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1.
Toshiyuki Sugawa 《Monatshefte für Mathematik》2003,50(7):61-68
The inner radius of univalence of a domain D with Poincaré density ρ
D
is the possible largest number σ such that the condition ∥ S
f
∥
D
= sup
w∈ D
ρ
D
(w)
−2∥ S
f
(z) ∥ ≤ σ implies univalence of f for a nonconstant meromorphic function f on D, where S
f
is the Schwarzian derivative of f. In this note, we give a lower bound of the inner radius of univalence for strongly starlike domains of order α in terms
of the order α. 相似文献
2.
We give a Fekete-Szeg? type inequality for an analytic function on the unit disk with Bloch seminorm ≤1. As an application
of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a
2
z
2 + a
3
z
3 + ⋯ on the unit disk with pre-Schwarzian norm ≤λ for a given λ > 0.
The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039.
Authors’ addresses: T. Sugawa and T. Terada, Department of Mathematics, Graduate School of Science, Hiroshima University,
Higashi-Hiroshima 739-8526, Japan
Current address: T. Sugawa, Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579,
Japan 相似文献
3.
Peter A. Lesky 《Monatshefte für Mathematik》2001,132(2):123-140
The explicit form and the three term recurrance relation for all the polynomial solutions in x and q
−x
from q-operator equations of second order are given. The known 17 q-orthogonal polynomial systems are special cases of 7 comprehensive q-systems.
(Eingegangen 27. M?rz 2000; in revidierter Fassung 2. November 2000) 相似文献
4.
In this paper we study invariant (α, β)-metrics on homogeneous spaces. We first give a method to construct invariant (α, β)-metrics
on homogeneous spaces. Then we obtain some conditions for some special type of (α, β)-metrics to be of Berwald type and Douglas
type. At last, we give a rigidity result concerning the Randers metrics and Matsumoto metrics of Berwald type on homogeneous
spaces.
Members of LPMC and supported by NSFC (no. 10671096) and NCET of China.
Second author was corresponding author.
Authors’ address: Huihui An and Shaoqiang Deng, School of Mathematical Sciences, Nankai University, Tianjin, 300071, People’s
Republic of China 相似文献
5.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
are finite for all
if and only if ∂Ω and ∂Π do not contain isolated points.
This work was supported by a grant of the Deutsche Forschungsgemeinschaft for F. G. Avkhadiev. 相似文献
6.
Kevin Ford 《Monatshefte für Mathematik》2008,153(3):205-216
We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0,1] random variables stays to one side of a given line.
Author’s address: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL
61801, USA 相似文献
7.
Toshiyuki Sugawa 《Mathematische Zeitschrift》2001,238(2):317-333
A compact set C in the Riemann sphere is called uniformly perfect if there is a uniform upper bound on the moduli of annuli which separate
C. Julia sets of rational maps of degree at least two are uniformly perfect. Proofs have been given independently by Ma né
and da Rocha and by Hinkkanen, but no explicit bounds are given. In this note, we shall provide such an explicit bound and,
as a result, give another proof of uniform perfectness of Julia sets of rational maps of degree at least two. As an application,
we provide a lower estimate of the Hausdorff dimension of the Julia sets. We also give a concrete bound for the family of
quadratic polynomials in terms of the parameter c.
Received: 7 June 1999; in final form: 9 November 1999 / Published online: 17 May 2001 相似文献
8.
Stephanie Halbeisen 《manuscripta mathematica》2000,103(2):169-182
The tangent cones of an inner metric Alexandrov space with finite Hausdorff dimension and a lower curvature bound are always inner metric spaces with nonnegative curvature. In this paper we construct an infinite-dimensional inner metric Alexandrov
space of nonnegative curvature which has in one point a tangent cone whose metric is not an inner metric.
Received: 20 October 1999 / Revised version: 8 May 2000 相似文献
9.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(4):343-350
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with H
k
= 0 and with two distinct principal curvatures, we give a characterization of torus the
. We extend recent results of Perdomo [9], Wang [10] and Otsuki [8]. 相似文献
10.
Hidetaka Hamada 《manuscripta mathematica》1999,99(3):359-369
Let M be a complex manifold with a exhaustion function ρ. Assume that ρ attains its minimum at a single point o and dρ≠ 0 on M\{o}. In this case, we will give a necessary condition and a sufficient condition for locally biholomorphic mappings on M to be biholomorphic and to have Φ-like images.
