Abbe sine condition
butâr-e sinus-e Abbe
Fr.: condition des sinus d'Abbe
In → geometric optics, a condition for eliminating → spherical aberration and → coma in an → optical system. It is expressed by the relationship: sin u'/U' = sin u/U, where u and U are the angles, relative to the → optical axis, of any two rays as they leave the object, and u' and U' are the angles of the same rays where they reach the image plane. A system which satisfies the sine condition is called → aplanatic.
adiabatic initial conditions
butârhâ-ye âqâzin-e bidarrow
Fr.: conditions initiales adiabatiques
The assumption whereby the density fluctuations in the very → early Universe would be produced by compressing or decompressing of all components of a homogeneous Universe. The adiabatic initial conditions lead to coherent oscillations in the form of peaks in the → temperature anisotropy spectrum. See also → acoustic peak, → baryon acoustic oscillation.
butârhâ-ye karân, ~ karâni
Fr.: conditions à la limite
1) Math: Restriction on the limits of applicability of an equation.
In a differential equation, conditions that allow to fix the constant
of integration and reach a unique solution. The number of boundary conditions
necessary to determine a solution matches the order of the equation.
1) Physics: The state of a physical system at a given time.
Also called → physical condition.
From O.Fr. condition, from L. condicionem (nom. condicio) "agreement, situation," from condicere "to speak with, talk together," from → com- "together" + dicere "to speak," from PIE *deik- "to point out;" cf. Av. daēs- "to show; assign; make known," Skt. dis- "to show, point toward," disati "shows," Gk. deiknunai "to show," O.H.G. zeigon, Ger. zeigen "to show," E. token "indication, sign."
Butâr, from Mid.Pers. but past tense stem of butan Mod.Pers. budan "to be, become," → exist, + -âr noun suffix (as in raftâr, jostâr, goftâr, kerdâr).
1) Imposing, containing, subject to, or depending on a condition or conditions; not absolute;
made or allowed on certain terms.
Fr.: introduction conditionnelle
A derivation rule that begins with an → assumption in a → subproof and allows for deriving a conditional outside the subproof. The derived conditional consists of the assumed proposition as the → antecedent and the derived conclusion in the subproof as the → consequent.
→ conditional; → introduction.
Fr.: probabilité conditionnelle
Of an event B in relationship to an event A, the probability that event B occurs given that event A has already occurred. The notation for conditional probability is P(B|A), read as the probability of B given A: P(B|A) = P(A ∩ B)/P(A). → Bayes' theorem.
Fr.: preuve conditionnelle
Fr.: proposition conditionelle
A compound → proposition in which one → clause asserts something as true provided that the other clause is true. A conditional statement consists of two parts, a hypothesis in the "if" clause and a conclusion in the "then"clause. For instance, "If it rains, then they cancel school." It rains is the hypothesis. "They cancel school" is the conclusion. The clause following if is traditionally called the → antecedent, whereas the clause following then is called the → consequent.
Fr.: condition de Dirichlet
One of the following conditions for a → Fourier series
Fr.: condition de Gamow
The constraint on the → baryon number density at T ~ 109 K in the early → expanding Universe. Gamow recognized that a key to the element buildup is the reaction n + p ↔ d + γ. Deuterium needs to be produced in sufficient abundance for higher elements to form, but if all → neutrons are immediately locked up into → deuterium, no higher elements can form either. The Gamow condition is expressed by nb<σv>t ~ 1, where nb is the baryon number density, σ is the cross section for the reaction at relative → velocity v, and t the expansion time-scale for the → Universe. This means that the time-scale for the above reaction is comparable to the expansion time. From this condition the baryon number density at the start of element buildup is found to be nb ~ (σvt)-1 ~ 1018 cm-3 at T = 109 K (P. J. E. Peebles, 2013, Discovery of the Hot Big Bang: What happened in 1948, arXiv.1310.2146).
Fr.: conditions initiales
1) Conditions at an initial time t = t0 from which a physical system or
a given set of mathematical equations evolves.
Fr.: conditions de saut
Very different values of pressure and density (or temperature or energy) across a shock wave.
Fr.: condition MHD
necessary and sufficient conditions
butârhâ-ye bâyesté o basandé
Fr.: conditions nécessaire et suffisante
If event A must occur for event B to occur, then it is said that A is → necessary for B. If event A may cause B but there could be some other cause as well, then it is said that A is sufficient to cause B. See also → if and only if (iff).
Fr.: condition physique
The state of a → physical system regarding its temperature, density, pressure, etc. at a given time.
Fr.: conditions de Rankine-Hugoniot
Hydrodynamics → conservation laws (which can be extended to → magnetohydrodynamics, MHD) which describe the physical conditions of material across a → shock front. A fluid is completely described by its velocity, density, pressure, specific heat ratio, and magnetic field (in the MHD case). Mass, momentum, and energy fluxes are conserved in the shock, leading to the Rankine-Hugoniot relations. Also called Rankine-Hugoniot jump conditions. See also → jump condition.
Fr.: conditions de Sakharov
The three conditions that are necessary for the generation of a
→ baryon asymmetry in the
→ early Universe. These conditions are:
Named after Andrei Sakharov (1921-1989), who in 1967 described these three minimum conditions (A. D. Sakharov, 1967, Zh. Eksp. Teor. Fiz. Pis'ma 5, 32; 1967, JETP Lett. 91B, 24); → condition.
Not limited by conditions; absolute.