N. Temme - Academia.edu (original) (raw)

Papers by N. Temme

Research paper thumbnail of Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

ETNA - Electronic Transactions on Numerical Analysis

Research paper thumbnail of Entropic uncertainty measures for large dimensional hydrogenic systems

Journal of Mathematical Physics

The entropic moments of the probability density of a quantum system in position and momentum spac... more The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system but also the entropic uncertainty measures of Rényi type, which allow one to find the most relevant mathematical formalizations of the position-momentum Heisenberg's uncertainty principle, the entropic uncertainty relations. It is known that the solution of difficult three-dimensional problems can be very well approximated by a series development in 1/D in similar systems with a nonstandard dimensionality D; moreover, several physical quantities of numerous atomic and molecular systems have been numerically shown to have values in the large-D limit comparable to the corresponding ones provided by the three-dimensional numerical self-consistent field methods. The D-dimensional hydrogenic atom is the main prototype of the physics of multidimensional many-electron systems. In this work, we rigorously determine the leading term of the Rényi entropies of the Ddimensional hydrogenic atom at the limit of large D. As a byproduct, we show that our results saturate the known position-momentum Rényi-entropy-based uncertainty relations.

Research paper thumbnail of Efficient algorithms for the inversion of the cumulative central beta distribution

Numerical Algorithms

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution a... more Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good nonlocal convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

Research paper thumbnail of Laplace type integrals: transformation to standard form and uniform asymptotic expansions

Quarterly of Applied Mathematics

Integrals are considered which can be transformed into the Laplace integral 00 FA(z) == r!>-..) [... more Integrals are considered which can be transformed into the Laplace integral 00 FA(z) == r!>-..) [ tAle -z 1 f (t)dt' where f is holomorphic, z is a large parameter, µ=>-.. / z is a uniformity parameter, µ~O. A uniform asymptotic expansion is given with error bounds for the remainders. Applications are given for special functions, with a detailed analysis for a ratio of gamma functions. Further applications are mentioned for Bessel functions and parabolic cylinder functions. Analogue results are given for loop integrals in the complex plane.

Research paper thumbnail of A sampling theory for dispersal-limited, niche-structured communities

Research paper thumbnail of Asymptotic Estimates of Stirling Numbers

Studies in Applied Mathematics, 1993

Research paper thumbnail of Asymptotic and closed from of a generalized incomplete gamma function

Research paper thumbnail of Chernoff's distribution and differential equations of parabolic and Airy type

Journal of Mathematical Analysis and Applications, 2015

We give a direct derivation of the distribution of the maximum and the location of the maximum of... more We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions, in particular involving integrals with respect to functions which can be called "incomplete Scorer functions". The relation is proved by showing that both integrals, as a function of two parameters, satisfy the same extended heat equation, and the maximum principle is used to show that these solution must therefore have the stated relation. Once this relation is established, a direct derivation of the distribution of the maximum and location of the maximum of Brownian motion minus a parabola is possible, leading to a considerable shortening of the original proofs.

Research paper thumbnail of The Error Function in the Study of Singularly Perturbed Convection-Diffusion Problems with Discontinuous Boundary Data

Mathematics in Industry, 2010

We show the importance of the error function in the approximation of the solution of singularly p... more We show the importance of the error function in the approximation of the solution of singularly perturbed convection-diffusion problems with discontinuous boundary conditions. It is observed that the error function (or a combination of them) provides an excellent approximation and reproduces accurately the effect of the discontinuities on the behaviour of the solution at the boundary and interior layers.

Research paper thumbnail of The Asymptotic Inversion of Certain Cumulative Distribution Functions

Mathematics in Industry, 2010

The inversion of cumulative distribution functions is an important topic in statistics, probabili... more The inversion of cumulative distribution functions is an important topic in statistics, probability theory and econometrics, in particular for computing percentage points of the distribution functions. The numerical inversion of these distributions needs accurate starting values, and for the standard distributions powerful asymptotic formulas can be used to obtain these values.. It is explained how a uniform asymptotic expansions of a standard form representing several well-known distribution functions can be used for the asymptotic inversion of these functions. As an example we consider the inversion of the hyperbolic cumulative distribution function.

