Results 111 to 120 of about 15,466 (317)

Structure relations for orthogonal polynomials on the unit circle [PDF]

, 2012
Structure relations for orthogonal polynomials with respect to Hermitian linear functionals are studied. Firstly, we prove that semi-classical orthogonal polynomials satisfy structure relations of the following type: ∑k=0s1βn,kPn+s1-k+∑k=0s2γn,kzkPn-1-k∗=
Branquinho, A., Rebocho, M.N., Rebocho, M. N.   +2 more
core   +1 more source

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, EarlyView.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Studies on the Method of Orthogonal Collocation III. The Use of Jacobi Orthogonal Polynomials for the Solution of Boundary Value Problems

Journal of King Saud University: Engineering Sciences, 1999
Previous work identified the kind of Jocobi polynomials suitable to solve boundary value problems of the diffusion type in a slab, cylinder or sphere.
Mostafa Ali Soliman, A.A. Ibrahim
doaj   +1 more source

Harnessing Machine Learning to Understand and Design Disordered Solids

Advanced Intelligent Discovery, EarlyView.
This review maps the dynamic evolution of machine learning in disordered solids, from structural representations to generative modeling. It explores how deep learning and model explainability transform property prediction into profound physical insight.
Muchen Wang, Yue Fan
wiley   +1 more source

Complementary Romanovski-Routh polynomials and their zeros

Trends in Computational and Applied Mathematics
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials.
L. L. Silva Ribeiro, A. Sri Ranga, Yen Chi Lun   +2 more
doaj   +1 more source

In Situ Contact Angle Measurement for Autonomous Spin Coating in Self‐Driving Labs

Advanced Intelligent Discovery, EarlyView.
A vision‐based add‐on transforms commercial spin coaters into autonomous modules of Self‐Driving Labs. Combining a width‐scaled U‐Net with classical geometric analysis, the system simultaneously measures contact angles and estimates substrate pose using a single camera.
Sven Fischer, Micha Hiegle, Holger Röhm
wiley   +1 more source

Orthonormal aberration decomposition for circular aperture and rectangular field with extension to multiple-aperture systems

AIP Advances
A new set of orthogonal polynomials and the traditional Zernike polynomials are combined to construct the wavefront of the sparse aperture (SA) optical system.
Baohua Chen, Quanying Wu, Junliu Fan, Songhongkang Yang, Zhixiang Li, Donghui Shen   +5 more
doaj   +1 more source

Orthogonal Polynomials with Singularly Perturbed Freud Weights. [PDF]

Entropy (Basel), 2023
Min C, Wang L.
europepmc   +1 more source

d-Orthogonal Analogs of Classical Orthogonal Polynomials [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2018
Classical orthogonal polynomial systems of Jacobi, Hermite and Laguerre have the property that the polynomials of each system are eigenfunctions of a second order ordinary differential operator. According to a famous theorem by Bochner they are the only systems on the real line with this property.
openaire   +2 more sources

On the zeros of orthogonal polynomials on the unit circle [PDF]

, 2013
Let {zn } be a sequence in the unit disk {z∈C:{pipe}z{pipe}
Alfaro, María Pilar, Bello-Hernández, Manuel [0000-0002-1833-4688], Montaner, Jesús María   +2 more
core   +1 more source