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1.
We present a new distance characterization of Aleksandrov spaces of non-positive curvature. By introducing a quasilinearization
for abstract metric spaces we draw an analogy between characterization of Aleksandrov spaces and inner product spaces; the
quasi-inner product is defined by means of the quadrilateral cosine—a metric substitute for the angular measure between two
directions at different points. Our main result states that a geodesically connected metric space is an Aleksandrov domain (also known as a CAT(0) space) if and only if the quadrilateral cosine does not exceed one for every two pairs of
distinct points in . We also observe that a geodesically connected metric space is an domain if and only if, for every quadruple of points in , the quadrilateral inequality (known as Euler’s inequality in ) holds. As a corollary of our main result we give necessary and sufficient conditions for a semimetric space to be an domain. Our results provide a complete solution to the Curvature Problem posed by Gromov in the context of metric spaces
of non-positive curvature.
相似文献
2.
Ameer Athavale 《Complex Analysis and Operator Theory》2008,2(3):417-428
Let be a strictly pseudoconvex bounded domain in with C
2 boundary . If a subnormal m-tuple T of Hilbert space operators has the spectral measure of its minimal normal extension N supported on , then T is referred to as a -isometry. Using some non-trivial approximation theorems in the theory of several complex variables, we establish a commutant
lifting theorem for those -isometries whose (joint) Taylor spectra are contained in a special superdomain Ω of . Further, we provide a function-theoretic characterization of those subnormal tuples whose Taylor spectra are contained in
Ω and that are quasisimilar to a certain (fixed) -isometry T (of which the multiplication tuple on the Hardy space of the unit ball in is a rather special example).
Submitted: September 9, 2007. Revised: October 10, 2007. Accepted: October 24, 2007. 相似文献
3.
We construct extremal stochastic integrals
of a deterministic function with respect to a random Fréchet () sup-measure. The measure is sup-additive rather than additive and is defined over a general measure space , where is a deterministic control measure. The extremal integral is constructed in a way similar to the usual stable integral, but with the maxima replacing the operation of summation. It is well-defined for arbitrary , and the metric metrizes the convergence in probability of the resulting integrals.This approach complements the well-known de Haan's spectral representation of max-stable processes with Fréchet marginals. De Haan's representation can be viewed as the max-stable analog of the LePage series representation of stable processes, whereas the extremal integrals correspond to the usual stable stochastic integrals. We prove that essentially any strictly stable process belongs to the domain of max-stable attraction of an Fréchet, max-stable process. Moreover, we express the corresponding Fréchet processes in terms of extremal stochastic integrals, involving the kernel function of the stable process. The close correspondence between the max-stable and stable frameworks yields new examples of max-stable processes with non-trivial dependence structures.This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University of Michigan and the NSF Grant DMS-0505747 at Boston University. 相似文献
4.
5.
Nic Koban 《Geometriae Dedicata》2007,124(1):133-141
We compute the geometric invariants of a product G × H of groups in terms of and . This gives a sufficient condition in terms of and for a normal subgroup of G × H with abelian quotient to be of type F
n
. We give an example involving the direct product of the Baumslag–Solitar group BS1,2 with itself.
相似文献
6.
The problem is considered of matching two sets of points in , by translation and rotation. There are many applications, for example in geodesy, computer vision and in the assessment
of manufactured parts. When the matching criterion is least squares, there is a well known solution process based on the singular
value decomposition of an matrix. Here we consider the use of the norm, which may be more appropriate than least squares in the context of wild points in the data. An algorithm is developed,
and is illustrated by some examples for the case . 相似文献
7.
Let be a saturated formation. We describe minimal non- -, minimal non- -, and minimal non-metabelian groups.
Dedicated to L. A. Shemetkov on the occasion of his seventieth birthday. 相似文献
8.
Ian Chiswell Thomas W. Müller Jan-Christoph Schlage-Puchta 《Archiv der Mathematik》2008,91(4):372-378
We establish (geometric) criteria for an -tree to be compact and to be locally compact. It follows that locally compact -trees are separable.
Received: 10 September 2007 相似文献
9.
In this paper, we introduce the notion of -decomposability of probability density functions in one dimension. Using -decomposability, we derive an inequality that applies to all symmetric unimodal densities. Our inequality involves only
the standard deviation of the densities concerned. The concept of -decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis. 相似文献
10.
