problème des ménages

SearchAdvancedHelp

(0.001 seconds)

11—20 of 155 matching pages

11: 11.12 Physical Applications

§11.12 Physical Applications

►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). …

12: Bibliography L

… ►

The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

ⓘ

Notes:

In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

External Links:

ISSN 0564-6162, Document, MathReview, ZentralBlatt

Referenced by:

§31.18.

Encodings:

BibTeX

… ►

The central two-point connection problem for the Heun class of ODEs. J. Phys. A 31 (18), pp. 4249–4261.

ⓘ

External Links:

ISSN 0305-4470, Document, MathReview, ZentralBlatt

Referenced by:

§31.12.

Encodings:

BibTeX

… ►

Problems of Mathematical Physics. Revised, enlarged and corrected English edition; translated and edited by Richard A. Silverman. With a supplement by Edward L. Reiss, Prentice-Hall Inc., Englewood Cliffs, N.J..

ⓘ

Notes:

Republished as Worked Problems in Applied Mathematics by Dover Publications, New York, 1979

External Links:

ISBN 0-486-63730-1, MathReview (J. Mathews), ZentralBlatt

Referenced by:

§10.43(v).

Encodings:

BibTeX

… ►

Traité des fonctions elliptiques et des intégrales Eulériennes. Huzard-Courcier, Paris.

ⓘ

Notes:

vol.1, 1825; vol.2, 1826; three supplements, 1828–1832.

Referenced by:

§19.14(ii), Ch.19.

Encodings:

BibTeX

… ►

On incomplete Airy functions and their application to diffraction problems. Radio Sci. 4 (10), pp. 959–969.

ⓘ

External Links:

ISSN 0048-6604, Document, MathReview (T. Erber)

Referenced by:

§9.14.

Encodings:

BibTeX

…

13: 30.13 Wave Equation in Prolate Spheroidal Coordinates

… ►

30.13.7 $${\nabla }^{2}w+{\kappa }^{2}w=0,$$

ⓘ

Defines:

$\kappa$: parameter (locally)

Symbols:

$w_j$: solution to DE

Referenced by:

§30.13(iv), §30.13(v), §30.14(iv), §30.14(iv), §30.14(v)

Permalink:

http://dlmf.nist.gov/30.13.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §30.13(iv), §30.13 and Ch.30

… ►where $w_1$, $w_2$, $w_3$ satisfy the differential equations … ►

§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids

►Equation (30.13.7) for $\xi \le {\xi }_0$, and subject to the boundary condition $w=0$ on the ellipsoid given by $\xi ={\xi }_0$, poses an eigenvalue problem with ${\kappa }^2$ as spectral parameter. …For the Dirichlet boundary-value problem of the region ${\xi }_1\le \xi \le {\xi }_2$ between two ellipsoids, the eigenvalues are determined from …

14: 23.21 Physical Applications

… ►In §22.19(ii) it is noted that Jacobian elliptic functions provide a natural basis of solutions for problems in Newtonian classical dynamics with quartic potentials in canonical form $(1-x^2)(1-k^2{x}^2)$. … ►

§23.21(ii) Nonlinear Evolution Equations

►Airault et al. (1977) applies the function $\mathrm{\wp }$ to an integrable classical many-body problem, and relates the solutions to nonlinear partial differential equations. For applications to soliton solutions of the Korteweg–de Vries (KdV) equation see McKean and Moll (1999, p. 91), Deconinck and Segur (2000), and Walker (1996, §8.1). …

15: Bibliography P

… ►

Unbiasedness of invariant tests for MANOVA and other multivariate problems. Ann. Statist. 8 (6), pp. 1326–1341.

ⓘ

External Links:

ISSN 0090-5364, FullText, MathReview (Takeaki Kariya), ZentralBlatt

Referenced by:

§35.9.

Encodings:

BibTeX

►

La Théorie des Fonctions de Bessel Exposée en vue de ses Applications à la Physique Mathématique. Centre National de la Recherche Scientifique, Paris (French).

ⓘ

External Links:

MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§10.63(ii).

Encodings:

BibTeX

… ►

Sur une généralisation des polynomes de Legendre. C. R. Acad. Sci. Paris 228, pp. 1363–1365.

ⓘ

External Links:

ISSN 0001-4036, MathReview (G. Szegö)

Referenced by:

§18.35(i).

Encodings:

BibTeX

►

Systèmes de polynomes biorthogonaux qui généralisent les polynomes ultrasphériques. C. R. Acad. Sci. Paris 228, pp. 1998–2000.

ⓘ

External Links:

ISSN 0001-4036, MathReview (G. Szegö)

Referenced by:

§18.35(i).

Encodings:

BibTeX

… ►

Numerical Solution of Sturm-Liouville Problems. Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.

ⓘ

External Links:

ISBN 0-19-853415-9, MathReview (L. Greenberg), ZentralBlatt

Referenced by:

§3.7(iv).

