Results 81 to 90 of about 40,478 (197)

A generalization of Mehta-Wang determinant and Askey-Wilson polynomials [PDF]

Discrete Mathematics & Theoretical Computer Science, 2013
Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the
Victor J. W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng   +3 more
doaj   +1 more source

Breaking Barriers in High‐Order Spectral Methods: The Intrinsic Matrix Approach

International Journal for Numerical Methods in Engineering, Volume 127, Issue 5, 15 March 2026.
ABSTRACT This paper introduces a unified framework in Hilbert spaces for applying high‐order differential operators in bounded domains using Chebyshev, Legendre, and Fourier spectral methods. By exploiting the banded structure of differentiation matrices and embedding boundary conditions directly into the operator through a scaling law relating ...
Osvaldo Guimarães, José R. C. Piqueira
wiley   +1 more source

On Saigo Fractional $q$-Calculus of a General Class of $q$-Polynomials [PDF]

Sahand Communications in Mathematical Analysis
In this paper, we derive Saigo fractional $q$-integrals of the general class of $q$-polynomials and demonstrate their application by investigating $q$-Konhouser biorthogonal polynomial,  $q$-Jacobi polynomials and basic analogue of the Kamp$\acute{e}$ de
Biniyam Shimelis, Dayalal Suthar
doaj   +1 more source

Multiple Wilson and Jacobi–Piñeiro polynomials

Journal of Approximation Theory, 2005
22 pages, 2 ...
Beckermann, B., Coussement, J., Van Assche, W.   +2 more
openaire   +3 more sources

Methods Based on Polynomial Chaos for Quadratic Delay Differential Equations With Random Parameters

Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 1, March 2026.
ABSTRACT We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos.
Roland Pulch
wiley   +1 more source

Riemann–Liouville Operator in Weighted L_p Spaces via the Jacobi Series Expansion

Axioms, 2019
In this paper, we use the orthogonal system of the Jacobi polynomials as a tool to study the Riemann−Liouville fractional integral and derivative operators on a compact of the real axis.
Maksim V. Kukushkin
doaj   +1 more source

Photonic Unitary Circuits for Quantum Information Processing

Advanced Quantum Technologies, Volume 9, Issue 3, March 2026.
Unitary transformations are the cornerstone of quantum computing, enabling reversible manipulation of quantum states. This review evaluates photonic waveguide architectures as an evolving solution for quantum computing, exploiting the unique properties of photons. It investigates current theoretical frameworks, material platforms, and design strategies.
Kevin Zelaya, Armando Perez‐Leija, Abdou Shetewy, Jonathan Friedman, Menglong He, Kambiz Jamshidi, Mohammad‐Ali Miri   +6 more
wiley   +1 more source

A new family of orthogonal polynomials in three variables

Journal of Inequalities and Applications, 2020
In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş, Iván Area, Esra Güldoğan   +2 more
doaj   +1 more source

Modified Bernstein Polynomials and Jacobi Polynomials in q-Calculus

, 2004
We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the $q$-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials.
Derriennic, Marie-Madeleine
core   +3 more sources

Bayesian Adaptive Polynomial Chaos Expansions

Stat, Volume 15, Issue 1, March 2026.
ABSTRACT Polynomial chaos expansions (PCEs) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare—especially with implementations in R.
Kellin N. Rumsey, Devin Francom, Graham Gibson, J. Derek Tucker, Gabriel Huerta   +4 more
wiley   +1 more source