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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations. [PDF]
Sci Rep, 2019 We discuss how positions of critical points of the three-dimensional Bose-Hubbard model can be accurately obtained from variance of the on-site atom number operator, which can be experimentally measured. The idea that we explore is that the derivative of
Prośniak OA, Łącki M, Damski B.
europepmc +4 more sources
Theoretical model of donor–donor and donor–acceptor energy transfer on a nanosphere [PDF]
Scientific ReportsIn this study, we introduce a novel advancement in the field of theoretical exploration. Specifically, we investigate the transfer and trapping of electronic excitations within a two-component disordered system confined to a finite volume.
Anna Synak +2 more
doaj +2 more sources
General model of nonradiative excitation energy migration on a spherical nanoparticle with attached chromophores [PDF]
Scientific ReportsTheory of multistep excitation energy migration within the set of chemically identical chromophores distributed on the surface of a spherical nanoparticle is presented.
L. Kułak, A. Schlichtholz, P. Bojarski
doaj +2 more sources
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
doaj +1 more source