Results 11 to 20 of about 133,004 (188)
Advanced Materials Interfaces, EarlyView., 2023 This review discusses the use of Surface‐Enhanced Raman Spectroscopy (SERS) combined with Artificial Intelligence (AI) for detecting antimicrobial resistance (AMR). Various SERS studies used with AI techniques, including machine learning and deep learning, are analyzed for their advantages and limitations.
Zakarya Al‐Shaebi +4 more
wiley +1 more source
Upward extension of the Jacobi matrix for orthogonal polynomials [PDF]
, 1995 Orthogonal polynomials on the real line always satisfy a three-term recurrence relation. The recurrence coefficients determine a tridiagonal semi-infinite matrix (Jacobi matrix) which uniquely characterizes the orthogonal polynomials.
Ronveaux, André, Van Assche, Walter
core +3 more sources
A connection between orthogonal polynomials on the unit circle and matrix orthogonal polynomials on the real line [PDF]
, 2002 Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal functions on the linear space of Laurent polynomials L, and ...
Alfaro +22 more
core +2 more sources
Equivalences of the Multi-Indexed Orthogonal Polynomials [PDF]
, 2013 Multi-indexed orthogonal polynomials describe eigenfunctions of exactly solvable shape-invariant quantum mechanical systems in one dimension obtained by the method of virtual states deletion.
Odake, Satoru
core +3 more sources
Some classical multiple orthogonal polynomials [PDF]
, 2001 Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximation (Hermite-Pade approximation) of a system of several ...
Al-Salam +23 more
core +4 more sources
Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle [PDF]
, 2001 We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials.
Ismail, Mourad E. H., Witte, Nicholas S.
core +2 more sources
Orthogonal Polynomials on the Unit Ball and Fourth-Order Partial Differential Equations [PDF]
, 2016 The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere.
Martínez, Clotilde, Piñar, Miguel A.
core +1 more source
Higher order matching polynomials and d-orthogonality [PDF]
, 2009 We show combinatorially that the higher-order matching polynomials of several families of graphs are d-orthogonal polynomials. The matching polynomial of a graph is a generating function for coverings of a graph by disjoint edges; the higher-order ...
Drake, Dan
core +2 more sources
On the Atkin Polynomials [PDF]
, 2013 We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identificationthen takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials.
El-Guindy, Ahmad, Ismail, Mourad E. H.
core +1 more source
Mehler-Heine asymptotics for multiple orthogonal polynomials
, 2016 Mehler-Heine asymptotics describe the behavior of orthogonal polynomials near the edges of the interval where the orthogonality measure is supported. For Jacobi polynomials and Laguerre polynomials this asymptotic behavior near the hard edge involves ...
Van Assche, Walter
core +1 more source