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1.
Marilyn Breen 《Journal of Geometry》2005,82(1-2):25-35
Let S be a simply connected orthogonal polygon in the plane. The set S is a union of two sets which are starshaped via staircase paths (i.e., orthogonally starshaped) if and only if for every
three points of S, at least two of these points see (via staircase paths) a common point of S. Moreover, the simple connectedness condition cannot be deleted. 相似文献
2.
Marilyn Breen 《Archiv der Mathematik》1997,68(1):60-64
Let S be a nonempty closed, simply connected set in the plane, and let α τ; 0. If every three points of 5 see a common point of
S via paths of length at most α, then for some point s0 of S, s0 sees each point of S via such a path. That is, S is starshaped via paths of length at most α.
Supported in part by NSF grant DMS-9207019 相似文献
3.
Marilyn Breen 《Journal of Geometry》2009,94(1-2):1-6
Let S be a simply connected orthogonal polygon in the plane. A family of examples will establish the following result. For every n ≥ 2, there exists no Krasnosel’skii number h(n) which satisfies this property: If every h(n) points of S are visible via staircase n-paths from a common point, then S is starshaped via staircase n-paths. 相似文献
4.
Marilyn Breen 《Periodica Mathematica Hungarica》2007,55(2):169-176
A Krasnosel’skii-type theorem for compact sets that are starshaped via staircase paths may be extended to compact sets that
are starshaped via orthogonally convex paths: Let S be a nonempty compact planar set having connected complement. If every
two points of S are visible via orthogonally convex paths from a common point of S, then S is starshaped via orthogonally convex paths. Moreover, the associated kernel Ker S has the expected property that every two of its points are joined in Ker S by an orthogonally convex path. If S is an arbitrary nonempty planar set that is starshaped via orthogonally convex paths, then for each component C of Ker S, every two of points of C are joined in C by an orthogonally convex path.
Communicated by Imre Bárány 相似文献
5.
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
6.
Albert Visser 《Archive for Mathematical Logic》2001,40(4):277-295
A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of
formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class
of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.
In Appendix A we prove that for theories with decidable identity we can take as the embeddings between domains in Kripke models
of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In
Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory.
Received: 4 February 1999 / Published online: 25 January 2001 相似文献
7.
Toshiyuki Sugawa 《Monatshefte für Mathematik》2003,139(1):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.
The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088.
A part of this work was carried out during his visit to the University of Helsinki under the exchange programme of scientists
between the Academy of Finland and the JSPS.
Received November 26, 2001; in revised form September 24, 2002
Published online May 9, 2003 相似文献
8.
Edmond E. Granirer 《Israel Journal of Mathematics》1990,69(3):321-336
LetG ⊂ Aut ℳ be a countable group, ℳ a Von Neumann algebra. LetE be a set of pure states on ℳ such thatG*E ⊂E, S
G be the set ofG invariant states on ℳ andS
E
G
=S
G ∩w* cl coE. We investigate in this paper some geometric properties for the setS
E
G
which turn out to be equivalent to amenability for the groupG. For example, we show thatS
E
G
⊂ ℳ* (S
E
G
has the WRNP) implies that ℳ contains minimal projections (ê containsfinite G invariant orbits) hold true, for all ℳ iffG is amenable. Furthermore we show that ifG is amenable thenS
G ∩M
*
⊥
contains a big set, thus improving results obtained by Ching Chou in [2]. These results imply that no action of an amenable
countable groupG on an arbitraryW* algebra ℳ iss — strongly ergodic. Moreover cardS
G ∩M
*
⊥
≧2
c
(see M. Choda [4], K. Schmidt [21] and compare with A. Connes and B. Weiss [5]).
The author gratefully acknowledges the support of an Izaak Walton Killam Memorial Senior Fellowship. 相似文献
9.
Marilyn Breen 《Aequationes Mathematicae》2010,79(1-2):99-110
Let S be a simply connected orthogonal polygon in the plane, and let n be fixed, n ≥ 1. If every two points of S are visible via staircase n-paths from a common point of S, then S is starshaped via staircase (n + 1)-paths. Moreover, the associated staircase (n + 1)-kernel is staircase (n + 1)-convex. The number two is best possible, and the number n + 1 is best possible for n ≥ 2. 相似文献
10.
Oleg Topală 《Journal of Geometry》2001,70(1-2):164-167
Let S be a simply connected orthogonal polygon in and let P(S) denote the intersection of all maximal starshaped via staircase paths orthogonal subpolygons in S. Our result: if , then there exists a maximal starshaped via staircase paths orthogonal polygon , such that . As a corollary, P(S) is a starshaped (via staircase paths) orthogonal polygon or empty. The results fail without the requirement that the set
S is simply connected.
Received 1 March 1999. 相似文献
11.
This paper aims to study the local convergence of a family of Euler-Halley type methods with a parameter α for solving nonlinear operator equations under the second-order generalized Lipschitz assumption. The radius r
α
of the optimal convergence ball and the error estimation of the method corresponding to α are estimated for each α ∈ ( − ∞ , + ∞ ). For each α > 0, we get r
α
≥ r
− α
and the upper bound of the error estimation of the method with α > 0 is not larger than the one with α < 0. For each α ≤ 0, we get the precise value of r
α
, which is closely linked to the dynamical property of the method applied to a real or a complex function, and the optimal
error estimation, which decreases when α→0 − . Results show that the method corresponding to α is better than the one corresponding to − α for each α > 0 and the Chebyshev-Euler method is the best among all methods in the family with α ∈ ( − ∞ , 0] from the view of both safe choice of the initial point and error estimation. 相似文献
12.
