries acting on a proper (not necessarily geodesic) δ -hyperbolic space X. For any continuous α-quasiconformal measure ν on ∂X assigning full measure to Λ
r
, the radial limit set of Γ, we produce a (nontrivial) measure μ on Γ for which ν is stationary. This means that the limit set together with ν forms a μ-boundary and ν is harmonic with respect to the random walk induced by μ. As a basic example, take
and Γ to be any geometrically finite Kleinian group with ν a Patterson-Sullivan measure for Γ. In the case when X is a CAT(−1) space and Γ is discrete with quasiconvex action, we show that (Λ
r
, ν) is the Poisson boundary for μ. In the course of the proofs, we establish sufficient conditions for a set of continuous functions to form a positive basis,
either in the L
1 or L
∞ norm, for the space of uniformly positive lower-semicontinuous functions on a general metric measure space.
The first author was supported in part by an NSF postdoctoral fellowship and DMS-0420432. The second author was supported
in part by an NSF postdoctoral fellowship. 相似文献
20.
In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained. 相似文献