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On the q-Charlier Multiple Orthogonal Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2015 We introduce a new family of special functions, namely $q$-Charlier multiple orthogonal polynomials. These polynomials are orthogonal with respect to $q$-analogues of Poisson distributions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained. An explicit representation in
Arves??, J., Ram??rez-Aberasturis, A.M.
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Multiple Meixner Polynomials on a Non-Uniform Lattice
Mathematics, 2020 We consider two families of type II multiple orthogonal polynomials. Each family has orthogonality conditions with respect to a discrete vector measure.
Jorge Arvesú +1 more
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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
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Global fluctuations for Multiple Orthogonal Polynomial Ensembles
Journal of Functional Analysis, 2021 We study the fluctuations of linear statistics with polynomial test functions for Multiple Orthogonal Polynomial Ensembles. Multiple Orthogonal Polynomial Ensembles form an important class of determinantal point processes that include random matrix models such as the GUE with external source, complex Wishart matrices, multi-matrix models and others ...
Maurice Duits +2 more
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Multiple Orthogonal Polynomials on the Unit Circle
Constructive Approximation, 2007 We introduce multiple orthogonal polynomials on the unit circle. We show how this is related to simultaneous rational approximation to Caratheodory functions (two-point Hermite-Pade approximation near zero and near infinity). We give a Riemann-Hilbert problem for which the solution is in terms of type I and type II multiple orthogonal polynomials on ...
Judit Mínguez Ceniceros +1 more
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The Symmetrization Problem for Multiple Orthogonal Polynomials [PDF]
, 2021 We analyze the effect of symmetrization in the theory of multiple orthogonal polynomials. For a symmetric sequence of type II multiple orthogonal polynomials satisfying a high-term recurrence relation, we fully characterize the Weyl function associated to the corresponding block Jacobi matrix as well as the Stieltjes matrix function.
Branquinho, Amílcar +1 more
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
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
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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 +6 more
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Transactions of the American Mathematical Society, Series BI analyze an unexpected connection between multiple orthogonal polynomials, d d -orthogonal polynomials, production matrices and branched continued fractions. This work can be viewed as a partial extension of Viennot’s combinatorial theory of orthogonal polynomials to the case where the production matrix is lower-Hessenberg but is not ...
Alan D. Sokal
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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 +9 more
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