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• 1
Online Resource
Berlin : : Mayo Foundation for Medical Education and Research,
In: Springer eBooks
Type of Medium: Online Resource
Pages: digital
ISBN: 9783642133992
Language: English
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• 2
Electronic Resource
Springer
Archive for mathematical logic 34 (1995), S. 257-261
ISSN: 1432-0665
Keywords: 03E35 ; 06E99
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract The countable sequences of cardinals which arise as cardinal sequences of superatomic Boolean algebras were characterized by La Grange on the basis of ZFC set theory. However, no similar characterization is available for uncountable cardinal sequences. In this paper we prove the following two consistency results: (1) Ifθ = 〈κ α :α 〈ω 1〉 is a sequence of infinite cardinals, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebraB such that θ is the cardinal sequence ofB. (2) Ifκ is an uncountable cardinal such thatκ 〈κ =κ andθ = 〈κ α :α 〈κ +〉 is a cardinal sequence such thatκ α ≥κ for everyα 〈κ + andκ α =κ for everyα 〈κ + such that cf(α)〈κ, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebraB such that θ is the cardinal sequence ofB.
Type of Medium: Electronic Resource
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• 3
Electronic Resource
Springer
Archive for mathematical logic 34 (1995), S. 257-261
ISSN: 1432-0665
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics
Notes: Abstract. The countable sequences of cardinals which arise as cardinal sequences of superatomic Boolean algebras were characterized by La Grange on the basis of ZFC set theory. However, no similar characterization is available for uncountable cardinal sequences. In this paper we prove the following two consistency results: (1) If $\theta =\langle\kappa_{\alpha}:\alpha 〈 \omega_1 \rangle$ is a sequence of infinite cardinals, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebra $B$ such that $\theta$ is the cardinal sequence of $B$ . (2) If $\kappa$ is an uncountable cardinal such that $\kappa^{〈 \kappa} = \kappa$ and $\theta = \langle\kappa_{\alpha}:\alpha 〈 \kappa^+ \rangle$ is a cardinal sequence such that $\kappa_{\alpha} \geq\kappa$ for every $\alpha 〈 \kappa^+$ and $\kappa_{\alpha} =\kappa$ for every $\alpha 〈 \kappa^+$ such that $\mbox{cf}(\alpha) 〈 \kappa$ , then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebra $B$ such that $\theta$ is the cardinal sequence of $B$ .
Type of Medium: Electronic Resource
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• 4
Unknown
Molecular Diversity Preservation International (MDPI)
Publication Date: 2020-04-18
Description: Clustering algorithms are necessary in Wireless Sensor Networks to reduce the energy consumption of the overall nodes. The decision of which nodes are the cluster heads (CHs) greatly affects the network performance. The centralized clustering algorithms rely on a sink or Base Station (BS) to select the CHs. To do so, the BS requires extensive data from the nodes, which sometimes need complex hardware inside each node or a significant number of control messages. Alternatively, the nodes in distributed clustering algorithms decide about which the CHs are by exchanging information among themselves. Both centralized and distributed clustering algorithms usually alternate the nodes playing the role of the CHs to dynamically balance the energy consumption among all the nodes in the network. This paper presents a distributed approach to form the clusters dynamically, but it is occasionally supported by the Base Station. In particular, the Base Station sends three messages during the network lifetime to reconfigure the s k i p value of the network. The s k i p , which stands out as the number of rounds in which the same CHs are kept, is adapted to the network status in this way. At the beginning of each group of rounds, the nodes decide about their convenience to become a CH according to a fuzzy-logic system. As a novelty, the fuzzy controller is as a Tagaki–Sugeno–Kang model and not a Mandami-one as other previous proposals. The clustering algorithm has been tested in a wide set of scenarios, and it has been compared with other representative centralized and distributed fuzzy-logic based algorithms. The simulation results demonstrate that the proposed clustering method is able to extend the network operability.
Electronic ISSN: 1424-8220
Topics: Chemistry and Pharmacology , Electrical Engineering, Measurement and Control Technology
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