editorial advances in lie groups and applications in...

Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2013 Article ID 178736 2 pageshttpdxdoiorg1011552013178736

EditorialAdvances in Lie Groups and Applications in Applied Sciences

Teoman Oumlzer1 Alexei F Cheviakov2 Shi Weichen3 Nail Migranov4 T Raja Sekhar5 andEmrullah YaGar6

1 Faculty of Civil Engineering Division of Mechanics Istanbul Technical University Maslak 34469 Istanbul Turkey2Department of Mathematics and Statistics University of Saskatchewan McLean Hall 106 Wiggins Road Saskatoon SK Canada3Department of Mechanical Engineering Shanghai Maritime University Haigang Avenue 1550 Shanghai 201306 China4Department of Engineering Physics Bashkir State University 100 Mingazheva Street Ufa Russia5 Department of Mathematics National Institute of Technology Rourkela Rourkela 769008 India6Department of Mathematics Faculty of Science and Letters Uludag University Bursa Turkey

Correspondence should be addressed to Teoman Ozer tozerituedutr

Received 9 December 2013 Accepted 9 December 2013

Copyright copy 2013 Teoman Ozer et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This special issue was planned to focus on most the recentadvances in the applications of Lie groups It covered a widearea of topics in interdisciplinary studies in mathematicsmechanics physics and finance We were particularly inter-ested in receiving novel contributions devoted to Lie groupsin particular applications to specific problems in appliedsciences We aimed to bring together contributions across avariety of applications of Lie groups and invite researchers tosubmit original research andor domain reviews in varioustopics Potential topics included but were not limited tothe following Lie algebras and Lie pseudogroups optimalcontrol topological groups representation theory of Liealgebras differential geometry finance dynamical systemsquantummechanics super-symmetry and superintegrabilityinformation theory Lie theory and symmetry methods indifferential fractal differential integrodifferential and dif-ference equations and further applications in physics andmechanics

From different areas of Lie groups and applications inapplied sciences mentioned above we have received papersabove thirty fromdifferent countries for consideration in thisspecial issue and eighteen papers have been accepted for thisspecial issue The brief descriptions for each of the acceptedpapers are given below

In their study ldquoInvariant operators of five-dimensionalnonconjugate subalgebras of the Lie algebra of the Poincaregroup P(14)rdquo V Fedorchuk and V Fedorchuk classify allfive dimensional nonconjugate subalgebras of the Lie algebra

of the Poincare group P(14) into classes of isomorphicsubalgebras In addition they construct invariant operatorsof the questioned algebras

In their study ldquoConservation laws of three-dimensionalperfect plasticity equations under von Mises yield criterionrdquo byS I Senashov and A Yakhno the authors seek conservationlaws of (1) vonMises plasticity equations in three dimensions(2) the plane stress equations and (3) the plane strainequations In the first case the conservation laws are foundvia Lie point symmetries and the Noetherrsquos theorem Forthe other two systems the approach of Vinogradov andKrasilrsquoshchik is used As a result for the plane stress and theplane strain equations linear homogeneous PDEs satisfied byconservation law fluxes are derived and applications of theobtained conservation laws to complete solution of specificCauchy problems are considered

In the study ldquoAlgebraic structures based on a classifyingspace of a compact Lie grouprdquo D-W Lee studies the algebraicstructures on the classifying space of a compact Lie group andby using the Milnor-Moore theorem he also investigates theconcrete primitive elements in the Pontrjagin algebra

In their study ldquoPost-Lie algebra structures on the Liealgebra gl(2C)rdquo Y Sheng and X Tang give a completeclassification of post-Lie algebra structures on the Lie algebraup to isomorphism

In their study ldquoGroup analysis and new explicit solutionsof simplified modified Kawahara equation with variable coeffi-cientsrdquo GWWang and T Z Xu study the simplifiedmodified

2 Abstract and Applied Analysis

Kawahara equation with variable coefficients by using Liesymmetry method They also present Lie algebra optimalsystem the similarity reduction forms and some invariantsolutions

In their study ldquoThe centroid of a Lie triple algebrardquo X Liuand L Chen completely determine the centroid of the tensorproduct of a simple Lie algebra and polynomial ring

