scholarly journals Maximal subsemigroups of finite transformation and diagram monoids

2018 ◽  
Vol 504 ◽  
pp. 176-216 ◽  
Author(s):  
James East ◽  
Jitender Kumar ◽  
James D. Mitchell ◽  
Wilf A. Wilson
Keyword(s):  
Maximal Subsemigroups ◽  
Finite Transformation

ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

2008 ◽  
Vol 01 (02) ◽  
pp. 189-202 ◽  
Author(s):  
I. Dimitrova ◽  
J. Koppitz
Keyword(s):  
Transformation Semigroups ◽  
Maximal Subsemigroups ◽  
Element Set

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.

scholarly journals Nonlocal Symmetry and Bäcklund Transformation of a Negative-Order Korteweg–de Vries Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jinxi Fei ◽  
Weiping Cao ◽  
Zhengyi Ma
Keyword(s):  
Vries Equation ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Nonlocal Symmetry ◽  
Linear Superposition ◽  
Residual Symmetry ◽  
Negative Order ◽  
De Vries ◽  
Finite Transformation ◽  
New Variables

The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By using Lie’s first theorem, we obtain the finite transformation for the localized residual symmetry. Furthermore, we localize the linear superposition of multiple residual symmetries and construct n-th Bäcklund transformation for this nKdV equation in the form of the determinants.

scholarly journals Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Man Jia
Keyword(s):  
Symmetry Reduction ◽  
Symmetry Analysis ◽  
Bäcklund Transformations ◽  
Cnoidal Waves ◽  
Nonlocal Symmetries ◽  
Interaction Solutions ◽  
Backlund Transformations ◽  
Akns System ◽  
Finite Transformation ◽  
Truncated Painlevé Expansion

An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.

Maximal subsemigroups of some semigroups of order-preserving mappings on a countably infinite set

2017 ◽  
Vol 29 (4) ◽  
Author(s):  
Tiwadee Musunthia ◽  
Jörg Koppitz
Keyword(s):  
Natural Numbers ◽  
Maximal Subsemigroups ◽  
Countably Infinite ◽  
Infinite Set

AbstractIn this paper, we study the maximal subsemigroups of several semigroups of order-preserving transformations on the natural numbers and the integers, respectively. We determine all maximal subsemigroups of the monoid of all order-preserving injections on the set of natural numbers as well as on the set of integers. Further, we give all maximal subsemigroups of the monoid of all bijections on the integers. For the monoid of all order-preserving transformations on the natural numbers, we classify also all its maximal subsemigroups, containing a particular set of transformations.

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