Research paper thumbnail of First order approximation of an elliptic 3D singular perturbation problem

A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is ... more A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error function.

Research paper thumbnail of Marginal stability of parallel whistler-mode waves (asymptotic analysis)

Annales Geophysicae, 1991

A new approach to the asymptotic analysis of the marginal stability of whistler-mode waves in a w... more A new approach to the asymptotic analysis of the marginal stability of whistler-mode waves in a weakly relativistic plasma makes it possible to generalize the results of previous papers to a wider range of parameters. In particular, it is pointed out that a decrease in electron density tends to stabilize whistler-mode instability, while an increase in electron temperature destabilizes or stabilizes it depending on the choice of the plasma model. However, the second effect is usually small when compared with the first one and can be neglected when analyzing the dynamics of whistler-mode waves in the earth's magnetosphere, as well as in the magnetospheres of other planets.

Research paper thumbnail of Some aspects of applied analysis: asymptotics, special functions and their numerical computation

Journal of Automated Reasoning - JAR, 1978

Research paper thumbnail of Polynomial asymptotic estimates of Gegenbauer, Laguerre, and Jacobi polynomials

Research paper thumbnail of Charge transfer in atom-surface collisions. On the validity of the semi-classical approximation

Surface Science, 1986

The classical limit of the quantum-mechanical theory, describing resonant electron transfer in at... more The classical limit of the quantum-mechanical theory, describing resonant electron transfer in atom-metal collisions, is studied. It is shown that the charge-transfer process can be described in terms of a classical master equation, if the position of the atomic valence level depends on atom-surface distance z. For the particular case of H-formation on cesiated tungsten (110), the difference between the quantal calculation and the solution of the classical master equation is less than 55[.

Research paper thumbnail of The Asymptotic Expansion of the Incomplete Gamma Functions

SIAM Journal on Mathematical Analysis, 1979

Earlier investigations on uniform asymptotic expansions of the incomplete gamma functions are rec... more Earlier investigations on uniform asymptotic expansions of the incomplete gamma functions are reconsidered. The new results include estimations for the remainder and the extension of the results to complex variables.

Research paper thumbnail of The Uniform Asymptotic Expansion of a Class of Integrals Related to Cumulative Distribution Functions

SIAM Journal on Mathematical Analysis, 1982

An asymptotic expansion is given for a class of integrals for large values of a parameter, which ... more An asymptotic expansion is given for a class of integrals for large values of a parameter, which corresponds with the degrees of freedom in a certain type of cumulative distribution functions. The expansion is uniform with respect to a variable related to the random variable of the distribution functions. Special cases include the chi-square distribution and the F-distribution.

Research paper thumbnail of Uniform Airy-Type Expansions of Integrals

SIAM Journal on Mathematical Analysis, 1994

The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathemat... more The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathematisch Centrum, which was founded on February 11 , 1946, as a nonprofit institution aiming at the promotion of mathematics, computer science, and their applications. It is sponsored by the Dutch Government through the Netherlands Organization for the Advancement of Research (N.W.O.).

Research paper thumbnail of Remarks on a Paper of A. Erdélyi

SIAM Journal on Mathematical Analysis, 1976

Research paper thumbnail of Analytical Methods for a Singular Perturbation Problem in a Sector

SIAM Journal on Mathematical Analysis, 1974

From the exact solution of an elliptic boundary value problem in a sector. asymptotic approximati... more From the exact solution of an elliptic boundary value problem in a sector. asymptotic approximations with respect to a small parameter are derived. The asymptotic expansion is uniformly valid in the boundary layers. Also the phenomena for the case of almost characteristic boundaries are discussed.

