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In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup Γ {\displaystyle \Gamma } of S L 2 ( R ) {\displaystyle \mathrm {SL} _{2}(\mathbb {R} )} as modular ...
The sawtooth wave (or saw wave) is a kind of non-sinusoidal waveform. It is so named based on its resemblance to the teeth of a plain-toothed saw with a zero rake angle. A single sawtooth, or an intermittently triggered sawtooth, is called a ramp waveform. The convention is that a sawtooth wave ramps upward and then sharply drops.
In mathematics, geology, and cartography, a surface map is a 2D perspective representation of a 3-dimensional surface. [1] Surface maps usually represent real-world entities such as landforms or the surfaces of objects. They can, however, serve as an abstraction where the third, or even all of the dimensions correspond to non-spatial data. In ...
This radiative ground wave is known as Norton surface wave, or more properly Norton ground wave, because ground waves in radio propagation are not confined to the surface. Another type of surface wave is the non-radiative, bound-mode Zenneck surface wave or Zenneck–Sommerfeld surface wave .
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Surface-wave inversion is the method by which elastic properties, density, and thickness of layers in the subsurface are obtained through analysis of surface-wave dispersion. [2] The entire inversion process requires the gathering of seismic data, the creation of dispersion curves, and finally the inference of subsurface properties.
As a simple example from the physics of magnetically confined plasmas, consider an axisymmetric system with circular, concentric magnetic flux surfaces of radius (a crude approximation to the magnetic field geometry in an early tokamak but topologically equivalent to any toroidal magnetic confinement system with nested flux surfaces) and denote the toroidal angle by and the poloidal angle by .