Results 101 to 110 of about 1,059,315 (385)
Determinant inequalities for sieved ultraspherical polynomials
International Journal of Mathematics and Mathematical Sciences, 2001 Paul Turan first observed that the Legendre polynomials satisfy the inequality Pn2(x)−Pn−1(x)Pn(x)>0 ...
J. Bustoz, I. S. Pyung
doaj +1 more source
Orthogonal Polynomials of Askey-Wilson Type [PDF]
arXiv, 2022 We study two families of orthogonal polynomials. The first is a finite family related to the Askey-Wilson polynomials but the orthogonality is on the real line. A limiting case of this family is an infinite system of orthogonal polynomials whose moment problem is indeterminate.
arxiv
Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2013 We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain. In particular, this is true if they are positive a.e.
A. Kroó, D. Lubinsky
semanticscholar +1 more source
Stimulated Raman Scattering with Optical Vortex Beams
Advanced Photonics Research, EarlyView.This study presents exact analytical expressions for stimulated Raman scattering with Laguerre‐Gaussian beams, revealing signal dependence on topological and hyperbolic momentum. The results provide a theoretical foundation for coherent Raman imaging and detecting orbital angular momentum of light via structured light in nonlinear optics.
Minhaeng Cho
wiley +1 more source
New Stability Criteria for Discrete Linear Systems Based on Orthogonal Polynomials
Mathematics, 2020 A new criterion for Schur stability is derived by using basic results of the theory of orthogonal polynomials. In particular, we use the relation between orthogonal polynomials on the real line and on the unit circle known as the Szegő transformation ...
Luis E. Garza +2 more
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A NEW CHARACTERIZATION OF SYMMETRIC DUNKL AND \(q\)-DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS
Ural Mathematical Journal, 2023 In this paper, we consider the following \(\mathcal{L}\)-difference equation $$\Phi(x) \mathcal{L}P_{n+1}(x)=(\xi_nx+\vartheta_n)P_{n+1}(x)+\lambda_nP_{n}(x),\quad n\geq0,$$where \(\Phi\) is a monic polynomial (even), \(\deg\Phi\leq2\), \(\xi_n ...
Yahia Habbachi
doaj +1 more source
, 2004 We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely ...
Alvarez-Nodarse R +24 more
core +1 more source
New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials [PDF]
, 2012 In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant.
I. Marquette, C. Quesne
semanticscholar +1 more source
Epileptiform Activity and Seizure Risk Follow Long‐Term Non‐Linear Attractor Dynamics
Advanced Science, EarlyView.This study leverages the HAVOK framework to model long‐term, nonlinear attractor dynamics underlying epileptiform activity and seizure risk in epilepsy patients. By identifying key forcing mechanisms driving chaotic transitions, the findings improve seizure risk forecasting over multi‐day cycles and provide a pathway for personalized, data‐driven ...
Richard E Rosch +4 more
wiley +1 more source
CPL‐Diff: A Diffusion Model for De Novo Design of Functional Peptide Sequences with Fixed Length
Advanced Science, EarlyView.This study presents a diffusion model for generating functional peptide sequence lengths using mask control. The model can generate antimicrobial, antifungal, and antiviral peptides with specific lengths on demand. The model learns the structure of peptides better and generates peptides with better physicochemical properties, and the model has good ...
Zhenjie Luo +5 more
wiley +1 more source