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A method is L-stable if it is A-stable and () as , where is the stability function of the method (the stability function of a Runge–Kutta method is a rational function and thus the limit as + is the same as the limit as ).
Miller twist rule is a mathematical formula derived by American physical chemist and historian of science Donald G. Miller (1927-2012) to determine the rate of twist to apply to a given bullet to provide optimum stability using a rifled barrel. [1]
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [1] [2]In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is
For = and =, the distribution is a Landau distribution (L) which has a specific usage in physics under this name. For α = 3 / 2 {\displaystyle \alpha =3/2} and β = 0 {\displaystyle \beta =0} the distribution reduces to a Holtsmark distribution with scale parameter c and shift parameter μ .
A Lyapunov function for an autonomous dynamical system {: ˙ = ()with an equilibrium point at = is a scalar function: that is continuous, has continuous first derivatives, is strictly positive for , and for which the time derivative ˙ = is non positive (these conditions are required on some region containing the origin).
The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations.
Jannik Bjerrum (son of Niels Bjerrum) developed the first general method for the determination of stability constants of metal-ammine complexes in 1941. [1] The reasons why this occurred at such a late date, nearly 50 years after Alfred Werner had proposed the correct structures for coordination complexes, have been summarised by Beck and Nagypál. [2]
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...