Results 81 to 90 of about 73,008 (249)
On zeros of discrete orthogonal polynomials
Journal of Approximation Theory, 2009 The authors establish sharp inequalities for the extreme zeros of the classical discrete orthogonal polynomials: Charlier, Krawtchouk, Meixner, and Hahn. Their approach is based on the corresponding difference equations. For Charlier, Krawtchouk, and Meixner polynomials the function bounding the zero spacing is unimodal, meanwhile for the Hahn case ...
Krasikov, Ilia, Zarkh, Alexander
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Harnessing Machine Learning to Understand and Design Disordered Solids
Advanced Intelligent Discovery, EarlyView.This review maps the dynamic evolution of machine learning in disordered solids, from structural representations to generative modeling. It explores how deep learning and model explainability transform property prediction into profound physical insight.
Muchen Wang, Yue Fan
wiley +1 more source
Orthogonal polynomials derived from the tridiagonal representation approach
, 2017 The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials whose ...
Alhaidari, A. D.
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Generalized Orthogonal Polynomials, Discrete KP and Riemann-Hilbert Problems [PDF]
Communications in Mathematical Physics, 1999 Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and tau-functions, expressed as Hermitian matrix integrals.
Adler, M., van Moerbeke, P.
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Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.This review aims to provide a broad understanding for interdisciplinary researchers in engineering and clinical applications. It addresses the development and control of magnetic actuation systems (MASs) in clinical surgeries and their revolutionary effects in multiple clinical applications.
Yingxin Huo +3 more
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On the asymptotics of orthogonal polynomials on the curve with a denumerable mass points
Journal of Numerical Analysis and Approximation Theory, 2007 We investigate the asymptotic behavior of orthogonal polynomials with respect to a measure of the type \(\sigma =\alpha +\gamma \), where \(\alpha \) is a measure concentrated on a rectifiable Jordan curve and \(\gamma \) is an infinite discrete measure.
Khaldi Rabah, Aggoune Fateh
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Discrete semi-classical orthogonal polynomials: Generalized Meixner
Journal of Approximation Theory, 1986 The property of quasiorthogonality of the derivative of semi classical orthogonal is extended to the discrete case for the generalized Meixner polynomials. The positive weigth \(\rho\) (x) is solution of the difference equation A(x) \(\rho\) (x\(+1)-B(x) \rho (x)=0\) with A(x) and B(x) polynomials of degree respectively \(\alpha\) and \(\beta\).
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A [3]Rotaxane Containing {Ti7Ga} Rings Linking CuII: Synthesis, Structure, and Spectroscopic Studies
Chemistry – A European Journal, EarlyView.Extended hybrid inorganic‐organic [2]‐ and [3]‐rotaxanes are reported based on heterometallic rings with threads that link CuII complexes; the crystal structures are reported, and the solution behavior is investigated by double electron electron resonance spectroscopy methods.
Selena J. Lockyer +7 more
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Self‐Similar Blowup for the Cubic Schrödinger Equation
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
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Journal of Inequalities and Applications, 2016 In this study, a high accuracy numerical method based on the spectral theory of compact operator for biharmonic eigenvalue equations on a spherical domain is developed.
Zhendong Luo
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