Received: 15 May 1998 / Revised version: 8 March 1999 相似文献
11.
Harald Niederreiter 《Monatshefte für Mathematik》2003,139(4):295-307
Extensible (polynomial) lattice rules have been introduced recently and they are convenient tools for quasi-Monte Carlo integration. It is shown in this paper that for suitable infinite families of polynomial moduli there exist generating parameters for extensible rank-1 polynomial lattice rules such that for all these infinitely many moduli and all dimensions s the quantity R
(s)
and the star discrepancy are small. The case of Korobov-type polynomial lattice rules is also considered.Received April 30, 2002; in revised form August 21, 2002
Published online April 4, 2003 相似文献
12.
This note should clarify how the behavior of certain invariant objects reflects the geometric convexity of balanced domains.
Authors’ addresses: Nikolai Nikolov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev
8, 1113 Sofia, Bulgaria; Peter Pflug, Carl von Ossietzky Universit?t Oldenburg, Institut für Mathematik, Fakult?t V, Postfach
2503, D-26111 Oldenburg, Germany 相似文献
13.
Pascal Lambrechts 《manuscripta mathematica》2000,103(2):143-160
A thickening of a finite CW-complex X is by definition a compact manifold M of the same simple homotopy type as X. We give a model for the cochain complex of the boundary of that manifold, C
*(δM), as a module over the cochain algebra C
*(X). We also show how to construct an algebraic model of the rational homotopy type of δC
*(M) from a model of X. Using this rational model, we prove a new formula for the rational Lusternik–Schnirelmann category of X.
Received: 24 September 1999 相似文献
14.
In an earlier work Hubert and the authors of this paper introduced and studied the notion of pseudorandomness of binary lattices.
Later in another paper the authors gave a construction for a large family of “good” binary lattices by using the quadratic
characters of finite fields. Here, a further large family of “good” binary lattices is constructed by using finite fields
and the notion of multiplicative inverse.
Authors’ addresses: Christian Mauduit, Institut de Mathématiques de Luminy, CNRS, UMR 6206, 163 avenue de Luminy, Case 907,
F-13288 Marseille Cedex 9, France; András Sárk?zy, Department of Algebra and Number Theory, E?tv?s Loránd University, Pázmány
Péter sétány 1/C, H-1117 Budapest, Hungary 相似文献
15.
J. Carlos Díaz-Ramos Eduardo García-Río Lieven Vanhecke 《Monatshefte für Mathematik》2006,149(4):303-322
We study some scalar curvature invariants on geodesic spheres and use them to characterize several kinds of Riemannian manifolds
such as homogenous manifolds and in particular, the two-point homogeneous spaces and the Damek-Ricci spaces. 相似文献
16.
Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class
of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all
weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself.
(Received 17 August 2000) 相似文献
17.
18.
Marilyn Breen 《Monatshefte für Mathematik》2003,139(2):105-109
Let S be a nonempty closed, simply connected set in the plane. For α > 0, let ℳ denote the family of all maximal subsets of S which are starshaped via paths of length at most α. Then ⋂{M : M in ℳ} is either starshaped via α-paths or empty. The result fails without the simple connectedness condition. However, even
with a simple connectedness requirement, there is no Helly theorem for intersections of sets which are starshaped via α-paths.
Received November 19, 2001; in revised form April 25, 2002
Published online November 18, 2002 相似文献
19.
Let f be a generalized holomorphic function on a connected open set
. It is proved that f equals zero if and only if there exists a smooth curve and a set A of positive (one-dimensional) measure such that f takes zero value on A. Also, a holomorphic generalized function different from zero on the disc, which takes zero values on a dense G
δ-set of the disc, is constructed. The generalized zero set of a holomorphic function is introduced and studied in an analogous
way. 相似文献
20.
Guoxin Wei 《Monatshefte für Mathematik》2006,149(3):251-258
By investigating hypersurfaces M
n
in the unit sphere S
n+1(1) with constant mean curvature and with two distinct principal curvatures, we give a characterization of the torus S
1(a) ×
, where
. We extend recent results of Hasanis et al. [5] and Otsuki [10]. 相似文献