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mathematical elegance qašangi-ye mazdâhik Fr.: élégance mathématique A mathematical solution or demonstration when it yields a result in a surprising way (e.g., from apparently unrelated theorems), is short, and is based on fundamental concepts. According to Henri Poincaré, what gives the feeling of elegance "is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. ... Elegance may result from the feeling of surprise caused by the un-looked-for occurrence together of objects not habitually associated. ... Briefly stated, the sentiment of mathematical elegance is nothing but the satisfaction due to some conformity between the solution we wish to discover and the necessities of our mind" (Henri Poincaré, Science and Method, 1908). According to Bertrand Russell, "Mathematics, rightly viewed, possesses not only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show" (Bertrand Russell, A History of Western Philosophy, 1945). → mathematical; → elegance. |
mathematical expectation omid-e mazdâhik, bayuseš-e ~, ~ riyâzi Fr.: espérance mathématique In probability and statistics, of a random variable, the summation or integration, over all values of the random variable, of the product of the value and its probability of occurrence. Also called → expectation, → expected value. → mathematical; → expectation. |
mathematical object barâxt-e mazdâhik, ~ riyâzi Fr.: objet mathématique An → abstract object dealt with in mathematics that has a definition, obeys certain properties, and can be the target of certain operations. It is often built out of other, already defined objects. Some examples are → numbers, → functions, → triangles, martices (→ matrix), → groups, and entities such as → vector spaces, and → infinite series. → mathematical; → object. |
mathematician mazdâhikdân Fr.: mathématicien An expert or specialist in → mathematics. M.E. mathematicion, from M.Fr. mathematicien, from mathematique, from L. mathematicus, → mathematics. Mazdâhikdân, from mazdâhik, → mathematics, + -dân "knower," present stem of dânestan "to know," → science. |
mathematics mazdâhik (#), riyâzi (#) Fr.: mathématique A broad-ranging field of knowledge dealing with the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. M.E. mathematic, from L. mathematica (ars), from Gk. mathematike (tekhne) "mathematical science," from mathema (gen. mathematos) "science, knowledge," (+ -ike, → -ics), related to manthein "to learn, to know" from PIE base *men- "to think," (cf. Av. mazdāh- "memory," as below, Lith. mandras "wide-awake," O.C.S. madru "wise, sage," Goth. mundonsis "to look at," Ger. munter "awake, lively"). Mazdâhik, from Av. mazdāh- "memory," mazdā-
"wisdom," mazdāθa- "what must be borne in mind;" from PIE
base *men- "to think," as above; cf.
Skt. medhā- "mental power, wisdom, intelligence;"
Gk. manthein, mathematike, as above. |
matrix mâtris (#) Fr.: matrice 1) An orderly array of numbers, algebraic symbols, or mathematical
functions, especially when such arrays are added and multiplied
according to certain rule; e.g. → Jordan matrix. From O.Fr. matrice, from L. matrix "female animal kept for breeding," in L.L. "womb, source, origin," from mater, → mother. Mâtris, loan from Fr., as above. |
matrix calculus afmârik-e mâtrishâ Fr.: calcul matriciel The treatment of matrices whose entries are functions. |
matrix inverse mâtris-e vârun Fr.: matrice inverse For a → square matrix whose → determinant is not zero, the unique matrix A^{-1} satisfying the relation AA^{-1} = A^{-1}A = I, where I is the → identity matrix. |
matter mâddé (#) Fr.: matière 1) Physical or corporeal substance in general, whether solid, liquid, or
gaseous, especially as distinguished from incorporeal substance, as spirit
or mind, or from qualities, actions, and the like. M.E. mater(e), materie, from O.Fr. mat(i)ere, materie, from L. materia "substance from which something is made," also "hard inner wood of a tree," from mater, → mother, PIE base *mater-, see below. Mâddé, variant mâyé "substance, essence; quantity, amount;"
Mid.Pers. mâtak/mâdak "substance, the essential element of anything; materials"
(Sogd. patmâδé "matter, substance"),
from mât, mâd "mother; substance" (see E. matter, as above),
from O.Pers./Av. mātar-
"mother;" cf. Ossetic mad/madae "mother;" Khotanese mâta "mother;"
Skt. mātár- "mother;" Gk. meter, mater; L. mater
(Fr. mère, Sp. madre);
O.E. môdor from P.Gmc. *mothær (O.S. modar, Dan. moder,
Du. moeder, Ger. Mutter); Lith. mote "wife." |
matter era dowrân-e mâddé (#) Fr.: ère dominée par la matière A critical change in the history of the Universe, which occurred after the radiation era, when the density of energy contained within matter exceeded the density of energy contained within radiation. This transition started about 5000 years after the Big Bang, when the temperature had fallen to 3 x 10^{4} K. Later, 380 000 years after the Big Bang, when the temperature was 3000 K, matter and radiation were no longer coupled together and the Universe became transparent. |
