Multiparametric and coloured extensions of the quantum group GLq(N)GL_q(N) and the Yangian algebra Y(glN)Y(gl_N) 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' $R$-matrix is found such that the resulting multiparametric $R$-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 $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ 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 $m$ is defined by the commutation relations $[P_0, P_\pm]$ $=$ $\pm P_\pm$, $[P_+, P_-]$ $=$ $\phi^{(m)}(P_0)$ where $\phi^{(m)}(P_0)$ is an $m$-th order polynomial in $P_0$ with the coefficients being constants or central elements of the algebra. It is shown that two given mutually commuting polynomial algebras of orders $l$ and $m$ can be combined to give two distinct $(l+m+1)$-th order polynomial algebras. This procedure follows from a generalization of the well known Jordan-Schwinger method of construction of $su(2)$ and $su(1,1)$ 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 $D \rightarrow PV$ and $D \rightarrow VV$, 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 $D \rightarrow PP$ decays vanish independently.Comment: 9 pages (+ 3 figures available upon request), UR-1316, ER-40685-766, IC/93/21

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

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