An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

1) If a → power series → converges for some nonzero value x₀, then it converges absolutely for any value of x, for which |x| < |x₀|.
2) If a power series → diverges for some nonzero value x₀, then it diverges for any value of x, for which |x| > |x₀|.

Named after the Norwegian mathematician Niels Henrik Abel (1802-1829); → theorem.

A measurement in which the comparison is directly with quantities whose units are basic units of the system. For example, the measurement of speed by measurements of distance and time is an absolute measurement, but the measurement of speed by a speedometer is not an absolute measurement. Note that the word absolute measurement implies nothing about → precision or → accuracy (IEEE Standard Dictionary of Electrical and Electronics Terms).

→ absolute; → measurement.

The intensity ratio among the couple of relatively adjacent → Balmer lines, for example Hα/Hβ and Hβ/Hγ, which have well-known theoretical values. They are used to determine the → interstellar extinction.

→ Balmer; → decrement.

A theorem in probability theory concerned with determining the → conditional probability of an event when another event has occurred. Bayes' theorem allows revision of the original probability with new information. Its simplest form is: P(A|B) = P(B|A) P(A)/P(B), where P(A): independent probability of A, also called prior probability; P(B): independent probability of B; P(B|A): conditional probability of B given A has occurred; P(A|B): conditional probability of A given B has occurred, also called posterior probability. Same as Bayes' rule.

Named after its proponent, the British mathematician Reverend Thomas Bayes (1702-1761). However, Bayes did not publish the theorem during his lifetime; instead, it was presented two years after his death to the Royal Society of London.

A statement of the → conservation of energy in the → steady flow of an → incompressible, → inviscid fluid. Accordingly, the quantity (P/ρ) + gz + (V²/2) is → constant along any → streamline, where P is the fluid → pressure, V is the fluid → velocity, ρ is the mass → density of the fluid, g is the acceleration due to → gravity, and z is the vertical → height. This equation affirms that if the internal velocity of the flow goes up, the internal pressure must drop. Therefore, the flow becomes more constricted if the velocity field within it increases. Same as the → Bernoulli equation.

After Daniel Bernoulli (1700-1782), the Swiss physicist and mathematician who put forward the theorem in his book Hydrodynamica in 1738; → theorem.

A rule for writing an equivalent expansion of an expression such as (a + b)ⁿ without having to perform all multiplications involved. → binomial expansion. The general expression is (a + b)ⁿ = &Sigma (n,k)a^kb^{n - k}, where the summation is from k = 0 to n, and (n,k) = n!/[r!(n - k)!]. For n = 2, (a + b)² = a² + 2ab + b². Historically, the binomial theorem as applied to (a + b)² was known to Euclid (320 B.C.) and other early Greek mathematicians. In the tenth century the Iranian mathematician Karaji (953-1029) knew the binomial theorem and its accompanying table of → binomial coefficients, now known as → Pascal's triangle. Subsequently Omar Khayyam (1048-1131) asserted that he could find the 4th, 5th, 6th, and higher roots of numbers by a special law which did not depend on geometric figures. Khayyam's treatise concerned with his findings is lost. In China there appeared in 1303 a work containing the binomial coefficients arranged in triangular form. The complete generalization of the binomial theorem for all values of n, including negative integers, was established by Isaac Newton (1642-1727).

→ binomial; → theorem.

For a four dimensional → space-time, the → Schwarzschild metric is the only solution of → Einstein's field equations which describes the gravitational field created by a spherically symmetrical distribution of mass. The theorem implies that the gravitational field outside a sphere is necessarily static, and that the metric inside a spherical shell of matter is necessarily flat.

The theorem was first demonstrated in 1923 by George David Birkhoff (1884-1944), an American mathematician; → theorem

The → electromagnetic radiation emitted by a → fast moving → charged particle when it passes within the strong → electric field of an → atomic nucleus and is → decelerated.

Bremsstrahlung, from Ger. Bremse "brake" + Strahlung "radiation," from strahlen "to radiate," from Strahl "ray," from O.H.G. strala "arrow, stripe;" PIE *ster- "to spread."

