Results 71 to 80 of about 80,472 (232)

Representation by Chebyshev Polynomials for Sums of Finite Products of Chebyshev Polynomials [PDF]

Symmetry, 2018
In this paper, we consider sums of finite products of Chebyshev polynomials of the first, third, and fourth kinds, which are different from the previously-studied ones. We represent each of them as linear combinations of Chebyshev polynomials of all kinds whose coefficients involve some terminating hypergeometric functions 2 F 1 .
Taekyun Kim 0001, Dae San Kim, Lee-Chae Jang, Dmitry V. Dolgy   +3 more
openaire   +1 more source

Operando X‐Ray Diffraction and Total Scattering Characterization of Battery Materials: Not Just a Pretty Picture

Advanced Energy Materials, EarlyView.
This review focuses on operando studies of battery materials by X‐ray diffraction (XRD) and total X‐ray scattering (TXS). This work highlights potential pitfalls and identify best‐practices for operando studies and reviews some unusual experiments to illustrate how these methods can be applied beyond the evaluation of the early‐stage cycling mechanisms
Amalie Skurtveit, Eira Tiberg North, Izar Capel Berdiell, Wouter Van Beek, David S. Wragg, Alexey Y. Koposov   +5 more
wiley   +1 more source

Decay analysis of bivariate Chebyshev coefficients for functions with limited regularity

Results in Applied Mathematics
The Chebyshev polynomial approximation is a useful tool to approximate smooth and non-smooth functions. In fact, for a sufficiently smooth function, the partial sum of Chebyshev series expansion provides optimal polynomial approximation.
Akansha
doaj   +1 more source

Machine Learning Interatomic Potentials for Energy Materials: Architectures, Training Strategies, and Applications

Advanced Energy Materials, EarlyView.
Machine learning interatomic potentials bridge quantum accuracy and computational efficiency for materials discovery. Architectures from Gaussian process regression to equivariant graph neural networks, training strategies including active learning and foundation models, and applications in solid‐state electrolytes, batteries, electrocatalysts ...
In Kee Park, Saeed Pourasad, Jinhong Mun, Arunkumar Chitteth Rajan, Tae Hyeon Park, Anand Rohit, Mohammad Zafari, Tan‐Lien Pham, Eunjae Jung, Bonseung Koo, Miran Ha, Gi Beom Sim, Hyun Gyu Park, Won Woong Choi, Kwanghyeon Jo, Soohaeng Yoo Willow, David ChangMo Yang, Chang Woo Myung, Geunsik Lee, Kwang S. Kim   +19 more
wiley   +1 more source

A rational spectral collocation method with adaptively transformed Chebyshev grid points [PDF]

, 2005
A spectral collocation method based on rational interpolants and adaptive grid points is presented. The rational interpolants approximate analytic functions with exponential accuracy by using prescribed barycentric weights and transformed Chebyshev ...
Tee, T. W., Trefethen, Lloyd N.
core  

The integer Chebyshev problem [PDF]

Mathematics of Computation, 1996
We are concerned with the problem of minimizing the supremum norm on an interval of a nonzero polynomial of degree at mostnnwith integer coefficients. This is an old and hard problem that cannot be exactly solved in any nontrivial cases. We examine the case of the interval[0,1][0,1]in most detail.
Peter B. Borwein, Tamás Erdélyi
openaire   +2 more sources

Data‐Driven High‐Throughput Volume Fraction Estimation From X‐Ray Diffraction Patterns

Advanced Intelligent Discovery, EarlyView.
Long exposure times and the need for manual evaluation limit the use of X‐ray diffraction in high‐throughput applications. This study presents a data‐driven approach addressing both issues. HiVE (a method for High‐throughput Volume fraction Estimation) performs composition estimation for high‐noise XRD patterns produced using polychromatic emission ...
Hawo H. Höfer, André Orth, Robert Wang, Ben Breitung, Simon Schweidler, Jasmin Aghassi‐Hagmann, Markus Reischl   +6 more
wiley   +1 more source

Chebyshev-Vandermonde Systems [PDF]

Mathematics of Computation, 1991
A Chebyshev-Vandermonde matrix \[ V = [ p j ( z k ) ] j , k = 0 n ∈
Reichel, Lothar, Opfer, Gerhard
openaire   +1 more source

RAMS: Residual‐Based Adversarial‐Gradient Moving Sample Method for Scientific Machine Learning in Solving Partial Differential Equations

Advanced Intelligent Discovery, EarlyView.
We propose a residual‐based adversarial‐gradient moving sample (RAMS) method for scientific machine learning that treats samples as trainable variables and updates them to maximize the physics residual, thereby effectively concentrating samples in inadequately learned regions.
Weihang Ouyang, Min Zhu, Wei Xiong, Si‐Wei Liu, Lu Lu   +4 more
wiley   +1 more source

Some results on generalization $\alpha-$Chebyshev wavelets [PDF]

Journal of Mahani Mathematical Research
In this paper, we introduce  generalized formulae for well-known functions such as $\alpha$-Chebyshev functions. We define $\alpha-$Chebyshev wavelets approximation and  generalization $\alpha-$wavelet coapproximation.
Hamid Mazaheri, Aabdul Wali Safi, Seayed Mohammad Jesmani   +2 more
doaj   +1 more source