A → morphism f : Y → X if, for any two morphisms u,v : X → Z, u f = v f implies u = v.
1) An incident in the course of a series of events.
From Fr. épisode from Gk. epeisodion "addition," noun use of neuter of epeisodios "coming in besides," from → epi- "in addition" + eisodos "a coming in, entrance" (from eis"into" + hodos "way," → period).
1) Pertaining to or of the nature of an episode.
A branch of philosophy that investigates the possibility, origins, nature, methods, and limits of human knowledge.
From Gk. episteme "knowledge," from Ionic Gk. epistasthai "to understand," literally "overstand," from → epi- "over, near" + histasthai "to stand;" cognate with Pers. istâdan "to stand," → standard; PIE base *sta- "to stand."
1) The date for which → orbital elements or the positions
of celestial objects are calculated. Specifying the epoch is important
because the apparent positions of objects in the sky change gradually due to
→ precession and → nutation,
while orbital elements change due to the gravitational effects of the
The standard epoch used in ephemerides (→ ephemeris)
and stellar catalogues at present is January 1, 2000, 12h (written also as 2000.0).
From M.L. epocha, from Gk. epokhe "pause, cessation, fixed point," from epekhein "to pause, take up a position," from epi- "on" + ekhein "to hold, to have;" cf. Av. hazah- "power, violence, superiority;" Skt. sahate "he masters," sáhas- "power, violence, might;" Goth. sigis; O.H.G. sigu; O.E. sige "victory;" PIE base *segh- "to hold."
Zimé, from Mid.Pers. zim "time, year, winter," from Av. zyam-, zayan- "winter," probably related to zaman "time" + nuance suffix -é.
Fr.: angle de phase initial
Same as the → initial phase angle.
epoch of thermalization
Fr.: époque de thermalisation
The period during the → early Universe before the → recombination era when the photons were hot enough to ionize hydrogen. The density was so high that the interactions between → matter and → radiation were very numerous. Therefore, matter and photons were in constant contact and their → temperatures were the same. As a result, the radiation became → thermalized, i.e. the → electromagnetic spectrum of the radiation became that of a → blackbody, a process called → thermalization. Since the time of recombination the photons of → cosmic background radiation have been free to travel uninhibited by interactions with matter. Thus, their distribution of energy is a perfect → blackbody curve, as predicted by the → Big Bang theory and shown by several observations, such as → Cosmic Background Explorer (COBE), → Wilkinson Microwave Anisotropy Probe (WMAP), and → Planck Satellite.
Fr.: paradoxe EPR
A thought experiment developed in 1935 by A. Einstein (1879-1955), Boris Podolsky (1896-1966), and Nathan Rosen (1909-1995) to demonstrate that there is a fundamental inconsistency in → quantum mechanics. They imagined two physical systems that are allowed to interact initially so that they will subsequently be defined by a single quantum mechanical state. For example, a neutral → pion at rest which decays into a pair of → photons. The pair of photons is described by a single two-particle → wave function. Once separated, the two photons are still described by the same wave function, and a measurement of one → observable of the first system will determine the measurement of the corresponding observable of the second system. For example, if photon 1 is found to have → spin up along the x-axis, then photon 2 must have spin down along the x-axis, since the final total → angular momentum of the two-photon system must be the same as the angular momentum of the initial state. This means that we know the spin of photon 2 even without measuring it. Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling (→ quantum entanglement). So, EPR argued that quantum mechanics was not a complete theory, but it could be corrected by postulating the existence of → hidden variables that furthermore would be "local". According to EPR, the specification of these local hidden parameters would predetermine the result of measuring any observable of the physical system. However, in 1964 John S. Bell developed a theorem, → Bell's inequality, to test for the existence of these hidden variables. He showed that if the inequality was satisfied, then no local hidden variable theory can reproduce the predictions of quantum mechanics. → Aspect experiment.
A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Phys. Rev. 41, 777 (15 May 1935); → paradox.
hamug, barâbar (#)
As great as; like or alike in quantity, degree, value.
From L. æqualis "uniform, identical, equal," from æquus "level, even, just," of unknown origin, + -alis, → -al.
Hamug, from Mid.Pers. hamôg "equal, like," from ham "the same; together; also" (O.Pers./Av. ham-; cf. Skt. sam-; also O.Pers./Av. hama- "one and the same;" Skt. sama-; Gk. homos-; originally identical with PIE numeral *sam- "one," from *som-) + suffix -og/-ok/-uk, as in nêrog "force" (from nar "man, male"), nêvakôk "good, nice" (from nêvak "good, beautiful, nice, favorable"), mastôk "drunk" (from mast "drunk, drunken"), câpuk "quick; active," sapuk "light, brisk."
1) The state or quality of being equal.
M.E. from L. aequalitat-, stem of aequalitats, → equal + -ity.
Hamugi noun of hamug, → equal.
Fr.: signe d'égalité
Same as → equals sign.
Fr.: égalisation; équalisation
The act of making equal or uniform.
Noun of equalize.
Fr.: égaliser; équaliser
To make equal; to make uniform.
From hamug, → equal + sâz contraction of sâzandé "doer, maker," from sâxtan, sâzidan "to make, form, fashion, prepare" (Mid.Pers. sâxtan, sâz- "to form, prepare, build, make;" Proto-Iranian *sac- "to fit, be suitable; to prepare").
Electronics: A device, usually an electric network, designed to correct for unequal attenuation of phase shift in the transmission of signals.
Agent noun from → equalize.
Fr.: signe égal
A mathematical symbol (=) that indicates equality of two expressions on each side of the sign. Same as → equality sign. The equals sign appears for the first time in Robert Recorde's book The Whetstone of Witte published in 1557. He was a Welsh physician and mathematician.
falak-e mo'adel (al-masir) (#)
In Ptolemy's → geocentric system, an imaginary point near the center of the → deferent but at a position opposite to that of the Earth from the center of the deferent. Ptolemy further supposed that the distance from the Earth to the center of the deferent was equal to the distance from the center of the deferent to the equant. He also claimed that the planet's deferent and the → epicycle described uniform circular motion around the equant.
L. aequant-, s. of aequans, pr.p. of aequare "to make equal."
Falak-e mo'adel (al-masir), literally "the sphere that equalizes (the path)," from Ar. falak "celestial orbit; sphere; heaven," from Babylonian pulluku + mo'adel "equalizing" (+ masir "path").
Fr.: mettre en équation
To put in the form of an equation; to state the equality of or between.
L. æquatus, p.p. of æquare "to make equal," from æquus "equal, level, even."
Infinitive form of hamug, → equal.
A statement asserting the equality of two numbers or two expressions. It consists of two parts, called sides or members of the equation, separated by the Same as → equality sign.
From L. æquation- "an equalizing," noun of → equate.
Verbal noun of hamugidan, → equate.
equation of motion
Fr.: équation de mouvement
1) Any equation that describes the motion of objects, i.e., variation of
velocity, distance covered, acceleration, etc., as a function of time;
e.g., V = V0 +
at, S = Vt + (1/2)at2.
equation of state
Fr.: équation d'état
In physics and thermodynamics, the equation that describes the relationship between pressure, density, and temperature, e.g. → ideal gas law, → van der Waals equation, → polytropic process, → virial equation of state.