Thomas Krainer 《Annals of Global Analysis and Geometry》2009,35(4):345-361
Let A be an elliptic operator on a compact manifold with boundary , and let be a covering map, where Y is a closed manifold. Let A
C
be a realization of A subject to a coupling condition C that is elliptic with parameter in the sector Λ. By a coupling condition we mean a nonlocal boundary condition that respects
the covering structure of the boundary. We prove that the resolvent trace for N sufficiently large has a complete asymptotic expansion as . In particular, the heat trace has a complete asymptotic expansion as , and the -function has a meromorphic extension to .
相似文献
11.
Complementing the results of (Lotta and Nacinovich, Adv. Math. 191(1): 114–146, 2005), we show that the minimal orbit M of a real form G of a semisimple complex Lie group in a flag manifold is CR-symmetric (see (Kaup and Zaitsev Adv. Math. 149(2):145–181, 2000)) if and only if the corresponding CR algebra admits a gradation compatible with the CR structure.
相似文献
12.
Pseudomonotone maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational
inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum
principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity of the map implies the “maximum principle sufficiency” and, in fact, is equivalent to it in a sense. We then present two
applications of pseudomonotone maps. First we show that pseudomonotone maps can be used instead of the much more restricted class of pseudomonotone+ maps in a cutting plane method. Finally, an application to a proximal point method is given.
相似文献
13.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献
14.
In this paper, motivated by a result due to Champion [Math. Program.99, 2004], we introduce a property for a conic quasi-convex vector-valued function in a general normed space. We prove that this property characterizes the zero duality gap for a class of the conic convex constrained optimization problem in the sense that if
this property is satisfied and the objective function f is continuous at some feasible point, then the duality gap is zero, and if this property is not satisfied, then there exists
a linear continuous function f such that the duality gap is positive. We also present some sufficient conditions for the property
The work of this author was partially supported by the National Natural Sciences Grant (No. 10671050) and the Excellent Young
Teachers Program of MOE, P.R.C. 相似文献
15.
Friedrich Haslinger 《Czechoslovak Mathematical Journal》2008,58(4):1247-1256
We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. 相似文献
16.
Simeon Zamkovoy 《Annals of Global Analysis and Geometry》2009,36(1):37-60
The canonical paracontact connection is defined and it is shown that its torsion is the obstruction the paracontact manifold
to be paraSasakian. A -homothetic transformation is determined as a special gauge transformation. The η-Einstein manifold are defined, it is proved
that their scalar curvature is a constant, and it is shown that in the paraSasakian case these spaces can be obtained from
Einstein paraSasakian manifolds with -homothetic transformations. It is shown that an almost paracontact structure admits a connection with totally skew-symmetric
torsion if and only if the Nijenhuis tensor of the paracontact structure is skew-symmetric and the defining vector field is
Killing.
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17.
Linus Carlsson 《Mathematische Zeitschrift》2009,261(1):189-200
We show a sufficient condition for a domain in to be a H
∞-domain of holomorphy. Furthermore if a domain has the Gleason property at a point and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several
other interesting properties.
相似文献
18.
For a given , we show that there exist two finite index subgroups of which are -quasisymmetrically conjugated and the conjugation homeomorphism is not conformal. This implies that for any there are two finite regular covers of the Modular once punctured torus T
0 (or just the Modular torus) and a -quasiconformal map between them that is not homotopic to a conformal map. As an application of the above results, we show
that the orbit of the basepoint in the Teichmüller space T(S
p
) of the punctured solenoid S
p
under the action of the corresponding Modular group (which is the mapping class group of S
p
[6], [7]) has the closure in T(S
p
) strictly larger than the orbit and that the closure is necessarily uncountable.
相似文献
19.
On Approximate Efficiency in Multiobjective Programming 总被引:2,自引:0,他引:2
This paper is focused on approximate (
-efficient) solutions of multiobjective mathematical programs. We introduce a new
-efficiency concept which extends and unifies different notions of approximate solution defined in the literature. We characterize these
-efficient solutions in convex multiobjective programs through approximate solutions of linear scalarizations, which allow us to obtain parametric representations of different
-efficiency sets. Several classical
-efficiency notions are considered in order to show the concepts introduced and the results obtained.This research was partially supported by Ministerio de Ciencia y Tecnología (Spain), project BFM2003-02194. 相似文献
20.
Changguo Wei 《Proceedings Mathematical Sciences》2008,118(4):517-524
Some results on A
-algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A
-algebras are A
-algebras or A
-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A
-algebra being an A
-algebra. 相似文献