Results 81 to 90 of about 49,043 (210)
Collocation Method via Jacobi Polynomials for Solving Nonlinear Ordinary Differential Equations
International Journal of Mathematics and Mathematical Sciences, 2011 We extend a collocation method for solving a nonlinear ordinary differential equation (ODE) via Jacobi polynomials. To date, researchers usually use Chebyshev or Legendre collocation method for solving problems in
Ahmad Imani, Azim Aminataei, Ali Imani
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Computer program ETC improves computation of elastic transfer matrices of Legendre polynomials P/0/ and P/1/ [PDF]
, 1967 Computer program ETC improves computation of elastic transfer matrices of Legendre polynomials P/0/ and P/1/. Rather than carrying out a double integration numerically, one of the integrations is accomplished analytically and the numerical integration ...
Gibson, G., Miller, M.
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Generalized q-Legendre polynomials
Journal of Computational and Applied Mathematics, 1993 The author finds the polynomials \(u_ n\) satisfying the 3-term recursion: \[ (1-q^{n+1}) (1+q^ n) u_{n+1} - f_ nu_ n + q^{2n- 1} (1-q^ n) (1+q^{N+1}) u_{n-1} = 0, \] where \[ f_ n = (1- q^{2n+1}) \left( 2q^ n-(1+q^ n) (1+q^{n+1}) \sum_{j=0}^ nq^{-jn} \left[ {n \over j} \right]_ q \left[ {n+j \over j} \right]_ qx_ j \right). \] For \(x_ 0=x\), \(x_ j=0\
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Nowcasting Swiss GDP Growth From Public Lead Texts: Simple Methods Are Sufficient
Oxford Bulletin of Economics and Statistics, EarlyView.ABSTRACT Public lead texts from Swiss newspapers contain most of the signal needed to nowcast Swiss GDP growth in real time. I build an indicator from daily topic‐specific sentiment and recession measures extracted from three Swiss newspapers and evaluate it in pseudo‐real time.
Marc Burri
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The Plant Phenome Journal, Volume 9, Issue 1, December 2026.Abstract High‐throughput phenotyping (HTP) techniques have brought new opportunities to understand and evaluate key traits in plant breeding programs. Combining multiple measures through time and random regression models permits a more comprehensive understanding of the genetic and environmental effects on trait expression over time. This study aims to
Felipe Sabadin +16 more
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On Fractional Orthonormal Polynomials of a Discrete Variable
Discrete Dynamics in Nature and Society, 2015 A fractional analogue of classical Gram or discrete Chebyshev polynomials is introduced. Basic properties as well as their relation with the fractional analogue of Legendre polynomials are presented.
I. Area +3 more
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Implementation of a Thermomechanical Model for Journal Bearings Using p‐FEM
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT Hydrodynamic journal bearings are essential machine parts that are used for applications with high rotational speeds. Their precise simulation requires the consideration of thermomechanical interactions between solids and fluid. During operation, the shear stresses in the fluid (lubricant film heights: 5–100 μm${\umu }\mathrm{m}$), lead to ...
Fabian Schmidtchen +4 more
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Legendre polynomial order selection in projection pursuit density estimation
Lietuvos Matematikos Rinkinys, 2013 Projection pursuit method and its application to probability density estimation is discussed. Method proposed by J.H. Friedman, based on projection density estimation using orthogonal Legendre polynomials, is analysed.
Mindaugas Kavaliauskas
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On the interval Legendre polynomials
Journal of Computational and Applied Mathematics, 2003 This paper deals with the extension of the classical Legendre polynomials to the interval theory by considering the family of interval polynomials \(\mathbb L_{n,k}(x) \) satisfying, for each natural number \(k\), the recursive formula \(\mathbb L_{0,k}(x)=[1-\frac 1k,1+\frac 1k]\), \(\mathbb L_{1,k}(x)=[1-\frac 1k,1+\frac 1k]x\), \(\mathbb L_{n+1,k}(x)
Patrı́cio, F. +2 more
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Nanophotonics, Volume 15, Issue 9, 13 May 2026.Mechanically reconfigurable metasurfaces enable high‐capacity optical storage and holography due to low cost/complexity. A differentiable inverse design framework maps meta‐atom geometries to multichannel optical responses via deep neural networks. Rotatable cascaded metasurfaces optimized through this pipeline achieve pixel‐level holography with 288 ...
Ting Ma +4 more
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