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Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013, Article ID 439767, 1 pagehttp://dx.doi.org/10.1155/2013/439767
EditorialSymmetries, Differential Equations, andApplications: Galois Bicentenary
Fazal M. Mahomed,1 Asghar Qadir,1,2 and Mehmet Pakdemirli3
1 Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics,University of the Witwatersrand, Wits 2050, South Africa
2 Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Islamabad, Pakistan3 Applied Mathematics and Computation Center, Celal Bayar University, 45040 Manisa, Turkey
Correspondence should be addressed to Fazal M. Mahomed; [email protected]
Received 3 June 2013; Accepted 3 June 2013
Copyright © 2013 Fazal M. Mahomed et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
This special issue commemorated the bicentenary of the birthof Evariste Galois who introduced the notion of a group andmade fundamental contributions to the solution of polyno-mial equations.The formal mathematical concept of symme-try thus came fromGalois theory. Symmetry was inauguratedandutilized in the solution of differential equations by SophusLie in the 1870s. The algebraic approach has thus become ofgreat importance in the theory and applications of differentialequations. There was a recent Conference SDEA2012 on thistopic held in Johannesburg from 23 to 27 January, 2012.SDEA2012 brought together researchers from all over theworld to exchange ideas, share their research findings, andidentify future research directions in symmetry and its mani-fold applications.
We invited the conference participants and researchers inthe field to contribute original research articles and reviewsto this special issue. We received many contributions whichranged from ordinary to partial differential equations as wellas applications.Therewas one review article on geometric lin-earization by one of the editors, Asghar Qadir, which coveredthe state of work in this interesting aspect. The topics of thepapers included the following:
(i) Lie theory in approximate and complex differentialequations,
(ii) Noether symmetries and their extensions,(iii) other methods for first integrals and conservation
laws,
(iv) linearization,(v) classification schemes,(vi) invariant characterization,(vii) stochastic differential equations,(viii) geometrical methods,(ix) computational mathematics,(x) classical mechanics, continuum mechanics, and gen-
eral relativity,(xi) equations of finance,(xii) mathematical modeling in the applied sciences and
engineering.
Acknowledgments
We express our sincere appreciation to the authors for theirvaluable contributions. Also the crucial work of all thereviewers is greatly acknowledged.
Fazal M. MahomedAsghar Qadir
Mehmet Pakdemirli
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