Hamiltonian structure

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11: 36.14 Other Physical Applications

… ►These are the structurally stable focal singularities (envelopes) of families of rays, on which the intensities of the geometrical (ray) theory diverge. …

12: 15.17 Mathematical Applications

… ►The three singular points in Riemann’s differential equation (15.11.1) lead to an interesting Riemann sheet structure. …

13: Richard A. Askey

… ►Askey was a member of the original editorial committee for the DLMF project, serving as an Associate Editor advising on all aspects of the project from the mid-1990’s to the mid-2010’s when the organizational structure of the DLMF project was reconstituted; see About the Project.

14: Bille C. Carlson

… ►Both contributions concerned the electronic structure of molecules and solids. …

15: 22.18 Mathematical Applications

… ►This circumvents the cumbersome branch structure of the multivalued functions $x(y)$ or $y(x)$, and constitutes the process of uniformization; see Siegel (1988, Chapter II). … ►This provides an abelian group structure, and leads to important results in number theory, discussed in an elementary manner by Silverman and Tate (1992), and more fully by Koblitz (1993, Chapter 1, especially §1.7) and McKean and Moll (1999, Chapter 3). The existence of this group structure is connected to the Jacobian elliptic functions via the differential equation (22.13.1). …

16: About the Project

… ► Olver, Editor-in-Chief and Mathematics Editor of the DLMF, the other Editors initiated an effort aimed at updating the organizational structure of the DLMF project. …

17: 36.13 Kelvin’s Ship-Wave Pattern

… ►The wake is a caustic of the “rays” defined by the dispersion relation (“Hamiltonian”) giving the frequency $\omega$ as a function of wavevector $𝐤$: …

18: 18.38 Mathematical Applications

… ►It has elegant structures, including $N$-soliton solutions, Lax pairs, and Bäcklund transformations. … ►Algebraic structures were built of which special representations involve Dunkl type operators. In the $q$-case this algebraic structure is called the double affine Hecke algebra (DAHA), introduced by Cherednik. …This gives also new structures and results in the one-variable case, but the obtained nonsymmetric special functions can now usually be written as a linear combination of two known special functions. …

19: Bibliography P

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Optical properties of layer antiferromagnets with ${\mathrm{K}}_2{\mathrm{NiF}}_4$ structure. J. Phys. C: Solid State Physics 2 (11), pp. 2012–2021.

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External Links:

Document

Referenced by:

§19.35(ii).

Encodings:

BibTeX

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The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic. Philos. Mag. (7) 37, pp. 311–317.

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External Links:

MathReview (C. J. Bouwkamp)

Referenced by:

§36.2(ii).

Encodings:

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20: Bibliography J

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The birth of the giant component. Random Structures Algorithms 4 (3), pp. 231–358.

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Notes:

With an introduction by the editors

External Links:

ISSN 1042-9832, Document, MathReview (Alan M. Frieze), ZentralBlatt

Referenced by:

§16.23(ii), §9.13(ii).

Encodings:

BibTeX

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Atomic Structure Theory: Lectures on Atomic Physics. Springer, Berlin and Heidelberg.

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External Links:

ISBN 978-3-540-68010-9

Referenced by:

§33.22(iv).

Encodings:

BibTeX

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