A Hofer-Type Norm of Hamiltonian Maps on Regular Poisson Manifold by Dawei Sun, Zhenxing Zhang

“…The norm between the Hamiltonian map and the induced Hamiltonian map on the quotient of Poisson manifold (M,{·,·}) by a compact Lie group Hamiltonian action is also compared.…”
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Higher Orbital Integrals, Cyclic Cocycles and Noncommutative Geometry by Yanli Song, Xiang Tang

“…Let G be a linear real reductive Lie group. Orbital integrals define traces on the group algebra of G. …”
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Symmetry Reductions of (2 + 1)-Dimensional CDGKS Equation and Its Reduced Lax Pairs by Na Lv, Xuegang Yuan, Jinzhi Wang

“…Moreover, we use the classical Lie group method to seek the symmetry groups of both the CDGKS equation and its Lax pair and then reduce them by the obtained symmetries. …”
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Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups by Masatomo Iwasa

“…Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. …”
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Linearization: Geometric, Complex, and Conditional by Asghar Qadir

“…Here, first the original work of Lie (and the early developments on it), and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory), are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.…”
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Symmetry Reductions, Exact Solutions, and Conservation Laws of a Modified Hunter-Saxton Equation by Andrew Gratien Johnpillai, Chaudry Masood Khalique

“…We study a modified Hunter-Saxton equation from the Lie group-theoretic point of view. The Lie point symmetry generators of the underlying equation are derived. …”
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Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation by G. Loaiza, Y. Acevedo, O.M.L. Duque, Danilo A. García Hernández

“…Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. …”
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Conservation Laws, Symmetry Reductions, and New Exact Solutions of the (2 + 1)-Dimensional Kadomtsev-Petviashvili Equation with Time-Dependent Coefficients by Li-hua Zhang

“…The (2 + 1)-dimensional Kadomtsev-Petviashvili equation with time-dependent coefficients is investigated. By means of the Lie group method, we first obtain several geometric symmetries for the equation in terms of coefficient functions and arbitrary functions of t. …”
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Adaptive Finite-Time Control on SE(3) for Spacecraft Final Proximity Maneuvers with Input Quantization by Sai Zhang, Zhen Yang

“…To realize the integrated control for spacecraft final proximity operation, the coupling kinematics and dynamics of attitude and position are modeled by feat of Lie group SE3. With a view to improving the convergence rate and reducing the chattering, an adaptive finite-time controller is proposed for the error tracking system with one-step theoretical proof of stability. …”
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A Lie Theory-Based Control Scheme for a Solar-Fed Encoderless SPMSM by Abirami Kalathy, Arpan Laha, Praveen Jain, Majid Pahlevani

“…This article proposes a novel Lie group controller for speed sensorless control of a surface-mounted Permanent Magnet Synchronous Motor (SPMSM) fed by a solar microinverter. …”
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Geometrical Applications of Split Octonions by Merab Gogberashvili, Otari Sakhelashvili

“…This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie group G2. This group generates specific rotations of (3 + 4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. …”
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Lie and Riccati Linearization of a Class of Liénard Type Equations by A. G. Johnpillai, C. M. Khalique, F. M. Mahomed

“…Since the class of equations also admits an eight-parameter Lie group of point transformations, we utilize the Lie-Tresse linearization theorem to obtain linearizing point transformations as well. …”
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An Improved Unscented Kalman Filter Applied to Positioning and Navigation of Autonomous Underwater Vehicles by Jinchao Zhao, Ya Zhang, Shizhong Li, Jiaxuan Wang, Lingling Fang, Luoyin Ning, Jinghao Feng, Jianwu Zhang

“…An estimation model for system noise, the adaptive Unscented Kalman Filter (UKF) algorithm was derived in light of the maximum likelihood criterion and optimized by applying the rolling-horizon estimation method, using the Newton–Raphson algorithm for the maximum likelihood estimation of noise statistics, and it was verified by simulation experiments using the Lie group inertial navigation error model. The results indicate that, compared with the UKF algorithm and the ARUKF, the improved algorithm reduces attitude angle errors by 45%, speed errors by 44%, and three-dimensional position errors by 47%. …”
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Cycle Intersection for SOp,q-Flag Domains by Faten Abu Shoga

“…A real form G0 of a complex semisimple Lie group G has only finitely many orbits in any given compact G-homogeneous projective algebraic manifold Z=G/Q. …”
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Lie symmetry analysis of bio-nano-slip flow in a conical gap between a rotating disk and cone with Stefan blowing by Hamadneh Nawaf N., Uddin Mohammed Jashim, Khan Waqar, Tanjila Rubina, Tamanna Nadia, Jaber Jamil J.

“…The governing system constitutes the continuity, momentum, energy, conservation of nanoparticle volume fraction (NPVF) equation, and density of the motile microorganism (DMM) equations. The Lie group approach is used to obtain invariant transformations. …”
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Large N limit of the Yang–Mills measure on compact surfaces II: Makeenko–Migdal equations and the planar master field by Antoine Dahlqvist, Thibaut Lemoine

“…This paper considers the large N limit of Wilson loops for the two-dimensional Euclidean Yang–Mills measure on all orientable compact surfaces of genus larger or equal to $1$ , with a structure group given by a classical compact matrix Lie group. Our main theorem shows the convergence of all Wilson loops in probability, given that it holds true on a restricted class of loops, obtained as a modification of geodesic paths. …”
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A Quantum Mermin-Wagner Theorem for a Generalized Hubbard Model by Mark Kelbert, Yurii Suhov

“…We assume that a connected Lie group G acts on M, represented by a Euclidean space or torus of dimension d'≤d, preserving the metric and the volume in M. …”
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