differential equation hamugeš-e degarsâneyi Fr.: équation différentielle An equation expressing a relationship between an → independent variable, x, an unknown → function, y = f(x), and its → derivatives. The general form of a differential equation is: F(x, y, y', y'', ..., y^{(n)}) = 0, or F(x,y, dy/dx, d^{2}y/dx^{2}, ..., d^{n}y/dx^{n}) = 0. See also: → ordinary differential equation; → partial differential equation; → linear differential equation; → exact differential equation; → first-order differential equation; → homogeneous linear differential equation; → nonhomogeneous linear differential equation; → differential equation with separated variables; → differential equation with separable variables. → differential; → equation. |
differential equation with separable variables hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâyi-pazir Fr.: équation différentielle à variables séparables A → differential equation of the form: M_{1}(x) N_{1}(y) dx + M_{2}(x) N_{2}(y) dy = 0, which can be reduced to a → differential equation with separated variables. → differential; → equation; → separate; → variable. |
differential equation with separated variables hamugeš-e degarsâne-yi bâ vartandehhâ-ye jodâ Fr.: équation différentielle à variables séparées A → differentail equation that can be transformed into the form: M(x)dx + N(x)dy = 0. → differential; → equation; → separate; → variable. |
diffusion equation hamugeš-e paxš Fr.: équation de diffusion An equation that expresses the time rate of change of a quantity in terms of the product of the diffusion coefficient and the → Laplacian operating on the quantity. For example the diffusion equation for temperature is: ∂T/∂t = D∇^{2}T. |
Dirac equation hamugeš-e Dirâk Fr.: équation de Dirac The equation that describes the behavior of an → electron in a way that combines the requirements of → quantum mechanics with the requirements of → special relativity. The Dirac equation predicted the existence of antimatter |
dispersion equation hamugeš-e pâšeš Fr.: équation de dispersion An equation representing the variation of → refractive index as a function of → wavelength; for example → Cauchy's equation and → Sellmeier's equation. → dispersion; → equation. |
Drake equation hamugeš-e Drake Fr.: équation de Drake A probabilistic argument used to estimate the number of
→ intelligent, communicating
→ extraterrestrial civilizations in the
→ Milky Way galaxy. The Drake equation is: Frank Donald Drake (1930-); → equation. |
Einstein's field equations hamugešhâ-ye meydân-e Einstein Fr.: équations de champ d'Einstein A system of ten non-linear → partial differential equations in the theory of → general relativity which relate the curvature of → space-time with the distribution of matter-energy. They have the form: G_{μν} = -κ T_{μν}, where G_{μν} is the → Einstein tensor (a function of the → metric tensor), κ is a coupling constant called the → Einstein gravitational constant, and T_{μν} is the → energy-momentum tensor. The field equations mean that the curvature of space-time is due to the distribution of mass-energy in space. A more general form of the field equations proposed by Einstein is: G_{μν} + Λg_{μν} = - κT_{μν}, where Λ is the → cosmological constant. Named after Albert Einstein (1879-1955); → field; → equation. |
elegant equation hamugeš-e qašang Fr.: équation élégante An equation with surprising simplicity that expresses a fundamental result relating several apparently unassociable elements. For example, → Euler's formula for the particular case of θ = π, and the → mass-energy relation. |
energy generation equation hamugeš-e âzâneš-e kâruž Fr.: équation de génération d'énergie Of a stellar → nuclear fusion, the equation describing the → energy generation rate as a function of → density and → temperature. → energy; → generation; → equation. |
equation hamugeš Fr.: équation 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 hamugeš-e jonbeš 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 = V_{0} +
at, S = Vt + (1/2)at^{2}. |
equation of state hamugeš-e hâlat 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. |
equation of state parameter pârâmun-e hamugeš-e hâlat Fr.: paramètre de l'équation d'état In cosmology, a → dimensionless parameter introduced by the → equation of state representing the ratio of the pressure to the energy density of a fluid, such as the → dark energy: w = p/ρ. The → deceleration or → acceleration of an → expanding Universe depends on this parameter (→ accelerating Universe). A number of numerical values of this parameter are as follows: for the → cosmological constant: w = -1, for → non-relativistic matter (present-day → baryons): w = 0, and for → relativistic matter (photons, neutrinos): w = +1/3. Together with Ω(dark energy) and Ω(matter), w provides a three-parameter description of the dark energy. The simplest parametrization of the dark energy is w = constant, although w might depend on → redshift. |
equation of the equinoxes hamugeš-e hamugânhâ Fr.: équation des équinoxes The difference between → apparent sidereal time and → mean sidereal time. It is due to the nutation of the Earth's polar axis of rotation about its precessional motion. It ranges from +0.8 to +1.2 seconds. Also known as → nutation in right ascension. |
equation of time hamugeš-e zamân Fr.: équation du temps The difference, due to Earth's elliptical orbit and variable orbital velocity, between apparent solar time and mean solar time. It varies throughout the year, and slightly from year to year. At present, it reaches extremes of about -14 minutes in February, and about +16 minutes in November. The equation of time is visually illustrated by an → analemma. |
Euler equation hamugeš-e Euler Fr.: équation d'Euler In → fluid mechanics, one of a set of → differential equations that govern the motion of a → compressible, → inviscid fluid. Euler equations correspond to the → Navier-Stokes equations with zero → viscosity. |
exact differential equation hamugeš-e degarsâneyi-ye razin Fr.: équation différentielle exacte A → differential equation composed of → continuous → differentiable functions for which certain conditions are fulfilled. The equation M(x,y)dx + N(x,y)dy = 0 is called exact if M(x,y) and N(x,y) are continuous differentiable functions for which the following relationship is fulfilled: ∂M/∂y = ∂N/∂x, and ∂M/∂y and ∂N/∂x are continuous in some region. → exact; → differential; → equation. |
exponential equation hamugeš-e nemâyi Fr.: équation exponentielle An equation in which unknowns appear as exponents. Examples: 2^{3x + 1} = 32. → exponential; → equation. |
field equation hamugeš-e meydân Fr.: équation de champ In a physical theory, an equation that describe how a fundamental force interacts with matter. Einstein's equations of → general relativity are called field equations since they describe the → gravitational field. Similarly, → Maxwell's equations describe the electromagnetic field. |