Results 11 to 20 of about 575,831 (281)
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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Mathematics, 2023 In this review paper, our aim is to study the current research progress of q-difference equations for generalized Al-Salam–Carlitz polynomials related to theta functions and to give an extension of q-difference equations for q-exponential operators and q-
Jian Cao +3 more
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Harmonizing results of ataxia rating scales: mFARS, SARA, and ICARS
Annals of Clinical and Translational Neurology, Volume 9, Issue 12, Page 2041-2046, December 2022., 2022 Abstract The ever‐increasing body of ataxia research provides opportunities for large‐scale meta‐analyses, systematic reviews, and data aggregation. Because multiple standardized scales are used to quantify ataxia severity, harmonization of these measures is necessary for quantitative data pooling. We applied the modified Friedreich Ataxia Rating Scale
Christian Rummey +5 more
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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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Discrete Hypergeometric Legendre Polynomials
Mathematics, 2021 A discrete analog of the Legendre polynomials defined by discrete hypergeometric series is investigated. The resulting polynomials have qualitatively similar properties to classical Legendre polynomials.
Tom Cuchta, Rebecca Luketic
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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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Performance analysis of control allocation using data‐driven integral quadratic constraints
Advanced Control for Applications, Volume 4, Issue 4, December 2022., 2022 Abstract A new method is presented for evaluating the performance of a nonlinear control allocation system within a linear control loop. To that end, a worst‐case gain analysis problem is formulated that can be readily solved by means of well‐established methods from robustness analysis using integral quadratic constraints (IQCs).
Manuel Pusch +2 more
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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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Sharing values of q-difference-differential polynomials
Advances in Difference Equations, 2020 This paper is devoted to the uniqueness of q-difference-differential polynomials of different types. Using the idea of common zeros and common poles (Chin. Ann. Math., Ser.
Jian Li, Kai Liu
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
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