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Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Transformation semigroup.'
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Journal articles on the topic "Transformation semigroup":
1
Haynes, Tyler. "Thickness in topological transformation semigroups." International Journal of Mathematics and Mathematical Sciences 16, no. 3 (1993): 493–502. http://dx.doi.org/10.1155/s0161171293000602.
This article deals with thickness in topological transformation semigroups (τ-semigroups). Thickness is used to establish conditions guaranteeing an invariant mean on a function space defined on aτ-semigroup if there exists an invariant mean on its functions restricted to a sub-τ-semigroup of the originalτ-semigroup. We sketch earlier results, then give many equivalent conditions for thickness onτ-semigroups, and finally present theorems giving conditions for an invariant mean to exist on a function space.
2
Jude. A., Omelebele, Udoaka O. G., and Udoakpan I. U. "Ranks of Identity Difference Transformation Semigroup." International Journal of Pure Mathematics 9 (March 30, 2022): 49–54. http://dx.doi.org/10.46300/91019.2022.9.10.
This study focuses on the ranks of identity difference transformation semigroup. The ideals of all the (sub) semigroups; identity difference full transformation semigroup (IDT_n), identity difference order preserving transformation semigroup, (IDO_n), identity difference symmetric inverse transformation semigroup( IDI_n), identity difference partial order preserving symmetric inverse transformation semigroup( IDPOI_n) and identity difference partial order preserving transformation semigroup ( IDPO_n) were investigated for rank and their combinatorial results obtained respectively.
3
Nenthein, S., and Y. Kemprasit. "On transformation semigroups which areℬ𝒬-semigroups." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–10. http://dx.doi.org/10.1155/ijmms/2006/12757.
A semigroup whose bi-ideals and quasi-ideals coincide is called aℬ𝒬-semigroup. The full transformation semigroup on a setXand the semigroup of all linear transformations of a vector spaceVover a fieldFinto itself are denoted, respectively, byT(X)andLF(V). It is known that every regular semigroup is aℬ𝒬-semigroup. Then bothT(X)andLF(V)areℬ𝒬-semigroups. In 1966, Magill introduced and studied the subsemigroupT¯(X,Y)ofT(X), where∅≠Y⊆XandT¯(X,Y)={α∈T(X,Y)|Yα⊆Y}. IfWis a subspace ofV, the subsemigroupL¯F(V,W)ofLF(V)will be defined analogously. In this paper, it is shown thatT¯(X,Y)is aℬ𝒬-semigroup if and only ifY=X,|Y|=1, or|X|≤3, andL¯F(V,W)is aℬ𝒬-semigroup if and only if (i)W=V, (ii)W={0}, or (iii)F=ℤ2,dimFV=2, anddimFW=1.
4
Dimitrova, I., and J. Koppitz. "ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS." Asian-European Journal of Mathematics 01, no. 02 (June 2008): 189–202. http://dx.doi.org/10.1142/s1793557108000187.
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.
5
Shirazi, Zadeh, and Nasser Golestani. "On classifications of transformation semigroups: Indicator sequences and indicator topological spaces." Filomat 26, no. 2 (2012): 313–29. http://dx.doi.org/10.2298/fil1202313s.
In this paper considering a transformation semigroup with finite height we define the notion of indicator sequence in such a way that any two transformation semigroups with the same indicator sequence have the same height. Also related to any transformation semigroup a topological space, called indicator topological space, is defined in such a way that transformation semigroups with homeomorphic indicator topological spaces have the same height. Moreover any two transformation semigroups with homeomorphic indicator topological spaces and finite height have the same indicator sequences.
6
Rakbud, Jittisak, and Malinee Chaiya. "Regularity of Semigroups of Transformations Whose Characters Form the Semigroup of a Δ -Structure." International Journal of Mathematics and Mathematical Sciences 2020 (December 27, 2020): 1–7. http://dx.doi.org/10.1155/2020/8872391.
In this paper, we make use of the notion of the character of a transformation on a fixed set X , provided by Purisang and Rakbud in 2016, and the notion of a Δ -structure on X , provided by Magill Jr. and Subbiah in 1974, to define a sub-semigroup of the full-transformation semigroup T X . We also define a sub-semigroup of that semigroup. The regularity of those two semigroups is also studied.
7
SINGHA, BOORAPA, JINTANA SANWONG, and R. P. SULLIVAN. "PARTIAL ORDERS ON PARTIAL BAER–LEVI SEMIGROUPS." Bulletin of the Australian Mathematical Society 81, no. 2 (January 26, 2010): 195–207. http://dx.doi.org/10.1017/s0004972709001038.
