Refining trigonometric inequalities by using Padé approximant [PDF]
Journal of Inequalities and Applications, 2018 A two-point Padé approximant method is presented for refining some remarkable trigonometric inequalities including the Jordan inequality, Kober inequality, Becker–Stark inequality, and Wu–Srivastava inequality. Simple proofs are provided.
Zhen Zhang, Huaqing Shan, Ligeng Chen
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Padé Approximant and Minimax Rational Approximation in Standard Cosmology
Galaxies, 2016 The luminosity distance in the standard cosmology as given by ΛCDM and, consequently, the distance modulus for supernovae can be defined by the Padé approximant.
Lorenzo Zaninetti
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Padé approximant meets federated learning: A nearly lossless, one-shot algorithm for evidence synthesis in distributed research networks with rare outcomes. [PDF]
J Biomed Inform, 2023 OBJECTIVE: We developed and evaluated a novel one-shot distributed algorithm for evidence synthesis in distributed research networks with rare outcomes.
Wu Q +6 more
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Padé approximant related to the Wallis formula [PDF]
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, in this paper we determine the coefficients a j $a_{j}$ and b j $b_{j}$ such that π = ( ( 2 n ) ! ! ( 2 n − 1 ) ! ! ) 2 { n k + a 1 n k − 1 + ⋯ + a k n k + 1 + b 1 n k + ⋯ + b k + 1 + O ( 1 n 2 k + 3 ) } , n → ∞ , $
Long Lin, Wen-Cheng Ma, Chao-Ping Chen
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Padé approximant related to asymptotics for the gamma function [PDF]
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, we determine the coefficients a j $a_{j}$ and b j $b_{j}$ ( 1 ≤ j ≤ k $1\leq j\leq k$ ) such that Γ ( x + 1 ) 2 π x ( x / e ) x = x k + a 1 x k − 1 + ⋯ + a k x k + b 1 x k − 1 + ⋯ + b k + O ( 1 x 2 k + 1 ) , x → ∞ ,
Xin Li, Chao-Ping Chen
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Analytical Dual Flip Angle R1 Calculation Outside the Small-Angle Regime. [PDF]
Magn Reson MedABSTRACT Purpose To evaluate a new analytical estimator for R1 and apparent proton density (A$$ A $$) from short‐TR dual flip angle data which does not rely on the small flip angle approximation and can thus be applied to a broader range of data, especially where relatively large flip angles are needed to achieve sufficient T1‐weighting for R1 ...
Edwards LJ +6 more
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Padé approximant related to inequalities involving the constant e and a generalized Carleman-type inequality [PDF]
Journal of Inequalities and Applications, 2017 Based on the Padé approximation method, in this paper we determine the coefficients a j $a_{j}$ and b j $b_{j}$ ( 1 ≤ j ≤ k $1\leq j \leq k$ ) such that 1 e ( 1 + 1 x ) x = x k + a 1 x k − 1 + ⋯ + a k x k + b 1 x k − 1 + ⋯ + b k + O ( 1 x 2 k + 1 ) , x →
Chao-Ping Chen, Hui-Jie Zhang
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A two-point-Padé-approximant-based method for bounding some trigonometric functions [PDF]
Journal of Inequalities and Applications, 2018 Inequalities are frequently used for solving practical engineering problem. There are two key issues of bounding inequalities; one is to find the bounds, and the other is to prove the bounds.
Xiao-Diao Chen +3 more
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A Critical Evaluation and Modification of the Padé–Laplace Method for Deconvolution of Viscoelastic Spectra [PDF]
Molecules, 2021 This paper shows that using the Padé–Laplace (PL) method for deconvolution of multi-exponential functions (stress relaxation of polymers) can produce ill-conditioned systems of equations.
Siamak Shams Es-haghi +1 more
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Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation
Kubik, 2022 Linear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed ...
Faizal Ade Rahmahuddin Abdullah +1 more
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