Remarks on Almost Cosymplectic 3-Manifolds with RICCI Operators by Quanxiang Pan, Yajie Wang

“…In this paper, we prove that the Ricci operator of M is transversely Killing if and only if M is locally isometric to a product space of an open interval and a surface of constant Gauss curvature, or a unimodular Lie group equipped with a left invariant almost cosymplectic structure. …”
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A Class of PDEs with Nonlinear Superposition Principles by Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou

“…Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. …”
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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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Normal forms of vector fields induced by holomorphic actions of the group SL(2,C) on a complex manifold by Benito Leonardo Ostos Cordero

“…In this work, we study actions of the Lie group SL(2,C) on a complex manifold of dimension three or higher. …”
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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 Closed Form of Higher-Order Cayley Transforms and Generalized Rodrigues Vectors Parameterization of Rigid Motion by Daniel Condurache, Mihail Cojocari, Ioan-Adrian Ciureanu

“…The transform is defined by the Lie algebra of three-dimensional vectors into the Lie group of proper orthogonal Euclidean tensors. The approach uses only elementary algebraic calculations with Euclidean vectors and tensors. …”
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Analysis of Stiffness Characteristic of Five-degree-of-freedom Hammer Riveting Robot based on Spiral Theory by Chunying Jiang, Xiangchen Liu, Changlong Ye, Huan Zhou, Xu Guan

“…In view of the characteristics of the 5-DOF hammer riveting robot， combining Lie group Lie algebra and spiral theory， its kinematics model is established and solved； use the exponential product formula to derive the Jacobian matrix of the robot，and use the stiffness mapping theory to solve the stiffness matrix of the robot； the finite element and Matlab simulation software are used to simulate and verify the end deformation under the general pose and the extreme pose，and the stiffness distribution map of the robot in the task space varying with the change of pose is given；the simulation result is compared with the theoretical calculation value and the error is not more than 10%，which verify the correctness and effectiveness of the established stiffness model and provide important reference for optimization of subsequent work path.…”
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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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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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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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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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