Results 91 to 100 of about 535,269 (286)
Spectral analysis for the exceptional Xm-Jacobi equation
Electronic Journal of Differential Equations, 2015 We provide the mathematical foundation for the $X_m$-Jacobi spectral theory. Namely, we present a self-adjoint operator associated to the differential expression with the exceptional $X_m$-Jacobi orthogonal polynomials as eigenfunctions.
Constanze Liaw +2 more
doaj
ON CUBATURE RULES ASSOCIATED TO WEYL GROUP ORBIT FUNCTIONS
Acta Polytechnica, 2016 The aim of this article is to describe several cubature formulas related to the Weyl group orbit functions, i.e. to the special cases of the Jacobi polynomials associated to root systems.
Lenka Háková +2 more
doaj +1 more source
Some generalized Jacobi polynomials
Computers & Mathematics with Applications, 2003 Following the work of the first author [Int. J. Math. Math. Sci. 24, No. 10, 673--689 (2000; Zbl 0967.33006)] in this paper the authors obtain the explicit expressions for the coefficients in the three term pure recurrence relation for generalized Jacobi polynomials defined by a positive weight function which involves a \(p\)th power of \((1-x)\).
Atia, M.J., Alaya, J., Ronveaux, A.
openaire +2 more sources
A Physics‐Informed Learning Framework to Solve the Infinite‐Horizon Optimal Control Problem
International Journal of Robust and Nonlinear Control, Volume 35, Issue 16, Page 6932-6944, 10 November 2025.ABSTRACT We propose a physics‐informed neural networks (PINNs) framework to solve the infinite‐horizon optimal control problem of nonlinear systems. In particular, since PINNs are generally able to solve a class of partial differential equations (PDEs), they can be employed to learn the value function of the infinite‐horizon optimal control problem via
Filippos Fotiadis +1 more
wiley +1 more source
Advances in Differential Equations, 2015 In this article, we introduce a numerical technique for solving a general form of the fractional optimal control problem. Fractional derivatives are described in the Caputo sense.
E. H. Doha +4 more
semanticscholar +1 more source
Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials [PDF]
, 2014 The possibility for the Jacobi equation to admit, in some cases, general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such polynomials are used here to build seed functions of a
B. Bagchi, Y. Grandati, C. Quesne
semanticscholar +1 more source
Divergent Jacobi polynomial series [PDF]
Proceedings of the American Mathematical Society, 1983 Fix real numbers α ⩾ β ⩾ − 1 2 \alpha \geqslant \beta \geqslant - \tfrac {1}{2} , with α > − 1 2 \alpha > - \tfrac {1}{2} , and equip [
openaire +2 more sources
Inf‐Sup Stable Non‐Conforming Finite Elements on Tetrahedra With Second‐ and Third‐Order Accuracy
Numerical Methods for Partial Differential Equations, Volume 41, Issue 6, November 2025.ABSTRACT We introduce a family of scalar non‐conforming finite elements with second‐ and third‐order accuracy with respect to the H1$$ {H}^1 $$‐norm on tetrahedra. Their vector‐valued versions generate, together with discontinuous pressure approximations of order one and two, respectively, inf‐sup stable finite element pairs with convergence order two ...
Loïc Balazi +3 more
wiley +1 more source
Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim +3 more
doaj +1 more source
The geometry and arithmetic of bielliptic Picard curves
Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley +1 more source