Results 71 to 80 of about 53,539 (221)

Some Types of Identities Involving the Legendre Polynomials

Mathematics, 2019
In this paper, a new non-linear recursive sequence is firstly introduced. Then, using this sequence, a computational problem involving the convolution of the Legendre polynomial is studied using the basic and combinatorial methods.
Shimeng Shen, Li Chen
doaj   +1 more source

Application of Genomic Random Regression Models for Genetic Parameter Estimations of Female Fertility Traits in Different Parities in German Holsteins

Journal of Animal Breeding and Genetics, EarlyView.
ABSTRACT The aim of the present study was to infer genetic (co) variance components and to estimate parity‐specific breeding values for the female fertility traits non‐return rate after 56 days, the interval from calving to first service and days open by applying random regression models on a time‐dependent parity scale. In this regard, we considered a
Sina Sakhaei‐far, Tong Yin, Sven König   +2 more
wiley   +1 more source

Algorithms for Solving Ordinary Differential Equations Based on Orthogonal Polynomial Neural Networks

Algorithms
This article proposes single-layer neural network algorithms for solving second-order ordinary differential equations, based on the principles of functional connection.
Roman Parovik
doaj   +1 more source

Accurate Evaluation of Polynomials in Legendre Basis

Journal of Applied Mathematics, 2014
This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double ...
Peibing Du, Hao Jiang, Lizhi Cheng
doaj   +1 more source

Smooth and compactly supported viscous sub-cell shock capturing for Discontinuous Galerkin methods

, 2018
In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used piecewise constant artificial viscosity method of Persson and Peraire as well as the piecewise
Almeida, J. L. S., Cantão, R. F., Glaubitz, J., Nogueira Jr., A. C., Silva, C. A. C.   +4 more
core   +1 more source

What If Each Voxel Were Measured With a Different Diffusion Protocol?

Magnetic Resonance in Medicine, Volume 95, Issue 4, Page 2277-2290, April 2026.
ABSTRACT Purpose Expansion of diffusion MRI (dMRI) both into the realm of strong gradients and into accessible imaging with portable low‐field devices brings about the challenge of gradient nonlinearities. Spatial variations of the diffusion gradients make diffusion weightings and directions non‐uniform across the field of view, and deform perfect ...
Santiago Coelho, Gregory Lemberskiy, Ante Zhu, Hong‐Hsi Lee, Nastaren Abad, Thomas K. F. Foo, Els Fieremans, Dmitry S. Novikov   +7 more
wiley   +1 more source

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\
openaire   +2 more sources

Some bounds related to the 2‐adic Littlewood conjecture

Mathematika, Volume 72, Issue 2, April 2026.
Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
wiley   +1 more source

On the Expansion of Legendre Polynomials in Bicomplex Space and Coupling with Fractional Operators

Axioms
In this paper, we introduce a novel version of the Legendre polynomials in the bicomplex system. We investigate the essential properties of the Legendre polynomial, focusing on its bicomplex structure, generating functions, orthogonality, and recurrence ...
Ahmed Bakhet, Shahid Hussain, Mohra Zayed, Aya M. Mourad   +3 more
doaj   +1 more source

Variational Modeling of Porosity Waves

PAMM, Volume 26, Issue 1, March 2026.
ABSTRACT Mathematical models for finite‐strain poroelasticity in an Eulerian formulation are studied by constructing their energy‐variational structure, which gives rise to a class of saddle‐point problems. This problem is discretized using an incremental time‐stepping scheme and a mixed finite element approach, resulting in a monolithic, structure ...
Andrea Zafferi, Dirk Peschka
wiley   +1 more source