About the Project



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1: 32.16 Physical Applications
§32.16 Physical Applications
Integrable Continuous Dynamical Systems
2: 21.10 Methods of Computation
  • Belokolos et al. (1994, Chapter 5) and references therein. Here the Riemann surface is represented by the action of a Schottky group on a region of the complex plane. The same representation is used in Gianni et al. (1998).

  • Tretkoff and Tretkoff (1984). Here a Hurwitz system is chosen to represent the Riemann surface.

  • 3: Stephen M. Watt
    His areas of research include algorithms and systems for computer algebra, programming languages and compilers, mathematical handwriting recognition and mathematical document analysis. He was one of the original authors of the Maple and Axiom computer algebra systems, principal architect of the Aldor programming language and its compiler at IBM Research, and co-author of the MathML and InkML W3C standards. …
    4: 28.27 Addition Theorems
    Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. …
    5: 29.19 Physical Applications
    §29.19(i) Lamé Functions
    Brack et al. (2001) shows that Lamé functions occur at bifurcations in chaotic Hamiltonian systems. …
    6: 8.24 Physical Applications
    §8.24(i) Incomplete Gamma Functions
    The function γ ( a , x ) appears in: discussions of power-law relaxation times in complex physical systems (Sornette (1998)); logarithmic oscillations in relaxation times for proteins (Metzler et al. (1999)); Gaussian orbitals and exponential (Slater) orbitals in quantum chemistry (Shavitt (1963), Shavitt and Karplus (1965)); population biology and ecological systems (Camacho et al. (2002)). …
    7: Simon Ruijsenaars
    His main research interests cover integrable systems, special functions, analytic difference equations, classical and quantum mechanics, and the relations between these areas. …
    8: Funding
  • Systems Integration for Manufacturing Applications Program of the Engineering Laboratory (formerly Manufacturing Engineering Laboratory)

  • 9: 26.22 Software
  • GAP (website). A system for computational discrete algebra.

  • Magma (website). A computational algebra system.

  • 10: Bruce R. Miller
    There, he carried out research in non-linear dynamics and celestial mechanics, developing a specialized computer algebra system for high-order Lie transformations. … In particular, he developed the LaTeXML system used for converting the  source documents into XML and MathML from which the DLMF website is constructed. …