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1101
Modeling and Control of Knee-Ankle-Toe Active Transfemoral Prosthesis
Published 2020-01-01“…Secondly, consider the cooperative movement of amputee and prosthesis, the kinematics model of prosthesis is established by Lie Groups and Lie Algebras, and the dynamic model of prosthesis is established by Lagrange equation. …”
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1102
Integrated Geometric Optimal Control of Spacecraft Attitude and Orbit Based on <italic>SE</italic>(3)
Published 2023-01-01“…Then, based on differential geometric theories, such as the variational principle, the left-invariant principle of Lie group, and the topology of Lie algebraic space, MPCP is applied to <inline-formula> <tex-math notation="LaTeX">$SE(3)$ </tex-math></inline-formula>. …”
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1103
Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants
Published 2020-10-01“…We analyze the adiabatic liquid dynamics, within which, following the general approach, the nature of the related Poissonian structure on the fluid motion phase space as a semidirect Banach groups product, and a natural reduction of the canonical symplectic structure on its cotangent space to the classical Lie-Poisson bracket on the adjoint space to the corresponding semidirect Lie algebras product are explained in detail. We also present a modification of the Hamiltonian analysis in case of a flow governed by isothermal liquid dynamics. …”
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1104
Energy-Preserving/Group-Preserving Schemes for Depicting Nonlinear Vibrations of Multi-Coupled Duffing Oscillators
Published 2024-01-01“…The main novelty is that we constructed the quadratic forms of the energy equations, the Lie-algebras and Lie-groups for the multi-coupled Duffing oscillator system. …”
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1105
Vertex operator algebras, Higgs branches, and modular differential equations
Published 2018-08-01“…We illustrate these ideas in a number of examples including a series of rank-one theories associated with the “Deligne-Cvitanović exceptional series” of simple Lie algebras, several families of Argyres-Douglas theories, an assortment of class S $$ \mathcal{S} $$ theories, and N=2 $$ \mathcal{N}=2 $$ super Yang-Mills with sun $$ \mathfrak{s}\mathfrak{u}(n) $$ gauge group for small-to-moderate values of n.…”
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1106
Towards Unifying Structures in Higher Spin Gauge Symmetry
Published 2008-02-01“…A common unifying structure of strongly homotopy Lie algebras underlying both approaches will be discussed. …”
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1107
A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry
Published 2021-10-01“…We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.…”
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1108
Disconnected 0-form and 2-group symmetries
Published 2023-07-01“…Examples of arbitrarily complex disconnected 0-form and 2-group symmetries in any spacetime dimension are furnished by gauge theories: with 1-form symmetries arising from the center of the gauge group, continuous 0-form symmetries arising as flavor symmetries acting on matter content, and finite 0-form symmetries arising from outer-automorphisms of gauge and flavor Lie algebras.…”
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1109
Qudit Entanglers Using Quantum Optimal Control
Published 2023-11-01“…We take advantage of both continuous, Lie algebraic control and digital, Lie group control. …”
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1110
Quiver theories and Hilbert series of classical Slodowy intersections
Published 2020-03-01“…The vacuum moduli spaces of many such theories can be parameterised by pairs of nilpotent orbits of Classical Lie algebras; they are transverse to one orbit and intersect the closure of the second. …”
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1111
Physics of infinite complex structure limits in eight dimensions
Published 2022-06-01“…As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. …”
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1112
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1114
Theory of Trotter Error with Commutator Scaling
Published 2021-02-01“…Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds, in general. …”
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1115
Quantum control with noisy fields: computational complexity versus sensitivity to noise
Published 2014-01-01“…The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system increases with the dimension of the Hilbert space representation of the algebra. …”
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1116
On a class of conformal E $$ \mathcal{E} $$ -models and their chiral Poisson algebras
Published 2023-06-01“…The case of degenerate E $$ \mathcal{E} $$ -models, in which a subalgebra of the current algebra is gauged, is more involved: the conformal condition yields a wider class of theories, which includes gauged WZW models but also other examples, seemingly different, which however sometimes turn out to be related to gauged WZW models based on other Lie algebras. For this class, we build non-local chiral fields of parafermionic-type as well as higher-spin local ones, forming classical W $$ \mathcal{W} $$ -algebras. …”
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1117
New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations
Published 2022-01-01“…Invariant submodels of rank one are constructed from two three-dimensional subalgebras of the corresponding Lie algebras, and exact solutions with a linear velocity field with inhomogeneous deformation are obtained. …”
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1118
Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invaria...
Published 2020-06-01“…Streater in the framework of Quantum Physics by Information Geometry for some Lie algebras, but only in the case of null cohomology. …”
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1119
Quantum robust control theory for Hamiltonian and control field uncertainty
Published 2021-01-01“…To provide guidelines as to the types of quantum control systems and control objectives for which asymptotic robustness analysis is important for accuracy, we introduce methods for assessing the Lie algebraic depth of quantum control systems, and illustrate through examples drawn from quantum information processing how such accurate methods for quantification of robustness to noise and uncertainty are more important for control strategies that exploit higher order quantum pathways. …”
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1120
Addendum to “Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o⋆(4) symmetries in unified o(4;C) setting” [Phys. Lett. B 754 (2016) 176–181]
Published 2017-07-01“…Applying reality conditions to the complex o(4;C) r-matrices we obtained the nonisomorphic classical r-matrices for all possible real forms of o(4;C): Euclidean o(4), Lorentz o(3,1), Kleinian o(2,2) and quaternionic o⋆(4) Lie algebras. In the case of o(4) and o(3,1) real symmetries these r-matrices give the full classifications of the inequivalent quasitriangular quantum deformations, however for o(2,2) and o⋆(4) the classifications are not full. …”
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