matter-dominated Universe giti-ye mâdde-ciré Fr.: Univers dominé par la matière A Universe in which the matter energy density (Ω_{m} ≈ 1) provides most of the total energy density. According to the → Big Bang model, in the early history of the → Universe a → radiation-dominated phase preceded the matter-dominated phase. This phase is characterized by R/R_{0} ∝ t^{2/3}, where R is the → cosmic scale factor and t is time. |
Maunder minimum kamine-ye Maunder Fr.: minimum de Maunder A period from about 1645 to 1715 when the number of → sunspots was unusually low. This → solar activity minimum is attested also through the increased content of carbon 14 in tree rings in that period. The reason is that the cosmic rays which produce ^{14}C reach the Earth in a greater number when there is weak solar activity (see also → radiocarbon dating). The Maunder minimum occurred during a period of cooling of the Earth, called the → Little Ice Age. The Maunder minimum is one of a number of periods of low solar activity, including the → Dalton minimum, the → Sporer minimum, the → Wolf minimum, and the → Oort minimum. After the British astronomer Edward Walter Maunder (1851-1928) who, along with Gustav Spörer of Germany, first called attention to this phenomenon; → minimum. |
maximum bišiné (#) Fr.: maximum The greatest value attained (or attainable) by a function; the opposite of minimum. From L. maximum, neuter of maximus "greatest," superlative of magnus "great, large" cognate with Pers. meh "great, large" (Mid.Pers. mah, mas; Av. maz-, masan-, mazant- "great, important," mazan- "greatness, majesty," mazišta- "greatest;" cf. Skt. mah-, mahant-; Gk. megas; PIE *meg- "great"). Bišiné, from biš "much, more; great" (from Mid.Pers. veš "more, longer; more frequently," related to vas "many, much" (Mod.Pers. bas); O.Pers. vasiy "at will, greatly, utterly;" Av. varəmi "I wish," vasô, vasə "at one's pleasure or will," from vas- "to will, desire, wish") + -in superlative suffix + -é nuance suffix. |
maximum density of water cagâli-ye bišine-ye âb Fr.: densité maximale de l'eau The density of pure water occurring at 3.98 °C, which is 1.0000 g cm^{-3}, or 1000 kg m^{-3}. Water when cooled down contracts normally until the temperature is 3.98 °C, after which it expands. Because the maximum density of water occurs at about 4 °C, water becomes increasingly lighter at 3 °C, 2 °C, 1 °C, and 0 °C (→ freezing point). The density of liquid water at 0 °C is greater than the density of frozen water at the same temperature. Thus water is heavier as a liquid than as a solid, and this is why ice floats on water. When a mass of water cools below 4 °C, the density decreases and allows water to rise to the surface, where freezing occurs. The layer of ice formed on the surface does not sink and it acts as a thermal isolator, thus protecting the biological environment beneath it. This property of water liquid is very unusual; molecules pack more closely than in the crystal structure of ice. The reason is that → hydrogen bonds between liquid water are not stable, they are continuously broken and new bonds are created. In the crystal structure of ice molecules have a fixed pattern creating empty space between molecules. |
maximum entropy method (MEM) raveš-e dargâšt-e bišiné Fr.: méthode d'entropie maximum A deconvolution algorithm which functions by minimizing a smoothness function in an image. The MEM seeks to extract as much information from a measurement as is justified by the data's signal-to-noise ratio. |
maximum light nur-e bišiné Fr.: maximum de lumière Of a → supernova, → peak luminosity. |
maximum likelihood šodvâri-ye bišiné Fr.: maximum de vraisemblance A statistical procedure based on choosing the value of the unknown parameter under which the probability of obtaining an observed sample is highest. → maximum; → likelihood. |
maxwell (Mx) maxwell (#) Fr.: maxwell The unit of → magnetic flux. The flux through 1 square cm normal to a magnetic field of 1 → gauss. It is equal to 10^{-8} → weber (Wb)s. After James Clerk Maxwell (1831-1879), British outstanding physicist, who made fundamental contributions to electromagnetic theory and the kinetic theory of gases. |
Maxwell bridge pol-e Maxwell Fr.: pont de Maxwell A type of → Wheatstone bridge used for measuring → inductance in terms of → resistance and → capacitance. |
Maxwell gap gâf-e Mawxell Fr.: division de Maxwell A division in Saturn's ring in the outer part of the C ring. It is about 87500 km from Saturn's center and is 500 km wide. The gap was discovered in 1980 by Voyager 1. Not discovered by J. C. Maxwell, but named in his honor; → maxwell; → gap. |
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