Fr.: théorème du binôme
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)akbn - 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).
Bio-, Gk., from bios "life," from PIE base *gweie- "to live;" cf. O.Pers./Av. gay- "to live," Av. gaya- "life," gaeθâ- "being, world, mankind," jivya-, jva- "aliving, alive," Skt. jivah "alive, living;" Mid.Pers. zivastan "to live," zivik, zivandag "alive, living," L. vivus "living, alive," vita "life," O.E. cwic "alive," E. quick, Lith. gyvas "living, alive."
Zist "life, existence," from zistan "to live," Mid.Pers. zivastan "to live," zivižn "life," O.Pers./Av. gay-, as explained above.
The retrieval and analysis of biochemical and biological data using mathematics and computer science, as in the study of genomes (Dictionary.com).
An expert or specialist in biology.
The study of living organisms and their interactions with the non living world.
The production and emission of light by a living organism as the result of a chemical reaction (→ chemiluminescence). In other words, bioluminescence is chemiluminescence from living organisms. It is widespread in the marine environment, but rare in terrestrial and especially freshwater environments.
A specialist in → biophysics.
The science that deals with biological structures and processes involving the application of physical principles and methods.
The part of a planet or moon within which life can occur. It may include the crust, oceans, and atmosphere.
qânun-e Biot-Savart (#)
Fr.: loi de Biot-Savart
The → magnetic field due to → electric current flowing in a long straight conductor is directly proportional to the current and inversely proportional to the distance of the point of observation from the conductor. The law is derivable from → Ampere's law, but was obtained experimentally by the authors.
Named after the French physicists Jean-Baptiste Biot (1774-1862) and Félix Savart (1791-1841); → law.
Fr.: environnement biotique
Ecology: The environment consisting of living organisms, which interact with each other and with their non-living surroundings.
The science concerned with the functions of life, or vital activity and force.
Having two poles; having two opposite main structures or components.
Fr.: flot bipolaire
Same as → bipolar outflow.
Fr.: jet bipolaire
One of two beams of high-temperature, ionized gas ejected in two opposite directions associated with a → protostar. The collimated jets, a consequence of the → accretion process, can extend over distances of several → light-years.
Fr.: nébuleuse bipolaire
An interstellar cloud of ionized gas with two main lobes which lie symmetrically on either side of a central star. The bipolar shape is generally due to the ejection of material by the central star in opposing directions.
Fr.: flot bipolaire
A flow of gaseous material in two opposite directions emanating from protostellar regions or from → evolved stars during the early post-→ AGB evolution. In protostellar regions → molecular outflows are pushed by → bipolar jets.
A property of some crystalline materials (e.g. calcite, quartz) which have different indices of refraction associated with different crystallographic directions. Therefore, the crystal splits incident transmitted light into two beams, each polarized perpendicularly to the other. Also called double refraction.
Došekast, from do- "two," → bi- + šekast "breaking," from šekastan "to break up," Mid.Pers. škastan, Av. skand- "to break."