Fr.: transformation affine
Any → transformation preserving → collinearity.
→ affine; → transformation.
Fr.: transformation de couleur
Empirical mathematical transformation applied to the observed magnitudes in order to convert them into a standard system, or into a different system.
→ color; → transformation.
Fr.: transformée de Fourier
A powerful mathematical tool which is the generalization of the → Fourier series for the analysis of non-periodic functions. The Fourier transform transforms a function defined on physical space into a function defined on the space of frequencies, whose values quantify the "amount" of each periodic frequency contained in the original function. The inverse Fourier transform then reconstructs the original function from its transformed frequency components. The integral F(α) = ∫ f(u)e-iαudu is called the Fourier transform of F(x) = (1/2π)∫ f(α)eiαxdx, both integrals from -∞ to + ∞.
→ Fourier analysis; → transform.
tarâdis-e Gâlile-yi (#)
Fr.: transformation galiléenne
The method of relating a measurement in one → reference frame to another moving with a constant velocity with respect to the first within the → Newtonian mechanics. The Galilean transformation between the coordinate systems (x,y,z,t) and (x',y',z',t') is expressed by the relations: x' = x - vt, y' = y, z' = z. Galilean transformations break down at high velocities and for electromagnetic phenomena and is superseded by the → Lorentz transformations.
→ Galilean; → transformation.
tarâdis-e gaz (#)
Fr.: transformation de jauge
A change of the fields of a gauge theory that does not change the value of any measurable quantity.
→ gauge; → transformation.
tarâdis-e Laplace (#)
Fr.: transformée de Laplace
An integral transform of a function obtained by multiplying the given function f(t) by e-pt, where p is a new variable, and integrating with respect to t from t = 0 to t = ∞.
Fr.: transformation de Legendre
A mathematical operation that transforms one function into another. Two differentiable functions f and g are said to be Legendre transforms of each other if their first derivatives are inverse functions of each other: df(x)/dx = (dg(x)/dx)-1. The functions f and g are said to be related by a Legendre transformation.
Fr.: transformation de Lorentz
A set of linear equations that expresses the time and space coordinates of one → reference frame in terms of those of another one when one frame moves at a constant velocity with respect to the other. In general, the Lorentz transformation allows a change of the origin of a coordinate system, a rotation around the origin, a reversal of spatial or temporal direction, and a uniform movement along a spatial axis. If the system S'(x',y',z',t') moves at the velocity v with respect to S(x,y,z,t) in the positive direction of the x-axis, the Lorentz transformations will be: x' = γ(x - vt), y' = y, z' = z, t' = γ [t - (vx/c2)], where c is the → velocity of light and γ = [1 - (v/c)2]-1/2. For the special case of velocities much less than c, the Lorentz transformation reduces to → Galilean transformation.
→ Lorentz; → transformation.
Fr.: transformation de similarité
1) A transformation that preserves angles and changes all distances in the same ratio.
→ similarity; → transformation.
1) tarâdis (#); 2) tarâdisidan (#)
Fr.: 1) transformée, transformation; 2) transformer
1) Math.: A mathematical quantity obtained from a given quantity
by an algebraic, geometric, or functional transformation.
tarâdiseš (#), tarâdis (#)
1) The act or process of transforming. The state of being transformed.
Verbal noun of → transform.
tarâdisgar (#), tarâdisandé (#)
A device that converts low voltages to higher voltages, or vice versa. A transformer consists of a primary coil and a secondary coil, both traversed by the same magnetic flux.
tarâdis-e yekâyi, ~ yekâni
Fr.: transformation unitaire
A transformation whose reciprocal is equal to its Hermitian conjugate.
→ unitary; → transformation.