A New Spectral Mittag-Leffler Weighted Method to Solve Variable Order Fractional Differential Equations by Abdulrazzaq T. Abed, Ekhlass S. Al-Rawi

“… Background: In many studies, spectral methods based on one of the orthogonal polynomials and weighted residual methods (WRMs) have been used to convert the variable-order fractional differential equation (VO-FDEs) into a system of linear or nonlinear algebraic equations, and then solve this system to obtain the approximate solution. …”
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Optimization of Time-Varying Temperature Profiles for Enhanced Beer Fermentation by Evolutive Algorithms by Pablo Ruarte, Nadia Pantano, Marianela Noriega, Cecilia Fernández, Emanuel Serrano, Gustavo Scaglia

“…This method integrates Fourier series and orthogonal polynomials for control action parameterization, in combination with evolutionary algorithms for parameter optimization. …”
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Bivariate Generalized Shifted Gegenbauer Orthogonal System by Mohammad A. Alqudah, Maalee N. Almheidat, Tareq Hamadneh

“…For K0,K1≥0, λ>−1/2, we examine Cr∗λ,K0,K1x, generalized shifted Gegenbauer orthogonal polynomials, with reference to the weight Wλ,K0,K1x=2λΓ2λ/Γλ+1/22x−x2λ−1/2Ix∈0,1dx+K0δ0+K1δ1, where the indicator function is denoted by Ix∈0,1 and δx indicates the Dirac δ−measure. …”
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An Electromagnetic Load Identification Method Based on the Polynomial Structure Selection Technique by Wengui Mao, Shixiong Pei, Jie Guo, Jianhua Li, Buyao Wang

“…Considering the weak correlation of the modal shape and Chebyshev orthogonal polynomial in the space-time independent electromagnetic load identification method, a proposed method combining the polynomial structure selection technique together with limited measured displacement responses is presented, in which an error reduction ratio is used to pick out the significant mode shape matrix and the Chebyshev orthogonal polynomial. …”
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Quasi-definiteness of generalized Uvarov transforms of moment functionals by D. H. Kim, K. H. Kwon

“…When σ is a quasi-definite moment functional with the monic orthogonal polynomial system {P n (x)}n=0∞, we consider a point masses perturbation τ of σ given by τ:=σ+λΣl=1 mΣk=0 ml((−1)kulk/k!)…”
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Estimation of Approximating Rate for Neural Network inLwp Spaces by Jian-Jun Wang, Chan-Yun Yang, Jia Jing

“…By adopting a set of orthogonal polynomial basis and under certain assumptions for the governing activation functions of the neural network, the upper bound on the degree of approximation can be obtained for the class of Soblove functions. …”
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Dynamic Analysis of the Nonlinear Chaotic System with Multistochastic Disturbances by Lingling Geng, Yongguang Yu, Shuo Zhang

“…The nonlinear chaotic system with multistochastic disturbances is investigated. Based on the orthogonal polynomial approximation, the method of transforming the system into an equivalent deterministic system is given. …”
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Generalized Synchronization of Stochastic Discrete Chaotic System with Poisson Distribution Coefficient by Shao-juan Ma, Duan Dong, Jie Zheng

“…Firstly, based on the orthogonal polynomial approximation theory of discrete random function in Hilbert spaces, the discrete chaotic system with random parameter is transformed into its equivalent deterministic system. …”
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Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller by Jie Ran, Yanmin Liu, Jun He, Xiang Li

“…Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. …”
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Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter by Jing Wang, Shaojuan Ma, Peng Hao, Hehui Yuan

“…The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. …”
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Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System by Jie Ran, Yu-Qin Li, Shao-Juan Ma, Juan Wu

“…Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. …”
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Vibration Analysis of Driving-Point System with Uncertainties Using Polynomial Chaos Expansion by Bin Xiao, Yu-long Zhou, Chao Gao, Shuang-Xia Shi, Ze-Xi Sun, Zong-biao Song

“…Considering the asymptotic probability density function of mode shape, the dynamic compliance is decomposed into the mean of mode shape and the subsystem represented as an orthogonal polynomial expansion. Following this, the vibration transmission analysis approach is proposed for the random vibration. …”
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A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters by Rugao Gao, Keping Zhou, Yun Lin

“…The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. …”
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Effect of supplementing epinephrine in maturation media on the developmental competence of buffalo oocytes by Ali Husnain, Abdul Khaliq, Talha Ashraf, Abdul Rehman, Muhammad Yasir Zahoor, Muhammad Binyameen, Amjad Riaz

“…The statistical model included the fixed effect of treatment and random replication. Orthogonal polynomial contrasts were built to assess the dose-response of epinephrine. …”
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