Encodings:

BibTeX

…

16: 14.31 Other Applications

… ►Applications of toroidal functions include expansion of vacuum magnetic fields in stellarators and tokamaks (van Milligen and López Fraguas (1994)), analytic solutions of Poisson’s equation in channel-like geometries (Hoyles et al. (1998)), and Dirichlet problems with toroidal symmetry (Gil et al. (2000)). … ►The conical functions ${𝖯}_{-\frac{1}{2}+\mathrm{i}\tau }^m\left(x\right)$ appear in boundary-value problems for the Laplace equation in toroidal coordinates (§14.19(i)) for regions bounded by cones, by two intersecting spheres, or by one or two confocal hyperboloids of revolution (Kölbig (1981)). These functions are also used in the Mehler–Fock integral transform (§14.20(vi)) for problems in potential and heat theory, and in elementary particle physics (Sneddon (1972, Chapter 7) and Braaksma and Meulenbeld (1967)). … ►

§14.31(iii) Miscellaneous

…

17: Bibliography R

… ►

General Computation Methods of Chebyshev Approximation. The Problems with Linear Real Parameters. Publishing House of the Academy of Science of the Ukrainian SSR, Kiev.

ⓘ

Notes:

English translation, AEC-TR-4491, United States Atomic Energy Commission

External Links:

MathReview (A. S. Householder)

Referenced by:

§3.11(iii).

Encodings:

BibTeX

… ►

Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome I. Gauthier-Villars, Paris.

ⓘ

Notes:

Préface de H. Villat

External Links:

MathReview (R. Campbell), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

BibTeX

►

Fonctions sphériques de Legendre et fonctions sphéroïdales. Tome II. Gauthier-Villars, Paris.

ⓘ

External Links:

MathReview (R. Campbell), ZentralBlatt

Referenced by:

Ch.14.

Encodings:

BibTeX

… ►

Sur quelques classes nouvelles de polynômes orthogonaux. C. R. Acad. Sci. Paris 188, pp. 1023–1025.

ⓘ

External Links:

ZentralBlatt

Referenced by:

(18.34.5_5).

Encodings:

BibTeX

… ►

The problem of an infinite plate under an inclined loading, with tables of the integrals of $\mathrm{Ai}(\pm \mathrm{x})$ and $\mathrm{Bi}(\pm \mathrm{x})$ . Quart. J. Mech. Appl. Math. 7 (1), pp. 1–7.

ⓘ

External Links:

Document, MathReview (A. Erdélyi), ZentralBlatt

Referenced by:

§9.16, 1st item.

Encodings:

BibTeX

…

18: 28.33 Physical Applications

… ►

§28.33(ii) Boundary-Value Problems

►Physical problems involving Mathieu functions include vibrational problems in elliptical coordinates; see (28.32.1). …The general solution of the problem is a superposition of the separated solutions. … ►

§28.33(iii) Stability and Initial-Value Problems

… ►References for other initial-value problems include: …

19: 30.14 Wave Equation in Oblate Spheroidal Coordinates

… ►The wave equation (30.13.7), transformed to oblate spheroidal coordinates $(\xi ,\eta ,\varphi )$, admits solutions of the form (30.13.8), where $w_1$ satisfies the differential equation ►

30.14.7 $$\frac{d}{d\xi }\left((1+{\xi }^2)\frac{d{w}_1}{d\xi }\right)-\left(\lambda +{\gamma }^2(1+{\xi }^2)-\frac{{\mu }^2}{1+{\xi }^2}\right)w_1=0,$$

ⓘ

Symbols:

$\frac{df}{dx}$: derivative of $f$ with respect to $x$ , $\xi$: oblate spheroidal coordinate, $w_j$: solution to DE, ${\gamma }^2={\kappa }^2{c}^2$: parameter, $\lambda$: real parameter and $\mu$: real parameter

A&S Ref:

21.6.3 (in different form)

Referenced by:

§30.14(iv), §30.14(iv)

Permalink:

http://dlmf.nist.gov/30.14.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §30.14(iv), §30.14 and Ch.30

… ►

30.14.8 $$w_1(\xi )=a_1{S}_n^{m(1)}(\mathrm{i}\xi ,\gamma )+b_1{S}_n^{m(2)}(\mathrm{i}\xi ,\gamma ).$$

ⓘ

Symbols:

$\mathrm{i}$: imaginary unit, $S_n^{m(j)}(z,\gamma )$: radial spheroidal wave function, $m$: nonnegative integer, $n\ge m$: integer degree, $b_j$: coefficients, $a_j$: coefficients, $\xi$: oblate spheroidal coordinate, $w_j$: solution to DE and ${\gamma }^2={\kappa }^2{c}^2$: parameter

Referenced by:

§30.14(v)

Permalink:

http://dlmf.nist.gov/30.14.E8

Encodings:

pMML, png, TeX

See also:

Annotations for §30.14(iv), §30.14 and Ch.30

… ►

§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids

►Equation (30.13.7) for $\xi \le {\xi }_0$ together with the boundary condition $w=0$ on the ellipsoid given by $\xi ={\xi }_0$, poses an eigenvalue problem with ${\kappa }^2$ as spectral parameter. …

20: Bibliography Q

… ►

A note on an open problem about the first Painlevé equation. Acta Math. Appl. Sin. Engl. Ser. 24 (2), pp. 203–210.

ⓘ

External Links:

ISSN 0168-9673, Document, MathReview (Dmitrii Petrovich Novikov), ZentralBlatt

Referenced by:

§32.11(i).

Encodings:

BibTeX

►

On two problems concerning means. J. Hangzhou Inst. Elec. Engrg. 17, pp. 1–7 (Chinese).

ⓘ

Notes:

In Chinese

Referenced by:

§19.9(i).

Encodings:

BibTeX

…