The branch of mathematics which deals with the properties and relations of numbers using symbols (usually letters of the alphabet) to represent numbers or members of a specified set; the generalization and extension of arithmetic.
Algebra, from M.L., from Ar. al jabr "reunion of broken bones," the first known use in the title of a book by the Persian mathematician and astronomer Abu Ja'far Mohammad ibn Musa al-Khwarizmi (c780-c850), who worked in Baghdad under the patronage of Caliph Al-Mamun. The full title of the tratise was Hisab al-Jabr w'al-Muqabala "Arithmetic of Completion and Balancing." → algorithm.
Jabr, from Ar. al jabr, as above.
Relating to, involving, or according to the laws of algebra.
Fr.: équation algébrique
An equation in the form of P = 0, where P is a → polynomial having a finite number of terms.
Fr.: fonction algébrique
A function expressed in terms of → polynomials and/or roots of polynomials. In other words, any function y = f(x) which satisfies an equation of the form P0(x)yn + P1(x)yn - 1 + ... + Pn(x) = 0, where P0(x), P1(x), ..., Pn(x) are polynomials in x.
adad-e jabri (#)
Fr.: nombre algébrique
A number, → real or → complex, that is a → root of a → non-zero polynomial equation whose → coefficients are all → rational. For example, the root x of the polynomial x2 - 2x + 1 = 0 is an algebraic number, because the polynomial is non-zero and the coefficients are rational numbers. The imaginary number i is algebraic, because it is the solution to x2 + 1 = 0.
That part of the Moon's shadow that extends beyond the → umbra. It is similar to the → penumbra in that the Sun is only partially blocked by the Moon. From within the antumbra, the Sun appears larger than the Moon which is seen in complete silhouette. An → annular eclipse is seen when an observer passes through the antumbra (F. Espenak, NASA).
Fr.: algèbre associative
An algebra whose multiplication is associative.
→ associative; → algebra.
asymptotic giant branch (AGB)
šâxe-ye nâhamsâvi-ye qulân
Fr.: branche asymptotique des géantes
A region of the → Hertzsprung-Russell diagram populated by evolving → low-mass to → intermediate-mass stars. These stars have an electron → degenerate core of carbon and oxygen surrounded by two burning shells of helium and hydrogen. The H and He-burning shells are activated alternately in the deep layers of the star. An extended and tenuous convection envelope, having a radius of 104-105 times the size of the core, lies above these shells. The loosely bound envelope is gradually eroded by the strong → stellar wind, which forms a dusty → circumstellar envelope out to several hundreds of stellar radii. The convective envelope, stellar atmosphere, and circumstellar envelope have a rich and changing chemical composition provided by → nucleosynthesis processes in the burning shells in the deep interior.
blue horizontal branch star
setâre-ye âbi-ye šâxe-ye ofoqi
Fr.: étoile bleue de la branche horizontale
A member of a population of blue stars appearing on the → horizontal branch in the → Hertzsprung-Russell diagram of the Galactic → halo populations and → globular clusters. Belonging to → spectral types B3 to A0, they have evolved past the → red giant stage and are burning helium in their core.
→ blue; → horizontal; → branch, → star.
jabr-e Booli (#)
Fr.: algèbre de Boole
Any of a number of possible systems of mathematics that deals with → binary digits instead of numbers. In Boolean algebra, a binary value of 1 is interpreted to mean → true and a binary value of 0 means → false. Boolean algebra can equivalently be thought of as a particular type of mathematics that deals with → truth values instead of numbers.
→ Boolean; → algebra. The term Boolean algebra was first suggested by Sheffer in 1913.
In Dirac's notation for describing a quantum state, a vector which together with → ket constitutes the dual vector → bracket. A bra is shown by <|, the mirror image of the symbol for a ket vector. The scalar product of a bra vector < B| and a ket vector |A> is written < B|A >, i.e. as a juxtaposition of the symbols for the bra and the ket vectors, that for the bra vector being on the left, and the two vertical lines being contracted to one for brevity.
From bra- the first syllable in → bracket.
In Dirac's notation, an expression which is a → scalar product of the dual vectors → bra and → ket which describe a quantum state. The bra vector appears on the left of the ket vector.
From M.Fr. braguette "codpiece armor."
Fr.: série de Brackette
A series of lines in the infrared spectrum of atomic hydrogen due to electron jumps between the fourth and higher energy levels (Br α has wavelength 4.052 μm, Br γ 2.166 μm).
Named after the American physicist Frederick Brackett (1896-1980); → series.
Fr.: angle de Bragg
The grazing angle between an incident beam of X-rays and a given set of crystal planes for which the secondary X-rays from the planes combine to give a single beam.
→ Bragg's law; → angle.
Fr.: loi de Bragg
A parallel beam of monochromatic X-rays of wavelength λ, incident on a given set of parallel crystal planes at a grazing angle θ will give rise to a reflected beam whenever: n λ = 2d . sinθ, where n is an integer representing the difference in path length, and d is the perpendicular distance between a pair of adjacent planes.
Named after William Lawrence Bragg (1890-1971), British physicist, who, in collaboration with his father, William Henry Bragg (1862-1942), joint Nobel Prize in Physics 1915, pioneered X-ray analysis and spectrometry; → law.
1) legâm, tormoz 2) legâmidan, tormoz kardan
Fr.: 1) frein; 2) freiner
1) A device for slowing or stopping a vehicle or other moving mechanism by
the absorption or transfer of the energy of momentum, usually by means of friction.
From O.Du. braeke "flax brake," from breken "to break."
Legâm originally "a horse bit," on the model of Fr. frein "horse bit; motor brake;" and Ger. Bremse "horse bit; brake;" tormoz, loan from Russ. тормоз.
The act or fact of stopping by means of or as if by means of a brake. See: → magnetic braking; → radiative braking; → tidal braking; → braking index.
Verbal noun of → brake.
Fr.: indice de freinage
A parameter indicating the rate at which a → pulsar slows down. Neutron stars are powered by → rotational energy and lose energy by accelerating particle → winds and by emitting → electromagnetic radiation. The → rotation frequency, Ω, thus decreases with time and this slowdown is usually described by the relation Ω. = - kΩn, where k is a positive constant which depends on the → moment of inertia and the → magnetic dipole moment of the → neutron star and n is the braking index. Conventionally, the braking index is derived by differentiation of the above equation, yielding n = ΩΩ.. / Ω.2. In a highly simplified model in which the spin-down torque arises from dipole radiation at the rotation frequency, one expects n = 3 (Johnston, S., Galloway, D., 1999, arXiv:astro-ph/9905058).
1) šâxé (#); 2) šâxé zadan (#)
Fr.: 1) branche; 2) se ramifier
1a) General: A shoot or arm-like limb of a tree; anything like a
limb of a tree; any offshoot from a main trunk.
M.E., from O.Fr. branche, from L.L. branca "a claw, paw."
1) Šâxé "branch," from Mid.Pers šâk, cf.
Mod.Pers. šâx, šax "branch; horn," Skt. sakha-
"a branch, a limb," Arm. cax, Lit. šaka,
O.S. soxa, PIE *kakhâ "branch."
The act of dividing into branches. → branching ratio.