An Etymological Dictionary of Astronomy and Astrophysics
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A high-contrast imaging technique that reduces minute temporal and spatial → seeing fluctuations and facilitates the detection of faint point sources, in close separation from their stars. It consists of the acquisition of a sequence of images with an → altazimuth mounting telescope while the instrument field derotator is switched off. This keeps the instrument and telescope optics aligned and allows the field of view to rotate with respect to the instrument. For each image, a reference → point spread function (PSF) is constructed from other appropriately selected images of the same sequence and subtracted to remove quasistatic PSF structure (Marois et al. 2006, ApJ 641, 556).

→ angular; → differential; → imaging.

An expression of the form x^m(a + bxⁿ)^pdx, where m, n, p, a, and b are constants.

→ binomial; → differential.

1) Noun.
1a) General: A difference or the amount of difference, as in rate, cost, quantity, degree, or quality, between things that are comparable.
1b) Math.: An infinitesimally small change in a variable; a function of two variables that is obtained from a given function, y = f(x), and that expresses the increment in the given function as the derivative of the function, f'(x), times the increment in the independent variable, written as dy = f'(x) dx.
1c) Electronics: Referring to a circuit, device, or machine whose principle of operation depends on the difference between two opposing effects.
2) Adjective.
2a) General: Of, relating to, or constituting a difference.
2b) Physics: Pertaining to or involving the difference of two or more motions, forces, etc.
2c) Math.: Pertaining to or involving a → derivative or derivatives.

From M.L. differentialis, from differenti(a), → difference, + → -al.

Degarsâné, from degarsân, → different + noun suffix -é.

The two branches of mathematics that make up the → calculus. → differential calculus; → integral calculus.

→ differential; → integral; → calculus.

A branch of calculus which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. → integral calculus.

→ differential; → calculus.

An equation expressing a relationship between an → independent variable, x, an unknown → function, y = f(x), and its → derivatives. The general form of a differential equation is: F(x, y, y', y'', ..., y⁽ⁿ⁾) = 0, or F(x,y, dy/dx, d²y/dx², ..., dⁿy/dxⁿ) = 0. See also: → ordinary differential equation; → partial differential equation; → linear differential equation; → exact differential equation; → first-order differential equation; → homogeneous linear differential equation; → nonhomogeneous linear differential equation; → differential equation with separated variables; → differential equation with separable variables.

→ differential; → equation.

A → differential equation of the form: M₁(x) N₁(y) dx + M₂(x) N₂(y) dy = 0, which can be reduced to a → differential equation with separated variables.

→ differential; → equation; → separate; → variable.

A → differentail equation that can be transformed into the form: M(x)dx + N(x)dy = 0.

→ differential; → equation; → separate; → variable.

The study of curved spaces using differential calculus.

→ differential; → geometry.

A device that is commonly used to measure the → seeing at optical astronomical sites. The DIMM delivers an estimate of the → Fried parameter based on measuring the variance of the differential image motion in two small apertures, usually cut out in a single larger telescope pupil by a mask. The DIMM concept was introduced by Stock & Keller (1960, in Stars and Stellar Systems, Vol. 1, ed. G. P. Kuiper & B. M. Middlehurst, p. 138), whereas its modern implementation was first described by Sarazin & Roddier (1990, A&A 227, 294).

→ differential; → image; → motion; → monitor.

A problem encountered in astronomical spectroscopy, which consists of a loss of light from some wavelengths due to → atmospheric dispersion. In simple terms, differential refraction means that at nonzero → zenith distances an object cannot be simultaneously placed at the same position within a → slit at all wavelengths. This problem becomes more important for increasing → airmass, larger → spectral range, and smaller → slitwidths. To remedy this drawback, the slit should always be oriented along a direction perpendicular to the horizon, since differential refraction occurs in that direction.

→ differential; → refraction.

1) Of a single body (such as a star or a gaseous planet), the axial rotation of equatorial latitudes faster than polar latitudes.
2) Of a galaxy, the orbiting of stars nearer the center faster than those at the edge.

→ differential; → rotation.

A system characterized by → differential rotation. In such a system the → angular velocity decreases as the distance from the rotation center increases.

→ differential; → rotating; → system.

If N(x,y) is a → function of two → independent variables, then dN = (∂N/∂x)dx + (∂N/∂y)dy is the exact differential.

→ exact; → differential.

A → differential equation composed of → continuous  → differentiable functions for which certain conditions are fulfilled. The equation M(x,y)dx + N(x,y)dy = 0 is called exact if M(x,y) and N(x,y) are continuous differentiable functions for which the following relationship is fulfilled: ∂M/∂y = ∂N/∂x, and ∂M/∂y and ∂N/∂x are continuous in some region.

→ exact; → differential; → equation.

A → differential equation containing only the first → derivative. For example, dy/dx = 3x and 2y(dy/dx) + 3x = 5.

→ first; → order; → differential; → equation.

A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I.

→ homogeneous; → linear; → differential; → equation.

An equation in which the → dependent variable y and all its differential coefficients occur only in the first degree. A linear differential equation of → order  order n has the form:
f_n(x)y⁽ⁿ⁾ + f_n-1(x)y^(n-1) + ... + f₁(x)y^' + f₀(x)y = Q(x),
where f₀(x), f₁(x), ..., f_n(x) and Q(x) are each continuous functions of x defined on a common interval I and f_n(x)≠ 0 in I. A linear differential equation cannot have, for example, terms such as y² or (y^')^1/2. See also: → homogeneous linear differential equation; → nonhomogeneous linear differential equation.

→ linear; → differential; → equation.

A differential equation that has been derived from an original nonlinear equation.

Linearized, p.p. of → linearize; → differential; → equation.

A → linear differential equation if Q(x)≠ 0 on interval I.

→ nonhomogeneous; → linear; → differential; → equation.