2024-03-28T08:25:46Zhttps://research-repository.st-andrews.ac.uk/oai/requestoai:research-repository.st-andrews.ac.uk:10023/33412023-04-18T09:47:16Zcom_10023_196com_10023_39com_10023_28com_10023_94com_10023_879com_10023_878col_10023_197col_10023_859col_10023_98col_10023_880
2013-02-07T12:34:47Z
urn:hdl:10023/3341
On disjoint unions of finitely many copies of the free monogenic semigroup
Abughazalah, Nabilah
Ruskuc, Nik
EPSRC
University of St Andrews. School of Mathematics and Statistics
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
QA Mathematics
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
2013-02-07T12:34:47Z
2013-02-07T12:34:47Z
2013-08
Journal article
Abughazalah , N & Ruskuc , N 2013 , ' On disjoint unions of finitely many copies of the free monogenic semigroup ' , Semigroup Forum , vol. 87 , no. 1 , pp. 243-256 . https://doi.org/10.1007/s00233-013-9468-9
0037-1912
PURE: 43731800
PURE UUID: d41e01b6-9344-42e3-91dc-d90bbf07eea1
Scopus: 84880642170
ORCID: /0000-0003-2415-9334/work/73702028
http://hdl.handle.net/10023/3341
https://doi.org/10.1007/s00233-013-9468-9
EP/I032282/1
eng
Semigroup Forum
This is an author version of this article. The final publication will be available at www.springerlink.com
oai:research-repository.st-andrews.ac.uk:10023/170722024-02-15T00:46:30Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2019-02-15T00:34:30Z
urn:hdl:10023/17072
Computing maximal subsemigroups of a finite semigroup
Donoven, C. R.
Mitchell, J. D.
Wilson, W. A.
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
Algorithms
Computational group theory
Computational semigroup theory
Maximal subsemigroups
QA Mathematics
Algebra and Number Theory
DAS
The third author wishes to acknowledge the support of his Carnegie Ph.D. Scholarship from the Carnegie Trust for the Universities of Scotland.
A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes. Determining which of these forms arise in a given finite semigroup is difficult, and no practical mechanism for doing so appears in the literature. We present an algorithm for computing the maximal subsemigroups of a finite semigroup S given knowledge of the Green's structure of S, and the ability to determine maximal subgroups of certain subgroups of S, namely its group H-classes. In the case of a finite semigroup S represented by a generating set X, in many examples, if it is practical to compute the Green's structure of S from X, then it is also practical to find the maximal subsemigroups of S using the algorithm we present. In such examples, the time taken to determine the Green's structure of S is comparable to that taken to find the maximal subsemigroups. The generating set X for S may consist, for example, of transformations, or partial permutations, of a finite set, or of matrices over a semiring. Algorithms for computing the Green's structure of S from X include the Froidure–Pin Algorithm, and an algorithm of the second author based on the Schreier–Sims algorithm for permutation groups. The worst case complexity of these algorithms is polynomial in |S|, which for, say, transformation semigroups is exponential in the number of points on which they act. Certain aspects of the problem of finding maximal subsemigroups reduce to other well-known computational problems, such as finding all maximal cliques in a graph and computing the maximal subgroups in a group. The algorithm presented comprises two parts. One part relates to computing the maximal subsemigroups of a special class of semigroups, known as Rees 0-matrix semigroups. The other part involves a careful analysis of certain graphs associated to the semigroup S, which, roughly speaking, capture the essential information about the action of S on its J-classes.