Research paper thumbnail of Asymptotic inversion of the binomial and negative binomial cumulative distribution functions

ETNA - Electronic Transactions on Numerical Analysis

Research paper thumbnail of Entropic uncertainty measures for large dimensional hydrogenic systems

Journal of Mathematical Physics

The entropic moments of the probability density of a quantum system in position and momentum spac... more The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system but also the entropic uncertainty measures of Rényi type, which allow one to find the most relevant mathematical formalizations of the position-momentum Heisenberg's uncertainty principle, the entropic uncertainty relations. It is known that the solution of difficult three-dimensional problems can be very well approximated by a series development in 1/D in similar systems with a nonstandard dimensionality D; moreover, several physical quantities of numerous atomic and molecular systems have been numerically shown to have values in the large-D limit comparable to the corresponding ones provided by the three-dimensional numerical self-consistent field methods. The D-dimensional hydrogenic atom is the main prototype of the physics of multidimensional many-electron systems. In this work, we rigorously determine the leading term of the Rényi entropies of the Ddimensional hydrogenic atom at the limit of large D. As a byproduct, we show that our results saturate the known position-momentum Rényi-entropy-based uncertainty relations.

Research paper thumbnail of Efficient algorithms for the inversion of the cumulative central beta distribution

Numerical Algorithms

Accurate and efficient algorithms for the inversion of the cumulative central beta distribution a... more Accurate and efficient algorithms for the inversion of the cumulative central beta distribution are described. The algorithms are based on the combination of a fourth-order fixed point method with good nonlocal convergence properties (the Schwarzian-Newton method), asymptotic inversion methods and sharp bounds in the tails of the distribution function.

Research paper thumbnail of Laplace type integrals: transformation to standard form and uniform asymptotic expansions

Quarterly of Applied Mathematics

Integrals are considered which can be transformed into the Laplace integral 00 FA(z) == r!>-..) [... more Integrals are considered which can be transformed into the Laplace integral 00 FA(z) == r!>-..) [ tAle -z 1 f (t)dt' where f is holomorphic, z is a large parameter, µ=>-.. / z is a uniformity parameter, µ~O. A uniform asymptotic expansion is given with error bounds for the remainders. Applications are given for special functions, with a detailed analysis for a ratio of gamma functions. Further applications are mentioned for Bessel functions and parabolic cylinder functions. Analogue results are given for loop integrals in the complex plane.

Research paper thumbnail of A sampling theory for dispersal-limited, niche-structured communities

Research paper thumbnail of Asymptotic Estimates of Stirling Numbers

Studies in Applied Mathematics, 1993

Research paper thumbnail of Asymptotic and closed from of a generalized incomplete gamma function

Research paper thumbnail of Chernoff's distribution and differential equations of parabolic and Airy type

Journal of Mathematical Analysis and Applications, 2015

We give a direct derivation of the distribution of the maximum and the location of the maximum of... more We give a direct derivation of the distribution of the maximum and the location of the maximum of one-sided and two-sided Brownian motion with a negative parabolic drift. The argument uses a relation between integrals of special functions, in particular involving integrals with respect to functions which can be called "incomplete Scorer functions". The relation is proved by showing that both integrals, as a function of two parameters, satisfy the same extended heat equation, and the maximum principle is used to show that these solution must therefore have the stated relation. Once this relation is established, a direct derivation of the distribution of the maximum and location of the maximum of Brownian motion minus a parabola is possible, leading to a considerable shortening of the original proofs.

Research paper thumbnail of The Error Function in the Study of Singularly Perturbed Convection-Diffusion Problems with Discontinuous Boundary Data

Mathematics in Industry, 2010

We show the importance of the error function in the approximation of the solution of singularly p... more We show the importance of the error function in the approximation of the solution of singularly perturbed convection-diffusion problems with discontinuous boundary conditions. It is observed that the error function (or a combination of them) provides an excellent approximation and reproduces accurately the effect of the discontinuities on the behaviour of the solution at the boundary and interior layers.

Research paper thumbnail of The Asymptotic Inversion of Certain Cumulative Distribution Functions

Mathematics in Industry, 2010

The inversion of cumulative distribution functions is an important topic in statistics, probabili... more The inversion of cumulative distribution functions is an important topic in statistics, probability theory and econometrics, in particular for computing percentage points of the distribution functions. The numerical inversion of these distributions needs accurate starting values, and for the standard distributions powerful asymptotic formulas can be used to obtain these values.. It is explained how a uniform asymptotic expansions of a standard form representing several well-known distribution functions can be used for the asymptotic inversion of these functions. As an example we consider the inversion of the hyperbolic cumulative distribution function.

