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Relevant bibliographies by topics / One-Parameter group of transformation

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Journal articles

Academic literature on the topic 'One-Parameter group of transformation'

Author: Grafiati

Published: 1 February 2025

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Journal articles on the topic "One-Parameter group of transformation"

1

Al-Shomrani, M. M. "Lie Groups Analysis and Contact Transformations for Ito System." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/342680.

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Generalized Ito systems of four coupled nonlinear evaluation equations are proposed. New classes of exact invariant solutions by using Lie group analysis are obtained. Moreover, we investigate the existence of a one-parameter group of contact transformations for a generalized Ito system. Consequently, we study the relationship between one-parameter group of a contact transformation and a one-parameter Lie point transformation for a generalized Ito system.

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2

Cieśliński, Jan L., and Dzianis Zhalukevich. "Spectral Parameter as a Group Parameter." Symmetry 14, no. 12 (2022): 2577. http://dx.doi.org/10.3390/sym14122577.

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A large class of integrable non-linear partial differential equations is characterized by the existence of the associated linear problem (in the case of two independent variables, known as a Lax pair) containing the so-called spectral parameter. In this paper, we present and discuss the conjecture that the spectral parameter can be interpreted as the parameter of some one-parameter groups of transformation, provided that it cannot be removed by any gauge transformation. If a non-parametric linear problem for a non-linear system is known (e.g., the Gauss–Weingarten equations as a linear problem for the Gauss–Codazzi equations in the geometry of submanifolds), then, by comparing both symmetry groups, we can find or indicate the integrable cases. We consider both conventional Lie point symmetries and the so-called extended Lie point symmetries, which are necessary in some cases. This paper is intended to be a review, but some novel results are presented as well.

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3

Levi, Inessa. "Group closures of one-to-one transformations." Bulletin of the Australian Mathematical Society 64, no. 2 (2001): 177–88. http://dx.doi.org/10.1017/s000497270003985x.

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For a semigroup S of transformations of an infinite set X let Gs be the group of all the permutations of X that preserve S under conjugation. Fix a permutation group H on X and a transformation f of X, and let 〈f: H〉 = 〈{hfh−1: h ∈ H}〉 be the H-closure of f. We find necessary and sufficient conditions on a one-to-one transformation f and a normal subgroup H of the symmetric group on X to satisfy G〈f:H〉 = H. We also show that if S is a semigroup of one-to-one transformations of X and GS contains the alternating group on X then Aut(S) = Inn(S) ≅ GS.

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4

Polikanova, I. V. "Measuring the arcs of the orbit of a one-parameter transformation group." Sibirskie Elektronnye Matematicheskie Izvestiya 17 (November 12, 2020): 1823–48. http://dx.doi.org/10.33048/semi.2020.17.124.

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5

Xue-zi, Xu, and Chen Huai-yong. "Application of one-parameter groups of transformation in mechanics." Applied Mathematics and Mechanics 11, no. 7 (1990): 679–86. http://dx.doi.org/10.1007/bf02017483.

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6

Drozhzhinov, Yu N., and B. I. Zav’yalov. "Asymptotically homogeneous generalized functions along trajectories defined by a general one-parameter transformation group." Doklady Mathematics 82, no. 3 (2010): 874–77. http://dx.doi.org/10.1134/s1064562410060098.

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7

Liu, Ping, Senyue Lou, and Lei Peng. "Second-Order Approximate Equations of the Large-Scale Atmospheric Motion Equations and Symmetry Analysis for the Basic Equations of Atmospheric Motion." Symmetry 14, no. 8 (2022): 1540. http://dx.doi.org/10.3390/sym14081540.

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In this paper, symmetry properties of the basic equations of atmospheric motion are proposed. The results on symmetries show that the basic equations of atmospheric motion are invariant under space-time translation transformation, Galilean translation transformations and scaling transformations. Eight one-parameter invariant subgroups and eight one-parameter group invariant solutions are demonstrated. Three types of nontrivial similarity solutions and group invariants are proposed. With the help of perturbation method, we derive the second-order approximate equations for the large-scale atmospheric motion equations, including the non-dimensional equations and the dimensional equations. The second-order approximate equations of the large-scale atmospheric motion equations not only show the characteristics of physical quantities changing with time, but also describe the characteristics of large-scale atmospheric vertical motion.

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8

Kulish, P. P. "A two-parameter quantum group and a gauge transformation." Journal of Mathematical Sciences 68, no. 2 (1994): 220–22. http://dx.doi.org/10.1007/bf01249335.

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9

Shilin, I. A., and Junesang Choi. "Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices." Axioms 13, no. 7 (2024): 452. http://dx.doi.org/10.3390/axioms13070452.

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Considering a representation space for a group of unimodular diag(1, −1, −1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some one-parameter subgroups. Finding the kernels of base transformation integral operators in terms of special functions, we consider the compositions of some of these transformations. Since composition is a ‘closed’ operation on the set of base transformations, we obtain some integral relations for the special functions involved in the above kernels.

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10

Abd-el-Malek, Mina B., and Medhat M. Helala. "Steady Flow of an Electrically Conducting Incompressible Viscoelastic Fluid over a Heated Plate." Zeitschrift für Naturforschung A 60, no. 1-2 (2005): 29–36. http://dx.doi.org/10.1515/zna-2005-1-205.

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The transformation group theoretic approach is applied to the problem of the flow of an electrically conducting incompressible viscoelastic fluid near the forward stagnation point of a heated plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the basic equations governing flow and heat transfer are reduced to a set of ordinary differential equations. These equations have been solved approximately subject to the relevant boundary conditions by employing the shooting numerical technique. The effect of the magnetic parameter M, the Prandtl number Pr and the non-dimensional elastic parameter representing the non- Newtonian character of the fluid k on velocity field, shear stress, temperature distribution and heat flux are carefully examined.

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