first degree equation
hamugeš-e daraje-ye yekom
Fr.: équiation du premier degré
first-order differential equation
hamugeš-e degarsâne-yi-ye râye-ye naxost
Fr.: équation différentielle du premier ordre
Fr.: équation de Fokker-Planck
A modified form of → Boltzmann's equation allowing for collision terms in an approximate way. It describes the rate of change of a particle's velocity as a result of small-angle collisional deflections.
After Dutch physicist Adriaan Fokker (1887-1972) and the German physicist Max Planck (1858-1947); → equation.
Fr.: équation de Fresnel
For an electromagnetic wave incident upon the interface between two media with different indices of refraction, one of a set of equations that give the → reflection coefficient and → transmission coefficient at the optical interface. These coefficients depend on the polarization degree of the incident wave.
Fr.: équation de Friedmann
An equation that expresses energy conservation in an → expanding Universe. It is formally derived from → Einstein's field equations of → general relativity by requiring the Universe to be everywhere → homogeneous and → isotropic. It is expressed by H2(t) = (8πG)/(3c2)ε(t) - (kc2)/R2(t), where H(t) is the → Hubble parameter, G is the → gravitational constant, c is the → speed of light, ε(t) is the → energy density, k is the → curvature of space-time, and R(t) is the → cosmic scale factor. See also → Big Bang, → accelerating Universe. See also → Friedmann-Lemaitre Universe.
Named after the Russian mathematician and physical scientist Aleksandr Aleksandrovich Friedmann (1888-1925), who was the first to formulate an → expanding Universe based on Einstein's theory of → general relativity ; → equation.
Fr.: équation des gaz
An equation that links the pressure and volume of a quantity of gas with the absolute temperature. For a gram-molecule of a perfect gas, PV = RT, where P = pressure, V = volume, T = absolute temperature, and R = the gas constant.
gravitational lens equation
hamugeš-e adasi-ye gerâneši
Fr.: équation de lentille gravitationnelle
The main equation of gravitational lens theory that sets a relation between the angular position of the point source and the observable position of its image.
Fr.: équation de Hamilton
One of a set of equations that describe the motion of a → dynamical system in terms of the → Hamiltonian function and the → generalized coordinates. For a → holonomic system with n degrees of freedom, Hamilton's equations are expressed by: q.i = ∂H/∂pi and p.i = - ∂H/∂qi, i = 1, ..., n.
homogeneous linear differential equation
hamugeš-e degarsâne-yi-ye xatti hamgen
Fr.: équation différentielle linéaire homogène
A → linear differential equation if the right-hand member is zero, Q(x) = 0, on interval I.
Fr.: équation hydrodynamique
Fluid mechanics: A → partial differential equation which describes the motion of an element of fluid subjected to different forces such as pressure, gravity, and frictions.
Fr.: équation hydrostatique
The equation describing the → hydrostatic equilibrium in a star, expressed as: dP/dr = -GMρ/r2, where P and M are the mass and pressure of a spherical shell with thickness dr at some distance r around the center of the star, ρ is the density of the gas, and G the → gravitational constant.
Fr.: équation d'induction
In magnetohydrodynamics, an equation that describes the transport of plasma and magnetic
field lines over time:
Fr.: équation intégrale
An equation involving an unknown function that appears as part of an integrand.
Fr.: équation de Kepler
An equation that enables the position of a body in an elliptical orbit to be calculated at any given time from its orbital elements. It relates the → mean anomaly of the body to its → eccentric anomaly.
Fr.: équation de Lagrange
A set of second order → differential equations for a system of particles which relate the kinetic energy of the system to the → generalized coordinates, the generalized forces, and the time. If the motion of a → holonomic system is described by the generalized coordinates q1, q2, ..., qn and the → generalized velocities q.1, q.2, ..., q.n, the equations of the motion are of the form: d/dt (∂T/∂q.i) - ∂T/∂q.i = Qi (i = 1, 2, ..., n), where T is the kinetic energy of the system and Qi the generalized force.
Fr.: équation de Lane-Emden
Named after the American astrophysicist Jonathan Homer Lane (1819-1880) and the Swiss astrophysicist Robert Emden (1862-1940); → equation
Fr.: équation de Langevin
Equation of motion for a weakly ionized cold plasma.
Paul Langevin (1872-1946), French physicist, who developed the theory of magnetic susceptibility of a paramagnetic gas; → equation.
Fr.: équation de Laplace
A → linear differential equation of the second order the solutions of which are important in many fields of science, mainly in electromagnetism, fluid dynamics, and is often used in astronomy. It is expressed by: ∂2V/ ∂x2 + ∂2V/ ∂y2 + ∂2V/ ∂z2 = 0. Laplace's equation can more concisely expressed by: ∇2V = 0. The function V may, for example, be the potential at any point in the electric field where there is no free charge. The general theory of solutions to Laplace's equation is known as potential theory.
Fr.: équation de Layzer-Irvine
The ordinary Newtonian energy conservation equation when expressed in expanding cosmological coordinates. More specifically, it is the relation between the → kinetic energy per unit mass associated with the motion of matter relative to the general → expansion of the Universe and the → gravitational potential energy per unit mass associated with the departure from a homogeneous mass distribution. In other words, it deals with how the energy of the → Universe is partitioned between kinetic and potential energy. Also known as → cosmic energy equation. In its original form, the Layzer-Irvine equation accounts for the evolution of the energy of a system of → non-relativistic particles, interacting only through gravity, until → virial equilibrium is reached. But it has recently been generalized to account for interaction between → dark matter and a homogeneous → dark energy component. Thus, it describes the dynamics of local dark matter perturbations in an otherwise homogeneous and → isotropic Universe (P. P. Avelino and C. F. V. Gomes, 2013, arXiv:1305.6064).
W. M. Irvine, 1961, Ph.D. thesis, Harvard University; D. Layzer, 1963, Astrophys. J. 138, 174; → equation.
Fr.: équation de Legendre
The → differential equation of the form: d/dx(1 - x2)dy/dx) + n(n + 1)y = 0. The general solution of the Legendre equation is given by y = c1Pn(x) + c2Qn(x), where Pn(x) are Legendre polynomials and Qn(x) are called Legendre functions of the second kind.
Named after Adrien-Marie Legendre (1752-1833), a French mathematician who made important contributions to statistics, number theory, abstract algebra, and mathematical analysis; → equation.