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The long-run cost curve is a cost function that models this minimum cost over time, meaning inputs are not fixed. Using the long-run cost curve, firms can scale their means of production to reduce the costs of producing the good. [1] There are three principal cost functions (or 'curves') used in microeconomic analysis:
The time constant is related to the RC circuit's cutoff frequency f c, by = = or, equivalently, = = where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in hertz (Hz).
Alternatively, as before, k may be taken to belong to the set {−1 ,0, +1} (for negative, zero, and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and may also be written R(t). Note that when k = +1, r is essentially a third angle along with θ and φ.
The concept was first introduced by S. Pancharatnam [1] as geometric phase and later elaborately explained and popularized by Michael Berry in a paper published in 1984 [2] emphasizing how geometric phases provide a powerful unifying concept in several branches of classical and quantum physics.
In condensed matter physics, relaxation is usually studied as a linear response to a small external perturbation. Since the underlying microscopic processes are active even in the absence of external perturbations, one can also study "relaxation in equilibrium" instead of the usual "relaxation into equilibrium" (see fluctuation-dissipation theorem).
In geometry, the sagitta (sometimes abbreviated as sag [1]) of a circular arc is the distance from the midpoint of the arc to the midpoint of its chord. [2] It is used extensively in architecture when calculating the arc necessary to span a certain height and distance and also in optics where it is used to find the depth of a spherical mirror ...
The most general form of Cauchy's equation is = + + +,where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.