Maximal compatible extensions of partial orders

AbstractWe give a complete description of maximal compatible partial orders on the mono-unary algebra (A, f), where f: A → A is an arbitrary unary operation.

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Partial Orders in Non-commutative $$L^p$$ Spaces Associated with Semi-finite von Neumann Algebras

Bulletin of the Malaysian Mathematical Sciences Society ◽

10.1007/s40840-021-01145-4 ◽

2021 ◽

Author(s):

Xinhui Wang ◽

Guoxing Ji

Keyword(s):

Von Neumann Algebras ◽

Partial Orders ◽

Von Neumann ◽

Finite Von Neumann Algebras

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Partial orders on conjugacy classes in the Weyl group and on unipotent conjugacy classes

Advances in Mathematics ◽

10.1016/j.aim.2021.107688 ◽

2021 ◽

Vol 383 ◽

pp. 107688

Author(s):

Jeffrey Adams ◽

Xuhua He ◽

Sian Nie

Keyword(s):

Weyl Group ◽

Partial Orders ◽

Conjugacy Classes

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THE NATURAL PARTIAL ORDER ON LINEAR SEMIGROUPS WITH NULLITY AND CO-RANK BOUNDED BELOW

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972714000793 ◽

2014 ◽

Vol 91 (1) ◽

pp. 104-115 ◽

Cited By ~ 1

Author(s):

SUREEPORN CHAOPRAKNOI ◽

TEERAPHONG PHONGPATTANACHAROEN ◽

PONGSAN PRAKITSRI

Keyword(s):

Semigroup Forum ◽

Partial Order ◽

Lower Bounds ◽

Partial Orders ◽

Natural Partial Order ◽

Linear Transformations ◽

Bounded Below

AbstractHiggins [‘The Mitsch order on a semigroup’, Semigroup Forum 49 (1994), 261–266] showed that the natural partial orders on a semigroup and its regular subsemigroups coincide. This is why we are interested in the study of the natural partial order on nonregular semigroups. Of particular interest are the nonregular semigroups of linear transformations with lower bounds on the nullity or the co-rank. In this paper, we determine when they exist, characterise the natural partial order on these nonregular semigroups and consider questions of compatibility, minimality and maximality. In addition, we provide many examples associated with our results.

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Modeling country risk ratings using partial orders

European Journal of Operational Research ◽

10.1016/j.ejor.2005.06.040 ◽

2006 ◽

Vol 175 (2) ◽

pp. 836-859 ◽

Cited By ~ 32

Author(s):

P.L. Hammer ◽

A. Kogan ◽

M.A. Lejeune

Keyword(s):

Country Risk ◽

Partial Orders

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Frequent Closed Partial Orders Mining in Sequences

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.846-847.1304 ◽

2013 ◽

Vol 846-847 ◽

pp. 1304-1307

Author(s):

Ye Wang ◽

Yan Jia ◽

Lu Min Zhang

Keyword(s):

Sequence Data ◽

Real Data ◽

Partial Orders ◽

Hard Problem ◽

Important Data ◽

Data Set ◽

Pruning Algorithm ◽

Equal Chance ◽

Np Hard Problem ◽

General Sequences

Mining partial orders from sequence data is an important data mining task with broad applications. As partial orders mining is a NP-hard problem, many efficient pruning algorithm have been proposed. In this paper, we improve a classical algorithm of discovering frequent closed partial orders from string. For general sequences, we consider items appearing together having equal chance to calculate the detecting matrix used for pruning. Experimental evaluations from a real data set show that our algorithm can effectively mine FCPO from sequences.

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Convex Bodies, Graphs and Partial Orders

Proceedings of the London Mathematical Society ◽

10.1112/s0024611500012168 ◽

2000 ◽

Vol 80 (2) ◽

pp. 415-450 ◽

Cited By ~ 4

Author(s):

Bela Bollobas ◽

Graham R. Brightwel

Keyword(s):

Convex Bodies ◽

Partial Orders

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True cofinality and bounding number for small products of partial orders

Annals of Pure and Applied Logic ◽

10.1016/s0168-0072(02)00041-6 ◽

2003 ◽

Vol 122 (1-3) ◽

pp. 87-106

Author(s):

Stefan Neumann

Keyword(s):

Partial Orders

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N-ARY OPERATIONS WITH LONG PRE-PERIODS

Asian-European Journal of Mathematics ◽

10.1142/s1793557109000170 ◽

2009 ◽

Vol 02 (02) ◽

pp. 201-212

Author(s):

K. Denecke ◽

Ch. Ratanaprasert

Keyword(s):

Unary Operation ◽

Equivalence Relations ◽

Finite Set

Iterating a unary operation f defined on the finite set A with |A| = k one obtains the descending chain [Formula: see text] The least integer λ(f) with Imfλ(f) = Imfλ(f)+1 is called the pre-period of f. The pre-period of f is an integer between 0 and k - 1. If λ(f) = k - 1 and k ≥ 1, then f is called a long-tailed (LT)-operation and if λ(f) = k - 2 for k ≥ 2, f is said to be an (LT1)-operation. Unary (LT)- and (LT1)-operations and their invariant equivalence relations are characterized in [5]. In [6] these results are extended to partial operations. In this paper we consider the iteration of n-ary operations for n > 1, define and characterize (LT)- and (LT1)- operations and their invariant equivalence relations. The results can be applied in all fields where iteration and recursion plays a role.

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