Results 61 to 70 of about 906 (173)

An accurate method for solving a singular second-order fractional Emden-Fowler problem

Advances in Difference Equations, 2018
In this paper, we study a singular second-order fractional Emden-Fowler problem. The reproducing kernel Hilbert space method (RKHSM) is employed to compute an approximation to the proposed problem.
Muhammed I Syam, HM Jaradat, Marwan Alquran, Safwan Al-Shara’   +3 more
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Recurrence Relations for Polynomials Orthonormal on Sobolev, Generated by Laguerre Polynomials

Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2018
Summary: In this paper we consider the system of polynomials \(l_{r,n}^{\alpha}(x)\) (\(r\) -- natural number, \(n=0, 1, \dots\)), orthonormal with respect to the Sobolev inner product (Sobolev orthonormal polynomials) of the following type \(\langle f,g\rangle=\sum_{\nu=0}^{r-1}f^{(\nu)}(0)g^{(\nu)}(0)+\int_{0}^{\infty} f^{(r)}(t)g^{(r)}(t)\rho(t)\,dt\
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Fitting discrete aspherical surface sag data using orthonormal polynomials

Optics Express, 2015
Characterizing real-life optical surfaces usually involves finding the best-fit of an appropriate surface model to a set of discrete measurement data. This process can be greatly simplified by choosing orthonormal polynomials for the surface description.
David, Hilbig, Ufuk, Ceyhan, Thomas, Henning, Friedrich, Fleischmann, Dietmar, Knipp   +4 more
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Orthonormal polynomials for elliptical wavefronts with an arbitrary orientation

Applied Optics, 2014
We generalize the analytical form of the orthonormal elliptical polynomials for any arbitrary aspect ratio to arbitrary orientation and give expression for them up to the 4th order. The utility of the polynomials is demonstrated by obtaining the expansion up to the 8th order in two examples of an off-axis wavefront exiting from an optical system with a
Díaz, José A., Navarro, Rafael
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On the Sharp Inequalities for Orthonormal Polynomials Along a Contour

Complex Analysis and Operator Theory, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. G. Abdullayev, G. A. Abdullayev
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Orthogonalizing q-Bernoulli polynomials

Demonstratio Mathematica
In this study, we utilize the Gram-Schmidt orthogonalization method to construct a new set of orthogonal polynomials called OBn(x,q){{\rm{OB}}}_{n}(x,q) from the q-Bernoulli polynomials.
Kuş Semra, Tuglu Naim
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On multipolar magnetic anomaly detection: multipolar signal subspaces, an analytical orthonormal basis, multipolar truncation and detection performance

EURASIP Journal on Advances in Signal Processing
In this paper, we consider the magnetic anomaly detection problem which aims to find ferromagnetic masses by estimating the weak perturbation they induce on local Earth’s magnetic field.
Clément Chenevas-Paule, Steeve Zozor, Laure-Line Rouve, Olivier J. J. Michel, Olivier Pinaud, Romain Kukla   +5 more
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Equiconvergence theorems for orthonormal polynomials [PDF]

Bulletin of the American Mathematical Society, 1944
Albert, G. E., Miller, L. H.
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An analysis of 24-h ambulatory blood pressure monitoring data using orthonormal polynomials in the linear mixed model. [PDF]

Blood Press Monit, 2014
Edwards LJ, Simpson SL.
europepmc   +1 more source

Zernike Polynomiales· for Opticl Ssytew. With Borizantal Recta_nguJar Aperture

Ibn Al-Haitham Journal for Pure and Applied Sciences, 2017
For  small   aberrations,  the  Â·suehl'  ratio of  an . im i'ng syStem • depends on trne aberration v·ariance. Its· aberration fu.nct1on ·is e:qJanded in terms 9f-l nike polynomials. which are_ oirrh6goilal over a circular apeltitte.
A, ,1J. AL-.llamdani, 8 Y. RAI-As di
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