Results 61 to 70 of about 219,144 (225)

Euler and the Legendre Polynomials

Euleriana, 2023
In this note we will present how Euler's investigations on various different subjects lead to certain properties of the Legendre polynomials. More precisely, we will show that the generating function and the difference equation for the Legendre polynomials was already written down by Euler in at least two different papers.
openaire   +2 more sources

Flow‐Critical Graphs

Journal of Graph Theory, EarlyView.
ABSTRACT Lovász et al. proved that every six‐edge‐connected graph has a nowhere‐zero three‐flow. In fact, they proved a more technical statement, which says that there exists a nowhere‐zero three‐flow that extends the flow prescribed on the incident edges of a single vertex z $z$ with bounded degree. We extend this theorem of Lovász et al.
Arnbjörg Soffía Árnadóttir, Zdeněk Dvořák, Bernard Lidický, Benjamin Moore, Evelyne Smith‐Roberge, Robert Šámal   +5 more
wiley   +1 more source

Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

Mathematics, 2018
In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we
Yuan He, Serkan Araci, Hari M. Srivastava, Mahmoud Abdel-Aty   +3 more
doaj   +1 more source

An Implicit Nodal–Staggered Finite Difference Scheme for Damped Shear Beam Models Without Rotational Inertia

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT We develop and analyze a fully discrete finite difference approximation for a damped shear beam model with mixed boundary conditions and no rotational inertia. The absence of a second‐order time derivative in the rotational equation gives rise to an asymmetric temporal structure.
Anderson de Jesus Araújo Ramos, André Fellipe Ribeiro de Almeida, Manoel Jeremias Dos Santos, Carlos Alberto da Silva Nonato   +3 more
wiley   +1 more source

On the q-Extension of Apostol-Euler Numbers and Polynomials [PDF]

, 2008
Recently, Choi et al. 2008 have studied the q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and multiple Hurwitz zeta function.
Lee-Chae Jang, Young-Hee Kim, Wonjoo Kim
core   +1 more source

Euler Pseudoprime Polynomials and Strong Pseudoprime Polynomials

Finite Fields and Their Applications, 2000
The subject of primality testing has become very important over the past few decades with a number of important results and concepts being developed. In this very interesting paper, the author uses a particular rank one Drinfeld module defined by M. van der Put to establish an analog of some of these results for \(\mathbb{F}_q[t]\).
openaire   +1 more source

Dynamic Performance Enhancement of a High‐Agility Hypersonic Mechanical System via a Learning‐Augmented Robust Control Architecture

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT The design of control systems for high‐agility mechanical systems operating in extreme environments is a significant challenge in nonlinear dynamics. This paper addresses the complex dynamic control problem of a hypersonic interceptor, modeled as a multi‐input multi‐output (MIMO) mechanical system characterized by strong aerodynamic cross ...
Mohammad Mahdi Soori, Seyed Hossein Sadati   +1 more
wiley   +1 more source

Assessing the ability of a stretched‐grid deep‐learning weather prediction model to capture physical balances

Quarterly Journal of the Royal Meteorological Society, EarlyView.
Regional deep learning weather prediction (DLWP) models, such as Bris, offer high resolution forecasts comparable with traditional numerical weather prediction (NWP) models. We evaluated Bris against the operational MetCoOp Ensemble Prediction System (MEPS) during extratropical cyclone Poly (July 5, 2023).
Francesco Pasquini, Michiel Baatsen, Bastien François, Natalie Theeuwes, Maurice Schmeits   +4 more
wiley   +1 more source

Summation formulas for the products of the Frobenius-Euler polynomials

, 2017
We present here a further investigation for the classical Frobenius-Euler polynomials. By making use of the generating function methods and summation transform techniques, we establish some summation formulas for the products of an arbitrary number of ...
Araci, Serkan, He, Yuan, Srivastava, H. M., Aracı, Serkan   +3 more
core   +1 more source

Optimal Gain Selection for the Arbitrary‐Order Homogeneous Differentiator

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Differentiation of noisy signals is a relevant and challenging task. Widespread approaches are the linear high‐gain observer acting as a differentiator and Levant's robust exact differentiator with a discontinuous right‐hand side. We consider the family of arbitrary‐order homogeneous differentiators, which includes these special cases.
Benjamin Calmbach, Jaime A. Moreno, Johann Reger   +2 more
wiley   +1 more source