منابع مشابه
Multiple covers with balls I: Inclusion-exclusion
Inclusion-exclusion is an effective method for computing the volume of a union of measurable sets. We extend it to multiple coverings, proving short inclusion-exclusion formulas for the subset of R covered by at least k balls in a finite set. We implement two of the formulas in dimension n = 3 and report on results obtained with our software.
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If a real scalar field is dominated by non-relativistic modes, then it approximately conserves its particle number and obeys an equation that governs a complex scalar field theory with a conserved global U(1) symmetry. From this fact, it is shown that the I-ball (oscillon) can be naturally understood as a projection (e.g., real part) of the non-relativistic Q-ball solution. In particular, we cl...
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Résumé. Cet article montre comment on peut utiliser la construction de Chu afin de simplifier la construction assez complexe de la catégorie ∗-autonome des boules qui sont réflexives et ζ-ζ∗-complètes donnée par le premier auteur dans les articles [Barr, 1976, 1979]. Abstract. This paper shows how the use of the “Chu construction” can simplify the rather complicated construction of the ∗-autono...
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This paper introduces the concept of critical ball. Critical balls are maximal balls which are necessary and sufficient to describe and rebuild sets, contrary to maximal balls where some redundancy exists. A general definition of a critical ball is given in continuous spaces and some of its main properties are depicted. Thanks to a slight modification of their definition, critical balls can als...
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Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level. The confidence balls are centered on adaptive estimators based on special local block thresholding rules. The radius is ...
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ژورنال
عنوان ژورنال: Physics Letters B
سال: 2003
ISSN: 0370-2693
DOI: 10.1016/s0370-2693(03)00344-7