On Probability that a Randomly Selected Set Has Some complexity-Theoretical Property

Author(s):  
Kojiro Kobayashi
Keyword(s):  
2005 ◽  
Vol 2 (1) ◽  
pp. 545-570
Author(s):  
David J. Livingstone
Keyword(s):  

2014 ◽  
Vol 97 (2) ◽  
pp. 257-287 ◽  
Author(s):  
KENGO MATSUMOTO ◽  
HIROKI MATUI

AbstractWe introduce a family of infinite nonamenable discrete groups as an interpolation of the Higman–Thompson groups by using the topological full groups of the groupoids defined by $\beta $-expansions of real numbers. They are regarded as full groups of certain interpolated Cuntz algebras, and realized as groups of piecewise-linear functions on the unit interval in the real line if the $\beta $-expansion of $1$ is finite or ultimately periodic. We also classify them by a number-theoretical property of $\beta $.


2003 ◽  
Vol 3 (10) ◽  
pp. 1171-1192 ◽  
Author(s):  
David Livingstone
Keyword(s):  

2017 ◽  
Vol 2 (30) ◽  
pp. 9829-9837 ◽  
Author(s):  
Sarinya Hadsadee ◽  
Rattanawalee Rattanawan ◽  
Ruangchai Tarsang ◽  
Nawee Kungwan ◽  
Siriporn Jungsuttiwong

2020 ◽  
Vol 18 (1) ◽  
pp. 400-416
Author(s):  
Gang Wang ◽  
Hua Mao

Abstract Using the notion of preconcept, we generalize Pawlak’s approximation operators from a one-dimensional space to a two-dimensional space in a formal context. In a formal context, we present two groups of approximation operators in a two-dimensional space: one is aided by an equivalence relation defined on the attribute set, and another is aided by the lattice theoretical property of the family of preconcepts. In addition, we analyze the properties of those approximation operators. All these results show that we can approximate all the subsets in a formal context assisted by the family of preconcepts using the above groups of approximation operators. Some biological examples show that the two groups of approximation operators provided in this article have potential ability to assist biologists to do the phylogenetic analysis of insects.


2016 ◽  
Vol 26 (05) ◽  
pp. 1071-1094
Author(s):  
Layla Sorkatti ◽  
Gunnar Traustason

In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension 10 over any field. It is known that symplectic alternating algebras over GF(3) correspond to a special rich class [Formula: see text] of 2-Engel 3-groups of exponent 27 and under this correspondence we will see that the nilpotent algebras correspond to a subclass of [Formula: see text] that are those groups in [Formula: see text] that have an extra group theoretical property that we refer to as being powerfully nilpotent and can be described also in the context of [Formula: see text]-groups where [Formula: see text] is an arbitrary prime.


2019 ◽  
Vol 20 (7) ◽  
pp. 975-981 ◽  
Author(s):  
László Csató

This article investigates the qualification for the Union of European Football Association (UEFA) Champions League (CL), the most prestigious club competition in European football, with respect to the theoretical property of strategyproofness. We find that in three seasons (2015-2016, 2016-2017, and 2017-2018), the UEFA Europa League titleholder might have been better off by losing its match against the CL titleholder in their domestic championship. A straightforward solution is suggested in order to avoid the occurrence of this paradox. The use of an incentive compatible rule would have a real effect on the qualification in these three seasons of the UEFA CL.


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