In their study ldquoInfinite-dimensional modular Lie superal-gebraΩrdquo X Xu and B Mu study ad-nilpotent elements of theinfinite-dimensional Lie superalgebra over a field of positivecharacteristic and classify the infinite-dimensional modularLie superalgebra

In their study ldquoReductions and new exact solutions ofZK gardner KP and modified KP equations via generalizeddouble reduction theoremrdquo R Naz et al study Lie symmetriesconservation laws reductions and new exact solutions ofZakharov-Kuznetsov (ZK) Gardner Kadomtsev-Petviashvili(GKP) and Modified Kadomtsev-Petviashvili (MKP) equa-tions

In their study ldquoThe automorphism group of the Lie ring ofreal skew-symmetric matricesrdquo J Xu B Zheng and L Yangstudy and characterize the automorphism group of the Liering

In their study ldquoThe natural filtration of finite dimensionalmodular Lie superalgebras of special typerdquo K Zheng and YZhang investigate the natural filtration of Lie superalgebraS(n m) of special type over a field of prime characteristicThey first construct the modular Lie superalgebra S(n m)and then they prove that the natural filtration of S(n m) isinvariant under its automorphisms

In the study ldquoA kind of infinite-dimensional Novikov alge-bras and its realizationsrdquo L Chen constructs a kind of infinite-dimensional Novikov algebras and presents its realization byhyperbolic sine functions and hyperbolic cosine functions

In the study ldquoA realization of Hom-Lie algebras by Iso-deformed commutator bracketrdquo X Li constructs classicalIso-Lie and Iso-Hom-Lie algebras in by twisted commuta-tor bracket through Iso-deformation and gives their Iso-automorphisms and isotopies

In their study ldquoFirst integrals integrating factors andinvariant solutions of the path equation based on Noether and120582-Symmetriesrdquo G Gun and T Ozer investigate the lambda-symmetry properties classification and the correspondingreduction forms and integrating factors of the path equationIn addition they apply the Jacobi last multiplier method as adifferent approach to determine the new forms of lambda-symmetries

In their study ldquoOn the homomorphisms of the Lie groupsSU(2) and 1198783rdquo F Ozdemir and H Ozekes construct all thehomomorphisms from the Heisenberg group to the 3-sphereBy defining a topology on these homomorphisms they regardthe set of these homomorphisms as a topological spaceNext using the kernels of homomorphisms they definean equivalence relation on this topological space and theyshow that the quotient space is a topological group which isisomorphic to 1198781

In their study ldquoA variational approach to an inhomoge-neous second-order ordinary differential systemrdquo BMuatjetjeja

and C M Khalique study the coupled inhomogeneousLane-Emden system from the Lagrangian formulation Theyclassify the system with respect to a first-order Lagrangianaccording to the Noether point symmetries and then obtainfirst integrals of the various cases

In their study ldquoExact solutions and conservation laws ofa (2 + 1)-dimensional nonlinear KP-BBM equationrdquo K RAdem and C M Khalique investigate the two-dimensionalnonlinear Kadomtsev-Petviashvili-Benjamin-Bona-Mahonyequation They obtain exact solutions and the conservationlaws

In their study ldquoLie group analysis and similarity solutionsfor mixed convection boundary layers in the stagnation-pointflow toward a stretching vertical sheetrdquo S S Chaharborjet al study the mixed convection boundary layers in thestagnation-point flow toward a stretching vertical sheet viasymmetry analysis

In their study ldquoAlgebraic properties of first integrals forscalar linear third-order ODEs of maximal symmetryrdquo K SMahomed and EMomoniat analyze the relationship betweenthe first integrals of the simplest linear third-order ODEsand their point symmetries They show that the maximal Liealgebra of a first integral for the simplest equation 119910101584010158401015840 = 0 isunique and four-dimensional

Acknowledgments

We would like to thank all the authors who sent their studiesand all the referees who spent time in the review process andfor their contributions and efforts to the success of the specialissue

Teoman OzerAlexei F Cheviakov

Shi WeichenNailMigranovT Raja SekharEmrullah Yasar

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Abstract and Applied Analysis

Kawahara equation with variable coefficients by using Liesymmetry method They also present Lie algebra optimalsystem the similarity reduction forms and some invariantsolutions