2019-02-15T00:34:30Z
2019-02-15T00:34:30Z
2018-07-01
2019-02-15
Journal article
Donoven , C R , Mitchell , J D & Wilson , W A 2018 , ' Computing maximal subsemigroups of a finite semigroup ' , Journal of Algebra , vol. 505 , pp. 559-596 . https://doi.org/10.1016/j.jalgebra.2018.01.044
0021-8693
ArXiv: http://arxiv.org/abs/1606.05583v1
ORCID: /0000-0002-5489-1617/work/73700795
ORCID: /0000-0002-3382-9603/work/85855348
https://hdl.handle.net/10023/17072
10.1016/j.jalgebra.2018.01.044
https://arxiv.org/abs/1606.05583v4
eng
Journal of Algebra
oai:research-repository.st-andrews.ac.uk:10023/84232023-04-18T10:07:24Zcom_10023_92com_10023_28com_10023_94com_10023_879com_10023_878col_10023_96col_10023_98col_10023_880
2016-03-16T12:30:03Z
urn:hdl:10023/8423
Effects of thermal conduction and compressive viscosity on the period ratio of the slow mode
Macnamara, Cicely Krystyna
Roberts, Bernard
PPARC - Now STFC
University of St Andrews. Applied Mathematics
University of St Andrews. Pure Mathematics
Sun: corona
Sun: oscillations
QB Astronomy
QC Physics
C.K.M. acknowledges financial support from the CarnegieTrust. Discussions with Dr. I. De Moortel and Prof. A. W. Hood are gratefully acknowledged
Aims: Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P2, between the period P1 of the fundamental mode and the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods: We consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. Results: For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. Conclusions: Damping typically has a small effect on the period ratio, suggesting that longitudinal structuring remains the most significant effect.
2016-03-16T12:30:03Z
2016-03-16T12:30:03Z
2010-06
Journal article
Macnamara , C K & Roberts , B 2010 , ' Effects of thermal conduction and compressive viscosity on the period ratio of the slow mode ' , Astronomy & Astrophysics , vol. 515 , A41 . https://doi.org/10.1051/0004-6361/200913409
0004-6361
PURE: 241566046
PURE UUID: 7b2d0981-a5ba-487d-8cbc-459360f156ff
Scopus: 77953277125
ORCID: /0000-0003-4961-6052/work/27162491
http://hdl.handle.net/10023/8423
https://doi.org/10.1051/0004-6361/200913409
PP/E001122/1
eng
Astronomy & Astrophysics
© 2010, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.aanda.org / https://dx.doi.org/10.1051/0004-6361/200913409
oai:research-repository.st-andrews.ac.uk:10023/171102024-02-17T00:42:18Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2019-02-21T00:33:45Z
urn:hdl:10023/17110
Maximal subsemigroups of finite transformation and diagram monoids
East, James
Kumar, Jitender
Mitchell, James D.
Wilson, Wilf A.
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
Maximal subsemigroups
Transformation semigroup
Diagram monoid
Permutation groups
Maximal subgroups
Graph
Maximal independent set
Partition monoid
QA Mathematics
T-NDAS
The first author gratefully acknowledges the support of the Glasgow Learning, Teaching, and Research Fund in partially funding his visit to the third author in July, 2014. The second author wishes to acknowledge the support of research initiation grant [0076|2016] provided by BITS Pilani, Pilani. The fourth author wishes to acknowledge the support of his Carnegie Ph.D. Scholarship from the Carnegie Trust for the Universities of Scotland.
We describe and count the maximal subsemigroups of many well-known transformation monoids, and diagram monoids, using a new unified framework that allows the treatment of several classes of monoids simultaneously. The problem of determining the maximal subsemigroups of a finite monoid of transformations has been extensively studied in the literature. To our knowledge, every existing result in the literature is a special case of the approach we present. In particular, our technique can be used to determine the maximal subsemigroups of the full spectrum of monoids of order- or orientation-preserving transformations and partial permutations considered by I. Dimitrova, V. H. Fernandes, and co-authors. We only present details for the transformation monoids whose maximal subsemigroups were not previously known; and for certain diagram monoids, such as the partition, Brauer, Jones, and Motzkin monoids. The technique we present is based on a specialised version of an algorithm for determining the maximal subsemigroups of any finite semigroup, developed by the third and fourth authors, and available in the Semigroups package for GAP, an open source computer algebra system. This allows us to concisely present the descriptions of the maximal subsemigroups, and to clearly see their common features.
