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binomial donâmin Fr.: 1) binôme; 2) binomial 1a) An algebraic expression containing 2 terms, as x + y and
2x^{2} - 3x. In other words, a → polynomial
with 2 terms. From L.L. binomi(us) "having two names," + → -al, → nominal. |
binomial coefficient hamgar-e donâmin Fr.: coefficient binomial
The factor multiplying the variable in a term of a → binomial expansion. For example, in (x + y)^{4} = x^{4} + 4x^{3}y + 6x^{2}y^{2} + 4xy^{3} + y^{4} 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)!]. → binomial; → coefficient. |
binomial differential degarsâne-ye donâmin Fr.: binôme différentiel An expression of the form x^{m}(a + bx^{n})^{p}dx, where m, n, p, a, and b are constants. → binomial; → differential. |
binomial distribution vâbâžeš-e donâmin 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)!] p^{x}.q^{n - 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}. → binomial; → distribution. |
binomial expansion gostareš-e donâmin Fr.: expansion binomiale A rule for the expansion of an expression of the form (x + y)^{n}. The variables x and y can be any → real numbers and n is an → integer. The general formula is known as the → binomial theorem. |
binomial nomenclature nâmgozâri-ye donâmin 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. → binomial; → nomenclature. |
binomial theorem farbin-e donâmin 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)a^{k}b^{n - k}, where the summation is from k = 0 to n, and (n,k) = n!/[r!(n - k)!]. For n = 2, (a + b)^{2} = a^{2} + 2ab + b^{2}. 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- zist- (#) Fr.: bio- 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. |
bioastronomy zistaxtaršenâsi (#) Fr.: bioastronomie A common branch of astronomy and biology dealing with the study of life throughout the Universe; synonymous with → astrobiology and → exobiology. Bioastronomy, from → bio- + → astronomy. Zistaxtaršenâsi, from zist-, → bio-, + axtaršenâsi, → astronomy. |
biodiversity zistgunâguni Fr.: biodiversité The → variety of → plant and → animal → species in a particular → environment. |
bioinformatics zist-azdâyik Fr.: bioinformatique The retrieval and analysis of biochemical and biological data using mathematics and computer science, as in the study of genomes (Dictionary.com). → bio-; → informatics. |
biologist zistšenâs (#) Fr.: biologiste An expert or specialist in biology. |
biology zistženâsi (#) Fr.: biologie The study of living organisms and their interactions with the non living world. |
bioluminescence zist-foruzesti Fr.: bioluminescence 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. → chemi-; → luminescence. |
biomarker zist-dâjgar Fr.: biomarqueur 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. |
biophysicist zistfizikdân (#) Fr.: biophysicien A specialist in → biophysics. |
biophysics zistfizik (#) Fr.: biophysique The science that deals with biological structures and processes involving the application of physical principles and methods. |
biosignature zist-nešânzad Fr.: biosignature A substance or phenomenon whose presence in an object such as a → meteorite or an → exoplanet indicates the existence of life. |
biosphere zistsepehr (#) Fr.: biosphère The part of a planet or moon within which life can occur. It may include the crust, oceans, and atmosphere. |
Biot-Savart law 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. |
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