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  2. Solenoid - Wikipedia

    en.wikipedia.org/wiki/Solenoid

    A finite solenoid is a solenoid with finite length. Continuous means that the solenoid is not formed by discrete coils but by a sheet of conductive material. We assume the current is uniformly distributed on the surface of the solenoid, with a surface current density K ; in cylindrical coordinates : K → = I l ϕ ^ . {\displaystyle {\vec {K ...

  3. Solenoid (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Solenoid_(mathematics)

    A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of an abelian compact topological group. Solenoids were first introduced by Vietoris for the n i = 2 {\displaystyle n_{i}=2} case, [ 2 ] and by van Dantzig the n i = n {\displaystyle n_{i}=n} case, where n ≥ 2 {\displaystyle n\geq 2} is fixed. [ 3 ]

  4. Chebyshev distance - Wikipedia

    en.wikipedia.org/wiki/Chebyshev_distance

    The two dimensional Manhattan distance has "circles" i.e. level sets in the form of squares, with sides of length √ 2 r, oriented at an angle of π/4 (45°) to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to (i.e. a linear transformation of) the planar Manhattan distance.

  5. Solenoid (engineering) - Wikipedia

    en.wikipedia.org/wiki/Solenoid_(engineering)

    The solenoid can be useful for positioning, stopping mid-stroke, or for low velocity actuation; especially in a closed loop control system. A uni-directional solenoid would actuate against an opposing force or a dual solenoid system would be self cycling. The proportional concept is more fully described in SAE publication 860759 (1986).

  6. Length of a module - Wikipedia

    en.wikipedia.org/wiki/Length_of_a_module

    In algebra, the length of a module over a ring is a generalization of the dimension of a vector space which measures its size. [1] page 153 It is defined to be the length of the longest chain of submodules.

  7. Infinite element method - Wikipedia

    en.wikipedia.org/wiki/Infinite_element_method

    The number of functions and points of interpolations define the accuracy of the element in the infinite direction. [1] The method is commonly used to solve acoustic problems and allows to respect the Sommerfeld condition of non-return of the acoustic waves and the diffusion of the pressure waves in the far field.

  8. Correlation function (statistical mechanics) - Wikipedia

    en.wikipedia.org/wiki/Correlation_function...

    One common correlation function is the radial distribution function which is seen often in statistical mechanics and fluid mechanics. The correlation function can be calculated in exactly solvable models (one-dimensional Bose gas, spin chains, Hubbard model) by means of Quantum inverse scattering method and Bethe ansatz. In an isotropic XY ...

  9. Infinite impulse response - Wikipedia

    en.wikipedia.org/wiki/Infinite_impulse_response

    This relationship is used in the Laplace transfer function of any analog filter or the digital infinite impulse response (IIR) filter T(z) of the analog filter. The bilinear transform essentially uses this first order approximation and substitutes into the continuous-time transfer function, H a ( s ) {\displaystyle H_{a}(s)}