2019-02-21T00:33:45Z
2019-02-21T00:33:45Z
2018-06-15
2019-02-21
Journal article
East , J , Kumar , J , Mitchell , J D & Wilson , W A 2018 , ' Maximal subsemigroups of finite transformation and diagram monoids ' , Journal of Algebra , vol. 504 , pp. 176-216 . https://doi.org/10.1016/j.jalgebra.2018.01.048
0021-8693
RIS: urn:51F957BCA043BD3D49090344FAA7E948
ORCID: /0000-0002-5489-1617/work/73700794
ORCID: /0000-0002-3382-9603/work/85855347
https://hdl.handle.net/10023/17110
10.1016/j.jalgebra.2018.01.048
eng
Journal of Algebra
oai:research-repository.st-andrews.ac.uk:10023/57932023-04-18T09:45:45Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2014-11-19T10:01:06Z
urn:hdl:10023/5793
Maximal subsemigroups of the semigroup of all mappings on an infinite set
East, J.
Mitchell, James David
Péresse, Y.
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
QA Mathematics
T-NDAS
BDC
R2C
In this paper we classify the maximal subsemigroups of the full transformation semigroup ΩΩ, which consists of all mappings on the infinite set Ω, containing certain subgroups of the symmetric group Sym (Ω) on Ω. In 1965 Gavrilov showed that there are five maximal subsemigroups of ΩΩ containing Sym (Ω) when Ω is countable, and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality. We classify the maximal subsemigroups of ΩΩ on a set Ω of arbitrary infinite cardinality containing one of the following subgroups of Sym (Ω): the pointwise stabiliser of a non-empty finite subset of Ω, the stabiliser of an ultrafilter on Ω, or the stabiliser of a partition of Ω into finitely many subsets of equal cardinality. If G is any of these subgroups, then we deduce a characterisation of the mappings f, g ∈ ΩΩ such that the semigroup generated by G ∪ {f, g} equals ΩΩ.
2014-11-19T10:01:06Z
2014-11-19T10:01:06Z
2015-03-01
Journal article
East , J , Mitchell , J D & Péresse , Y 2015 , ' Maximal subsemigroups of the semigroup of all mappings on an infinite set ' , Transactions of the American Mathematical Society , vol. 367 , no. 3 , pp. 1911-1944 . https://doi.org/10.1090/S0002-9947-2014-06110-2
0002-9947
PURE: 23107193
PURE UUID: d622aa4b-0740-4abc-883a-339349d48c2d
ArXiv: http://arxiv.org/abs/1104.2011v2
Scopus: 84916620178
ORCID: /0000-0002-5489-1617/work/73700777
WOS: 000351857000014
http://hdl.handle.net/10023/5793
https://doi.org/10.1090/S0002-9947-2014-06110-2
eng
Transactions of the American Mathematical Society
© 2014. American Mathematical Society. First published in Transactions of the American Mathematical Society 2014.
oai:research-repository.st-andrews.ac.uk:10023/152142022-07-08T10:30:01Zcom_10023_94com_10023_28com_10023_879com_10023_878col_10023_98col_10023_880
2018-07-10T23:33:02Z
urn:hdl:10023/15214
Equilibrium states, pressure and escape for multimodal maps with holes
Demers, Mark F.
Todd, Mike
University of St Andrews. Pure Mathematics
QA Mathematics
T-NDAS
BDC
R2C
MD was partially supported by NSF grants DMS 1101572 and DMS 1362420. MT was partially supported by NSF grants DMS 0606343 and DMS 0908093.
For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant measures and equilibrium states and prove a relation between the rate of escape and pressure with respect to these potentials. As a consequence, we obtain a Bowen formula: we express the Hausdorff dimension of the set of points which never exit through the hole in terms of the relevant pressure function. Finally, we obtain an expression for the derivative of the escape rate in the zero-hole limit.
