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One-parameter Lie group

4. Analytical similarity solution of non-linear equation using one-parameter infinitesimal Lie group of transformation

4. Analytical similarity solution of non-linear equation using one-parameter infinitesimal Lie group of transformation

... using Lie-infinitesimal transformation technique. Sophus Lie has developed the Lie transformation technique which maps a given differential equation to ...continuous group of transformations ...

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Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method

Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method

... the one-step property of Lie-group is usually not shared by other numerical methods because those methods do not belong to the Lie-group ...a one-step estimation method to es- ...

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Lie group structures on automorphism groups of real analytic CR manifolds

Lie group structures on automorphism groups of real analytic CR manifolds

... the parameter ǫ in the identities. Indeed, the parameter ǫ appears always in an appropriate place so that the results concerning the parametriza- tion of solutions of singular analytic systems given in the ...

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A Discourse On Applications Of Lie Groups And Lie Algebras

A Discourse On Applications Of Lie Groups And Lie Algebras

... topological group to be Hausdorff is ...topological group to be connected has been ...research one can extend these ideas to prove that a Lie group is always ...―Any Lie ...

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Lie Symmetries, 1 Dimensional Optimal System and Optimal Reductions of (1 + 2) Dimensional Nonlinear Schrödinger Equation

Lie Symmetries, 1 Dimensional Optimal System and Optimal Reductions of (1 + 2) Dimensional Nonlinear Schrödinger Equation

... a Lie algebra is a list of conjugacyin equivalent s-parameter subgroups with the property that any other subgroup is conjugate to precisely one subgroup in the ...the Lie algebra is equivalent ...

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The first isomorphism theorem of lie group for fuzzy topographic topological mapping

The first isomorphism theorem of lie group for fuzzy topographic topological mapping

... Lie group is situated at the intersection of two basic areas of mathematics: algebra and geometry. A Lie group is a group. It is also a differentiable (smooth) manifold. Finally, the ...

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Nonclassical Symmetry Solutions for 4th Order Phase Field Reaction-Diffusion

Nonclassical Symmetry Solutions for 4th Order Phase Field Reaction-Diffusion

... a one-parameter transformation, an analytic function of a single real parameter , connected to the identity transformation at = 0, that leaves invariant the system consisting of a target PDE together ...

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Lie symmetry analysis for Kawahara-KdV equations

Lie symmetry analysis for Kawahara-KdV equations

... [3] B. J. Cantwell, Introduction to Symmetry Analysis, Cambridge University Press, (2002). [4] W. Gang-Wei, L. Xi-Qiang and Z. Ying-Yuan, Lie Symmetry Analysis and Invariant Solutions of the Generalized ...

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Some Coefficients Method Of Solving Riccati Equation By Lie Group Symmetry

Some Coefficients Method Of Solving Riccati Equation By Lie Group Symmetry

... more difficult problem solving the Riccati Equation by inspired guesswork, or geometric intuition, the steps used when solving all first order differential equations involve some assumptions and guesses of the form of ...

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Lie Symmetries, One Dimensional Optimal System and Optimal Reduction of (2 + 1) Coupled nonlinear Schrödinger Equations

Lie Symmetries, One Dimensional Optimal System and Optimal Reduction of (2 + 1) Coupled nonlinear Schrödinger Equations

... infinite-dimensional Lie algebra  ∞ of the Lie sym- metry group of the 2D-CNLS equations is derived which covered the results obtained in ...the one- dimensional optimal system of an ...

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On the flag geometry of simple group of Lie type and multivariate cryptography

On the flag geometry of simple group of Lie type and multivariate cryptography

... Deformations of such nonlinear map by two special elements of affine group acting on the plainspace can produce a computable in polynomial time nonlinear transformation. The information on adjacency graph, list of ...

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Stability properties of one parameter flows

Stability properties of one parameter flows

... theorem in this chapter is that every flow without fixed points on a compact manifold M which is topologically stable has the pseudo orbit tracing property... Using this work particularl[r] ...

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Normal Lie subsupergroups and non abelian supercircles

Normal Lie subsupergroups and non abelian supercircles

... and Lie supergroups are of particular interest in modern physics and mathematics as ...the Lie supergroups as symmetry groups for Hamiltonian supermechanics [1, 8, 9] and supergauge theory [7, 12, 17], ...

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Operator Methods and SU(1,1) Symmetry in  the Theory of Jacobi and of Ultraspherical Polynomials

Operator Methods and SU(1,1) Symmetry in the Theory of Jacobi and of Ultraspherical Polynomials

... in one formula) and it deals with also Laguerre polynomials under the heading of the chapter about Jacobi ...form one finds a lot of formulae for Orthogonal polynomials also in a book of Bell [22] which we ...

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Lie symmetry analysis of stochastic SIRS model

Lie symmetry analysis of stochastic SIRS model

... In this paper, we introduce stochastic effects into a deterministic SIRS model. In nature, infection of disease are impacted by diverse complex biological process. Therefore one could believe on the existence of ...

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Lie group analysis and similarity solutions for hydro-magnetic Maxwell fluid through a porous medium

Lie group analysis and similarity solutions for hydro-magnetic Maxwell fluid through a porous medium

... permeability parameter k increases the horizontal velocity component u increases, while the vertical velocity component v ...Hall parameter m, which indicate that for small values of t (or at initial values ...

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Logarithmic Convexity of the One-Parameter Mean Values

Logarithmic Convexity of the One-Parameter Mean Values

... 2000 Mathematics Subject Classification. Primary 26A48, 26A51; Secondary 26B25, 26D07. Key words and phrases. Logarithmic convexity, monotonicity, one-parameter mean values. The first author was supported ...

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CONFIDENCE INTERVALS FOR THE SCALE PARAMETER OF A TWO-PARAMETER WEIBULL DISTRIBUTION: ONE SAMPLE PROBLEM

CONFIDENCE INTERVALS FOR THE SCALE PARAMETER OF A TWO-PARAMETER WEIBULL DISTRIBUTION: ONE SAMPLE PROBLEM

... shape parameter β equals 1 and all scale parameters θ for all sample ...shape parameter β increases, the coverage prob- abilities of the exact and asymptotic confidence intervals are also close to the ...

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Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups

Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups

... As mentioned in the introduction, associated to each G is a classifying space BG. We will not use BG directly in our results, but some results of Adams’ et. al. on BG will be relevant to our later discussions so we ...

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On the Structure of Infinitesimal Automorphisms of the Poisson Lie Group SU(2,R)

On the Structure of Infinitesimal Automorphisms of the Poisson Lie Group SU(2,R)

... Poisson-Lie group SU ( 2,  ) . We will calculate, firstly, all Pois- son-Lie structures through the correspondence with Lie bialgebra; secondly, we will show that these Poisson-Lie ...

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