Results 31 to 40 of about 2,693 (191)

Numerical solutions for fractional optimal control problems using Mü‎‎‎‎‎‎‎ntz-Legendre polynomials [PDF]

Journal of Mahani Mathematical Research
This study introduces a novel method using the Müntz-Legendre polynomials for numerically solving fractional optimal control problems. Utilizing the unique properties of Müntz-Legendre polynomials when dealing with fractional operators, these polynomials
Mohammad Sahabi, Allahbakhsh Yazdani Cherati   +1 more
doaj   +1 more source

CFD modeling and sensitivity‐guided design of silicon filament CVD reactors

AIChE Journal, EarlyView.
Abstract Filament‐based chemical vapor deposition (CVD) for silicon (Si) coatings is often treated as an adaptation of planar deposition. But this overlooks fundamental shifts in transport phenomena and reaction kinetics. In filament CVD, the filament acts as a substrate, heat source, and flow disruptor simultaneously. In this work, we ask: What really
G. P. Gakis, G. Loachamín‐Suntaxi, I. G. Aviziotis, E. D. Koronaki, P. P. Filippatos, G. Chatzigiannakis, S. P. A. Bordas, D. Davazoglou, A. G. Boudouvis   +8 more
wiley   +1 more source

Insights into New Generalization of q-Legendre-Based Appell Polynomials: Properties and Quasi Monomiality

Mathematics
In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced.
Naeem Ahmad, Waseem Ahmad Khan
doaj   +1 more source

Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations

Advances in Mathematical Physics, 2020
Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials.
Haidong Qu, Xiaopeng Yang, Zihang She
doaj   +1 more source

Design, Control, and Clinical Applications of Magnetic Actuation Systems: Challenges and Opportunities

Advanced Intelligent Systems, Volume 7, Issue 3, March 2025.
This review aims to provide a broad understanding for interdisciplinary researchers in engineering and clinical applications. It addresses the development and control of magnetic actuation systems (MASs) in clinical surgeries and their revolutionary effects in multiple clinical applications.
Yingxin Huo, Lidong Yang, Tiantian Xu, Dong Sun   +3 more
wiley   +1 more source

Novel Results on Legendre Polynomials in the Sense of a Generalized Fractional Derivative

Mathematical and Computational Applications
In this article, new results are investigated in the context of the recently introduced Abu-Shady–Kaabar fractional derivative. First, we solve the generalized Legendre fractional differential equation.
Francisco Martínez, Mohammed K. A. Kaabar, Inmaculada Martínez   +2 more
doaj   +1 more source

Modified F‐tests for assessing tree radial growth under linear‐circular regression models with correlated errors: A comprehensive toolbox rooted in G. E. P. Box's theorems

Canadian Journal of Statistics, EarlyView.
Abstract Annual tree growth is a complex biological process. Modelling radial growth in the trunk by linear‐circular regression with one mode and correlated errors has allowed the definition and assessment of a preferred direction for 1 and 2 years. Here, modified F$$ F $$‐tests are presented for 3 years, 1 mode/year; 1 year, 2 modes for possible main ...
Pierre Dutilleul, Tomoaki Imoto, Kunio Shimizu   +2 more
wiley   +1 more source

On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials

Mathematics, 2020
The generalization of Rodrigues’ formula for orthogonal matrix polynomials has attracted the attention of many researchers. This generalization provides new integral and differential representations in addition to new mathematical results that are ...
Mohra Zayed, Mahmoud Abul-Ez, Mohamed Abdalla, Nasser Saad   +3 more
doaj   +1 more source

Nonlinear permuted Granger causality

Canadian Journal of Statistics, EarlyView.
Abstract Granger causality is an established, contentious method that seeks causal temporal connections via association and precedence. While not true causal inference, it assists in mapping networks of information flow that may warrant further study.
Noah D. Gade, Jordan Rodu
wiley   +1 more source

On Legendre numbers

International Journal of Mathematics and Mathematical Sciences, 1985
The Legendre numbers, an infinite set of rational numbers are defined from the associated Legendre functions and several elementary properties are presented. A general formula for the Legendre numbers is given. Applications include summing certain series
Paul W. Haggard
doaj   +1 more source