It is undecidable whether the Knuth-Bendix completion procedure generates a crossed pair

2005 ◽  
pp. 348-359 ◽  
Author(s):  
Paliath Narendran ◽  
Jonathan Stillman
Keyword(s):  
Crossed Pair

scholarly journals On (p,1)-total labelling of plane graphs with independent crossings

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1091-1100 ◽  
Author(s):  
Xin Zhang ◽  
Guizhen Liu ◽  
Yong Yu
Keyword(s):  
Planar Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
Discrete Math ◽  
Plane Graph ◽  
Plane Graphs ◽  
High Maximum ◽  
Crossed Pair ◽  
Large Girth

Two distinct crossings are independent if the end-vertices of the crossed pair of edges are mutually different. If a graph G has a drawing in the plane so that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, it is proved that the (p, 1)-total labelling number of every IC-planar graph G is at most ?(G) + 2p ? 2 provided that ?(G) ? ? and 1(G) ? 1, where (?, 1) ? {(6p + 2, 3), (4p + 2, 4), (2p + 5, 5)}. As a consequence, we generalize and improve some results obtained in [F. Bazzaro, M. Montassier, A. Raspaud, (d, 1)-Total labelling of planar graphs with large girth and high maximum degree, Discrete Math. 307 (2007) 2141-2151].

scholarly journals Idempotent-separating extensions of regular semigroups

2005 ◽  
Vol 2005 (18) ◽  
pp. 2945-2975
Author(s):  
A. Tamilarasi
Keyword(s):  
Automorphism Group ◽  
Regular Semigroup ◽  
Extension Theory ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Compatibility Conditions ◽  
Regular Semigroups ◽  
Biordered Set ◽  
Crossed Pair ◽  
Necessary And Sufficient

For a regular biordered setE, the notion ofE-diagram and the associated regular semigroup was introduced in our previous paper (1995). Given a regular biordered setE, anE-diagram in a categoryCis a collection of objects, indexed by the elements ofEand morphisms ofCsatisfying certain compatibility conditions. With such anE-diagramAwe associate a regular semigroupRegE(A)havingEas its biordered set of idempotents. This regular semigroup is analogous to automorphism group of a group. This paper provides an application ofRegE(A)to the idempotent-separating extensions of regular semigroups. We introduced the concept of crossed pair and used it to describe all extensions of a regular semigroup S by a groupE-diagramA. In this paper, the necessary and sufficient condition for the existence of an extension ofSbyAis provided. Also we study cohomology and obstruction theories and find a relationship with extension theory for regular semigroups.

Microwave Correlation Measurement Crossed-pair Antennas Techniques Diagnosis of Breast Cancer

2007 ◽  
Vol 18 (1) ◽  
Author(s):  
M Mimi ◽  
K Laidi
Keyword(s):  
Breast Cancer ◽  
Correlation Measurement ◽  
Crossed Pair

Electrically Long Dipoles in a Crossed Pair for Closed-Form Estimation of an Incident Source’s Polarization

2019 ◽  
Vol 67 (8) ◽  
pp. 5569-5581 ◽  
Author(s):  
Salman Khan ◽  
Kainam Thomas Wong
Keyword(s):  
Closed Form ◽  
Crossed Pair
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