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A method of constructing the frame of a directed graph

100%
Hofuku I., Oshima K.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 4
823-837
EN
In web search engines, such as Google, the ranking of a particular keyword is determined by mathematical tools, e.g., Pagerank or Hits. However, as the size of the network increases, it becomes increasingly difficult to use keyword ranking to quickly find the information required by an individual user. One reason for this phenomenon is the interference of superfluous information with the link structure. The World Wide Web can be expressed as an enormous directed graph. The purpose of the present study is to provide tools for studying the web as a directed graph in order to find clues to the solution of the problem of interference from superfluous information, and to reform the directed graph to clarify the relationships between the nodes.
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Perron-Frobenius and Krein-Rutman theorems for tangentially positive operators

63%
Kanigowski A., Kryszewski W.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2240-2263
EN
We study several aspects of a generalized Perron-Frobenius and Krein-Rutman theorems concerning spectral properties of a (possibly unbounded) linear operator on a cone in a Banach space. The operator is subject to the so-called tangency or weak range assumptions implying the resolvent invariance of the cone. The further assumptions rely on relations between the spectral and essential spectral bounds of the operator. In general we do not assume that the cone induces the Banach lattice structure into the underlying space.
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