2018-07-10T23:33:02Z
2018-07-10T23:33:02Z
2017-09
2018-07-11
Journal article
Demers , M F & Todd , M 2017 , ' Equilibrium states, pressure and escape for multimodal maps with holes ' , Israel Journal of Mathematics , vol. 221 , no. 1 , pp. 367-424 . https://doi.org/10.1007/s11856-017-1547-2
0021-2172
PURE: 12702692
PURE UUID: 750bb93c-2ed9-43ed-aba6-a0873cb1c373
Scopus: 85023194658
ORCID: /0000-0002-0042-0713/work/54181517
WOS: 000411583200012
http://hdl.handle.net/10023/15214
https://doi.org/10.1007/s11856-017-1547-2
eng
Israel Journal of Mathematics
© Hebrew University of Jerusalem 2017. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1007/s11856-017-1547-2
oai:research-repository.st-andrews.ac.uk:10023/21312023-04-18T09:42:52Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2011-12-23T11:08:36Z
urn:hdl:10023/2131
Generators and relations for subsemigroups via boundaries in Cayley graphs
Gray, R
Ruskuc, Nik
EPSRC
EPSRC
EPSRC
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
Semigroup
Generators
Presentations
Cayley graph
Subsemigroup
Reidemeister-Schreier rewriting
QA Mathematics
Given a finitely generated semigroup S and subsemigroup T of S we define the notion of the boundary of T in S which, intuitively, describes the position of T inside the left and right Cayley graphs of S. We prove that if S is finitely generated and T has a finite boundary in S then T is finitely generated. We also prove that if S is finitely presented and T has a finite boundary in S then T is finitely presented. Several corollaries and examples are given.
2011-12-23T11:08:36Z
2011-12-23T11:08:36Z
2011-11
Journal article
Gray , R & Ruskuc , N 2011 , ' Generators and relations for subsemigroups via boundaries in Cayley graphs ' , Journal of Pure and Applied Algebra , vol. 215 , no. 11 , pp. 2761-2779 . https://doi.org/10.1016/j.jpaa.2011.03.017
0022-4049
PURE: 5158279
PURE UUID: ab2695c1-8bc5-44a7-9e4f-a46efd512876
Scopus: 79956008214
ORCID: /0000-0003-2415-9334/work/73702072
http://hdl.handle.net/10023/2131
https://doi.org/10.1016/j.jpaa.2011.03.017
EP/C523229/1
EP/E043194/1
EP/H011978/1
eng
Journal of Pure and Applied Algebra
This is an author version of this article. The definitive version (c) 2011 Elsevier B.V. is available from www.sciencedirect.com
oai:research-repository.st-andrews.ac.uk:10023/21372023-04-18T09:42:57Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2011-12-23T13:08:41Z
urn:hdl:10023/2137
Growth rates for subclasses of Av(321)
Albert, M.H.
Atkinson, M.D.
Brignall, R
Ruskuc, Nik
Smith, R
West, J
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
QA Mathematics
Pattern classes which avoid 321 and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates.
2011-12-23T13:08:41Z
2011-12-23T13:08:41Z
2010-10-22
Journal article
Albert , M H , Atkinson , M D , Brignall , R , Ruskuc , N , Smith , R & West , J 2010 , ' Growth rates for subclasses of Av(321) ' , Electronic Journal of Combinatorics , vol. 17 , no. 1 , R141 .
1097-1440
PURE: 5162387
PURE UUID: abfae055-4852-434d-9b3d-19bb2ab2c87d
Scopus: 78149431471
ORCID: /0000-0003-2415-9334/work/73702023
http://hdl.handle.net/10023/2137
http://www.combinatorics.org/Volume_17/v17i1toc.html
eng
Electronic Journal of Combinatorics
(c) The authors. Published in the Electronic Journal of Combinatorics at http://www.combinatorics.org/
oai:research-repository.st-andrews.ac.uk:10023/118792023-04-18T23:36:18Zcom_10023_196com_10023_39com_10023_58com_10023_19com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_59col_10023_98col_10023_880
2017-10-18T15:30:13Z
urn:hdl:10023/11879
Two variants of the froidure-pin algorithm for finite semigroups
Jonusas, Julius
Mitchell, J. D.
Pfeiffer, M.
European Commission
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
University of St Andrews. School of Computer Science
Algorithms
Green's relations
Monoids
Semigroups
QA Mathematics
Mathematics(all)
DAS
In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing the structure of a finite semigroup from a generating set. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup. If U is any semigroup, and A is a subset of U, then we denote by <A> the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about <A>, that has been found using the Froidure-Pin Algorithm, to compute the semigroup <A∪B>. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for <A∪B> from that for <A>. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm.