AbstractMarques-Smith and Sullivan [‘Partial orders on transformation semigroups’, Monatsh. Math.140 (2003), 103–118] studied various properties of two partial orders on P(X), the semigroup (under composition) consisting of all partial transformations of an arbitrary set X. One partial order was the ‘containment order’: namely, if α,β∈P(X) then α⊆β means xα=xβ for all x∈dom α, the domain of α. The other order was the so-called ‘natural order’ defined by Mitsch [‘A natural partial order for semigroups’, Proc. Amer. Math. Soc.97(3) (1986), 384–388] for any semigroup. In this paper, we consider these and other orders defined on the symmetric inverse semigroup I(X) and the partial Baer–Levi semigroup PS(q). We show that there are surprising differences between the orders on these semigroups, concerned with their compatibility with respect to composition and the existence of maximal and minimal elements.
8
Konieczny, Janusz. "A new definition of conjugacy for semigroups." Journal of Algebra and Its Applications 17, no. 02 (January 23, 2018): 1850032. http://dx.doi.org/10.1142/s0219498818500329.
The conjugacy relation plays an important role in group theory. If [Formula: see text] and [Formula: see text] are elements of a group [Formula: see text], [Formula: see text] is conjugate to [Formula: see text] if [Formula: see text] for some [Formula: see text]. The group conjugacy extends to inverse semigroups in a natural way: for [Formula: see text] and [Formula: see text] in an inverse semigroup [Formula: see text], [Formula: see text] is conjugate to [Formula: see text] if [Formula: see text] and [Formula: see text] for some [Formula: see text]. In this paper, we define a conjugacy for an arbitrary semigroup [Formula: see text] that reduces to the inverse semigroup conjugacy if [Formula: see text] is an inverse semigroup. (None of the existing notions of conjugacy for semigroups has this property.) We compare our new notion of conjugacy with existing definitions, characterize the conjugacy in basic transformation semigroups and their ideals using the representation of transformations as directed graphs, and determine the number of conjugacy classes in these semigroups.
9
Luangchaisri, Panuwat, Thawhat Changphas, and Chalida Phanlert. "Left (right) magnifying elements of a partial transformation semigroup." Asian-European Journal of Mathematics 13, no. 01 (August 3, 2018): 2050016. http://dx.doi.org/10.1142/s1793557120500163.
An element [Formula: see text] of a semigroup [Formula: see text] is a called a left (respectively right) magnifying element of [Formula: see text] if [Formula: see text] (respectively [Formula: see text]) for some proper subset [Formula: see text] of [Formula: see text]. In this paper, left magnifying elements and right magnifying elements of a partial transformation semigroup will be characterized. The results obtained generalize the results of Magill [K. D. Magill, Magnifying elements of transformation semigroups, Semigroup Forum, 48 (1994) 119–126].
10
Marques-Smith, M. Paula O., and R. P. Sullivan. "The ideal structure of nilpotent-generated transformation semigroups." Bulletin of the Australian Mathematical Society 60, no. 2 (October 1999): 303–18. http://dx.doi.org/10.1017/s0004972700036418.
In 1987 Sullivan determined the elements of the semigroup N(X) generated by all nilpotent partial transformations of an infinite set X; and later in 1997 he studied subsemigroups of N(X) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X. We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.
A semigroup is simply a set with an associative binary operation; computational semigroup theory is the branch of mathematics concerned with developing techniques for computing with semigroups, as well as investigating semigroups with the help of computers. This thesis explores both sides of computational semigroup theory, across several topics, especially in the finite case. The central focus of this thesis is computing and describing maximal subsemigroups of finite semigroups. A maximal subsemigroup of a semigroup is a proper subsemigroup that is contained in no other proper subsemigroup. We present novel and useful algorithms for computing the maximal subsemigroups of an arbitrary finite semigroup, building on the paper of Graham, Graham, and Rhodes from 1968. In certain cases, the algorithms reduce to computing maximal subgroups of finite groups, and analysing graphs that capture information about the regular I-classes of a semigroup. We use the framework underpinning these algorithms to describe the maximal subsemigroups of many families of finite transformation and diagram monoids. This reproduces and greatly extends a large amount of existing work in the literature, and allows us to easily see the common features between these maximal subsemigroups. This thesis is also concerned with direct products of semigroups, and with a special class of semigroups known as Rees 0-matrix semigroups. We extend known results concerning the generating sets of direct products of semigroups; in doing so, we propose techniques for computing relatively small generating sets for certain kinds of direct products. Additionally, we characterise several features of Rees 0-matrix semigroups in terms of their underlying semigroups and matrices, such as their Green's relations and generating sets, and whether they are inverse. In doing so, we suggest new methods for computing Rees 0-matrix semigroups.
