Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Mulim, Henrique Alberto Pinto, Luis Fernando Batista Zampar, Aline Mourão, Gerson Barreto Valloto, Altair Antônio Pedrosa, Victor Breno
Published in
Annals of Animal Science

The experiments reported in this research paper were aimed at assessing the genetic responses of a Holstein cow population, as a response to the variations in environmental temperature, through the analysis of the effects resulting from the genotype by environment interaction (GEI), based on reaction norms. Therefore, milk production data was colle...

Bakaleinikov, L. A. Tropp, E. A.
Published in
Computational Mathematics and Mathematical Physics

AbstractAn asymptotic expansion of the Legendre polynomials \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{P}_{n}}\left( x \right)$$\end{document} in inverse powers ...

Ghorbani, Asghar Baleanu, Dumitru
Published in
Advances in Difference Equations

A simple scheme is proposed for computing N×N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$N \times N$\end{document} spectral differentiation matrices of fractional or...

Shokoohinia, Mohammad Reza Fateh, Mohammad Mehdi Gholipour, Reza
Published in
SN Applied Sciences

In this work, an adaptive dynamic sliding mode control approach is proposed for robotic systems via uncertainty estimators with exponential convergence rate. The uncertainties are estimated using various uncertainty estimators such as the Fourier series expansion, Legendre polynomials and adaptive fuzzy systems. Also, for each uncertainty estimator...

wang, tingting qiao, liang

By using the analysis methods and the properties of Chebyshev polynomials of the first kind, this paper studies certain symmetry sums of the Legendre polynomials, and gives some new and interesting identities and inequalities for them, thus improving certain existing results.

Silva, Delvan Alves Costa, Claudio Nápolis Silva, Alessandra Alves Silva, Hugo Teixeira Lopes, Paulo Sávio Silva, Fabyano Fonseca Veroneze, Renata Thompson, Gertrude Aguilar, Ignacio Carvalheira, Júlio
...
Published in
Journal of animal breeding and genetics = Zeitschrift fur Tierzuchtung und Zuchtungsbiologie

Autoregressive (AR) and random regression (RR) models were fitted to test-day records from the first three lactations of Brazilian Holstein cattle with the objective of comparing their efficiency for national genetic evaluations. The data comprised 4,142,740 records of milk yield (MY) and somatic cell score (SCS) from 274,335 cows belonging to 2,32...

He, Yuan
Published in
Advances in Difference Equations

In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials. By making use of some analytic and combinatorial methods, we establish some new expressions for sums of products of arbitrary numbers of Chebyshev polynomials of the first and second ...

kukushkin, maksim v.

In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann&ndash / Liouville fractional integral and derivative operators on a compact of the real axis. This approach has some advantages and allows us to complete the previously known results of the fractional calculus theory by means of reformulating them i...