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61.
62.
Marilyn Breen 《Journal of Geometry》1989,36(1-2):8-16
LetS be a compact, simply connected set inR
2. If every boundary point ofS is clearly visible viaS from at least one of the three pointsa, b, c, thenS is a union of three starshaped sets whose kernels containa, b, c, respectively. The result fails when the number three is replaced by four.As a partial converse, ifS is a union of three starshaped sets whose kernels containa, b, c, respectively, then the set of points in the boundary ofS clearly visible from at least one ofa, b, orc is dense in the boundary ofS.Supported in part by NSF grant DMS-8705336. 相似文献
63.
This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart. 相似文献
64.
The authors give a consistent affirmative response to a question of Juhász, Soukup and Szentmiklóssy: If GCH fails, there are (many) extraresolvable, not maximally resolvable Tychonoff spaces. They show also in ZFC that for ω<λ?κ, no maximal λ-independent family of λ-partitions of κ is ω-resolvable. In topological language, that theorem translates to this: A dense, ω-resolvable subset of a space of the form (DI(λ)) is λ-resolvable. 相似文献
65.
Martin Loebl 《Advances in Mathematics》2007,211(2):546-565
We define a q-chromatic function and q-dichromate on graphs and compare it with existing graph functions. Then we study in more detail the class of general chordal graphs. This is partly motivated by the graph isomorphism problem. Finally we relate the q-chromatic function to the colored Jones function of knots. This leads to a curious expression of the colored Jones function of a knot diagram K as a chromatic operator applied to a power series whose coefficients are linear combinations of long chord diagrams. Chromatic operators are directly related to weight systems by the work of Chmutov, Duzhin, Lando and Noble, Welsh. 相似文献
66.
Piotr Borodulin-Nadzieja 《Topology and its Applications》2007,154(18):3107-3124
We investigate properties of minimally generated Boolean algebras. It is shown that all measures defined on such algebras are separable but not necessarily weakly uniformly regular. On the other hand, there exist Boolean algebras small in terms of measures which are not minimally generated. We prove that under CH a measure on a retractive Boolean algebra can be nonseparable. Some relevant examples are indicated. Also, we give two examples of spaces satisfying some kind of Efimov property. 相似文献
67.
S. Heinze P. Kurz D. Wortmann G. Bihlmayer S. Blügel 《Applied Physics A: Materials Science & Processing》2002,75(1):25-36
In this paper we present a density functional theory investigation of complex magnetic structures in ultra-thin films. The
focus is on magnetically frustrated antiferromagnetic Cr and Mn monolayers deposited on a triangular lattice provided by a
Ag (111) substrate. This involves non-collinear magnetic structures, which we treat by first-principles calculations on the
basis of the vector spin-density formulation of the density functional theory. We find for Cr/Ag (111) a coplanar non-collinear
periodic 120° Néel structure, for Mn/Ag (111) a row-wise antiferromagnetic structure, and for Fe/Ag (111) a ferromagnetic
structure as magnetic ground states. The spin-polarized scanning tunneling microscope (SP–STM) operated in the constant-current
mode is proposed as a powerful tool to investigate complex atomic-scale magnetic structures of otherwise chemically equivalent
atoms. We discuss a recent application of this operation mode of the SP–STM on Mn/W (110), which led to the first observation
of a two-dimensional antiferromagnet on a non-magnetic metal. The future potential of this approach is demonstrated by calculating
SP–STM images for different magnetic structures of Cr/Ag (111). The results show that the predicted non-collinear magnetic
ground state structure can clearly be discriminated from competing magnetic structures. A general discussion of the application
of different operation modes of the SP–STM is presented on the basis of the model of Tersoff and Hamann.
Received: 07 May 2001 / Accepted: 23 July 2001 / Published online: 3 April 2002 相似文献
68.
Summary The paper addresses the problem of the implementation of nonhomogeneous essential Dirichlet type boundary conditions in thep-version of the finite element method.Partially supported by the Office of Naval Research under Grant N-00014-85-K-0169Research partially supported by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant Number AFOSR 85-0322 相似文献
69.
70.
Norbert Poschadel 《Mathematische Semesterberichte》2002,49(1):45-54
Zusammenfassung. Eine Abbildung zwischen metrischen R?umen hei?t abstandsvertr?glich, wenn der Abstand der Bilder zweier Punkte nur vom Abstand der Punkte selbst abh?ngt. Wir zeigen, dass eine Abbildung genau dann abstandsvertr?glich ist, wenn der Cauchyschen Funktionalgleichung genügt, also ein Endomorphismus der Gruppe ist. Ein entsprechendes Resultat gilt auch für die abstandsvertr?glichen Abbildungen des Kreises (mit der Multiplikation komplexer Zahlen als Gruppenverknüpfung). Damit kann man sowohl alle messbaren abstandsvertr?glichen Abbildungen von bzw. in sich angeben, als auch einen Nachweis für die Existenz nichtmessbarer abstandsvertr?glicher Abbildungen auf und erbringen.
Eingegangen am 20. Juni 2001 / Angenommen am 13. September 2001 相似文献