2017-10-18T15:30:13Z
2017-10-18T15:30:13Z
2018-02-08
Journal article
Jonusas , J , Mitchell , J D & Pfeiffer , M 2018 , ' Two variants of the froidure-pin algorithm for finite semigroups ' , Portugaliae Mathematica , vol. 74 , no. 3 , pp. 173-200 . https://doi.org/10.4171/PM/2001
0032-5155
PURE: 249695343
PURE UUID: 3d9792a3-36ee-443b-be0d-ad884fc89944
ArXiv: http://arxiv.org/abs/1704.04084v1
Scopus: 85041706757
ORCID: /0000-0002-9881-4429/work/47356677
ORCID: /0000-0002-5489-1617/work/73700820
WOS: 000427321500002
http://hdl.handle.net/10023/11879
https://doi.org/10.4171/PM/2001
http://arxiv.org/abs/1704.04084v1
676541
eng
Portugaliae Mathematica
© 2017, Portuguese Mathematical Society. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version.
oai:research-repository.st-andrews.ac.uk:10023/52322023-04-18T09:53:11Zcom_10023_92com_10023_28com_10023_94com_10023_792com_10023_39com_10023_879com_10023_878col_10023_96col_10023_98col_10023_795col_10023_880
2014-08-25T15:31:04Z
urn:hdl:10023/5232
The effect of slip length on vortex rebound from a rigid boundary
Sutherland, D.
Macaskill, C.
Dritschel, D.G.
University of St Andrews. University of St Andrews
University of St Andrews. Pure Mathematics
University of St Andrews. Applied Mathematics
University of St Andrews. Marine Alliance for Science & Technology Scotland
University of St Andrews. Scottish Oceans Institute
QC Physics
The problem of a dipole incident normally on a rigid boundary, for moderate to large Reynolds numbers, has recently been treated numerically using a volume penalisation method by Nguyen van yen, Farge, and Schneider [Phys. Rev. Lett.106, 184502 (2011)]. Their results indicate that energy dissipating structures persist in the inviscid limit. They found that the use of penalisation methods intrinsically introduces some slip at the boundary wall, where the slip approaches zero as the Reynolds number goes to infinity, so reducing to the no-slip case in this limit. We study the same problem, for both no-slip and partial slip cases, using compact differences on a Chebyshev grid in the direction normal to the wall and Fourier methods in the direction along the wall. We find that for the no-slip case there is no indication of the persistence of energy dissipating structures in the limit as viscosity approaches zero and that this also holds for any fixed slip length. However, when the slip length is taken to vary inversely with Reynolds number then the results of Nguyen van yen et al. are regained. It therefore appears that the prediction that energy dissipating structures persist in the inviscid limit follows from the two limits of wall slip length going to zero, and viscosity going to zero, not being treated independently in their use of the volume penalisation method.
2014-08-25T15:31:04Z
2014-08-25T15:31:04Z
2013-09-23
Journal article
Sutherland , D , Macaskill , C & Dritschel , D G 2013 , ' The effect of slip length on vortex rebound from a rigid boundary ' , Physics of Fluids , vol. 25 , no. 9 , 093104 . https://doi.org/10.1063/1.4821774
1070-6631
PURE: 143238593
PURE UUID: 345d91b2-3bd8-4a8a-a9b0-19adebe4f74e
Scopus: 84885026819
ORCID: /0000-0001-6489-3395/work/64697799
http://hdl.handle.net/10023/5232
https://doi.org/10.1063/1.4821774
http://www.scopus.com/inward/record.url?eid=2-s2.0-84885026819&partnerID=8YFLogxK
eng
Physics of Fluids
© 2013 AIP Publishing LLC
oai:research-repository.st-andrews.ac.uk:10023/19982023-04-18T09:42:54Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2011-09-02T14:57:54Z
urn:hdl:10023/1998
Presentations of inverse semigroups, their kernels and extensions
Carvalho, C.A.
Gray, R
Ruskuc, Nik
EPSRC
EPSRC
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
Inverse semigroup presentations
Reidemeister-Schreier
Kernel
Finiteness conditions
QA Mathematics
"Part of this work was done while Gray was an EPSRC Postdoctoral Research Fellow at the University of St Andrews, Scotland"
Let S be an inverse semigroup and let π:S→T be a surjective homomorphism with kernel K. We show how to obtain a presentation for K from a presentation for S, and vice versa. We then investigate the relationship between the properties of S, K and T, focusing mainly on finiteness conditions. In particular we consider finite presentability, solubility of the word problem, residual finiteness, and the homological finiteness property FPn. Our results extend several classical results from combinatorial group theory concerning group extensions to inverse semigroups. Examples are also provided that highlight the differences with the special case of groups.
