Diophantine approximation

2021 ◽  
Vol 34 (2) ◽  
pp. 205-229
Author(s):  
Noriko Hirata-Kohno
Keyword(s):  
Number Theory ◽  
Diophantine Approximation ◽  
Recent Progress ◽  
Padé Approximation ◽  
Pade Approximation ◽  
Fundamental Properties ◽  
Subspace Theorem ◽  
Diophantine Problems

This article gives an introductory survey of recent progress on Diophantine problems, especially consequences coming from Schmidt’s subspace theorem, Baker’s transcendence method and Padé approximation. We present fundamental properties around Diophantine approximation and how it yields results in number theory.

Modeling of Rails Expressed using Pade Approximation Considering Frequency Dependent Effect

2017 ◽  
Vol 137 (2) ◽  
pp. 147-153
Author(s):  
Akinori Hori ◽  
Hiroki Tanaka ◽  
Yuichiro Hayakawa ◽  
Hiroshi Shida ◽  
Keiji Kawahara ◽  
...  
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Frequency Dependent ◽  
Dependent Effect

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

Long-offset moveout for VTI using Padé approximation

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C219-C227 ◽  
Author(s):  
Hanjie Song ◽  
Yingjie Gao ◽  
Jinhai Zhang ◽  
Zhenxing Yao
Keyword(s):  
Padé Approximation ◽  
Pade Approximation ◽  
Practical Applications ◽  
Long Offset ◽  
Wide Range ◽  
Isotropic Media ◽  
Transversally Isotropic ◽  
Error Accumulation ◽  
Anisotropy Parameters ◽  
Vti Media

The approximation of normal moveout is essential for estimating the anisotropy parameters of the transversally isotropic media with vertical symmetry axis (VTI). We have approximated the long-offset moveout using the Padé approximation based on the higher order Taylor series coefficients for VTI media. For a given anellipticity parameter, we have the best accuracy when the numerator is one order higher than the denominator (i.e., [[Formula: see text]]); thus, we suggest using [4/3] and [7/6] orders for practical applications. A [7/6] Padé approximation can handle a much larger offset and stronger anellipticity parameter. We have further compared the relative traveltime errors between the Padé approximation and several approximations. Our method shows great superiority to most existing methods over a wide range of offset (normalized offset up to 2 or offset-to-depth ratio up to 4) and anellipticity parameter (0–0.5). The Padé approximation provides us with an attractive high-accuracy scheme with an error that is negligible within its convergence domain. This is important for reducing the error accumulation especially for deeper substructures.

Non-spherical particles sedimentation in an incompressible Newtonian medium by Padé approximation

2015 ◽  
Vol 278 ◽  
pp. 248-256 ◽  
Author(s):  
A.S. Dogonchi ◽  
M. Hatami ◽  
Kh. Hosseinzadeh ◽  
G. Domairry
Keyword(s):  
Padé Approximation ◽  
Spherical Particles ◽  
Pade Approximation
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