2
East, James Phillip Hinton. "On Monoids Related to Braid Groups and Transformation Semigroups." School of Mathematics and Statistics, 2006. http://hdl.handle.net/2123/2438.
East, James Phillip Hinton. "On Monoids Related to Braid Groups and Transformation Semigroups." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/2438.
We consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a finitely generated subsemigroup of S? If so, what is the least number n such that for every countable subset F of S there exist n elements of S that generate a subsemigroup of S containing F as a subset. (ii) Given a subset U of S, what is the least cardinality of a subset A of S such that the union of A and U is a generating set for S? (iii) Define a preorder relation ≤ on the subsets of S as follows. For subsets V and W of S write V ≤ W if there exists a countable subset C of S such that V is contained in the semigroup generated by the union of W and C. Given a subset U of S, where does U lie in the preorder ≤ on subsets of S? Semigroups S for which we answer question (i) include: the semigroups of the injec- tive functions and the surjective functions on a countably infinite set; the semigroups of the increasing functions, the Lebesgue measurable functions, and the differentiable functions on the closed unit interval [0, 1]; and the endomorphism semigroup of the random graph. We investigate questions (ii) and (iii) in the case where S is the semigroup Ω[superscript Ω] of all functions on a countably infinite set Ω. Subsets U of Ω[superscript Ω] under consideration are semigroups of Lipschitz functions on Ω with respect to discrete metrics on Ω and semigroups of endomorphisms of binary relations on Ω such as graphs or preorders.
5
Umar, Abdullahi. "Semigroups of order-decreasing transformations." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/2834.
Let X be a totally ordered set and consider the semigroups of orderdecreasing (increasing) full (partial, partial one-to-one) transformations of X. In this Thesis the study of order-increasing full (partial, partial one-to-one) transformations has been reduced to that of order-decreasing full (partial, partial one-to-one) transformations and the study of order-decreasing partial transformations to that of order-decreasing full transformations for both the finite and infinite cases. For the finite order-decreasing full (partial one-to-one) transformation semigroups, we obtain results analogous to Howie (1971) and Howie and McFadden (1990) concerning products of idempotents (quasi-idempotents), and concerning combinatorial and rank properties. By contrast with the semigroups of order-preserving transformations and the full transformation semigroup, the semigroups of orderdecreasing full (partial one-to-one) transformations and their Rees quotient semigroups are not regular. They are, however, abundant (type A) semigroups in the sense of Fountain (1982,1979). An explicit characterisation of the minimum semilattice congruence on the finite semigroups of order-decreasing transformations and their Rees quotient semigroups is obtained. If X is an infinite chain then the semigroup S of order-decreasing full transformations need not be abundant. A necessary and sufficient condition on X is obtained for S to be abundant. By contrast, for every chain X the semigroup of order-decreasing partial one-to-one transformations is type A. The ranks of the nilpotent subsemigroups of the finite semigroups of orderdecreasing full (partial one-to-one) transformations have been investigated.
6
Jacques, Matthew. "Composition sequences and semigroups of Möbius transformations." Thesis, Open University, 2016. http://oro.open.ac.uk/48415/.
Motivated by the theory of Kleinian groups and by the theory of continued fractions, we study semigroups of Möbius transformations. Like Kleinian groups, semigroups have limit sets, and indeed each semigroup is equipped with two limit sets. We find that limit sets have an internal structure with features similar to the limit sets of Kleinian groups and the Julia sets of iterates of analytic functions. We introduce the notion of a semidiscrete semigroup, and find that this property is akin to the discreteness property for groups. We study semigroups of Möbius transformations that fix the unit disc, and lay the foundations of a theory for such semigroups. We consider the composition sequences generated by such semigroups, and show that every such composition sequence converges pointwise in the open unit disc to a constant function whenever the identity element does not lie in the closure of the semigroup. We establish various results that have counterparts in the theory of Fuchsian groups. For example we show that aside from a certain exceptional family, any finitely-generated semigroup S is semidiscrete precisely when every two-generator semigroup contained in S is semidiscrete. We show that the limit sets of a nonelementary finitely-generated semidiscrete semigroup are equal (and non-trivial) precisely when the semigroup is a group. We classify two-generator semidiscrete semigroups, and give the basis for an algorithm that decides whether any two-generator semigroup is semidiscrete. We go on to study finitely-generated semigroups of Möbius transformations that map the unit disc strictly within itself. Every composition sequence generated by such a semigroup converges pointwise in the open unit disc to a constant function. We give conditions that determine whether this convergence is uniform on the closed unit disc, and show that the cases where convergence is not uniform are very special indeed.