Research paper thumbnail of First order approximation of an elliptic 3D singular perturbation problem

A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is ... more A three-dimensional elliptic singular perturbation problem with discontinuous boundary values is considered. The solution of the problem is written in terms of a double integral. A saddle point analysis is used to obtain a first approximation, which is expressed in terms of a function that can be viewed as a generalization of the complementary error function.

Research paper thumbnail of Marginal stability of parallel whistler-mode waves (asymptotic analysis)

Annales Geophysicae, 1991

A new approach to the asymptotic analysis of the marginal stability of whistler-mode waves in a w... more A new approach to the asymptotic analysis of the marginal stability of whistler-mode waves in a weakly relativistic plasma makes it possible to generalize the results of previous papers to a wider range of parameters. In particular, it is pointed out that a decrease in electron density tends to stabilize whistler-mode instability, while an increase in electron temperature destabilizes or stabilizes it depending on the choice of the plasma model. However, the second effect is usually small when compared with the first one and can be neglected when analyzing the dynamics of whistler-mode waves in the earth's magnetosphere, as well as in the magnetospheres of other planets.

Research paper thumbnail of Some aspects of applied analysis: asymptotics, special functions and their numerical computation

Journal of Automated Reasoning - JAR, 1978

Research paper thumbnail of Polynomial asymptotic estimates of Gegenbauer, Laguerre, and Jacobi polynomials

Research paper thumbnail of Charge transfer in atom-surface collisions. On the validity of the semi-classical approximation

Surface Science, 1986

The classical limit of the quantum-mechanical theory, describing resonant electron transfer in at... more The classical limit of the quantum-mechanical theory, describing resonant electron transfer in atom-metal collisions, is studied. It is shown that the charge-transfer process can be described in terms of a classical master equation, if the position of the atomic valence level depends on atom-surface distance z. For the particular case of H-formation on cesiated tungsten (110), the difference between the quantal calculation and the solution of the classical master equation is less than 55[.

Research paper thumbnail of The Asymptotic Expansion of the Incomplete Gamma Functions

SIAM Journal on Mathematical Analysis, 1979

Earlier investigations on uniform asymptotic expansions of the incomplete gamma functions are rec... more Earlier investigations on uniform asymptotic expansions of the incomplete gamma functions are reconsidered. The new results include estimations for the remainder and the extension of the results to complex variables.

Research paper thumbnail of The Uniform Asymptotic Expansion of a Class of Integrals Related to Cumulative Distribution Functions

SIAM Journal on Mathematical Analysis, 1982

An asymptotic expansion is given for a class of integrals for large values of a parameter, which ... more An asymptotic expansion is given for a class of integrals for large values of a parameter, which corresponds with the degrees of freedom in a certain type of cumulative distribution functions. The expansion is uniform with respect to a variable related to the random variable of the distribution functions. Special cases include the chi-square distribution and the F-distribution.

Research paper thumbnail of Uniform Airy-Type Expansions of Integrals

SIAM Journal on Mathematical Analysis, 1994

The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathemat... more The Centre for Mathematics and Computer Science is a research institute of the Stichting Mathematisch Centrum, which was founded on February 11 , 1946, as a nonprofit institution aiming at the promotion of mathematics, computer science, and their applications. It is sponsored by the Dutch Government through the Netherlands Organization for the Advancement of Research (N.W.O.).

Research paper thumbnail of Remarks on a Paper of A. Erdélyi

SIAM Journal on Mathematical Analysis, 1976

Research paper thumbnail of Analytical Methods for a Singular Perturbation Problem in a Sector

SIAM Journal on Mathematical Analysis, 1974

From the exact solution of an elliptic boundary value problem in a sector. asymptotic approximati... more From the exact solution of an elliptic boundary value problem in a sector. asymptotic approximations with respect to a small parameter are derived. The asymptotic expansion is uniformly valid in the boundary layers. Also the phenomena for the case of almost characteristic boundaries are discussed.