Fr.: 1) binôme; 2) binomial
1a) An algebraic expression containing 2 terms, as x + y and
2x2 - 3x. In other words, a → polynomial
with 2 terms.
Fr.: coefficient binomial
The factor multiplying the variable in a term of a → binomial expansion. For example, in (x + y)4 = x4 + 4x3y + 6x2y2 + 4xy3 + y4 the binomial coefficients are 1, 4, 6, 4, and 1. In general, the r-th binomial coefficient in the expression (x + y)n is: (n,r) = n!/[r!(n - r)!].
Fr.: binôme différentiel
An expression of the form xm(a + bxn)pdx, where m, n, p, a, and b are constants.
Fr.: distribution binomiale
A probability distribution for independent events for which there are only two possible outcomes i.e., success and failure. The probability of x successes in n trials is: P(x) = [n!/x!(n - x)!] px.qn - x, where p is the probability of success and q = 1 - p the probability of failure on each trial. These probabilities are given in terms of the → binomial theorem expansion of (p + q)n.
Fr.: expansion binomiale
Fr.: nomenclature binomiale
A system introduced by Carl von Linné (1707-1778), the Swedish botanist, in which each organism is identified by two names. The first is the name of the genus (generic name), written with a capital letter. The second is the name of the species (specific name). The generic and specific names are in Latin and are printed in italic type. For example, human beings belong to species Homo sapiens.
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 biologic feature that is measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacological responses to a therapeutic intervention. For example, prostate specific antigen (PSA) is a biomarker for cancer of the prostate.
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.