Optimal ray sequences of rational functions connected with the Zolotarev problem

1994 ◽  
Vol 10 (2) ◽  
pp. 235-273 ◽  
Author(s):  
A. L. Levin ◽  
E. B. Saff
Keyword(s):  
Rational Functions ◽  
Zolotarev Problem ◽  
Ray Sequences

scholarly journals Erratum: Optimal ray sequences of rational functions connected with the zolotarev problem

1996 ◽  
Vol 12 (3) ◽  
pp. 437-438 ◽  
Author(s):  
A. L. Levin ◽  
E. B. Saff
Keyword(s):  
Rational Functions ◽  
Zolotarev Problem ◽  
Ray Sequences

scholarly journals Estimates for derivatives of rational functions and the fourth Zolotarev problem

2008 ◽  
Vol 19 (02) ◽  
pp. 253-260 ◽  
Author(s):  
A. L. Lukashov
Keyword(s):  
Rational Functions ◽  
Zolotarev Problem ◽  
Derivatives Of

scholarly journals Optimal Rational Functions for the Generalized Zolotarev Problem in the Complex Plane

2000 ◽  
Vol 38 (5) ◽  
pp. 1409-1424 ◽  
Author(s):  
B. Le Bailly ◽  
J. P. Thiran
Keyword(s):  
Complex Plane ◽  
Rational Functions ◽  
Zolotarev Problem

Rates of Best Uniform Rational Approximation of Analytic Functions by Ray Sequences of Rational Functions

1999 ◽  
Vol 15 (2) ◽  
pp. 155-173 ◽  
Author(s):  
V. A. Prokhorov ◽  
E. B. Saff
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Rational Functions ◽  
Ray Sequences

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Padé approximants and noise: rational functions

1999 ◽  
Vol 105 (1-2) ◽  
pp. 285-297 ◽  
Author(s):  
Jacek Gilewicz ◽  
Maciej Pindor
Keyword(s):  
Rational Functions ◽  
Padé Approximants ◽  
Pade Approximants

scholarly journals Global Well-Posedness of the Ocean Primitive Equations with Nonlinear Thermodynamics

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Peter Korn
Keyword(s):  
Equation Of State ◽  
Equations Of State ◽  
Boussinesq Equations ◽  
Climate Science ◽  
Rational Functions ◽  
Ocean Dynamics ◽  
Global Ocean ◽  
Primitive Equations ◽  
Well Posedness ◽  
Nonlinear Thermodynamics

AbstractWe consider the hydrostatic Boussinesq equations of global ocean dynamics, also known as the “primitive equations”, coupled to advection–diffusion equations for temperature and salt. The system of equations is closed by an equation of state that expresses density as a function of temperature, salinity and pressure. The equation of state TEOS-10, the official description of seawater and ice properties in marine science of the Intergovernmental Oceanographic Commission, is the most accurate equations of state with respect to ocean observation and rests on the firm theoretical foundation of the Gibbs formalism of thermodynamics. We study several specifications of the TEOS-10 equation of state that comply with the assumption underlying the primitive equations. These equations of state take the form of high-order polynomials or rational functions of temperature, salinity and pressure. The ocean primitive equations with a nonlinear equation of state describe richer dynamical phenomena than the system with a linear equation of state. We prove well-posedness for the ocean primitive equations with nonlinear thermodynamics in the Sobolev space $${{\mathcal {H}}^{1}}$$ H 1 . The proof rests upon the fundamental work of Cao and Titi (Ann. Math. 166:245–267, 2007) and also on the results of Kukavica and Ziane (Nonlinearity 20:2739–2753, 2007). Alternative and older nonlinear equations of state are also considered. Our results narrow the gap between the mathematical analysis of the ocean primitive equations and the equations underlying numerical ocean models used in ocean and climate science.

Some inequalities for the rational functions with prescribed poles and restricted zeros

2021 ◽  
Author(s):  
M. H. Gulzar ◽  
B. A. Zargar ◽  
Rubia Akhter
Keyword(s):  
Rational Functions ◽  
Restricted Zeros

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

Sign in / Sign up

Export Citation Format

Share Document