Results 31 to 40 of about 32,914 (238)

Trigonometric Approximation by Modulus of Smoothness in Lp,α (X)

Al-Mustansiriyah Journal of Science, 2021
In this paper, we study the approximate properties of functions by means of trigonometric polynomials in weighted spaces. Relationships between modulus of smoothness of function derivatives and those of the jobs themselves are introduced. In the weighted
Mohammed Hamad Fayyadh, Alaa Adnan Auad
doaj   +1 more source

On generalized trigonometric functions and series of rational functions

, 2017
Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$.
Yu, Han
core   +1 more source

Some Trigonometric Polynomials with Extremely Small Uniform Norm

, 2014
An example of trigonometric polynomials with extremely small uniform norm is given. This example demonstrates the potential limits for extension of Sidon's inequality for lacunary polynomials in a certain ...
Grigoriev, Pavel G., Radomskii, Artyom O.   +1 more
core   +1 more source

A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types

Mathematics, 2019
We study some properties of Sheffer sequences for some special polynomials with complex Changhee and Daehee polynomials introducing their complex versions of the polynomials and splitting them into real and imaginary parts using trigonometric polynomial ...
Dojin Kim
doaj   +1 more source

Orthonormal Systems in Linear Spans

, 2012
We show that any $N$-dimensional linear subspace of $L^2(\mathbb{T})$ admits an orthonormal system such that the $L^2$ norm of the square variation operator $V^2$ is as small as possible. When applied to the span of the trigonometric system, we obtain an
Chevet, Garsia, Marcus, Milman
core   +1 more source

On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

Mathematics, 2020
We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para ...
Jorge A. Borrego-Morell, Cleonice F. Bracciali, Alagacone Sri Ranga   +2 more
doaj   +1 more source

q-Ultraspherical polynomials for q a root of unity

, 1996
Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra.
A. F. Nikiforov, A. V. Odesskii, A. Zhedanov, A. Zhedanov, Alexei Zhedanov, B. N. Zakhariev, D. B. Fairlie, R. Askey, R. Askey, S. Skorik, T. S. Chihara, V. Spiridonov, Vyacheslav Spiridonov, W. Al-Salam   +13 more
core   +2 more sources

Flexible Memory: Progress, Challenges, and Opportunities

Advanced Intelligent Discovery, EarlyView.
Flexible memory technology is crucial for flexible electronics integration. This review covers its historical evolution, evaluates rigid systems, proposes a flexible memory framework based on multiple mechanisms, stresses material design's role, presents a coupling model for performance optimization, and points out future directions.
Ruizhi Yuan, Sen Chen, Minghui Guo, Ziliang Cui, Yujie Du, Jing Liu   +5 more
wiley   +1 more source

Analytical and Numerical Soliton Solutions of the Shynaray II‐A Equation Using the G′G,1G$$ \left(\frac{G^{\prime }}{G},\frac{1}{G}\right) $$‐Expansion Method and Regularization‐Based Neural Networks

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Nonlinear differential equations play a fundamental role in modeling complex physical phenomena across solid‐state physics, hydrodynamics, plasma physics, nonlinear optics, and biological systems. This study focuses on the Shynaray II‐A equation, a relatively less‐explored parametric nonlinear partial differential equation that describes ...
Aamir Farooq, H. W. A. Riaz, Sadique Rehman, M. Mamun Miah, Wen Xiu Ma   +4 more
wiley   +1 more source

Single Smooth Waveform Command‐Shaping Control of Overhead Crane Systems Utilizing Two‐Stage Acceleration–Deceleration Profile for Short‐Moving Point‐to‐Point Maneuver

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Modern industrial demand for efficient material handling in confined spaces has driven the need for overhead cranes capable of short‐distance point‐to‐point maneuvers without compromising payload stability. Conventional three‐stage shaper profiles, experiencing acceleration, cruising, and deceleration, become inefficient or infeasible for ...
Mohammed Alfares, Jasem Baroon, Khaled Alhazza   +2 more
wiley   +1 more source