Results 151 to 160 of about 411,141 (342)

On the modifications of classical orthogonal polynomials: The symmetric case

Approximation Theory and its Applications, 1998
We consider the modifcations of the monic Hermite and Gegenbauer polynomials via the addition of one point mass at the origin. Some properties of the resulting polynomials are studied: three-term recurrence relation, differential equation, ratio asymptotics, hypergeometric representation as well as, for large n, the behaviour of their zeros.
Álvarez Nodarse, Renato, Marcellán Español, Francisco   +1 more
openaire   +3 more sources

Critical Energies and Wigner Functions of the Stationary States of the Bose Einstein Condensates in a Double‐Well Trap

Advanced Quantum Technologies, EarlyView.
The critical parameters and energies, at which the wave function of the Bose Einstein Condensate in a double well trap exhibit the symmetry breaking, are estimated. The phase space representation of the states is obtained trough the Wigner function and the trends of the negativities are analyzed.
D. J. Nader, E. Serrano‐Ensástiga
wiley   +1 more source

Nice q-analogs of orthogonal polynomials with nice moments: Some simple examples [PDF]

arXiv
In this note I collect some typical examples of orthogonal polynomials with simple moments where both moments and orthogonal polynomials have nice q-analogs.
arxiv  

New Characterizations of Discrete Classical Orthogonal Polynomials

Journal of Approximation Theory, 1997
AbstractWe prove that if both {Pn(x)}∞n=0and {∇rPn(x)}∞n=rare orthogonal polynomials for any fixed integer r⩾1, then {Pn(x)}∞n=0must be discrete classical orthogonal polynomials. This result is a discrete version of the classical Hahn's theorem stating that if both {Pn(x)}∞n=0and {(d/dx)rPn(x)}∞n=rare orthogonal polynomials, then {Pn(x)}∞n=0are ...
Kwon, KH Kwon, Kil Hyun, Lee, DW, Park, SB   +2 more
openaire   +3 more sources

Applications of Artificial Intelligence in Neurological Voice Disorders

World Journal of Otorhinolaryngology - Head and Neck Surgery, EarlyView.
ABSTRACT Neurological voice disorders, such as Parkinson's disease, laryngeal dystonia, and stroke‐induced dysarthria, significantly impact speech production and communication. Traditional diagnostic methods rely on subjective assessment, whereas artificial intelligence (AI) offers objective, noninvasive, and scalable solutions for voice analysis. This
Dongren Yao, Aki Koivu, Kristina Simonyan   +2 more
wiley   +1 more source

Alternative Orthogonal Polynomials [PDF]

arXiv, 2004
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences that are the result of the inverse orthogonalization procedure.
arxiv  

Generalized coherent states for classical orthogonal polynomials [PDF]

, 2002
V. V. Borzov
openalex   +3 more sources

The generalized Hausman test for detecting non‐normality in the latent variable distribution of the two‐parameter IRT model

British Journal of Mathematical and Statistical Psychology, EarlyView.
Abstract This paper introduces the generalized Hausman test as a novel method for detecting the non‐normality of the latent variable distribution of the unidimensional latent trait model for binary data. The test utilizes the pairwise maximum likelihood estimator for the parameters of the latent trait model, which assumes normality of the latent ...
Lucia Guastadisegni, Silvia Cagnone, Irini Moustaki, Vassilis Vasdekis   +3 more
wiley   +1 more source

New fractional-order shifted Gegenbauer moments for image analysis and recognition

Journal of Advanced Research, 2020
Orthogonal moments are used to represent digital images with minimum redundancy. Orthogonal moments with fractional-orders show better capabilities in digital image analysis than integer-order moments.
Khalid M. Hosny, Mohamed M. Darwish, Mohamed Meselhy Eltoukhy   +2 more
doaj  

Modelling non‐linear psychological processes: Reviewing and evaluating non‐parametric approaches and their applicability to intensive longitudinal data

British Journal of Mathematical and Statistical Psychology, EarlyView.
Abstract Psychological concepts are increasingly understood as complex dynamic systems that change over time. To study these complex systems, researchers are increasingly gathering intensive longitudinal data (ILD), revealing non‐linear phenomena such as asymptotic growth, mean‐level switching, and regulatory oscillations.
Jan I. Failenschmid, Leonie V. D. E. Vogelsmeier, Joris Mulder, Joran Jongerling   +3 more
wiley   +1 more source