1,522 research outputs found
Multiparametric and coloured extensions of the quantum group and the Yangian algebra through a symmetry transformation of the Yang-Baxter equation
Inspired by Reshetikhin's twisting procedure to obtain multiparametric
extensions of a Hopf algebra, a general `symmetry transformation' of the
`particle conserving' -matrix is found such that the resulting
multiparametric -matrix, with a spectral parameter as well as a colour
parameter, is also a solution of the Yang-Baxter equation (YBE). The
corresponding transformation of the quantum YBE reveals a new relation between
the associated quantized algebra and its multiparametric deformation. As
applications of this general relation to some particular cases, multiparametric
and coloured extensions of the quantum group and the Yangian algebra
are investigated and their explicit realizations are also discussed.
Possible interesting physical applications of such extended Yangian algebras
are indicated.Comment: 21 pages, LaTeX (twice). Interesting physical applications of the
work are indicated. To appear in Int. J. Mod. Phys.
Jordan-Schwinger realizations of three-dimensional polynomial algebras
A three-dimensional polynomial algebra of order is defined by the
commutation relations ,
where is an -th order polynomial in
with the coefficients being constants or central elements of the algebra.
It is shown that two given mutually commuting polynomial algebras of orders
and can be combined to give two distinct -th order polynomial
algebras. This procedure follows from a generalization of the well known
Jordan-Schwinger method of construction of and algebras from
two mutually commuting boson algebras.Comment: 10 pages, LaTeX2
Control of Nonaffine Nonlinear Discrete Time Systems using Reinforcement-learning-Based Linearly Parameterized Neural Networks
A nonaffine discrete-time system represented by the nonlinear autoregressive moving average with eXogenous input (NARMAX) representation with unknown nonlinear system dynamics is considered. An equivalent affinelike representation in terms of the tracking error dynamics is first obtained from the original nonaffine nonlinear discrete-time system so that reinforcement-learning-based near-optimal neural network (NN) controller can be developed. The control scheme consists of two linearly parameterized NNs. One NN is designated as the critic NN, which approximates a predefined long-term cost function, and an action NN is employed to derive a near-optimal control signal for the system to track a desired trajectory while minimizing the cost function simultaneously. The NN weights are tuned online. by using the standard Lyapunov approach, the stability of the closed-loop system is shown. The net result is a supervised actor-critic NN controller scheme which can be applied to a general nonaffine nonlinear discrete-time system without needing the affinelike representation. Simulation results demonstrate satisfactory performance of the controlle
Annihilation Diagrams in Two-Body Nonleptonic Decays of Charmed Mesons
In the pole-dominance model for the two-body nonleptonic decays of charmed
mesons and , it is shown that the
contributions of the intermediate pseudoscalar and the axial-vector meson poles
cancel each other in the annihilation diagrams in the chiral limit. In the same
limit, the annihilation diagrams for the decays vanish
independently.Comment: 9 pages (+ 3 figures available upon request), UR-1316, ER-40685-766,
IC/93/21
Optimal Adaptive Output Regulation of Uncertain Nonlinear Discrete-Time Systems using Lifelong Concurrent Learning
This Paper Addresses Neural Network (NN) based Optimal Adaptive Regulation of Uncertain Nonlinear Discrete-Time Systems in Affine Form using Output Feedback Via Lifelong Concurrent Learning. First, an Adaptive NN Observer is Introduced to Estimate Both the State Vector and Control Coefficient Matrix, and its NN Weights Are Adjusted using Both Output Error and Concurrent Learning Term to Relax the Persistency Excitation (PE) Condition. Next, by Utilizing an Actor-Critic Framework for Estimating the Value Functional and Control Policy, the Critic Network Weights Are Tuned Via Both Temporal Different Error and Concurrent Learning Schemes through a Replay Buffer. the Actor NN Weights Are Tuned using Control Policy Errors. to Attain Lifelong Learning for Performing Effectively during Multiple Tasks, an Elastic Weight Consolidation Term is Added to the Critic NN Weight Tuning Law. the State Estimation, Regulation, and the Weight Estimation Errors of the Observer, Actor and Critic NNs Are Demonstrated to Be Bounded When Performing Tasks by using Lyapunov Analysis. Simulation Results Are Carried Out to Verify the Effectiveness of the Proposed Approach on a Vander Pol Oscillator. Finally, Extension to Optimal Tracking is Given Briefly
Energy level statistics of electrons in a 2D quasicrystal
A numerical study is made of the spectra of a tight-binding hamiltonian on
square approximants of the quasiperiodic octagonal tiling. Tilings may be pure
or random, with different degrees of phason disorder considered. The level
statistics for the randomized tilings follow the predictions of random matrix
theory, while for the perfect tilings a new type of level statistics is found.
In this case, the first-, second- level spacing distributions are well
described by lognormal laws with power law tails for large spacing. In
addition, level spacing properties being related to properties of the density
of states, the latter quantity is studied and the multifractal character of the
spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available
upon request, LATEX, report-number els
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