Results 61 to 70 of about 136,517 (223)

Polynomial‐shaped electrodes for adaptive X‐ray optics

Journal of Synchrotron Radiation, EarlyView.
A shaped electrode design for lithium niobate adaptive X‐ray mirrors connects actuator degrees of freedom to specific polynomial orders, enabling general shape control and the correction of defocus, coma and fourth‐order aberrations with a limited number of inputs.For adaptive mirrors on X‐ray beamlines and optical systems, we describe a strategy for ...
Kenneth A. Goldberg, Francesco Marzari, Grant D. Cutler   +2 more
wiley   +1 more source

Extended forms of Legendre-Laguerre-based hybrid polynomials and their characteristics via fractional operator approach

Journal of Inequalities and Applications
This study presents an extensive generalization of Legendre–Laguerre polynomials along with their Appell-type counterparts. Using the quasi-monomiality approach, we establish core analytical features, including recurrence relations, associated ...
Waseem Ahmad Khan, Shahid Ahmad Wani, Mohammad Ayman-Mursaleen, Ketan Kotecha, Prakash Jadhav   +4 more
doaj   +1 more source

Coordinating representation registers: linear algebra students' understanding of orthogonal Legendre polynomials in the inner product space ℙn in a technology-assisted learning environment

Annales de Didactique et de Sciences Cognitives, 2018
The purpose of this research study was to understand how linear algebra students in a university in the United States make sense of the orthogonal Legendre polynomials as vectors of the inner product space ℙn in a DGS (Dynamic Geometry Software)-MATLAB ...
Günhan Caglayan
doaj   +1 more source

The Product of Two Legendre Polynomials [PDF]

Proceedings of the Glasgow Mathematical Association, 1953
1. It is known that any polynomial in μ. can be expanded as a linear function of Legendre polynomials [1]. In particular, we haveThe earlier coefficients, say A0, A2, A4 may easily be found by equating the coefficients of μp+q, μp+q-2, μp+q-4 on the two sides of (1).
openaire   +2 more sources

Residual permutation tests for feature importance in machine learning

British Journal of Mathematical and Statistical Psychology, EarlyView.
Abstract Psychological research has traditionally relied on linear models to test scientific hypotheses. However, the emergence of machine learning (ML) algorithms has opened new opportunities for exploring variable relationships beyond linear constraints.
Po‐Hsien Huang
wiley   +1 more source

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
doaj   +1 more source

Investigating the Properties and Dynamic Applications of Δ_h Legendre–Appell Polynomials

Mathematics
This research aims to introduce and examine a new type of polynomial called the Δh Legendre–Appell polynomials. We use the monomiality principle and operational rules to define the Δh Legendre–Appell polynomials and explore their properties.
Noor Alam, Shahid Ahmad Wani, Waseem Ahmad Khan, Hasan Nihal Zaidi   +3 more
doaj   +1 more source

Plots of Legendre Polynomials

, 2016
Plot the Legendre polynomials, which appear in many mathematical problems, notably those involving systems with circular symmetryComponente Curricular::Educação Superior::Ciências Exatas e da Terra ...
Wolfram, Stephen
core   +2 more sources

Genetic Associations of Functional Longevity With Sexual Precocity and Growth Traits in Nellore Beef Cattle

Journal of Animal Breeding and Genetics, EarlyView.
ABSTRACT Functional longevity (FL) is a complex trait that integrates many attributes directly contributing to the successful retention and productivity of a cow within the herd. Consequently, improving FL in beef cattle increases herd profitability. This study aimed to estimate the genetic associations between two alternative FL definitions and traits
Dalila Ribeiro dos Santos, Gabriele de Souza Silva Fernandes, Arione Augusti Boligon, Mário Luiz Santana, Gilberto Romeiro de Oliveira Menezes, Denise Rocha Ayres, Annaiza Braga Bignardi, Rodrigo Junqueira Pereira   +7 more
wiley   +1 more source

The telephone polynomials: An Appell-type orthogonal polynomials connecting Hermite–Laguerre polynomials

Nuclear Physics B
This article investigates a new Appell-type sequence, the telephone polynomials, which extend the classical telephone (involution) numbers. We present their fundamental algebraic properties, structural characterizations, and diverse interconnections with
Kalika Prasad, Munesh Kumari
doaj   +1 more source