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problème des ménages


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1: 26.15 Permutations: Matrix Notation
For the problem of derangements, r j ( B ) = ( n j ) . …
Example 1
The problème des ménages asks for the number of ways of seating n married couples around a circular table with labeled seats so that no men are adjacent, no women are adjacent, and no husband and wife are adjacent. …
2: 29.19 Physical Applications
Simply-periodic Lamé functions ( ν noninteger) can be used to solve boundary-value problems for Laplace’s equation in elliptical cones. …
§29.19(ii) Lamé Polynomials
Ward (1987) computes finite-gap potentials associated with the periodic Korteweg–de Vries equation. Shail (1978) treats applications to solutions of elliptic crack and punch problems. …
3: 26.20 Physical Applications
Other articles on this subject are de Bruijn (1981) and Rouvray (1995). … Applications of combinatorics, especially integer and plane partitions, to counting lattice structures and other problems of statistical mechanics, of which the Ising model is the principal example, can be found in Montroll (1964), Godsil et al. (1995), Baxter (1982), and Korepin et al. (1993). … Other applications to problems in engineering, crystallography, biology, and computer science can be found in Beckenbach (1981) and Graham et al. (1995).
4: 6.17 Physical Applications
Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. For applications in astrophysics, see also van de Hulst (1980). …
5: 9.16 Physical Applications
These examples of transitions to turbulence are presented in detail in Drazin and Reid (1981) with the problem of hydrodynamic stability. … Airy functions play a prominent role in problems defined by nonlinear wave equations. … This reference provides several examples of applications to problems in quantum mechanics in which Airy functions give uniform asymptotic approximations, valid in the neighborhood of a turning point. …In the case of the rainbow, the scattering amplitude is expressed in terms of Ai ( x ) , the analysis being similar to that given originally by Airy (1838) for the corresponding problem in optics. An application of the Scorer functions is to the problem of the uniform loading of infinite plates (Rothman (1954b, a)).
6: Bibliography H
  • E. Hairer, S. P. Nørsett, and G. Wanner (1993) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.
  • E. Hairer, S. P. Nørsett, and G. Wanner (2000) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.
  • E. Hairer and G. Wanner (1996) Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.
  • G. H. Hardy and J. E. Littlewood (1925) Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.
  • S. P. Hastings and J. B. McLeod (1980) 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.
  • 7: 21.9 Integrable Equations
    Typical examples of such equations are the Korteweg–de Vries equation …
    See accompanying text
    Figure 21.9.2: Contour plot of a two-phase solution of Equation (21.9.3). … Magnify
    Furthermore, the solutions of the KP equation solve the Schottky problem: this is the question concerning conditions that a Riemann matrix needs to satisfy in order to be associated with a Riemann surface (Schottky (1903)). …
    8: Bibliography J
  • L. Jager (1997) Fonctions de Mathieu et polynômes de Klein-Gordon. C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).
  • L. Jager (1998) Fonctions de Mathieu et fonctions propres de l’oscillateur relativiste. Ann. Fac. Sci. Toulouse Math. (6) 7 (3), pp. 465–495 (French).
  • D. J. Jeffrey, R. M. Corless, D. E. G. Hare, and D. E. Knuth (1995) Sur l’inversion de y α e y au moyen des nombres de Stirling associés. C. R. Acad. Sci. Paris Sér. I Math. 320 (12), pp. 1449–1452.
  • N. Joshi and A. V. Kitaev (2005) The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis. J. Reine Angew. Math. 583, pp. 29–86.
  • N. Joshi and M. D. Kruskal (1992) The Painlevé connection problem: An asymptotic approach. I. Stud. Appl. Math. 86 (4), pp. 315–376.
  • 9: 7.21 Physical Applications
    Dawson’s integral appears in de-convolving even more complex motional effects; see Pratt (2007). …
    10: Bibliography D
  • D. Dai, M. E. H. Ismail, and X. Wang (2014) Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Constr. Approx. 40 (1), pp. 61–104.
  • C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire M x + N . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
  • A. Decarreau, M.-Cl. Dumont-Lepage, P. Maroni, A. Robert, and A. Ronveaux (1978a) Formes canoniques des équations confluentes de l’équation de Heun. Ann. Soc. Sci. Bruxelles Sér. I 92 (1-2), pp. 53–78.
  • H. Delange (1991) Sur les zéros réels des polynômes de Bernoulli. Ann. Inst. Fourier (Grenoble) 41 (2), pp. 267–309 (French).
  • R. C. Desai and M. Nelkin (1966) Atomic motions in a rigid sphere gas as a problem in neutron transport. Nucl. Sci. Eng. 24 (2), pp. 142–152.