systems

SearchAdvancedHelp

(0.001 seconds)

21—30 of 100 matching pages

21: 12.17 Physical Applications

§12.17 Physical Applications

… ► … ►Dean (1966) describes the role of PCFs in quantum mechanical systems closely related to the one-dimensional harmonic oscillator. …

22: 28.32 Mathematical Applications

… ►

§28.32(i) Elliptical Coordinates and an Integral Relationship

… ►Kernels $K$ can be found, for example, by separating solutions of the wave equation in other systems of orthogonal coordinates. … ►

§28.32(ii) Paraboloidal Coordinates

►The general paraboloidal coordinate system is linked with Cartesian coordinates via …

23: 14.31 Other Applications

… ►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)). …

24: Mark J. Ablowitz

… ►Widespread interest in Painlevé equations re-emerged in the 1970s and thereafter partially due to the connection with IST and integrable systems. …

25: Mourad E. H. Ismail

… ►Ismail serves on several editorial boards including the Cambridge University Press book series Encyclopedia of Mathematics and its Applications, and on the editorial boards of 9 journals including Proceedings of the American Mathematical Society (Integrable Systems and Special Functions Editor); Constructive Approximation; Journal of Approximation Theory; and Integral Transforms and Special Functions. …

26: Morris Newman

… ►Department of Commerce Gold Medal in 1966 for his work on algorithms for solving integral linear systems exactly by using congruence techniques. …

27: 3.1 Arithmetics and Error Measures

… ►

§3.1(i) Floating-Point Arithmetic

►Computer arithmetic is described for the binary based system with base 2; another system that has been used is the hexadecimal system with base 16. … ►Computer algebra systems use exact rational arithmetic with rational numbers $p/q$, where $p$ and $q$ are multi-length integers. …

28: 31.17 Physical Applications

… ►Then … ►

§31.17(ii) Other Applications

►Heun functions appear in the theory of black holes (Kerr (1963), Teukolsky (1972), Chandrasekhar (1984), Suzuki et al. (1998), Kalnins et al. (2000)), lattice systems in statistical mechanics (Joyce (1973, 1994)), dislocation theory (Lay and Slavyanov (1999)), and solution of the Schrödinger equation of quantum mechanics (Bay et al. (1997), Tolstikhin and Matsuzawa (2001), and Hall et al. (2010)). …

29: 28.33 Physical Applications

… ►

McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.

… ►

Daymond (1955) for vibrating systems.

… ►If the parameters of a physical system vary periodically with time, then the question of stability arises, for example, a mathematical pendulum whose length varies as $\cos \left(2\omega t\right)$. … ►

McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

…

30: About MathML

… ►As a general rule, using the latest available version of your chosen browser, plugins and an updated operating system is helpful. …