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1.
The Bartle–Dunford–Schwartz integral for scalar functions with respect to vector measures is characterized by means of Riemann-type
sums based on partitions of the domain into countably many measurable sets. In this setting, two natural notions of integrability
(Birkhoff integrability and Kolmogoroff integrability) turn out to be equivalent to Bartle–Dunford–Schwartz integrability.
A. Fernández, F. Mayoral and F. Naranjo were supported by MEC and FEDER (project MTM2006–11690–C02–02) and La Junta de Andalucía. J. Rodríguez was supported by MEC and FEDER (project MTM2005-08379), Fundación Séneca (project 00690/PI/04) and the Juan de la Cierva Programme (MEC and FSE). 相似文献
2.
Anirvan Chakraborty Probal Chaudhuri 《Annals of the Institute of Statistical Mathematics》2014,66(2):303-324
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite dimensional data, there have been some recent attempts to develop depth functions for data in infinite dimensional spaces. In this paper, we consider some notions of depth in infinite dimensional spaces and study their properties under various stochastic models. Our analysis shows that some of the depth functions available in the literature have degenerate behaviour for some commonly used probability distributions in infinite dimensional spaces of sequences and functions. As a consequence, they are not very useful for the analysis of data satisfying such infinite dimensional probability models. However, some modified versions of those depth functions as well as an infinite dimensional extension of the spatial depth do not suffer from such degeneracy and can be conveniently used for analyzing infinite dimensional data. 相似文献
3.
Functional approach to the random mean of a compound Cox process 总被引:1,自引:0,他引:1
The parametric process and counting statistics of a marked point process whose marks belong to a given subset of the mark
space of a compound Cox process are derived in this paper by means of functional data analysis. They are illustrated by means
of an example and simulation study with different intensity processes for the CCP.
This work was partially supported by projects MTM2004-05992 of Dirección General de Investigación, and MTM2004-04230 of Plan
Nacional de I+D+I, Ministerio de Ciencia y Tecnología jointly by the FEDER. 相似文献
4.
R. Ayala L.M. Fernández J.A. Vilches 《Bulletin of the Brazilian Mathematical Society》2009,40(2):225-235
We get a characterization theorem for equivalent discrete Morse functions defined on simplicial complexes in terms of their
gradient vector field. As a consequence, we also characterize them in the 1-dimensional case by using critical elements.
The authors are partially supported by the P.A.I. project (Junta de Andalucia, SPAIN, 2009/FQM-189 and 327) and by the MEC-FEDER
grants MTM2007-61284 and MTM2007-65726 (MEC, SPAIN, 2007). 相似文献
5.
In this paper we study the influence of the partial cover and avoidance property on the subgroups of some relevant families of subgroups in a finite group. 相似文献
6.
In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures
in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator,
for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory:
it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain
the asymptotic behavior of Sobolev orthogonal polynomials. We also obtain some non-trivial results about these Sobolev spaces
with respect to measures; in particular, we prove a main result in the theory: they are Banach spaces.
J.M. Rodriguez supported in part by three grants from M.E.C. (MTM 2006-13000-C03-02, MTM 2006-11976 and MTM 2007-30904-E),
Spain, and by a grant from U.C.III M./C.A.M. (CCG07-UC3M/ESP-3339), Spain.
J.M. Sigarreta supported in part by a grant from M.E.C. (MTM 2006-13000-C03-02), Spain, and by a grant from U.C.III M./C.A.M.
(CCG07-UC3M/ESP-3339), Spain. 相似文献
7.
We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor.
Applications on cup-one products, Toda brackets and Whitehead products are considered.
The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865
and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract. 相似文献
8.
Sara López-Pintado Ying Sun Juan K. Lin Marc G. Genton 《Advances in Data Analysis and Classification》2014,8(3):321-338
We propose notions of simplicial band depth for multivariate functional data that extend the univariate functional band depth. The proposed simplicial band depths provide simple and natural criteria to measure the centrality of a trajectory within a sample of curves. Based on these depths, a sample of multivariate curves can be ordered from the center outward and order statistics can be defined. Properties of the proposed depths, such as invariance and consistency, can be established. A simulation study shows the robustness of this new definition of depth and the advantages of using a multivariate depth versus the marginal depths for detecting outliers. Real data examples from growth curves and signature data are used to illustrate the performance and usefulness of the proposed depths. 相似文献
9.
A new numerical quadrature formula on the unit circle 总被引:1,自引:0,他引:1
In this paper we study a quadrature formula for Bernstein–Szegő measures on the unit circle with a fixed number of nodes and
unlimited exactness. Taking into account that the Bernstein–Szegő measures are very suitable for approximating an important
class of measures we also present a quadrature formula for this type of measures such that the error can be controlled with
a well-bounded formula.
This work was supported by Ministerio de Educación y Ciencia under grants number MTM2005-01320 (E. B. and A. C.) and MTM2006-13000-C03-02
(F. M.). 相似文献
10.
In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space.
Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva
theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic
cooperative games among others are particular cases of this general theory.
The research of the authors is partially supported by Spanish DGICYT grant numbers MTM2004-0909, HA2003-0121, HI2003-0189,
MTM2007-67433-C02-01, P06-FQM-01366. 相似文献