2011-09-02T14:57:54Z
2011-09-02T14:57:54Z
2011-06-01
Journal article
Carvalho , C A , Gray , R & Ruskuc , N 2011 , ' Presentations of inverse semigroups, their kernels and extensions ' , Journal of the Australian Mathematical Society , vol. 90 , no. 3 , pp. 289-316 . https://doi.org/10.1017/S1446788711001297
1446-7887
PURE: 5160166
PURE UUID: f4d51f78-f930-4cb9-b02d-1eb994b2bfa4
Scopus: 84856402640
ORCID: /0000-0003-2415-9334/work/73702058
http://hdl.handle.net/10023/1998
https://doi.org/10.1017/S1446788711001297
EP/E043194/1
EP/H011978/1
eng
Journal of the Australian Mathematical Society
This is an author version of the article. The published version copyright (c) Australian Mathematical Publishing Association Inc. 2011 is available from http://journals.cambridge.org
oai:research-repository.st-andrews.ac.uk:10023/166182023-04-18T23:53:05Zcom_10023_94com_10023_28com_10023_879com_10023_878col_10023_98col_10023_880
2018-12-04T11:30:08Z
urn:hdl:10023/16618
Phases of physics in J.D. Forbes’ Dissertation Sixth for the Encyclopaedia Britannica (1856)
Falconer, Isobel Jessie
University of St Andrews. Pure Mathematics
J.D. Forbes
James David Forbes
Encyclopaedia Britannica
Nineteenth-century science
Natural philosophy
Discipline formation
Associational culture
Scientific discovery
Scientific genius
Intellectual spirit
QC Physics
QH Natural history
History and Philosophy of Science
Mathematics (miscellaneous)
Physics and Astronomy (miscellaneous)
T-NDAS
This paper takes James David Forbes’ Encyclopaedia Britannica entry, Dissertation Sixth, as a lens to examine physics as a cognitive, practical, and social, enterprise. Forbes wrote this survey of eighteenth- and nineteenth-century mathematical and physical sciences, in 1852-6, when British “physics” was at a pivotal point in its history, situated between a discipline identified by its mathematical methods – originating in France - and one identified by its university laboratory institutions. Contemporary encyclopaedias provided a nexus for publishers, the book trade, readers, and men of science, in the formation of physics as a field. Forbes was both a witness, whose account of the progress of physics or natural philosophy can be explored at face value, and an agent, who exploited the opportunity offered by the Encyclopaedia Britannica in the mid nineteenth century to enrol the broadly educated public, and scientific collective, illuminating the connection between the definition of physics and its forms of social practice. Forbes used the terms “physics” and “natural philosophy” interchangeably. He portrayed the field as progressed by the natural genius of great men, who curated the discipline within an associational culture that engendered true intellectual spirit. Although this societal mechanism was becoming ineffective, Forbes did not see university institutions as the way forward. Instead, running counter to his friend William Whewell, he advocated inclusion of the mechanical arts (engineering), and a strictly limited role for mathematics. He revealed tensions when the widely accepted discovery-based historiography conflicted with intellectual and moral worth, reflecting a nineteenth-century concern with spirit that cuts across twentieth-century questions about discipline and field.
