isomonodromy problems

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21: Alexander I. Bobenko

… ►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E. …

22: Annie A. M. Cuyt

… ►Her main research interest is in the area of numerical approximation theory and its applications to a diversity of problems in scientific computing. …

23: Brian D. Sleeman

… ► thesis was Some Boundary Value Problems Associated with the Heun Equation. …

24: Hans Volkmer

… ►His book Multiparameter Eigenvalue Problems and Expansion Theorems was published by Springer as Lecture Notes in Mathematics No. …

25: 27.13 Functions

… ►The basic problem is that of expressing a given positive integer $n$ as a sum of integers from some prescribed set $S$ whose members are primes, squares, cubes, or other special integers. …The subsections that follow describe problems from additive number theory. … ►

§27.13(iii) Waring’s Problem

►This problem is named after Edward Waring who, in 1770, stated without proof and with limited numerical evidence, that every positive integer $n$ is the sum of four squares, of nine cubes, of nineteen fourth powers, and so on. Waring’s problem is to find, for each positive integer $k$, whether there is an integer $m$ (depending only on $k$) such that the equation …

26: 12.17 Physical Applications

… ►By using instead coordinates of the parabolic cylinder $\xi ,\eta ,\zeta$, defined by … ►Buchholz (1969) collects many results on boundary-value problems involving PCFs. … ►Problems on high-frequency scattering in homogeneous media by parabolic cylinders lead to asymptotic methods for integrals involving PCFs. For this topic and other boundary-value problems see Boyd (1973), Hillion (1997), Magnus (1941), Morse and Feshbach (1953a, b), Müller (1988), Ott (1985), Rice (1954), and Shanmugam (1978). …

27: Bibliography H

… ►

Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.

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Notes:

A reprinting with corrections appeared in 2000.

External Links:

ISBN 3-540-56670-8, MathReview, ZentralBlatt

Referenced by:

§3.7(v), §3.7(i).

Encodings:

BibTeX

►

Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.

ⓘ

External Links:

ISBN 3-540-56670-8, Document, MathReview

Referenced by:

§32.17.

Encodings:

BibTeX

►

Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.

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External Links:

ISBN 3-540-60452-9, MathReview, ZentralBlatt

Referenced by:

§3.7(v).

Encodings:

BibTeX

… ►

Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.

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Notes:

Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.

External Links:

ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt

Referenced by:

§27.13(iii).

Encodings:

BibTeX

… ►

A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

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External Links:

ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

Referenced by:

§32.11(ii).

Encodings:

BibTeX

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28: 21.10 Methods of Computation

… ►In addition to evaluating the Fourier series, the main problem here is to compute a Riemann matrix originating from a Riemann surface. …

29: 32.16 Physical Applications

… ►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …

30: 10.73 Physical Applications

… ►Bessel functions first appear in the investigation of a physical problem in Daniel Bernoulli’s analysis of the small oscillations of a uniform heavy flexible chain. For this problem and its further generalizations, see Korenev (2002, Chapter 4, §37) and Gray et al. (1922, Chapter I, §1, Chapter XVI, §4). … ►Laplace’s equation governs problems in heat conduction, in the distribution of potential in an electrostatic field, and in hydrodynamics in the irrotational motion of an incompressible fluid. … ►This equation governs problems in acoustic and electromagnetic wave propagation. … ►More recently, Bessel functions appear in the inverse problem in wave propagation, with applications in medicine, astronomy, and acoustic imaging. …