Results 11 to 20 of about 230,209 (328)
Manifolds of difference polynomials [PDF]
Transactions of the American Mathematical Society, 1948 1. It is the purpose of this paper to develop in some detail the structure of the manifolds determined by systems of difference polynomials. Our results will necessarily be confined to the case of polynomials in an abstract field, since a suitable existence theorem for analytic difference equations is not available. The ideal theory, developed by J. F.
Richard M. Cohn
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An existence theorem for difference polynomials [PDF]
Proceedings of the American Mathematical Society, 1966 Introduction. The abstract varieties (also called manifolds) of difference algebra [2], [3] have not heretofore had a realization as sets of functions comparable to the realization provided for differential manifolds by the analytic existence theorem for differential equations (see [4], particularly p. 23).
Richard M. Cohn
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On the generalized difference polynomials [PDF]
Pacific Journal of Mathematics, 1990 Laurenţiu Panaitopol, D. M. Stefanescu
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On the difference and sum of basic sets of polynomials [PDF]
Pacific Journal of Mathematics, 1961 M.N. Mikhail, M. Nassif
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Differential-Difference Properties of Hypergeometric Polynomials [PDF]
Mathematics of Computation, 1975 We develop differential-difference properties of a class of hypergeometric polynomials which are a generalization of the Jacobi polynomials. The formulas are analogous to known formulas for the classical orthogonal polynomials.
Jet Wimp
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On a difference equation for generalizations of Charlier polynomials
Journal of Approximation Theory, 1999 11 ...
H. Bavinck, Roelof Koekoek
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International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary In this contribution, we propose a detailed study of interpolation‐based data‐driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, that is, we analyze frequency‐response data.
Quirin Aumann, Ion Victor Gosea
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Data‐driven performance metrics for neural network learning
International Journal of Adaptive Control and Signal Processing, EarlyView., 2023 Summary Effectiveness of data‐driven neural learning in terms of both local mimima trapping and convergence rate is addressed. Such issues are investigated in a case study involving the training of one‐hidden‐layer feedforward neural networks with the extended Kalman filter, which reduces the search for the optimal network parameters to a state ...
Angelo Alessandri +2 more
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Zeros of difference polynomials
Journal of Approximation Theory, 1992 Studies --- both analytic and numerical --- on polynomials have been of immense interest for long. Here the authors deal in detail with various questions relating to the zeros of difference polynomials. Particularly, defining the difference operator by \(\Delta f(x)=f(x+1)-f(x)\), the polynomial \(\Delta^ mx^ n\) of degree \((n-m)\) having \((n-m ...
John J. Warvik, Ronald J. Evans
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Polynomial Differences in the Primes [PDF]
, 2014 We establish, utilizing the Hardy-Littlewood Circle Method, an asymptotic formula for the number of pairs of primes whose differences lie in the image of a fixed polynomial. We also include a generalization of this result where differences are replaced with any integer linear combination of two primes.
Alex Rice, Neil Lyall
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