2018-12-04T11:30:08Z
2018-12-04T11:30:08Z
2018-12-03
Journal article
Falconer , I J 2018 , ' Phases of physics in J.D. Forbes’ Dissertation Sixth for the Encyclopaedia Britannica (1856) ' , History of Science , vol. OnlineFirst . https://doi.org/10.1177/0073275318811443
0073-2753
PURE: 256188128
PURE UUID: 9f7201fe-4479-4233-8164-87c14dfe74e2
Scopus: 85058821712
ORCID: /0000-0002-7076-9136/work/51470233
WOS: 000625756900003
http://hdl.handle.net/10023/16618
https://doi.org/10.1177/0073275318811443
http://arxiv.org/abs/1810.06063
eng
History of Science
© 2018, the Author(s). This work has been made available online in accordance with the publisher's policies. This is the author created accepted version manuscript following peer review and as such may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1177/0073275318811443
oai:research-repository.st-andrews.ac.uk:10023/19972024-03-24T00:40:25Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2011-09-02T13:27:55Z
urn:hdl:10023/1997
Simple extensions of combinatorial structures
Brignall, R
Ruskuc, Nik
Vatter, V
EPSRC
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
QA Mathematics
An interval in a combinatorial structure R is a set I of points which are related to every point in R \ I in the same way. A structure is simple if it has no proper intervals. Every combinatorial structure can be expressed as an inflation of a simple structure by structures of smaller sizes — this is called the substitution (or modular) decomposition. In this paper we prove several results of the following type: An arbitrary structure S of size n belonging to a class C can be embedded into a simple structure from C by adding at most f (n) elements. We prove such results when C is the class of all tournaments, graphs, permutations, posets, digraphs, oriented graphs and general relational structures containing a relation of arity greater than 2. The function f (n) in these cases is 2, ⌈log2(n + 1)⌉, ⌈(n + 1)/2⌉, ⌈(n + 1)/2⌉, ⌈log4(n + 1)⌉, ⌈log3(n + 1)⌉ and 1, respectively. In each case these bounds are the best possible.
2011-09-02T13:27:55Z
2011-09-02T13:27:55Z
2011-07
Journal article
Brignall , R , Ruskuc , N & Vatter , V 2011 , ' Simple extensions of combinatorial structures ' , Mathematika , vol. 57 , no. 2 , pp. 193-214 . https://doi.org/10.1112/S0025579310001518
0025-5793
ORCID: /0000-0003-2415-9334/work/73702074
https://hdl.handle.net/10023/1997
10.1112/S0025579310001518
GR/S53503/01
eng
Mathematika
oai:research-repository.st-andrews.ac.uk:10023/27602023-04-18T09:42:52Zcom_10023_196com_10023_39com_10023_94com_10023_28com_10023_879com_10023_878col_10023_197col_10023_98col_10023_880
2012-06-13T11:31:01Z
urn:hdl:10023/2760
Green index in semigroups : generators, presentations and automatic structures
Cain, A.J.
Gray, R
Ruskuc, Nik
EPSRC
EPSRC
University of St Andrews. Pure Mathematics
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
Green index
Presentations
Automatic semigroup
Finiteness conditions
QA Mathematics
The Green index of a subsemigroup T of a semigroup S is given by counting strong orbits in the complement S n T under the natural actions of T on S via right and left multiplication. This partitions the complement S nT into T-relative H -classes, in the sense of Wallace, and with each such class there is a naturally associated group called the relative Schützenberger group. If the Rees index ΙS n TΙ is finite, T also has finite Green index in S. If S is a group and T a subgroup then T has finite Green index in S if and only if it has finite group index in S. Thus Green index provides a common generalisation of Rees index and group index. We prove a rewriting theorem which shows how generating sets for S may be used to obtain generating sets for T and the Schützenberger groups, and vice versa. We also give a method for constructing a presentation for S from given presentations of T and the Schützenberger groups. These results are then used to show that several important properties are preserved when passing to finite Green index subsemigroups or extensions, including: finite generation, solubility of the word problem, growth type, automaticity (for subsemigroups), finite presentability (for extensions) and finite Malcev presentability (in the case of group-embeddable semigroups).
2012-06-13T11:31:01Z
2012-06-13T11:31:01Z
2012
Journal article
Cain , A J , Gray , R & Ruskuc , N 2012 , ' Green index in semigroups : generators, presentations and automatic structures ' , Semigroup Forum , vol. Online First . https://doi.org/10.1007/s00233-012-9406-2
0037-1912
PURE: 5158227
PURE UUID: bd48078c-8bad-484a-b52a-288031114e6a
Scopus: 84871329719
ORCID: /0000-0003-2415-9334/work/73702084
http://hdl.handle.net/10023/2760
https://doi.org/10.1007/s00233-012-9406-2
EP/H011978/1
EP/E043194/1
eng
Semigroup Forum
This is an author version of this work. The original publication (c) Springer Science+Business Media, LLC 2012 is available at www.springerlink.com