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The Reynolds-averaged Navier–Stokes equations (RANS equations) are time-averaged equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [1]
The equation of the circle being y 2 + x(x − n / m 2) = 0, the right hand side is the value of y 2 on the circle. Solution with angle trisector. A cubic equation with real coefficients can be solved geometrically using compass, straightedge, and an angle trisector if and only if it has three real roots.: Thm. 1
In mathematics, the Volterra integral equations are a special type of integral equations. [1] They are divided into two groups referred to as the first and the second kind. A linear Volterra equation of the first kind is. where f is a given function and x is an unknown function to be solved for. A linear Volterra equation of the second kind is.
Langevin equation. In physics, a Langevin equation (named after Paul Langevin) is a stochastic differential equation describing how a system evolves when subjected to a combination of deterministic and fluctuating ("random") forces. The dependent variables in a Langevin equation typically are collective (macroscopic) variables changing only ...
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. [1] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
An ordinary differential equation ( ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y ), which, therefore, depends on x. Thus x is often called the independent variable of the equation.
HHL algorithm. The Harrow–Hassidim–Lloyd algorithm or HHL algorithm is a quantum algorithm for numerically solving a system of linear equations, designed by Aram Harrow, Avinatan Hassidim, and Seth Lloyd. The algorithm estimates the result of a scalar measurement on the solution vector to a given linear system of equations. [1]
In physics, the Landau–Lifshitz–Gilbert equation (usually abbreviated as LLG equation), named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the dynamics (typically the precessional motion) of magnetization M in a solid. It is a modified version by Gilbert of the original equation ...
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