In this paper, we explore the problem of isochronicity at infinity for a class of polynomial differential system. The technique is based on taking infinity into the origin by means of a homeomorphism. Simultaneously, ...
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In this paper, we explore the problem of isochronicity at infinity for a class of polynomial differential system. The technique is based on taking infinity into the origin by means of a homeomorphism. Simultaneously, we derive a recursive algorithm to compute period constants at the origin of the transformed system. At the end, as an application of our algorithm, we study pseudo-isochronous center conditions at infinity for a class of septic system.
The direct problem of light scattering for a fiber optic Bragg grating is considered. The formulation and solution of the problem based on the transfer-matrix method are discussed. A modification of the method is prop...
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The direct problem of light scattering for a fiber optic Bragg grating is considered. The formulation and solution of the problem based on the transfer-matrix method are discussed. A modification of the method is proposed which reduces it to a computationally convenient universal recursive algorithm similar to the Thomas algorithm. Using the finite volume method in the coupled-mode approximation, the elements of transfer matrices were calculated with local third-order accuracy in coordinate on a nonuniform computational grid. Numerical calculations for the direct scattering problem for a Bragg grating with apodization and nonlinear chirp were performed using the recursive algorithm. Numerical simulations confirmed the significant increase in the accuracy of calculations when solving the scattering problem on a nonuniform grid.
Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algori...
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Exponential tail bounds are derived for solutions of max-recursive equations and for max-recursive random sequences, which typically arise as functionals of recursive structures, of random trees or in recursive algorithms. In particular they arise in the worst case analysis of divide and conquer algorithms, in parallel search algorithms or in the height of random tree models. For the proof we determine asymptotic bounds for the moments or for the Laplace transforms and apply a characterization of exponential tail bounds due to Kasahara (1978).
This paper deals with the parameter estimation problem of Hammerstein state-space models with different nonlinearities. The basic idea is to develop a recursive algorithm which estimate jointly the system model parame...
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This paper deals with the parameter estimation problem of Hammerstein state-space models with different nonlinearities. The basic idea is to develop a recursive algorithm which estimate jointly the system model parameters and the state variables by combining the adjustable model method, the least squares technique and the Kalman filter. A numerical example is provided to test the flexibility and the effectiveness of the proposed algorithm.
A recursive instrumental variable algorithm is proposed for estimating the structural parameters of a simultaneous equation model with autoregressive error terms. The choice of the instruments is discussed in order to...
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A recursive instrumental variable algorithm is proposed for estimating the structural parameters of a simultaneous equation model with autoregressive error terms. The choice of the instruments is discussed in order to obtain asymptotically efficient estimation of the structural parameters.
The Turing machine model is extended to allow for recursive calls and the basic theory of these machines is developed. The model is also used to study the following additional topics: The time and storage needed to im...
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The Turing machine model is extended to allow for recursive calls and the basic theory of these machines is developed. The model is also used to study the following additional topics: The time and storage needed to implement recursive algorithms by non-recursive algorithms, the storage needed to implement non-deterministic algorithms by deterministic algorithms, and the implementation of recursive algorithms by means of stack machines. Some attention is given to time bounds but the emphasis is on storage-bounded computations.
A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature ...
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A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature of the approach is to obtain the "simplest" formula which reduces the computation demand to minimum. At each order of the normal form computation, the formula generates a set of algebraic equations for computing the normal form and nonlinear transformation. Moreover, the new recursive method is not required for solving large matrix equations, instead it solves linear algebraic equations one by one. Thus the new method is computationally efficient. In addition, unlike the conventional normal form theory which uses separate nonlinear transformations at each order, this approach uses a consistent nonlinear transformation through all order computations. This enables one to obtain a convenient, one step transformation between the original system and the simplest normal form. The new method can treat general differential equations which are not necessarily assumed in a conventional normal form. The method is applied to consider Hopf and Bogdanov-Takens singularities, with examples to show the computation efficiency. Maple programs have been developed to provide an "automatic" procedure for applications.
The usefulness of the controllability maximum principle is presently extended through a demonstration of its ability to find estimates of projections of the controllable set onto a lower-dimension (two- dimensional) s...
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The usefulness of the controllability maximum principle is presently extended through a demonstration of its ability to find estimates of projections of the controllable set onto a lower-dimension (two- dimensional) space. Three- or four-dimensional problems may now be 'solved' with approximately the same degree of difficulty as previously associated with two-dimensional problems. The method is applicable to both linear and nonlinear systems. (O.C.)
We establish consistency and derive asymptotic distributions for estimators of the coefficients of a subset vector autoregressive (SVAR) process. Using a martingale central limit theorem, we first derive the asymptoti...
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We establish consistency and derive asymptotic distributions for estimators of the coefficients of a subset vector autoregressive (SVAR) process. Using a martingale central limit theorem, we first derive the asymptotic distribution of the subset least squares (LS) estimators. Exploiting the similarity of closed form expressions for the LS and Yule-Walker (YW) estimators, we extend the asymptotics to the latter. Using the fact that the subset Yule-Walker and recently proposed Burg estimators satisfy closely related recursive algorithms, we then extend the asymptotic results to the Burg estimators. All estimators are shown to have the same limiting distribution. (C) 2003 Elsevier Inc. All rights reserved.
This paper describes an algorithm which builds a ``Peano scanning,"" i.e., the reciprocal mapping, from [0, 1]n to [0, 1], of the well-known ``Peano curve."" This Peano scanning is applied to a set...
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This paper describes an algorithm which builds a ``Peano scanning,"" i.e., the reciprocal mapping, from [0, 1]n to [0, 1], of the well-known ``Peano curve."" This Peano scanning is applied to a set of points in [0, 1]n and gives a one-dimensional image of it. Several applications of this technique have already been developed and are presented in this paper.
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