Marilyn Breen 《Journal of Geometry》1999,65(1-2):50-53
Let
be a finite family of compact sets in the plane, and letk be a fixed natural number. If every three (not necessarily distinct) members of
have a union which is simply connected and starshaped viak-paths, then
and
is starshaped viak-paths. Analogous results hold for paths of length at most , > 0, and for staircase paths, although not for staircasek-paths.Supported in part by NSF grant DMS-9504249 相似文献
13.
Marilyn Breen 《Monatshefte für Mathematik》2006,148(2):91-100
For n ≥ 1, define p (n) to be the smallest natural number r for which the following is true: For
any finite family of simply connected orthogonal polygons in the plane and points x and y in
, if every r (not necessarily distinct) members of
contain a common staircase n-path from x to y, then
contains such a path. We show that p(1) = 1 and p(n) = 2 (n − 1) for n ≥ 2. The numbers p(n) yield an improved Helly theorem for intersections of sets starshaped via staircase n-paths.
Moreover, we establish the following dual result for unions of these sets: Let
be any finite family of orthogonal polygons in the plane, with
simply connected. If every three (not necessarily distinct) members of
have a union which is starshaped via staircase n-paths, then T is starshaped via staircase (n + 1)-paths. The number n + 1 in the theorem is best for every n ≥ 2. 相似文献
14.
Zakhar Kabluchko 《Extremes》2009,12(4):401-424
To each max-stable process with α-Fréchet margins, α ∈ (0,2), a symmetric α-stable process can be associated in a natural way. Using this correspondence, we deduce known and new results on spectral
representations of max-stable processes from their α-stable counterparts. We investigate the connection between the ergodic properties of a stationary max-stable process and
the recurrence properties of the non-singular flow generating its spectral representation. In particular, we show that a stationary
max-stable process is ergodic iff the flow generating its spectral representation has vanishing positive recurrent component.
We prove that a stationary max-stable process is ergodic (mixing) iff the associated SαS process is ergodic (mixing). We construct non-singular flows generating the max-stable processes of Brown and Resnick. 相似文献
15.
Let N be an H-type group of homogeneous dimension Q. We study the space of biradial Schwartz functions on N by means of the Gelfand transform. This enables us to characterize the class of biradial homogeneous distributions on N of degree α, with 0 ? α< Q, which are away from the identity, via the Gelfand transform.
(Received 26 April 2000; in revised form December 2000) 相似文献
16.
R. Shen 《Acta Mathematica Hungarica》2009,124(4):363-369
We study the relationship between the product and other basic operations (namely σ, π, α and β) of generalized topologies. Also we discuss the connectedness, generalized connectedness and compactness of products of generalized
topologies. It is proved that the connectedness and compactness are preserved under the product of generalized topologies,
which shows that the definition of product of generalized topologies is quite reasonable. 相似文献
17.
We denote by ℳ
R
n
the test neighbourhood sufficient to extract the Euclidean Medial Axis of any n-dimensional discrete shape whose inner radius is no greater than R. In this paper, we study properties of discrete Euclidean disks overlappings so as to prove that in any given dimension n, ℳ
R
n
tends to the set of visible vectors as R tends to infinity. 相似文献
18.
Reinhard Winkler 《Monatshefte für Mathematik》2002,135(4):333-343
Let be a homomorphism with dense image in the compact group C. If is a continuity set, i.e. its topological boundary has Haar measure 0, then is called a Hartman set. If M is aperiodic then S contains the essential information about (C, ι) or, equivalently, about the dynamical system (C, T) where T is the ergodic group rotation . Using Pontryagin’s duality the paper presents a new method to get this information from S: The set S induces a filter on which is an isomorphism invariant for (C, T) and turns out to be a complete invariant for ergodic group rotations. If one takes , , , , one gets the interesting special case of Kronecker sequences (nα) which are classical objects in number theory and diophantine analysis.
Received 3 November 2000; in final form 25 January 2002 相似文献
19.
Marilyn Breen 《Journal of Geometry》2001,71(1-2):26-33
Let S be a simply connected orthogonal polygon in the plane, and assume that S is two-guardable (but not starshaped) via staircase paths. If K is a component of two-kernel (S), then the set of partners of points in K determines a second component K' of two-kernel (S). Thus the components occur in pairs. Moreover, each component is geodesically convex. The results fail without the requirement
that S be simply connected.
Received 2 November 1999; revised 28 September 2000. 相似文献
20.
J. E. van den Berg 《Acta Mathematica Hungarica》2000,87(1-2):153-172
This paper investigates closure properties possessed by certain classes of finite subdirect products of prime rings. If ℳ
is a special class of prime rings then the class ℳ∞ of all finite subdirect products of rings in ℳ is shown to be weakly special. A ring S is said to be a right tight extension [resp. tight extension] of a subring R if every nonzero right ideal [resp. right ideal and left ideal] of S meets R nontrivially. Every hereditary class of semiprime rings closed under tight extensions is weakly special. Each of the following
conditions imposed on a semiprime ring yields a hereditary class closed under right tight extensions: ACC on right annihilators;
finite right Goldie dimension; right Goldie. The class of all finite subdirect products of uniformly strongly prime rings
is shown to be closed under tight extensions, answering a published question.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献