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The mathematics of filtering and its applications
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Iterative procedures for identification of nonlinear interconnected systems
This work addresses the identification problem of a discrete-time nonlinear system composed by linear and nonlinear subsystems. Systems in this class will be represented by Linear Fractional
Transformations. Iterative identification procedures are examined, that alternate between the estimation of the linear and the nonlinear components. The burden of identification falls naturally on the nonlinear subsystem, as techniques for identification of linear systems have long been established. Two approaches are
examined. A point-wise identification of the nonlinearity, recently proposed in the literature, is applied and its advantages and
drawbacks are outlined. An alternative procedure that employs piecewise affine approximation techniques is proposed. Numerical examples demonstrate the efficiency of the proposed algorithm
Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity
Specializing properly the parameters contained in the maximal cyclic
representation of the non-restricted A-type quantum algebra at roots of unity,
we find the unique primitive vector in it. We show that the submodule generated
by the primitive vector can be identified with an irreducble highest weight
module of the finite dimensional A-type quantum algebra which is defined as the
subalgebra of the restricted quantum algebra at roots of unity.Comment: LaTeX(2e), 17 page
A Construction of Solutions to Reflection Equations for Interaction-Round-a-Face Models
We present a procedure in which known solutions to reflection equations for
interaction-round-a-face lattice models are used to construct new solutions.
The procedure is particularly well-suited to models which have a known fusion
hierarchy and which are based on graphs containing a node of valency . Among
such models are the Andrews-Baxter-Forrester models, for which we construct
reflection equation solutions for fixed and free boundary conditions.Comment: 9 pages, LaTe
Symmetric Linear Backlund Transformation for Discrete BKP and DKP equation
Proper lattices for the discrete BKP and the discrete DKP equaitons are
determined. Linear B\"acklund transformation equations for the discrete BKP and
the DKP equations are constructed, which possesses the lattice symmetries and
generate auto-B\"acklund transformationsComment: 18 pages,3 figure
Exploiting structure in piecewise affine identification of LFT systems
Identification of interconnected systems is a challenging problem in which it is crucial to exploit the available knowledge about the interconnection structure. In this paper, identification of discrete-time nonlinear systems composed by interconnected linear
and nonlinear systems, is addressed. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear components. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine (PWA) identification techniques are employed for modelling the nonlinearity. A numerical
example analyzes the benefits of the proposed structure-exploiting identification algorithm compared to applying black-box PWA identification techniques to the overall system
Basic Representations of A_{2l}^(2) and D_{l+1}^(2) and the Polynomial Solutions to the Reduced BKP Hierarchies
Basic representations of A_{2l}^(2) and D_{l+1}^(2) are studied. The weight
vectors are represented in terms of Schur's -functions. The method to get
the polynomial solutions to the reduced BKP hierarchies is shown to be
equivalent to a certain rule in Maya game.Comment: January 1994, 11 page
Reflectionless analytic difference operators I. algebraic framework
We introduce and study a class of analytic difference operators admitting
reflectionless eigenfunctions. Our construction of the class is patterned after
the Inverse Scattering Transform for the reflectionless self-adjoint
Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice
solitons
A Symmetric Generalization of Linear B\"acklund Transformation associated with the Hirota Bilinear Difference Equation
The Hirota bilinear difference equation is generalized to discrete space of
arbitrary dimension. Solutions to the nonlinear difference equations can be
obtained via B\"acklund transformation of the corresponding linear problems.Comment: Latex, 12 pages, 1 figur
Fundamental Cycle of a Periodic Box-Ball System
We investigate a soliton cellular automaton (Box-Ball system) with periodic
boundary conditions. Since the cellular automaton is a deterministic dynamical
system that takes only a finite number of states, it will exhibit periodic
motion. We determine its fundamental cycle for a given initial state.Comment: 28 pages, 6 figure
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