7
Garba, Goje Uba. "Idempotents, nilpotents, rank and order in finite transformation semigroups." Thesis, University of St Andrews, 1992. http://hdl.handle.net/10023/13703.
Жуковська, Тетяна Григорівна, and Tetiana H. Zhukovska. "Напівгрупи перетворень булеану пов’язані з відношенням включення." Thesis, Інститут математики НАН України, 2008. http://esnuir.eenu.edu.ua/handle/123456789/1512.
Жуковська Тетяна Григорівна - старший викладач кафедри геометрії і алгебри Східноєвропейського національного університету імені Лесі Українки Напівгрупи перетворень булеану пов’язані з відношенням включення були розглянуті в доповіді. The transformations semigroup of the boolean related to the relation of the inclusion were considered in the report.
9
Morris, Owen Christopher. "On a class of one-parameter operator semigroups with state space Rn x Zm generated by pseudo-differential operators." Thesis, Swansea University, 2013. https://cronfa.swan.ac.uk/Record/cronfa42779.
The thesis shows that, under suitable conditions, a pseudo-differential operator, defined on some "nice" set of functions on Rn x Zm, with continuous negative definite symbol q(x,xi,o) extends to a generator of a Feller semigroup. Sections 1-5 are the preliminary sections, these sections discuss some harmonic analysis concerning locally compact Abelian groups. The essence of this thesis are Sections 6-13, which deals with obtaining the estimates required for the fulfilment of the conditions of the Hille-Yosida-Ray theorem.
10
Brown, Thomas John. "The theory of integrated empathies." Pretoria : [s.n.], 2005. http://upetd.up.ac.za/thesis/available/etd-08242006-120817.
Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. Providence, Rhode Island: American Mathematical Society, 2016.
Jentsch, Peter C., and Chrystopher L. Nehaniv. "Exploring Tetris as a Transformation Semigroup." In Springer Proceedings in Mathematics & Statistics, 71–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63591-6_7.
Farahbakhsh, Isaiah, and Chrystopher L. Nehaniv. "Spatial Iterated Prisoner’s Dilemma as a Transformation Semigroup." In Springer Proceedings in Mathematics & Statistics, 47–57. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63591-6_5.
Magill, K. D. "The Countability Indices of Certain Transformation Semigroups." In Semigroups and Their Applications, 91–97. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-3839-7_12.
Beaudry, Martin. "Testing membership in commutative transformation semigroups." In Automata, Languages and Programming, 542–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-18088-5_47.
Tiwari, S. P., and Shambhu Sharan. "On Coverings of Rough Transformation Semigroups." In Lecture Notes in Computer Science, 79–86. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21881-1_14.
Fleischer, Lukas, and Manfred Kufleitner. "Green’s Relations in Finite Transformation Semigroups." In Computer Science – Theory and Applications, 112–25. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58747-9_12.
Conference papers on the topic "Transformation semigroup":
1
Trendafilov, Ivan D., and Dimitrinka I. Vladeva. "On some semigroups of the partial transformation semigroup." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12): Proceedings of the 38th International Conference Applications of Mathematics in Engineering and Economics. AIP, 2012. http://dx.doi.org/10.1063/1.4766807.
Li, Xiang. "Isomorphisms of Maximal Subsemigroups of D-classes of Finite Full Transformation Semigroup." In Proceedings of the 2018 3rd International Conference on Communications, Information Management and Network Security (CIMNS 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/cimns-18.2018.34.
MENDES-GONÇALVES, SUZANA. "ISOMORPHISM PROBLEMS FOR TRANSFORMATION SEMIGROUPS." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708700_0015.
SULLIVAN, R. P. "TRANSFORMATION SEMIGROUPS: PAST, PRESENT AND FUTURE." In Proceedings of the International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792310_0016.
FERNANDES, VíTOR H. "PRESENTATIONS FOR SOME MONOIDS OF PARTIAL TRANSFORMATIONS ON A FINITE CHAIN: A SURVEY." In Semigroups, Algorithms, Automata and Languages. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776884_0015.
Mora, W., and Y. Kemprasit. "Regular Elements of Generalized Order-Preserving Transformation Semigroups." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0033.
ANANICHEV, D. S., and M. V. VOLKOV. "SOME RESULTS ON ČERNÝ TYPE PROBLEMS FOR TRANSFORMATION SEMIGROUPS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702616_0002.
Muradov, Firudin Kh. "Ternary semigroups of topological transformations of open sets of finite-dimensional Euclidean spaces." In FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042197.
Muradov, Firudin Kh. "On the ternary semigroups of homeomorphic transformations of bounded closed sets with nonempty interior of finite-dimensional Euclidean spaces." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040311.
