We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding i...We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.展开更多
This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simpl...This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simple off-diagonal bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighbourhood of the origin.Numerical examples compare the obtained results with the approximation power of diagonal Chisholm approximant and Taylor polynomial approximant.展开更多
This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that t...This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.展开更多
This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Herm...This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.展开更多
The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each o...The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.展开更多
This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a tra...This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field.Using a perturbation method coupled with a special type of Hermite-Pade' approximation technique,the simplified governing non-linear equation is solved and the important properties of overall flow structure including velocity field,temperature field and thermal criticality conditions are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers,irreversibility distribution ratio and the Bejan number in the flow field.展开更多
文摘We extend a theorem of Ivanev and Saff to show that for the Hermite-Pade interpolant at the roots of unity to a function meromorphic in the unit disc, its leading coefficients vanish if and only if the corresponding interpolani to a related function vanishes at given points outside the unit disc. The result is then extended to simultaneous Hermite-Pade interpolation to a finite set of functions.
基金Supported by National Natural Science Foundation of China( 699730 1 0,1 0 2 71 0 2 2 )
文摘This paper analyses the local behavior of the simple off-diagonal bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin.It is shown that the simple off-diagonal bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighbourhood of the origin.Numerical examples compare the obtained results with the approximation power of diagonal Chisholm approximant and Taylor polynomial approximant.
基金supported by the National Research Foundation of South Africa Thuthuka Programme
文摘This study is devoted to the investigation of thermal criticality for a reactive gravity driven thin film flow of a third-grade fluid with adiabatic free surface down an inclined isothermal plane. It is assumed that the reaction is exothermic under Arrhenius kinetics, neglecting the consumption of the material. The governing non-linear equations for conservation of momentum and energy are obtained and solved by using a new computational approach based on a special type of Hermite-Padé approximation technique implemented in MAPLE. This semi-numerical scheme offers some advantages over solutions obtained with traditional methods such as finite differences, spectral method, and shooting method. It reveals the analytical structure of the solution function. Important properties of overall flow structure including velocity field, temperature field, thermal criticality, and bifurcations are discussed.
基金Supported by the NNSF of China(10271022, 60373093)Supported by the Science and Technology Development Foundation of Education Department of Liaoning Province(2004C060)
文摘This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Padé form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.
文摘The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.
文摘This study is devoted to investigate the inherent irreversibility and thermal stability in a reactive electrically conducting fluid flowing steadily through a channel with isothermal walls under the influence of a transversely imposed magnetic field.Using a perturbation method coupled with a special type of Hermite-Pade' approximation technique,the simplified governing non-linear equation is solved and the important properties of overall flow structure including velocity field,temperature field and thermal criticality conditions are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers,irreversibility distribution ratio and the Bejan number in the flow field.