Legâm-tâbeš, from legâm, → brake, + tâbeš, → radiation.

If f(x) and φ(x) are two → continuous functions on the → interval [a,b] and → differentiable within it, and φ'(x) does not vanish anywhere inside the interval, there will be found, in [a,b], some point x = c, such that [f(b) - f(a)] / [φ(b) - φ(a)] = f'(c) / φ'(c).

→ Cauchy's equation; → theorem.

A statement about the characteristics of the sampling distribution of means of → random samples from a given → statistical population. For any set of independent, identically distributed random variables, X₁, X₂,..., X_n, with a → mean μ and → variance σ², the distribution of the means is equal to the mean of the population from which the samples were drawn. Moreover, if the original population has a → normal distribution, the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases.

→ central; → limit; → theorem.

A theorem stating that the → Fourier transform of the convolution of f(x) and g(x) is equal to the product of the Fourier transform of f(x) and g(x): F{f*g} = F{f}.F{g}.

→ convolution; → theorem.

The → absolute acceleration of a point P, which is moving with respect to a local → reference frame that is also in motion, is equal to the vector sum of:
a) the acceleration P would have if it were fixed to the moving system;
b) the acceleration of P with respect to the local moving system; and
c) a compound supplementary → Coriolis acceleration.

→ Coriolis effect; → theorem.

1) The amount lost in the process of decreasing.
2) Math.: The quantity by which a variable is decreased. A negative → increment.
3) Physics: 1) The ratio of the amplitude of an oscillation to that of its succeeding oscillation in an underdamped vibrating system. 2) The intensity ratio of a series of spectral lines of the same nature, such as → Balmer decrement.

L decrementum, from decre(tus), → decrease + -mentum noun suffix -ment.

Kâheh, from kâh- present stem of kâhidan, → decrease + noun suffix -é.

Same as → Gauss's theorem.

→ divergence; → theorem.

Math: A theorem that asserts the existence of at least one object, such as the → solution to a → problem or → equation.

→ existence; → theorem.

Farthest from the center or middle; outermost; exceeding the bounds of moderation. → extreme adaptive optics; → extreme HB star; → extreme horizontal branch star; → extreme infrared; → extreme mass ratio inspiral; → extreme ultraviolet; → extremely metal-poor star.

From L. extremus "outermost, utmost," superlative of exterus, "outer," comparative of ex "out of," → ex-.

Ostom "outermost, utmost" (Av. (ustəma- "outermost, highest, ultimate"), superlative of ost "out," → ex-, + -tom superlative suffix, from Mid.Pers. -tom (xwaštom "most pleasant," nevaktom "best," wattom "worst"), from O.Pers. -tama- (fratama- "first, front"); Av. -təma- (amavastəma- "strongest," hubaiδitəma- "most sweet-scented," baēšazyôtəma- "most healing," fratəma- "first, front"); cf. Skt. tama-.

An → adaptive optics system with high-contrast imaging and spectroscopic capabilities. Extreme adaptive optics systems enable the detection of faint objects (e.g., → exoplanets) close to bright sources that would otherwise overwhelm them. This is accomplished both by increasing the peak intensity of point-source images and by removing light scattered by the atmosphere and the telescope optics into the → seeing disk.

→ extreme; → adaptive; → optics.

Same as → extreme horizontal branch star.

→ extreme horizontal branch star.

The hottest variety of stars on the → horizontal branch with temperatures ranging from 20,000 to 40,000 K. EHB stars are distinguished from normal horizontal branch stars by having extremely thin, inert hydrogen envelopes surrounding the helium-burning core. They are hot, dense stars with masses in a narrow range near 0.5 Msun. These stars have undergone such extreme mass loss during their first ascent up the giant branch that only a very thin hydrogen envelope survives. Stars identified as EHB stars are found in low metallicity globular clusters as an extension of the normal HB.

→ extreme; → horizontal; → branch; → star.

A portion of the far infrared radiation, including wavelengths between 100 and 1,000 microns.

→ extreme; → infrared.