In their study ldquoThe centroid of a Lie triple algebrardquo X Liuand L Chen completely determine the centroid of the tensorproduct of a simple Lie algebra and polynomial ring

In their study ldquoInfinite-dimensional modular Lie superal-gebraΩrdquo X Xu and B Mu study ad-nilpotent elements of theinfinite-dimensional Lie superalgebra over a field of positivecharacteristic and classify the infinite-dimensional modularLie superalgebra

In their study ldquoReductions and new exact solutions ofZK gardner KP and modified KP equations via generalizeddouble reduction theoremrdquo R Naz et al study Lie symmetriesconservation laws reductions and new exact solutions ofZakharov-Kuznetsov (ZK) Gardner Kadomtsev-Petviashvili(GKP) and Modified Kadomtsev-Petviashvili (MKP) equa-tions

In their study ldquoThe automorphism group of the Lie ring ofreal skew-symmetric matricesrdquo J Xu B Zheng and L Yangstudy and characterize the automorphism group of the Liering

In their study ldquoThe natural filtration of finite dimensionalmodular Lie superalgebras of special typerdquo K Zheng and YZhang investigate the natural filtration of Lie superalgebraS(n m) of special type over a field of prime characteristicThey first construct the modular Lie superalgebra S(n m)and then they prove that the natural filtration of S(n m) isinvariant under its automorphisms

In the study ldquoA kind of infinite-dimensional Novikov alge-bras and its realizationsrdquo L Chen constructs a kind of infinite-dimensional Novikov algebras and presents its realization byhyperbolic sine functions and hyperbolic cosine functions

In the study ldquoA realization of Hom-Lie algebras by Iso-deformed commutator bracketrdquo X Li constructs classicalIso-Lie and Iso-Hom-Lie algebras in by twisted commuta-tor bracket through Iso-deformation and gives their Iso-automorphisms and isotopies

In their study ldquoFirst integrals integrating factors andinvariant solutions of the path equation based on Noether and120582-Symmetriesrdquo G Gun and T Ozer investigate the lambda-symmetry properties classification and the correspondingreduction forms and integrating factors of the path equationIn addition they apply the Jacobi last multiplier method as adifferent approach to determine the new forms of lambda-symmetries

In their study ldquoOn the homomorphisms of the Lie groupsSU(2) and 1198783rdquo F Ozdemir and H Ozekes construct all thehomomorphisms from the Heisenberg group to the 3-sphereBy defining a topology on these homomorphisms they regardthe set of these homomorphisms as a topological spaceNext using the kernels of homomorphisms they definean equivalence relation on this topological space and theyshow that the quotient space is a topological group which isisomorphic to 1198781

In their study ldquoA variational approach to an inhomoge-neous second-order ordinary differential systemrdquo BMuatjetjeja

and C M Khalique study the coupled inhomogeneousLane-Emden system from the Lagrangian formulation Theyclassify the system with respect to a first-order Lagrangianaccording to the Noether point symmetries and then obtainfirst integrals of the various cases

In their study ldquoExact solutions and conservation laws ofa (2 + 1)-dimensional nonlinear KP-BBM equationrdquo K RAdem and C M Khalique investigate the two-dimensionalnonlinear Kadomtsev-Petviashvili-Benjamin-Bona-Mahonyequation They obtain exact solutions and the conservationlaws

In their study ldquoLie group analysis and similarity solutionsfor mixed convection boundary layers in the stagnation-pointflow toward a stretching vertical sheetrdquo S S Chaharborjet al study the mixed convection boundary layers in thestagnation-point flow toward a stretching vertical sheet viasymmetry analysis

In their study ldquoAlgebraic properties of first integrals forscalar linear third-order ODEs of maximal symmetryrdquo K SMahomed and EMomoniat analyze the relationship betweenthe first integrals of the simplest linear third-order ODEsand their point symmetries They show that the maximal Liealgebra of a first integral for the simplest equation 119910101584010158401015840 = 0 isunique and four-dimensional

Acknowledgments

We would like to thank all the authors who sent their studiesand all the referees who spent time in the review process andfor their contributions and efforts to the success of the specialissue

Teoman OzerAlexei F Cheviakov

Shi WeichenNailMigranovT Raja SekharEmrullah Yasar








Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









editorial advances in lie groups and applications in...

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