Results 31 to 40 of about 71,161 (303)

A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]

, 2009
A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M., Arvesú J., Arvesú J., C. Esposito, Chihara T.S., J. Arvesú, Lee D.W., Nikiforov A.F., Nikiforov A.F., Nikishin E.M., Piñeiro L.R.   +10 more
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Application of uncertainty design optimization based on polynomial chaos expansions and maximum entropy method in ship design

Zhongguo Jianchuan Yanjiu, 2023
ObjectivesThe key to uncertainty design optimization (UDO) is uncertainty quantification (UQ), but the traditionally used Monte Carlo (MC) method can be time-consuming and computationally expensive.
Xiao WEI, Heng LI, Chenran HUANG
doaj   +1 more source

Electrostatic Partners and Zeros of Orthogonal and Multiple Orthogonal Polynomials

Constructive Approximation, 2022
AbstractFor a given polynomial P with simple zeros, and a given semiclassical weight w, we present a construction that yields a linear second-order differential equation (ODE), and in consequence, an electrostatic model for zeros of P. The coefficients of this ODE are written in terms of a dual polynomial that we call the electrostatic partner of P ...
Martinez-Finkelshtein, Andrei, Orive, Ramón, Sánchez Lara, Joaquín Francisco   +2 more
openaire   +3 more sources

Biomedical Multimedia Encryption by Fractional-Order Meixner Polynomials Map and Quaternion Fractional-Order Meixner Moments

IEEE Access, 2022
Chaotic systems are widely used in signal and image encryption schemes. Therefore, the design of new chaotic systems is always useful for improving the performance of encryption schemes in terms of security. In this work, we first demonstrate the chaotic
Achraf Daoui, Mohamed Yamni, Hicham Karmouni, Mhamed Sayyouri, Hassan Qjidaa, Musheer Ahmad, Ahmed A. Abd El-Latif   +6 more
doaj   +1 more source

Hypergeometric multiple orthogonal polynomials [PDF]

, 2021
This thesis is devoted to the analysis of multiple orthogonal polynomials for indices on the so-called step-line with respect to absolutely continuous measures on the positive real line, whose moments are given by ratios of Pochhammer symbols (also known as rising factorials).
openaire   +1 more source

Multidimensional Toda Lattices: Continuous and Discrete Time [PDF]

, 2016
In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates.
Aptekarev, Alexander I., Derevyagin, Maxim, Miki, Hiroshi, Van Assche, Walter   +3 more
core   +1 more source

Multiple Orthogonal Polynomials of two real variables [PDF]

Journal of Mathematical Analysis and Applications
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e approximation, random matrix theory or integrable systems.
Lidia Fernández, Juan Antonio Villegas
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Multi-indexed (q-)Racah Polynomials [PDF]

, 2012
As the second stage of the project multi-indexed orthogonal polynomials, we present, in the framework of `discrete quantum mechanics' with real shifts in one dimension, the multi-indexed (q-)Racah polynomials.
Andrews G E, Bannai E, Chakrabarti R, Darboux G, Fernández D J, Gendenshtein L E, Gladwell G M L, Grandati Y, Gómez-Ullate D, Ho C-L, Ho C-L, Ismail M E H, Koekoek R Swarttouw R F, Krein M G, Odake S, Odake S, Odake S, Parthasarathy P R, Quesne C, Quesne C, Quesne C, Ryu Sasaki, Sasaki R, Satoru Odake, Vinet L Zhedanov A   +24 more
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials [PDF]

Transactions of the American Mathematical Society, 2020
We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey--Wilson, multiple continuous dual $q$-Hahn, and multiple Al ...
Nuwacu, Jean Paul, Van Assche, Walter
openaire   +3 more sources

Mach-Zehnder Interferometer Sensor Curvature Demodulation Method Based on the Orthogonal Decomposition of Spectral Curves

IEEE Access, 2020
This paper proposes a curvature demodulation of Mach-Zehnder interferometer (MZI) sensors based on complete spectral information. An MZI sensor composed of two waist-enlarged single mode fibers (SMFs) was fabricated.
Mingyao Liu, Jingliang Wang, Yi Liu, Yuegang Tan, Kang Yun, Liu Hong, Han Song, Xiangsheng Zeng, Ping Xia, Zhao Li   +9 more
doaj   +1 more source